mathematics year 1 curriculum planning …oakwoodlive.net/curriculum/maths/maths - new curriculum...

Fluency Reasoning Problem Solving

MATHEMATICS

YEAR 1

CURRICULUM PLANNING

TOOLKIT


Y1: Number and Place Value

Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count forwards from 80 to 110

Count backwards from 105

Notes:

Aut 1 Aut 2 Spr 1 Spr 2 Sum1 Sum 2

Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens Find p 39 in a book

Make a label to show how many things were in your collection

Count groups of 10 each of 2p, 5p and 10p coins

Notes:


Given a number, identify one more and one less There are twenty nine beads in this pot. I am putting one more bead in the pot. How many are in there now? How did you know? How can

you check?

This time there are forty beads in the pot. I take out one bead. How many beads are left in the pot? How did you know? How can you check?

Start with a different number of beads in the pot. Ask your partner to put another bead in or take one out and then say how many there are in

the pot. How will you know if your partner is right?

Notes:


Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least I'm giving each of you a strip of card with some numbers on [five numbers at random from 0 to 30].

Point to the number which is worth most. Now point to the number which is worth least.

Make these numbers using tens and ones apparatus and put them in order.

Why have you put this number there?

Notes:


Read and write numbers from 1 to 20 in numerals and words Make some labels for collections using numbers and words.

Notes:


https://www.ncetm.org.uk/resources/42431


Non statutory guidance

Pupils practise counting (1, 2, 3), ordering (e.g. first, second, third), or to indicate a quantity (e.g. 3 apples, 2 centimetres), including solving simple concrete problems, until they are fluent.

Pupils begin to recognise place value in numbers beyond 20 by reading, writing, counting and comparing numbers up to 100, supported by objects and pictorial representations.

They practise counting as reciting numbers and counting as enumerating objects, and counting in twos, fives and tens from different multiples to develop their recognition of patterns in the number system (e.g. odd and even

numbers), including varied and frequent practice through increasingly complex questions.

They recognise and create repeating patterns with objects and with shapes.

Quick links Resources (Years 1-6)

Cross-curricular and real life

connections

Making connections to other topics

NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS

SUGGESTED ACTIVITIES

GAPS AND MISCONCEPTIONS TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Place value grids & digit cards

Place value partitioning tool

Place value charts

Place value arrow cards

Place value counters

Counting stick

Beadstrings

Number lines

Dienes

Washing lines with numerals

Vertical number lines (thermometer)

Tens grouping objects: eg

Cuisenaire, unifix, multilink, straws,

(Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice

Games: collecting objects or track

games

Jars filled with objects e.g. cotton

reels, matchsticks

Outdoor score boards and timers for

PE activities

Counters or matchsticks

Ordering numbers/Moving

digits/Beadsticks/Place

Value/Thermometer ITPs

Learners will encounter numbers and place value in many

contexts:

Ages of family members and friends. Teenagers

are of particular interest!

Numerals as labels on buses, car etc., telephone

numbers

Page numbers in books and magazines (ordinal)

Games of all kinds, e.g. board games, computer

games, football scores

Preparing for parties, planning activities and

events, counting supplies

Measuring, money and time

There are many opportunities to link work on number and

place value with other areas of the mathematics curriculum.

E.g. when teaching is focused on measurement, children will

be recording lengths, heights, mass, amounts of money,

capacity and time – all requiring a good understanding of

number structure and place value.

http://mathstoolkit.wix.com/mathstoolkit#!contact/con8

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http://mathstoolkit.wix.com/mathstoolkit#!place-value-activities/c2g2

http://www.annery-kiln.eu/gaps-misconceptions/


http://www.annery-kiln.eu/gaps-misconceptions/all-images.html

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Y1: Addition and Subtraction

Read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs

Use the vocabulary add, subtract, minus, equals, is the same value as, total, more than, fewer/less than.

Explain that things on both sides of the equals sign have the same value

Know that the ‘total’ can be presented on either side of the equals sign

Complete ‘empty box’ number sentences

Notes:


Represent and use number bonds and related subtraction facts within 20

I’m thinking of a number. I’ve subtracted 6 and the answer is 8. What number was I thinking of? Explain how you know.

I’m thinking of a number. I’ve added 7 and the answer is 18. What number was I thinking of? Explain how you know.

I know that 6 and 4 is 10. How can I find 7 + 4? How could you work it out?

Notes:


Add and subtract one-digit and two-digit numbers to 20, including zero

What is 37 subtract 10? How did you work that out? How could you show that using cubes/a number line/a 100-square? What would 37

subtract 20 be?

Make up some difference questions with the answer 5. Can you show how to solve them using counters? Can you show how to find the

answer on a number line?

Notes:


Solve one-step problems that involve addition and subtraction, using concrete objects

and pictorial representations, and missing number problems such as 7 = ☐ – 9

Make up some additions with the answer 15. Try to put them in different ways, like this: 10 + 5 = 15. The total of 10 and 5 is 15. 10 and 5

more makes 15.

How many ways can you show me that 9 subtract 3 is 6?

Make up some subtractions with the answer 5. Try to put them in different ways, like this: 11 – 6 = 5. The difference between 6 and 11 is 5.

Notes:





Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 + 7 = 16; 16 – 7 = 9; 7 = 16 – 9). They should realise the effect of adding or subtracting zero. This establishes addition and

subtraction as related operations.

Pupils combine and increase numbers, counting forwards and backwards.

They discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than

and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly.

Quick links Resources

(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS


GAPS AND MISCONCEPTIONS

TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings

Structured number

lines

Empty number

lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards

Place value cards

& counters

100 squares

Pegs on hanger

Number rhymes

Practical objects

linked to topic

Slider box cards

Dice

Number grid/

Number scales/

Number facts/

Difference/

Number line ITPs

Learners will encounter addition and

subtraction:

Within the science curriculum there are

opportunities to connect with addition and

subtraction, for example, in the programmes of

study the children are expected to use their

local environment throughout the year to

explore and answer questions about animals in

their habitat. They need to be able to sort and

group them. This would give opportunities for

children add and subtract to find totals and

differences.

Within the geography curriculum, the children

are expected to identify seasonal and daily

weather patterns in the United Kingdom and

the location of hot and cold areas of the world

in relation to the Equator and the North and

South Poles. When they do this they could use

subtraction to find differences in the

temperatures of the different areas.

Within the history curriculum, the children are

expected to explore where the people and

events they study fit within a chronological

framework. This could involve using subtraction

or counting on to find time differences between

these events. They could use addition to find,

for example the number of years the people

they studied lived or the lengths of reign of

different Kings and Queens.

Multiplication and division

When working on addition and subtraction and/or multiplication and division, there are

opportunities to make connections between them, for example:

Multiplication must be understood both as ‘repeated addition’ and as ‘scaling’. Likewise, division

is both ‘repeated subtraction’ and reduction (multiply by a scale factor of less than 1). You should

model these concepts using manipulatives including bead strings and arrays. For example:

Give each child a bead string with 20 beads on it. Ask them to find 3 multiplied by 4 by moving 3

beads at a time four times giving 12. Next, ask them to divide 12 by 3 by

taking away groups of 3. As they do this you could demonstrate what they are

doing on a number line. It is important that the children use practical

apparatus before using a number line because a number line alone is too

abstract for some children.

Give the children 12 counters and ask them to set these out in three rows of four on a piece of

paper or a whiteboard: Discuss how they can make 12 by adding four three times, and, if they

turn their array around they can add three four times. They could record these as addition and

multiplication number sentences.

Fractions

When working on addition and subtraction and/or fractions there are opportunities to make

connections between them, for example:

You could give the children opportunities to find halves and quarters of different quantities, for

example 20. They could find half by dividing by two or sharing single a set of 20 objects into two

piles. They could then count how many are in each half and then add them together to check that

when they do they get the whole amount. They could do the same for quarters, adding two

groups to find two quarters or ½ and three for ¾.

Measurement

When working on addition and subtraction and/or measurement there are opportunities to make


You could ask the children to measure different lengths in metres using metre sticks or

centimetres using rulers. They could then find totals or differences of pairs of lengths. They could

repeat this for measuring masses in kilograms and capacities or volumes in litres.







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Y1: Multiplication and Division

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Children should be able to:

Use practical apparatus, arrays and images to help solve multiplication and division problems such as:

Ben had 5 football stickers. His friend Tom gave him 5 more, how many does he have altogether?

Share 12 sweets between two children. How many do they each have?

Find half of and double a number or quantity:

16 children went to the park at the weekend. Half that number went swimming. How many children went swimming?

I think of a number and halve it. I end up with 9, what was my original number?

Notes:



Through grouping and sharing small quantities, pupils begin to understand: multiplication and division; doubling numbers and quantities; and finding simple fractions of objects, numbers and quantities.

They make connections between arrays, number patterns, and counting in twos, fives and tens.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings

Socks on washing lines

Hands counting

Straws (bunching)

Structured number lines & empty

number lines

100 squares

Timestable squares, blank 12 x 12

grid

Counting stick

Money – 2p, 5p, 10p

Loop cards

Arrays: Eggs in boxes, Chocolate,

Cake trays

Grouping/Number dials/Remainders after division/Multiplication array/Number grid/Multiplcation grid ITP

Learners will encounter multiplication and division in:

Money - when shopping and recognising prices of items,

ordering items by price, finding quantities in multiple

purchases, sales prices, sharing costs.

Measurement - calculating area and perimeter, finding

journey distances, reading and calculating scales,

adjusting recipe quantities.

Data - interpreting and evaluating data, calculating

amounts from pie charts and pictograms.








http://mathstoolkit.wix.com/mathstoolkit#!multiplication-and-division/c5mw






Y1: Fractions

Recognise, find and name a half as one of two equal parts of an object, shape or quantity

Here is a set of 12 pencils

How many is half the set?

Shade one quarter of each shape

Notes:


Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity

Four Children share 12 strawberries into equal parts. How many strawberries will each child have?

Notes:





Pupils are taught half and quarter as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole.


(Years 1-6)

Cross-curricular and

real life connections


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OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Fraction wall Fraction plates Fraction strips Fraction cards Shapes Counting stick Number lines Other representations of fractions: clock faces, chocolate bars Fraction videos Numicon, Cuisenaire Fractions/Area/Moving digits/Decimal numberline ITP

Fractions, in particular halves and

quarters, can be linked to many

different ‘real-life’ contexts.

Children naturally use the term

‘half’ or ‘halve’ in general

conversation. Encourage them,

and the adults working with them,

to refine their use of the word, and

try to use it accurately.

‘Introduction to Fractions’ from

Nrich provides a series of 7 useful

activities for connecting fractions

to other activities, in the form of a

trail.

When teaching and learning is focused on fractions in Year 1, there are many links that can be

made to other areas of the mathematics curriculum;

Number and place value:

Identify and represent numbers using objects and pictorial representations including the number

line, and use the language of: equal to, more than, less than (fewer), most, least.

Addition and subtraction:

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial

representations, and missing number problems such as

7 = ☐ – 9.

Multiplication and division:

Solve one-step problems involving multiplication and division, by calculating the answer using

concrete objects, pictorial representations and arrays with the support of the teacher.

Measurement:

Compare, describe and solve practical problems for:

lengths and heights [for example, long/short, longer/shorter, tall/short,

double/half]

mass/weight [for example, heavy/light, heavier than, lighter than] capacity and volume [for

example, full/empty, more than, less than, half, half full, quarter]

time [for example, quicker, slower, earlier, later]







http://mathstoolkit.wix.com/mathstoolkit#!fractions-/cc6t








http://nrich.maths.org/5540


Y1: Measurement

Compare, describe and solve practical problems for:

lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]

mass/weight [for example, heavy/light, heavier than, lighter than]

capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]

time [for example, quicker, slower, earlier, later] Use their experience of standard units to make realistic estimates, answering questions such as:

Is the table taller or shorter than a metre?

Is this doll taller or shorter than one of the class rulers?

Does this bottle hold more or less than the litre jug?

Which of these things do you think will weigh less than a kilogram?

Notes:


Measure and begin to record the following:

lengths and heights

mass/weight

capacity and volume

time (hours, minutes, seconds) Use standard units to measure and compare objects. For example, they place metre sticks end-to-end to find out how much wider the hall is

than the classroom. They use a litre jug to measure how much more the washing-up bowl holds than the cola bottle.

Notes:


Recognise and know the value of different denominations of coins and notes

Distinguish coins by sorting them and start to understand their value. They begin to recognise that some coins have a greater value than

others, and will buy more: for example, 2p is worth more than 1p; 5p is worth more than 2p; £2 is worth more than £1. They play money

games and collect 1p or 2p coins to the value of 10p and begin to count up ‘how much this is altogether’. They extend their activities in the

classroom shop, paying for items that cost 1p, 3p, 5p, 7p or 9p using only 2p coins, and receiving the appropriate amount of change in 1p

coins. They use coins to help them to respond to questions such as:

Michael had £5. He spent £3. How much did he have left?

Rosie had a 10p coin. She spent 3p. How much change did she get?

How much altogether is 1p and 2p and 5p?

Sunita spent 5p and 6p on toffees. What did she pay altogether?

Chews cost 2p each. How much do three chews cost?

An apple costs 12p. Which two coins would pay for it? What combinations of 3 coins would pay for it?

Notes:




Sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] Continue to develop the concept of time in terms of time passing and sequencing events in familiar story or day-to-day routines.

They use terms such as morning, afternoon and evening, yesterday and tomorrow.

They learn to order the days of the week and learn that weekend days are Saturday and Sunday.

They listen to stories and rhymes about time, such as The Very Hungry Caterpillar or The Bad-Tempered Ladybird by Eric Carle,

Monster Monday by Susanna Gretz or Hard Boiled Legs by Michael Rosen and Quentin Blake.

Notes:


Recognise and use language relating to dates, including days of the week, weeks, months and years Order the months of the year and make a 12-page classroom calendar with pictures of each month, writing significant events underneath,

such as Divali, Pancake Day or Midsummer’s Day, or the dates of their birthdays

Notes:


Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times Read time to the hour and half hour on a clock with hands and recognise half past the hour in day-to-day routines. They use time lines or

clocks to help them to respond to questions such as:

It’s half past seven. What time will it be in four hours’ time? What time was it two hours ago?

John went to the park at 9 o’clock. He left at half past eleven. How long was he at the park?

Notes:




The pairs of terms: mass and weight, volume and capacity, are used interchangeably at this stage.

Pupils move from using and comparing different types of quantities and measures using non-standard units, including discrete (e.g. counting) and continuous (e.g. liquid) measurement, to using manageable common

standard units.

In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers.

Pupils use the language of time, including telling the time throughout the day, first using o’clock and then half past.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Mass/weight:

Weights - kg’s & g’s, multilink

Equipment: bathroom

scales,weighing scales, balances,

Force metres

Length & height (area):

Equipment: rulers, Metre sticks, cm2

paper, Trundle wheels, Measuring

tapes

Capasity & volume:

Equiment: measuring jugs, bottles,

containers, spoons, measuring

spoons, buckets, cups

Time: Equipment: Demonstration clock with geared hands, Analogue clocks, Digital clocks, Timelines Money: Coins, notes, money fans, tills Measuring scales/Ruler/Thermometer/Measuring cylinder/Tell time/Area ITPs

Learners will encounter measurement:

Within the science curriculum there are opportunities to

connect with measurement, for example, the children are

expected to use simple measurements and equipment

(e.g. hand lenses, egg timers) to gather data, carry out

simple tests, record simple data, and talk about what they

have found out and how they found it out. They can also

connect measurement with the four seasons by observing

and describing how day length varies.

Within the history curriculum, the children are expected to

explore where the people and events they study fit within a

chronological framework. This could involve plotting the

years of different events on a number line.

Within the design and technology curriculum there are

opportunities to connect with measurement when the

children carry out practical activities that might require

accurate measuring of lengths.

Addition and Subtraction

When working on measurement and/or addition and

subtraction, there are opportunities to make connections

between them, for example:

You could ask the children to measure different lengths in

metres using metre sticks or centimetres using rulers. They

could then find totals of or differences between pairs of

lengths. They could repeat this for measuring masses in

kilograms and capacities or volumes in litres.

The children could use coins to find totals and differences of

small amounts of money, for example one 10 pence and two

2 pence coins.

Fractions

When working on measurement and/or fractions there are

opportunities to make connections between them, for

example:

You could give the children opportunities to measure half a

metre/kilogram/litre and to find the equivalence in the

smaller unit of centimetres/grams/millilitres.

You could give the children clocks and ask them to find

different half past times. You could ask problems such as, ‘I

got to school at half past seven, Bertie arrived an hour later.

Show me what time he got to school.’







http://mathstoolkit.wix.com/mathstoolkit#!measurement/c1b36







Y1: Geometry: Properties of Shapes

Recognise and name common 2-D and 3-D shapes, including:

2-D shapes [for example, rectangles (including squares), circles and triangles]

3-D shapes [for example, cuboids (including cubes), pyramids and spheres]

Give each child this shape

Child A Child B Child C Child D

Look at the Shape I have given you. Tell me one thing about the shape.

Hand each child this shape.

Child A:cylinder

Child B:triangular prism

Child C:cone

Child D:cube

Look at the shape I have given you. Tell me one thing about the shape.

(Give each child two different shapes.)

Tell me something that is the same about the two shapes.

Now tell me something that is different abiout the two shapes.

One shape has 2 long sides and 2 short sides.

Tick (✔) it.

Fred draws round the bottom of a cone.

Tick (✔) the shape that Fred draws.

Notes:





Pupils handle common 2-D and 3-D shapes, naming these and related everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

2D shapes, 3D shapes, Polydron, Shape tiles

Protractors, Angle measures, Set squares

Isometric dot paper, squared paper, tracing

paper

Rulers

Geostrips

Pin boards, Geo boards and elastic bands,

Art straws and construction kits

Isometric grids/Symmetry/Fixpoints/Polygon/Calculating angles ITP

There are many opportunities to continue to explore

properties of shape, and apply mathematical

understanding of this area, in other curriculum subjects.

P.E. - Making shapes with your own body in

gymnastics and dance

Geography – looking at shapes within the natural

environment, on maps and plans

Small world play – different shaped pieces and

containers used in sand and water play and shapes cut

out in modelling dough.

Design Technology – when using construction kits

children can be encouraged to describe their work

using vocabulary associated with the properties of

shapes

Shapes in the environment, shape packaging and

those in artwork and pictures.

Teachers should use every relevant subject to develop

pupils’ mathematical fluency. Confidence in numeracy

and other mathematical skills is a precondition of

success across the national curriculum.

(National Curriculum in England Framework Document,

September 2013, p9)






http://mathstoolkit.wix.com/mathstoolkit#!geometry---properties-of-shape/cngc







Y1: Geometry: Position and Direction

Describe position, direction and movement, including whole, half, quarter and three-

quarter turns

Look at the map. Go to start. Follow this route from there. Go to the fourth house on the right. Draw a ring around it.

Look at this map

Desi's house is the 2nd on the left. Tick ( ✔) it.

Notes:





Pupils use the language of position, direction and motion, including: left and right, top, middle and bottom, on top of, in front of, above, between, around, near, close and far, up and down, forwards and backwards, inside and

outside. Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with movement on a clock face.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Logo

Bee bots

Compass

Square papers

Geo strips

Tracing paper

Co-ordinates ITP

Aspects of position, direction and movement can be

integrated with work in other areas of the curriculum.

PE and dance lessons prove easy contexts in which to

apply and consolidate skills. Games can include

instructions relating to position and direction, e.g. labelling

the corners of a room the ‘N, S, E and W’

Action songs, rhymes and games such as ‘Simon Says…’

can be adapted to include directional instructions

Many popular children’s stories can provide engaging

contexts for this mathematical work.‘We’re Going on a

Bear Hunt’ (Rosen, M.& Oxenbury, H.,1997, Walker

Books) is a good example where the vocabulary of

position, direction and movement can be used in

context.‘Rosie’s Walk’ (Hutchins, P, 1998, Bodley Head)

and ‘Katie Morag Delivers the Mail’(Hedderiwck, M, 2-1-,

Red Fox): both provide superb contexts in which to teach

an understanding of directional maps and models

Small world play resources, using play mats and figures,

can provide excellent settings for creating real life

scenarios (traffic following set routes, animals being

delivered to a zoo, stacking classroom shop shelves with

supplies etc.) to physically demonstrate and practise key

skills.

Work within geometry relating to position and direction can

be linked to other areas of the mathematics curriculum. For

example, when using clock faces and hoops relating to

position, key elements can be reinforced.






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MATHEMATICS

YEAR 2

CURRICULUM PLANNING

TOOLKIT



Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

Use their knowledge of counting on from or back to zero in steps of 2, 3, 5 and 10 to answer multiplication and division questions such as 7 ×

2 and 40 ÷ 5. They understand that one way to work out 40 ÷ 5, for example, is to find out how many fives make 40. They know that this can

be done by counting forwards in fives from zero or backwards in fives from 40.

Write the missing numbers in each of these patterns.

Notes:


Recognise the place value of each digit in a two-digit number (tens, ones)

What is the value of … ? (point to digits in the list above)

Notes:


Identify, represent and estimate numbers using different representations, including the number line Children should be able to represent numbers using equipment such as bundles of ten and single art-straws, 10p and 1p coins and number

lines.

Look at the squares of chocolate

There are 16 squares

Notes:


Tick(✔) the sum that matches the

picture

5+2+9=16

5+6+5=16

6+6+4=16

6+2+8=16

8+3+5=16



Compare and order numbers from 0 up to 100; use <, > and = signs

Here are two signs

Use these signs to make these correct

52 ☐ 17

18 ☐ 91

50 ☐ 34

Children should be able to order a set of two-digit numbers, such as 52, 25, 5, 22, 2, 55. They explain their decisions. They understand and

use the < and > symbols; for example, they write a two-digit number to make the statement 56 > ☐ true.

Notes:


Read and write numbers to at least 100 in numerals and in words

Children should be able to answer questions, such as:

What numbers can you make using two of these digits: 3, 6, 0?

Write down each number you make. Read those numbers to me. Can you write the largest of the numbers in words?

Notes:


Use place value and number facts to solve problems

Notes:




Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of three

to support their later understanding of a third.

As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including

spatial representations.

Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems

that emphasise the value of each digit in two-digit numbers. They begin to understand zero as a place holder


(Years 1-6) Cross-curricular and real life

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TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Place value grids & digit

cards

Place value partitioning

tool

Place value charts



Counting stick

Beadstrings

Number lines

Dienes

Washing lines with

numerals

Vertical number lines

(thermometer)


Cuisenaire, unifix,

multilink, straws,

(Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice

Games: collecting objects

or track games

Jars filled with objects e.g.

cotton reels, matchsticks

Outdoor score boards and

timers for PE activities





Learners will encounter number and place value

in other subjects:

Within the science curriculum there are opportunities

to connect with number and place value, for example,

in the notes and guidance it suggests that the children

might work scientifically by sorting and classifying

things according to whether they are living, dead or

were never alive, and recording their findings using

charts. The results from their findings can be

compared and ordered.

Within the geography curriculum, the children are

expected to identify seasonal and daily weather

patterns in the United Kingdom and the location of hot

and cold areas of the world in relation to the Equator

and the North and South Poles. When they do this

they could order the different temperatures and

compare using the greater and less than symbols.

Within the history curriculum, the children are

expected to explore where the people and events

they study fit within a chronological framework. This

could involve ordering the dates of events and the

coronations of different Kings and Queens and

placing these on a class number line.

Addition and subtraction

When working on number and place value and/or addition and subtraction,

there are opportunities to make connections between them:

Pupils should be taught to

read, write and interpret mathematical statements involving addition (+),

subtraction (–) and equals (=) signs

represent and use number bonds and related subtraction facts within 20

add and subtract one-digit and two-digit numbers to 20, including zero

solve one-step problems that involve addition and subtraction, using concrete

objects and pictorial representations, and missing number problems such as

7 = ☐ – 9.


When working on number and place value and/or multiplication and division,

there are opportunities to make connections between them:

Pupils should be taught to:

solve one-step problems involving multiplication and division, by calculating the

answer using concrete objects, pictorial representations and arrays with the

support of the teacher.

Measurement

When working on number and place value and/or measurement there are



choose and use appropriate standard units to estimate and measure

length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity

(litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers

and measuring vessels

compare and order lengths, mass, volume/capacity and record the results using

>, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to

make a particular value














Solve problems with addition and subtraction:

Using concrete objects and pictorial representations, including those involving numbers, quantities and measures

Applying their increasing knowledge of mental and written methods

Use partitioning, counting strategies and knowledge of number bonds to add or subtract a one-digit number or a multiple of 10 to any two-digit

number. To work out 86 – 50, for example, they might partition and calculate:

86 – 50 = 80 + 6 – 50 = 80 – 50 + 6 = 30 + 6 = 36

Similarly, to find the total number of people on a bus with 14 people on the top deck and 8 below, they might use:

14 + 8 = 14 + 6 + 2 = 20 + 2 = 22

Children add or subtract two-digit numbers using practical and informal methods and their knowledge of the relationships between operations.

For example, they count back along a number line to find 64 – 25 or count up from 67 to find the answer to 94 – 67. They represent such

calculations as number sentences. They calculate the value of an unknown in a number sentence such as ☐ ÷ 2 = 6 or 85 – ☐ = 29. They

recognise, for example, that to answer 85 – ☐ = 29 they could use the related addition 29 + ☐ = 85

Notes:


Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 Extend their knowledge and use of number facts, and use partitioning and number bonds to add and subtract numbers mentally to answer

questions such as 60 – ☐ = 52 or 35 = 20 + ☐. They make jottings where appropriate to support their thinking.

Answer problems such as:

Look at this number sentence: ☐ + ☐ = 20. What could the two missing numbers be? What else?

Can you tell me all the pairs of numbers that make 20?

Notes:




Add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

A two-digit number and ones

A two-digit number and tens

Two two-digit numbers

Adding three one-digit numbers

Use partitioning, counting strategies and knowledge of number bonds to add or subtract a one-digit number or a multiple of 10 to any two-

digit number. To work out 86 – 50, for example, they might partition and calculate:

86 – 50 = 80 + 6 – 50 = 80 – 50 + 6 = 30 + 6 = 36

Similarly, to find the total number of people on a bus with 14 people on the top deck and 8 below, they might use:

14 + 8 = 14 + 6 + 2 = 20 + 2 = 22

Children add or subtract two-digit numbers using practical and informal methods and their knowledge of the relationships between

operations. For example, they count back along a number line to find 64 – 25 or count up from 67 to find the answer to 94 – 67. They

represent such calculations as number sentences. They calculate the value of an unknown in a number sentence such as ☐ ÷ 2 = 6 or 85 –

☐ = 29. They recognise, for example, that to answer 85 – ☐ = 29 they could use the related addition 29 + ☐ = 85

Notes:


Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot Understand that addition can be done in any order and use this to solve an addition by rearranging the numbers to simplify the operation.

They need to understand that two numbers can be taken away from each other but that the answers will not be the same.

Notes:


Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems Check their addition and subtraction with a calculation that uses the inverse operation.

Answer questions, such as:

Look at this number sentence: 74 – 13 = 61

Write three more number sentences using these numbers. How do you know, without calculating, that they are correct?

What addition facts can you use to help you calculate these?

12 – 5, 19 – 8

Explain how the addition facts helped you.

I think of a number, I subtract 19 and the answer is 30. What is my number? How do you know?

Notes:



Non statutory guidance Pupils extend their understanding of the language of addition and subtraction to include sum and difference.

Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate 30 + 70 = 100; 100– 70 = 30 and 70 = 100 – 30. They check their

calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition.

Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.



connections


NRICH OVERVIEW

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ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings

Structured number lines

Empty number lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards

Place value cards & counters

100 squares

Pegs on hanger

Number rhymes

Practical objects linked to topic

Slider box cards

Dice

Number grid/Number scales/Number

facts/Difference/Number line ITPs

Within the science curriculum there are opportunities to

connect with addition and subtraction, for example, in the

notes and guidance it suggests that the children might

work scientifically by sorting and classifying things

according to various criteria, and recording their findings

using charts. This could include finding totals and

differences using the strategies for addition and

subtraction that they have covered in class.

Within the geography curriculum, the children are expected

to identify seasonal and daily weather patterns in the

United Kingdom and the location of hot and cold areas of

the world in relation to the Equator and the North and

South Poles. When they do this they could the numerical

differences in the seasonal average temperatures.

Within the history curriculum, the children are expected to

explore events beyond living memory that are significant

nationally or globally. When they do this they could plot

relevant dates on a number line and compare how long

they went on for by counting on or back along it. They also

need to explore the lives of significant individuals in the

past who have contributed to national and international

achievements. The children could plot the years in which

they were born and died on a number line and work out, by

counting on or back, for how many years they lived. They

could then compare the ages of different people and work

out how much older one person was than another.

Number and place value

(requirements include) Pupils should be taught to:

count in steps of 2, 3, and 5 from 0, and in tens from any

number, forward and backward

recognise the place value of each digit in a two-digit number

(tens, ones)

use place value and number facts to solve problems.

Measurement

When working on number and place value and/or

measurement there are opportunities to make connections



recognise and use symbols for pounds (£) and pence (p);

combine amounts to make a particular value

find different combinations of coins that equal the same

amounts of money

solve simple problems in a practical context involving

addition and subtraction of money of the same unit,

including giving change















Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers The children should be able to:

Recognise a multiple of 2, 5 or 10 and use their knowledge of multiplication facts to find corresponding division facts. They can say which

numbers are odd and which are even.

e.g. 2 x 5 = 10, show me three more number facts using these numbers.

Is 34 an odd number? How do you know?

Notes:


Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs Children should be able to:

Find missing numbers or symbols in a calculation:

4 x __ = 20, __ ÷ 10 = 3

Anna has 3 boxes of cakes. Each box contains 5 cakes. How many cakes does she have altogether? Show how you worked this out.

Notes:


Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot Children should be able to:

Use their knowledge of triangles of numbers to show related number facts.

e.g. If 6 x 2 = 12 then 2 x 6 = 12 and 12 ÷ 6 = 2.

Notes:


Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts Children should be able to:

Use various methods and apparatus to help them solve word problems such as:

There are 10 lollies in a bag. Charlie needs 30 lollies for his party. How many bags does he need to buy? Show how you worked this out.

Notes:




Non statutory guidance Pupils use a variety of language to describe multiplication and division.

Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5

multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations.

Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to

fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).



connections


NRICH OVERVIEW

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ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings


Hands counting

Straws (bunching)


number lines

100 squares


grid

Counting stick


Loop cards


Cake trays

Grouping/Number dials/Remainders

after division/Multiplication

array/Number grid/Multiplcation grid

ITP


Money – shopping: finding quantities in multiple

purchases, sales prices, sharing costs.

Measurement - calculating area and perimeter, finding

journey distances, reading and calculating scales,

adjusting recipe quantities.

Data – interpreting and evaluating data, calculating

amounts from pie charts and pictograms.














Y2: Fractions

Recognise, find, name and write fractions ⅓, ¼, 2⁄4 and ¾ of a length, shape, set of objects or quantity Using bar models to represent and unpick a fraction word problem

Harrison and Sam were talking and Harrison said that if he doubled Sam's age and added 2 he would get 12

Notes:


Write simple fractions e.g. ½ of 6 = 3 and recognise the equivalence of two quarters and one half

Would a chocolate lover rather have ½ or 3⁄5 of this bar of chocolate? Explain your answer.

Notes:





Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be

calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet ¾ as the first example of a non-unit fraction.

Pupils should count in fractions up to 10, starting from any number and using the ½ and 2⁄4equivalence on the number line (for example, 1 ¼ , 1 2⁄4 (or 1½ ), 1¾ , 2). This reinforces the concept of fractions as numbers and

that they can add up to more than one.



connections


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Fraction wall

Fraction plates

Fraction strips

Fraction cards

Shapes

Counting stick

Number lines

Other representations of fractions:

clock faces, chocolate bars

Fraction videos

Numicon, Cuisenaire

Fractions/Area/Moving

digits/Decimal numberline ITP

Fractions, in particular halves and quarters, can be linked

to many different ‘real-life’ contexts. Children naturally use

the term ‘half’ or ‘halve’ in general conversation.

Encourage them, and the adults working with them, to

refine their use of the word, and try to use it accurately.

‘Introduction to Fractions’ from Nrich provides a series

of 7 useful activities for connecting fractions to other

activities, in the form of a trail.

When teaching and learning about fractions in Year 2, links

can be made with other areas of the Year 2 Mathematics

curriculum;

Number and place value:

identify, represent and estimate numbers using

different representations, including the number line

Addition and subtraction:

solve problems with addition and subtraction:

using concrete objects and pictorial

representations, including those involving

numbers, quantities and measure

applying their increasing knowledge of mental and

written methods

From Multiplication and division:

solve problems involving multiplication and

division, using materials, arrays, repeated

addition, mental methods, and multiplication and

division facts, including problems in contexts.

Measurement:

tell and write the time to five minutes, including

quarter past/to the hour and draw the hands on a

clock face to show these times

know the number of minutes in an hour and the

number of hours in a day.

















Y2: Measurement

Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

Suggest sensible units you might use to measure: the height of your table; how much water is in a cup; the weight of my reading book; how

long it takes me to wash my hands.

Choose a piece of equipment to help you measure: the weight of your shoe; how long the classroom is; how long this lesson lasts; how

much water a cup holds.

How long is this line? Now draw a line 2 cm longer than this one.

How much water is in this measuring jug?

Find an object in the classroom that you think is about 10 cm long.

About how heavy do you think your pencil case is?

If I programme my floor turtle to go forward three metres is there enough room in the classroom? How could you measure to find out?

Notes:


Compare and order lengths, mass, volume/capacity and record the results using >, < and = Megan and Jack are growing beans. Megan’s plant is 25 cm tall. Jack’s is 38 cm tall. Whose plant is the taller? By how much? Can you

compare them using > or < ?

Notes:


Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value Holly has these coins.

Harry has the same amount of money but has six coins. What are they? Is there only one possible answer?

Notes:


Find different combinations of coins that equal the same amounts of money

Holly has these coins.

Harry has the same amount of money but has six coins. What are they? Is there only one possible answer?

Notes:


Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change Jess has saved 62p. She spends 15p. How much money does she have left? She pays with a 50p piece. How much change does she get?

Notes:




Compare and sequence intervals of time

What time does this clock show?

Draw a clock showing the time five minutes later.

Show your school day on clock faces: when do you leave home, have breaks, go back home, etc.

Notes:


Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times What time does this clock show?

Draw a clock showing the time five minutes later.

Show your school day on clock faces: when do you leave home, have breaks, go back home, etc.?

Notes:


Know the number of minutes in an hour and the number of hours in a day

Notes:



Non statutory guidance Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations.

Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’.

They become fluent in telling the time on analogue clocks and recording it.

Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.



connections


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TOOL

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PROGRESSION MAPS

REASONING MAPS

Mass/weight:


Equipment: bathroom


Force metres




tapes

Capasity & volume:




Time: Equipment: Demonstration clock with geared hands, Analogue clocks, Digital clocks, Timelines, Timetables Money: Coins, notes, money fans, tills Measuring scales/Ruler/Thermometer/Measuring cylinder/Tell time/Area ITPs

Learners will encounter measurement in various ways in

everyday life. Time, money, temperature, weighing

ingredients are just some of them.

Time is a sequence of events that relates to our daily life.

Clocks / watches and calendars are tools that measure

time.

We use money to buy the things we need. Using money

involves using different mathematics skills like counting,

adding, and subtracting amounts of money.

Measurement skills are extensively used in every kitchen,

every recipe. In school, opportunities arise in other

subjects such as science – measuring plant growth and

monitoring and recording temperatures, or P.E. –

measuring long jumps, counting skips, timing races etc.

Take cross-curricular opportunities to deepen children’s

understanding of units of measurement. For example, ask

them to:

find out what measures their parents use in their

jobs or in the home;

take measurements of jumps or throws in PE

lessons;

use measures in art, design and technology

lessons, discussing degrees of accuracy.



count in steps of 2, 3, and 5 from 0, and in tens

from any number, forward and backward

recognise the place value of each digit in a two-

digit number (tens, ones)

identify, represent and estimate numbers using

different representations, including the number

line

compare and order numbers from 0 up to 100; use

<, > and = signs

read and write numbers to at least 100 in

numerals and in words

use place value and number facts to solve

problems.















Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line

Notes:


Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

Notes:


Identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

Notes:


Compare and sort common 2-D and 3-D shapes and everyday objects Children can sort two sets of 2D and 3D shapes in 2 or more different ways using different criteria each time. For example, they might

choose ‘dimensions’ or ‘right angled’ Notes:




Non statutory guidance Pupils handle and name a wider variety of common 2-D and 3-D shapes including: quadrilaterals and cuboids, prisms, cones and polygons, and identify the properties of each shape (e.g. number of sides, number of faces).

Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.

Pupils read and write names for shapes that are appropriate for their word reading and spelling.

Pupils draw lines and shapes using a straight edge.



connections


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paper

Rulers

Geostrips




Children need to be encouraged to use the language

associated with shape in order to describe the physical

world and their environment. Understanding how things

fit together (or when and why they do not) is important

for making connections.

For example, building anything involves a lot of critical

consideration about shape in three dimensions, as well

as angles. Reading maps and simple plans also

involves an understanding of the relationship between

2-D and 3-D shape.

Geometry (position and direction)

Within other areas of the mathematics curriculum for

Year2, there will be opportunities to link work on

Geometry (properties of shape) with:

use mathematical vocabulary to describe

position, direction and movement, including

movement in a straight line and distinguishing

between rotation as a turn and in terms of right

angles for quarter, half and three-quarter turns

(clockwise and anti- clockwise).















Order and arrange combinations of mathematical objects in patterns and sequences Describe the patterns in sequences and predict what comes next in the sequence and continue the pattern.

Notes:


Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

Recognise whole, half and quarter turns. They describe turns and give and follow instructions to turn. For example, they give instructions to

a friend to follow a route around the playground. They make and draw half and quarter turns from the same starting point using, for example,

two geostrips.

Use the grid to help you complete this table.

Watch me as I rotate (turn) this picture of a clown.

trees B2

slide

seesaw

A3

Notes:



Fluency Reasoning Problem Solving (Rotate the clown smoothly and continuously through a full turn, keeping it facing the children a t all times.)Which of the pictures shows what

the clown will look like if I rotate (turn) my picture a half turn?

Tick the picture

(Do not rotate your picture this time)

Non statutory guidance Pupils should work with patterns of shapes, including those in different orientations.

Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and

programming robots using instructions given in right angles).



connections


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TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Logo

Bee bots

Compass

Square papers

Geo strips

Tracing paper

Co-ordinates ITP

Learners will encounter geometry: position and direction:

When studying animals, including those in micro-habitats,

the children could compare the way different animals

move. They could record these in tables or on charts, for

example, finding out animals that fly, swim, crawl or run.

They could observe how they do this. #Do they travel in

straight lines, move in a circular motion or dart about in

different directions

Within the geography curriculum, the children are expected

to use simple compass directions (North, South, East and

West) and locational and directional language (e.g. near

and far; left and right) to describe the location of features

and routes on a map. Give children the opportunity to

identify places on maps and to work out in which direction

they need to travel to get from one place to another.

In real life we all make turns and move in different

directions in everything we do without thinking about it.

You could ask the children to consider turns and moves

they make while listening to you. You could ask them to

make a diagram of moves they make around the

classroom, for example, from the classroom door to where

they sit and then to the carpet area. You could also ask

them to describe turns they make using the vocabulary of

Geometry: properties of shape


identify and describe the properties of 2-D shapes,

including the number of sides and line symmetry in

a vertical line

identify and describe the properties of 3-D shapes,

including the number of edges, vertices and faces

identify 2-D shapes on the surface of 3-D shapes

[for example, a circle on a cylinder and a triangle

on a pyramid]

compare and sort common 2-D and 3-D shapes

and everyday objects.

You could give the children a selection of 3D-shapes,

discuss their properties in terms of numbers of faces, sides

and vertices and shapes of faces and then ask them to make

patterns using their shapes according to their own criteria,

for example alternating shapes with rectangular faces and

shapes with circular faces. They could show their pattern for

other children to guess the rule. You could repeat this idea

for pictures of 2D-shapes, discussing properties including

symmetry first.













Fluency Reasoning Problem Solving clockwise, anti-clockwise, right and left. You could ask

them to think about their journeys to school or to a

favourite place. Did they notice the directions from home to

their chosen place? Probably not! Ask them to notice and

make a record of this next time they make the journey. You

could ask them to think about the turns and positions they

make when doing simple tasks like turning a door handle

or brushing their teeth.

Y2: Statistics

Interpret and construct simple pictograms, tally charts, block diagrams and simple tables Class 2 make a graph

5 children have blue eyes. Show this on a graph. More children have brown eyes than green eyes.

How many more?

Notes:


Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity Look at this pictogram

There are 12 boys in class 5.

Show this on a pictogram.

Notes:




A shop sold 10 ice lollies on Wednesday.

How many lollies were sold on Monday?

How many more lollies were sold on Tuesday than on Wednesday?


Ask and answer questions about totalling and comparing categorical data Some children rolled toy cars down a slope

How far did the blue car roll?

How much further did the green car roll than the red car?

Additional questions:

Which car rolled the furthest?

Make up a question about the red car and the yellow car.

Jane made a tally chart

How many more gulls than blackbirds did she see?

Additional questions:

Make up a question comparing the numbers of sparrows and blackbirds that Jane saw?

How many fewer thrushes than magpies did she see:-

12

2

10

3

Some children were asked to choose their favourite animal in the zoo. This table shows the results.

How many more girls than boys chose the giraffes?

How many more boys chose lions than elephants?

Which animal was chosen by the greatest number of children?

Notes:



Non statutory guidance Pupils record, interpret, collate, organise and compare information (e.g. using many-to-one correspondence with simple ratios 2, 5, 10).


Cross-curricular and real life connections Making connections to other

topics

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Carroll diagrams

Venn diagrams, hoops

Tables

Pictograms

Block graphs

Bar graphs

Multilink towers

Data Handling/Handygraph/Line

graph/ ITP

Tracing paper

Protractors

There are many opportunities to use skills developed through work on

statistics and data, across other curriculum areas.

In Science ;

Living things and their habitats

Non-statutory guidance: Pupils might work scientifically by:

sorting and classifying things according to whether they are living,

dead or were never alive, and recording their findings using

charts.

Plants

Non-statutory guidance: Pupils might work scientifically by:

observing and recording, with some accuracy, the growth of a

variety of plants as they change over time from a seed or bulb, or

observing similar plants at different stages of growth; setting up a

comparative test to show that plants need light and water to stay

healthy.

Uses of everyday materials

Non-statutory guidance Pupils might work scientifically by:

comparing different sound sources and looking for patterns;

carrying out tests to find the best places to locate fire bells in

school.

Sound

Non-statutory guidance Pupils should be encouraged to think

about unusual and creative uses for everyday materials. They

could ask questions about the movement of objects such as toy

cars on different surfaces; comparing them, by measuring how far

they go; ordering their findings and recording their observations

and measurements, for example by constructing tables and

charts, and drawing on their results to answer their questions.

Real life connections.

Link with activities that go on in school to give statistics work some

relevance and purpose.

Ask children to plan for how they might find out;

How many children walk to school?

What type of library books are borrowed the most often?

Discuss any graphs or tables that connect to other subjects or in

papers or on the internet that the children would find interesting.

Atlases are a great source of different types of graphs to discuss.

Number and Place Value


count in steps of 2, 3, and 5 from 0, and in

tens from any number, forward and

backward

recognise the place value of each digit in a

two-digit number (tens, ones)

identify, represent and estimate numbers

using different representations, including

the number line

compare and order numbers from 0 up to

100; use <, > and = signs

read and write numbers to at least 100 in

numerals and in words

use place value and number facts to solve

problems







http://mathstoolkit.wix.com/mathstoolkit#!geometry---position-and-direction/cn5v







MATHEMATICS

YEAR 3

CURRICULUM PLANNING

TOOLKIT



Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given

number

Count on from zero in steps of 2, 3, 4, 5, 8, 50, 100; b) Give me the number 100 less than 756

recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

For each of these numbers: 428, 205, 130, 25, 7, 909.

Tell me: How many hundreds? How many tens it has? How many ones?

Notes:


Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

Notes:


Compare and order numbers up to 1000

Sort these numbers into ascending order: 95, 16, 98, 74, 2, 0, 100

Notes:


Identify, represent and estimate numbers using different representations

Show me 642 on a number line, with Dienes apparatus, with place value cards, on a Gattegno grid;

What number is halfway between 65 and 95? How do you know?

Notes:


Read and write numbers up to 1000 in numerals and in words

Notes:


Solve number problems and practical problems involving these ideas

Jack walks 645 metres to school. Suzy walks 100 metres less. How far does Suzy walk?

What is 1 more than 485? Than 569? Than 299?

What number needs to go into each triangle? Explain why?

642 = 600 + Δ + 2 967 = Δ + 60 + 7

Notes:





Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100. They use larger numbers to at least 1000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (e.g. 146 = 100 and 40 and 6, 146 = 130 and 16). Using a variety of representations, including those related to measure, pupils continue to count in ones, tens and hundreds, so that they become fluent in the order and place value of numbers to 1000.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS



Place value charts



Counting stick

Beadstrings

Number lines

Dienes





(Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice


games


reels, matchsticks


PE activities






contexts and begin to explore their significance.

Comparing quantities in real life contexts such as

counting those present in school or having school

dinners

Comparing measures such as length, weight or

volume of different objects

Organising data can draw attention to aspects of

place value for instance through collecting information

about pets that others have or the distances that they

travel to get to school.

School sports day can offer opportunities for counting

and measuring and comparing quantities

Activities such as counting the number of seeds in a

packet can support children’s understandings of large

numbers and help them to see the value of strategies

such as rounding to the nearest 10

In fractions work:

Pupils count up and down in tenths; recognise that tenths

arise from dividing an object into 10 equal parts and in

dividing one-digit numbers or quantities by 10

Pupils connect tenths to place value, decimal measures and

to division by 10. They begin to understand unit and non-unit

fractions as numbers on the number line and deduce

relations between them such as size and equivalence (non-

statutory)

In work on measures:

Measure and compare: lengths (m/cm/mm); Mass (kg/g);

volume (l/ml)

Pupils continue to measure using appropriate tools and

units, progressing to a wider range of measures, including

comparing and using mixed units (e.g. 1kg and 200g) and

simple equivalents of mixed units (e.g. 5m = 500cm)

The comparison of measures should also include simple

scaling by integers (non-statutory)
















Add and subtract numbers mentally, including:

a three-digit number and ones

a three-digit number and tens

a three-digit number and hundreds

What number is 27 more than 145? What number is 19 more than 145? Explain how you worked out these two calculations.

Work out the missing digits:

3☐ + ☐2 = 85

Work out these subtraction calculations:

72 – 5 372 – 68 270 – 3

82 – 15 132 – 28 70 – 66

Did you use the same method for each calculation? If not, why not? Explain your methods to a friend and compare your methods with

theirs.

Notes:


Add and subtract numbers with up to three digits, using formal written methods of

columnar addition and subtraction

Paul says 172 – 15 = 163. Write down an addition calculation that you could do to check this.

Paul’s working is: 170 – 10 = 160 and 5 – 2 = 3 so 172 – 15 = 163

Can you identify where Paul has gone wrong?

Notes:


Estimate the answer to a calculation and use inverse operations to check answers

Notes:


Solve problems, including missing number problems, using number facts, place value,

and more complex addition and subtraction.

Notes:




Non statutory guidance Pupils practise solving varied addition and subtraction questions. For mental calculations with two-digit numbers, the answers could exceed 100.

Pupils use their understanding of place value and partitioning, and practise using column addition and subtraction with increasingly large numbers up to three digits to become fluent (see Mathematics Appendix 1).


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings


Empty number lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards


100 squares

Pegs on hanger

Number rhymes


Slider box cards

Dice




contexts and begin to explore their significance.

Comparing quantities in real life contexts such

as counting those present in school or having

school dinners

Comparing measures such as length, weight or

volume of different objects

Organising data can draw attention to aspects of

place value for instance through collecting

information about pets that others have or the

distances that they travel to get to school.

School sports day can offer opportunities for

counting and measuring and comparing

quantities

Activities such as counting the number of seeds

in a packet can support children’s

understandings of large numbers and help them

to see the value of strategies such as rounding

to the nearest 10

Making connections to other topics within this year

group

In fractions work:

Pupils count up and down in tenths; recognise that tenths

arise from dividing an object into 10 equal parts and in

dividing one-digit numbers or quantities by 10

Pupils connect tenths to place value, decimal measures and

to division by 10. They begin to understand unit and non-unit

fractions as numbers on the number line and deduce

relations between them such as size and equivalence (non-

statutory)

In work on measures:

Measure and compare: lengths (m/cm/mm); Mass (kg/g);

volume (l/ml)

Pupils continue to measure using appropriate tools and

units, progressing to a wider range of measures, including

comparing and using mixed units (e.g. 1kg and 200g) and

simple equivalents of mixed units (e.g. 5m = 500cm)

The comparison of measures should also include simple

scaling by integers (non-statutory)

https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239129/PRIMARY_national_curriculum_-_Mathematics.pdf
















Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Multiply seven by three; what is four multiplied by nine? Etc.

Circle three numbers that add to make a multiple of 4

11 12 13 14 15 16 17 18 19

Leila puts 4 seeds in each of her pots. She uses 6 pots and has 1 seed left over. How many seeds did she start with?

At Christmas, there are 49 chocolates in a tin and Tim shares them between himself and 7 other members of the family. How many

chocolates will each person get?

Notes:


Write and calculate mathematical statements for multiplication and division using the

multiplication tables that they know, including for two-digit numbers times one-digit

numbers, using mental and progressing to formal written methods One orange costs nineteen pence. How much will three oranges cost?

Mark drives 19 miles to work every day and 19 miles back. He does this on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays. How

many miles does he travel to work and back in one week?

Notes:


Solve problems, including missing number problems, involving multiplication and

division, including positive integer scaling problems and correspondence problems in

which n objects are connected to m objects

Miss West needs 28 paper cups. She has to buy them in packs of 6

How many packs does she have to buy?

Notes:




Non statutory guidance Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables. Pupils develop efficient mental methods, for example, using commutativity and associativity (for example,4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and multiplication and division facts(for example, using 3 × 2 = 6, 6 ÷ 3 = 2

and 2 = 6 ÷ 3) to derive related facts(for example,30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).

Pupils develop reliable written methods for multiplication and division, starting with calculations of two - digit numbers by one - digit numbers and progressing to the formal written methods of short multiplication and division.

Pupils solve simple problems in contexts, deciding which of the four operations to use and why. These include measuring and scaling contexts, (for example, four times ashigh, eight times as long etc.) and correspondence

problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings


Hands counting

Straws (bunching)


number lines

100 squares


grid

Counting stick


Loop cards


Cake trays




ITP

Learners will encounter aspects of multiplication and

division when working on area, relating to arrays. Problem

solving work involving finding all possibilities and

combinations also draws on knowledge of multiplication

tables facts.

Fractions work within other curriculum areas and in real life

links naturally to multiplication and division work.

The notion of equal groups can emerge in many different

activities and contexts, e.g. when packing boxes,

purchasing quantities of items for several people etc.

When focusing on aspects of ‘Number and Place Value’ in

Year 3, in particular when counting in steps of 4, 8, 50 and

100, children will have the opportunity to link with work on

multiplication and division.

When interpreting and presenting data using bar charts,

pictograms and tables in Year 3, children can use their

knowledge of multiplication facts when creating and reading

scales and data sets.












Y3: Fractions

Count up and down in tenths; recognise that tenths arise from dividing an object into 10

equal parts and in dividing one-digit numbers or quantities by 10


Use decimal notation for tenths

Divide single digits or whole numbers by 10

Explain how finding 1/10 is the same as dividing by 10

Here is part of a number line. Write in the numbers missing from the two empty boxes.

Notes:


Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit

fractions with small denominators


Recognise and write unit and non-unit fractions of shapes.

Unit Fractions. Unit means one. Here are some examples of unit fractions.

Can you spot the pattern? A unit fraction is one part of a whole that is divided into equal parts.

Non-unit fractions. Unit means one, so non-unit is any number apart from one. Here are some examples of non-unit fractions.

Understand that the number on the bottom of a fraction tells me how many pieces the whole is divided into

What fraction of this shape is shaded? How do you know? Is there another way that you can describe the fraction?

Find fractions of amounts

Here are 21 apples. Put a ring around one third of them.

Notes:




Recognise and use fractions as numbers: unit fractions and non-unit fractions with small

denominators


Position fractions on a number line; eg. mark fractions such as ½, 3 ½ and 2 3/10 on a number line marked from zero to 5.

A fraction of each shape is shaded. Match each fraction to the correct place on the number line. One has been done for you.

Notes:


Recognise and show, using diagrams, equivalent fractions with small denominators


Identify pairs of fractions that total 1.

Circle two fractions that have the same value

Notes:


Add and subtract fractions with the same denominator within one whole

[for example, 5⁄7 + 1⁄7 = 6⁄7 ]

This could also be done by using drawings and in the array form:

For addition:

and for subtraction:

Notes:



Compare and order unit fractions with the same denominator


Would you rather have 1/3 of 30 sweets

Notes:


Solve problems that involve all of the above

Children should be able to answer questions like:

15 grapes are shared equally onto five plates. What fraction of the grapes is on each plate?

Meg has 20 pet stickers to go on this page:

1/4 of them are dog stickers

1/2 of them are cat stickers

The rest are rabbit stickers

How many rabbit stickers does she have?

Notes:




Pupils connect tenths to place value, decimal measures and to division by 10.

They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to

measure.

Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.

They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity.

Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Fraction wall

Fraction plates

Fraction strips

Fraction cards

Shapes

Counting stick

Number lines

Other representations of fractions: clock faces,

chocolate bars

Fraction videos

Numicon, Cuisenaire

Fractions/Area/Moving digits/Decimal

numberline ITP

Learners will encounter fractions in:

Sharing: build on children’s earliest experiences

of fractions which are associated with sharing

food, toys and money etc. with family and

friends.

Money – shopping: comparing prices, sales (1/2

price) Measurement: Link to scaling and

proportion, for example, halving recipes

Fractions all around us: What fractions can you

see in the classroom, around the school, in the

local environment? For example, what fraction of

the class are boys, girls or adults? What fraction

of the class have pets?

Making Links across the curriculum: Read this

article on the NCETM website for ideas on a

multitude of cross curricular links.

Connect fractions to a clock face and to reading the time. It

is quarter past 12. What time will it be two and three quarter

hours later?

Begin to extend their knowledge of the number system to

include decimal numbers and fractions they have met so far.

Make connections with a range of representations, for

example: arrow cards, Dienes, bead string, 100 squares.

Understand the difference between fractions as ordinal

numbers (as numbers on a number line), fractions as being

a special kind of cardinal number (the answer to 1/2 of a

number depends on the quantity you are using) and fractions

as operators (What is ½ of 30? What is 2/3 of 45?).

Connect fractions to a range of units of measurement. For

example how many millilitres in ½ a litre? What is ¾ of 2kg?

Connect fractions to division through the concepts of equal

sharing and grouping. For example equal sharing between 2

people results in them having a half each. Equal sharing

between four people results in them having a quarter each.

OR There are 4 groups of 3 in 12, so 3 must be a quarter of

12.


















Y3: Measurement

Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity

(l/ml) Children should be able to:

Length: Show something that they think is just shorter/longer than a metre/centimetre/millimetre. They should be able to check whether they are

right.

Mass: Say which object in the classroom is heavier than 100 g/kilogram/half-kilogram and know how to check if they are correct.

Read scales such as this:

Capacity: Find a container that they think would hold one litre and check to find out if they were correct.

General: Say what each division on this scale is worth and explain how they worked this out.

Notes:


Measure the perimeter of simple 2-D shapes


Measure the sides of regular polygons in centimetres and millimetres and find their perimeters in centimetres and millimetres?

Notes:


Add and subtract amounts of money to give change, using both £ and p in practical

contexts


Solve problems like this:

Jake wants to buy a comic that costs £1. He saves 25p one week and 40p the next. How much more money does he need to buy the

comic?

Add these prices: £6.73, £9.10 and £7.00 to find the total. Find out how much they need to add to get £23?

Notes:


Tell and write the time from an analogue clock, including using Roman numerals from I to

XII, and 12-hour and 24-hour clocks


Read times like this in analogue and digital formats, including those with Roman numerals.

Notes:




Solve problems such as: Ben’s clock says 7:50 when he gets up. Place the hands on this clock to show this time.

Estimate and read time with increasing accuracy to the nearest minute; record and

compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock,

a.m./p.m., morning, afternoon, noon and midnight


Solve problems such as:

Kevin leaves home at quarter past 8 and arrives in school at 20 to 9. How long is his journey? How did you work this out?

How long is it between the times shown on these two clocks? How did you work it out?(oral question)

Notes:


Know the number of seconds in a minute and the number of days in each month, year and

leap year


Solve problems such as: Millie has a 100 ml bottle of medicine. She takes one fifth of the medicine each day. How many days does she take the

medicine for? How much medicine does she take each day? What calculation did you do to work this out?

Notes:


Compare durations of events

(for example to calculate the time taken by particular events or tasks)


Solve problems such as:

Estimate how long your favourite TV programme lasts. Use a television guide to work out how close your estimation was.

It takes 35 minutes to walk from home to school. I need to be there by 8.55 am. What time do I need to leave home?

How much does it cost to hire a rowing boat for three hours?

Notes:




Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (e.g. 1kg and 200g) and simples equivalents of mixed units (e.g.

5m = 500cm).

The comparison of measures should also include simple scaling by integers (e.g. a given quantity or measure is twice as long or five times as high) and this connects to multiplication.

Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units and giving change using manageable amounts. They record £ and p separately. The decimal

recording of money is introduced formally in year 4.

Pupils use both analogue and digital 12-hour clocks and record their times. In this way they become fluent in and prepared for using digital 24-hour clocks in year 4. Quick links Resources

(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING

BARRIERS

ARTICLES

VIDEOS


GAPS AND

MISCONCEPTIONS TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Mass/weight: Weights - kg’s & g’s, multilink

Equipment: bathroom scales,weighing

scales, balances, Force metres




tapes

Capasity & volume:




Time: Equipment: Demonstration clock with geared hands, Analogue clocks, Digital clocks, Timelines, Timetables Money: Coins, notes, money fans, tills Measuring scales/Ruler/Thermometer/Measuring cylinder/Tell time/Area ITPs

Measurement is a practical application of mathematics in real life. For example, during most days of our lives we work with money. We often estimate and/or calculate length, mass, capacity and time e.g. how long it will take us to travel somewhere, what time we need to leave home to get to an appointment, how much water to put in the kettle to make a mug of coffee.

Within the science curriculum there are many opportunities to connect with measurement, for example in the Programme of Study: working scientifically, it states that during years 3 and 4, pupils should be taught to use practical scientific methods, processes and skills through the teaching of the programme of study content, e.g.

setting up simple practical enquiries, comparative and fair tests

making systematic and careful observations and, where appropriate, taking accurate measurements using standard units, using a range of equipment, including thermometers and data loggers

Within history, see, for example:

Roman numbers

The history of our money

The history of length

The history of mass

The history of volume and capacity

The history of time

Within art, see for example, the work of Kandinsky.

Addition and subtraction Add and subtract numbers mentally including:

a three-digit number and ones

a three-digit number and tens

a three-digit number and hundreds Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction When working on measurement and/or addition and subtraction there are opportunities to make connections between them, for example: Finding totals and change in money problems, e.g. Ali spent £2.50 on a packet of pencils and £4.75 on a pencil case. What was her change from £10? Adding/subtracting different lengths, masses or capacities e.g. Sam had two litres of juice in a jug. He poured 750ml into his flask. How much juice was left in the jug? Solving problems that involve adding times and finding the differences between them e.g. Sally went to the park at 4 o’clock, she left for home at 5:15. For how long was she at the park? The train left Leicester station at 2:15pm. It took one hour and 55 minutes to arrive in London. At what time did the train arrive in London? Multiplication and division Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables When working on measurement and/or multiplication and division there are opportunities to make connections between them, for example: Comparing measurements, e.g. this pencil is 5cm in length. That pencil is 3 times longer. How long is the longer pencil? Fractions Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers of quantities by 10 Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators When working on measurement and/or fractions there are opportunities to make connections between them, for example: A millimetre is 1/10 of a centimetre, ½ a kilogram is 500g, 1/10 of a litre is 100ml Showing ¼ past, ½ past and ¼ to the hour on an analogue clock ¼ of an hour is 15 minutes, ½ and hour is 30 minutes, ¾ of an hour is 45 minutes.























Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in

different orientations and describe them

The requirements for Year 3 in Geometry: Properties of Shapes are quite explicit and exemplars are not particularly helpful. It is helpful, however,

to understand that, in Year 3, pupils should be expected to demonstrate understanding in this area by:

using appropriate mathematical vocabulary to describe the features of common 2-D and 3-D shapes including semicircles, hemispheres

and prisms

sorting and classifying collections of 2-D shapes in different ways using a range of properties including: ‘all sides are of equal length,’

‘has at least one right angle’ or ‘has at least one line of symmetry’

recording their classifications on Venn and Carroll diagrams, including diagrams involving more than one criterion.

Notes:


Recognise angles as a property of shape or a description of a turn

Notes:


Identify right angles, recognise that two right angles make a half-turn, three make three

quarters of a turn and four a complete turn; identify whether angles are greater than or less

than a right angle

Notes:


Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Notes:





Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the

properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.

Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING

BARRIERS

ARTICLES

VIDEOS

SUGGESTED

ACTIVITIES

GAPS AND

MISCONCEPTIONS

TOOL

MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

2D shapes, 3D shapes, Polydron, Shape tiles Protractors, Angle

measures, Set squares

Isometric dot paper,

squared paper, tracing

paper

Rulers

Geostrips

Pin boards, Geo boards

and elastic bands,

Art straws and

construction kits


Learners will encounter geometry (properties of shapes) in a number of contexts: Within the art curriculum there are opportunities to connect with geometry: properties of shape, for example, in the requirements the children should be taught to improve their mastery of art and design techniques, including drawing, painting and sculpture with a range of materials (e.g. pencil, charcoal, paint, clay). You could ask the children to make a selection of 3D shapes, such as, spheres, cubes, cuboids and pyramids out of clay and then put them together to make a sculpture of their own design. An activity like this should include a discussion of each shape’s properties, what they can do and where they are seen in real life. The art curriculum also requires the children to be taught about great artists, architects and designers in history. The Art of Mathematics articles in the Primary Magazine explore the works of many artists. In each article there is a short history of the artist and many mathematical activities to explore through their art work. Within the design and technology curriculum, the children should be taught the knowledge, understanding and skills needed to design and make things working in a range of relevant contexts. You could give the children opportunities to make packaging for something to be sold. This could involve exploring nets of cubes and cuboids. In real life, shape and pattern are everywhere. You could ask the children to explore shape in their environment. What 3D shapes can they see in the classroom? What 2D shapes can they see in patterns? You could follow the ideas on Islamic patterns in The Art of Mathematics in issue 13 of the Primary Magazine. You could show the children the works of famous artists such as Mondrian and Kandinsky and ask the children to explore the shapes that they can see, the angles, parallel and perpendicular lines and so on. The Art of Mathematics in the Primary Magazine provides a useful resource for this.

Fractions When working on geometry: properties of shape and/or fractions, there are opportunities to make connections between them, for example: In the guidance for fractions it states that the children should continue to recognise fractions in the context of shape. Give children the opportunity to explore these during shape and fractions lessons in order to reinforce and consolidate their learning in both areas. For example, you could ask the children to draw a variety of regular and irregular shapes and explore which ones can be divided into halves, thirds, quarters etc. It is important that the children consider that equal fractions of a shape have the same area rather than parts that look the same which is often how they are presented in textbooks and worksheets. You could ask the children to cut up pieces of their shapes to find out if they are the same. For example, they could draw the rectangle below and its two diagonals:

The resulting parts don’t all look the same, but each is a quarter. Can the children prove this? They could, for example, cut out each triangle and then cut it in half. These pieces are eighths. Two eighths are equal to a quarter therefore the triangles are all quarters. You might give the children a tangram like this: Ask them to identify each of the shapes (right angled isosceles triangles, parallelogram and square). They then cut the pieces out and explore the fractions that they can make. For example, the small red triangle is half of the parallelogram, the area of square is half that of the green triangle, the red triangle is a quarter of the green triangle. You could give the children a selection of 3D shapes and ask them to visualise and sketch what they would become if cut in half. For example a sphere would become a hemisphere, a cube would become a cuboid. They could make triangular prisms out of card or plasticine and explore what these would look like if cut into thirds or quarters. What is the same about them, what is different? Measurement When working on geometry: properties of shape and/or measurement, there are opportunities to make connections between them, for example: One of the requirements in measurement is that the children should be taught to measure the perimeter of simple 2D shapes. You could ask the children to draw regular and irregular triangles, rectangles (including squares), pentagons and hexagons. Once they have, they measure their perimeters. Can they find a quick way of finding the perimeter of regular shapes? Can they make up a formula for this? They may be able to come up with l x n, where l = length and n = number of sides. So, for example a pentagon with sides of 4cm would be 4cm x 5 (20cm). In the guidance for measurement it encourages the comparison of measurements through simple scaling by integers and link this to multiplication. You could ask the children to draw small shapes and then measure their sides to the nearest centimetre. They could then scale these up so that they are, for example, twice the size or five times bigger. They could then draw their shapes again to the new measurements and compare the two.




















Y3: Statistics

Interpret and present data using bar charts, pictograms and tables

Process, present and interpret data to pose and answer questions. They use all representations such as Venn and Carroll diagrams, bar charts,

pictograms. They collect data quickly onto a class tally chart. Children recognise that a tally involves grouping in fives and that this helps them to

count the frequencies quickly and accurately. They produce a simple pictogram and/or bar chart, where a symbol represents 2 units.

Children sort and classify objects, numbers or shapes according to two criteria, and display this work on Venn and Carroll diagrams.

Notes:


Solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many

fewer?’] using information presented in scaled bar charts and pictograms and tables.

Collect, represent and interpret data in order to answer a question that is relevant to them, for example:

What new addition to the school play equipment would you like?

Which class race shall we choose for sports day?

They decide on the information they need to collect and collect it efficiently. They collate the information on a tally chart or frequency table, then

use this to make simple frequency diagrams such as bar charts, using ICT where appropriate. They discuss the outcomes, responding to questions

such as:

Which items had fewer than five votes?

Would the table be the same if we asked Year 6?

How might the table change if everyone had two votes?

Children present their conclusions to others, identifying key points that should be included. They make suggestions as to how this data could be

used; for example, they may decide that they need to investigate the price of different equipment or discuss what they need to do to prepare for

their chosen race.

Notes:





Pupils understand and use simple scales (e.g. 2, 5, 10 units per cm) in pictograms and bar charts with increasing accuracy.

They continue to interpret data presented in many contexts.


(Years 1-6)


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TOOL

MENTAL IMAGES

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Carroll diagrams


Tables

Pictograms

Block graphs

Bar graphs

Multilink towers

Data

Handling/Handygraph/Line

graph/ ITP

Tracing paper

Protractors

Learners will encounter statistics in:

Within the science curriculum there are

opportunities to work with statistics, for example,

in working scientifically there is a requirement

that the children record findings using simple

scientific language, drawings, labelled diagrams,

keys, bar charts, and tables. In the section on

magnets children should sort materials into

those that are magnetic and those that are not.

This can be done using tables or single criteria

Venn and Carroll diagrams.

Within the geography curriculum, the children

are expected to describe and understand key

aspects of:

physical geography, including: climate

zones, biomes and vegetation belts,

rivers, mountains, volcanoes and

earthquakes, and the water cycle

human geography, including: types of

settlement and land use, economic

activity including trade links, and the

distribution of natural resources

including energy, food, minerals and

water

Give the children opportunities to gather relevant

data and present it in tables, bar charts or

pictograms and then analyse their findings.


When working on statistics and/or number and place value, there are opportunities to

make connections between them, for example:

When learning about number and place value the children are expected to count in

and use multiples of 2, 3, 4, 5, 8, 10, 50 and 100. When presenting data, the children

are expected to use simple scales for example, 2, 5, 10 units per centimetre, in

pictograms and bar charts. The connections between the two are obvious! Give the

children opportunities to practise using the required multiples when creating bar

charts and pictograms. You could ask the class to pick their favourite food, pet or

sport from a given list and then to make a bar chart or pictogram choosing the scale

that they think is most appropriate.


When working on statistics and/or addition and subtraction, there are opportunities to

make connections between them, for example:

The requirements for statistics include solving one and two step problems, answering

‘How many more?’ and ‘How many fewer?’ questions using information that is

presented in bar charts, pictograms and tables. Clearly, solving such problems

requires the ability to add and subtract. When covering these concepts you could

provide the children with copies of bar charts, pictograms and tables and ask them to

then make up and solve problems involving addition and subtraction.

Properties of shape

When working on statistics and/or geometry: properties of shape, there are


During the children’s work on properties of shape, give them opportunities to sort a

variety of 2D and/or 3D shapes into Venn and Carroll diagrams according to criteria

that they choose for themselves.














MATHEMATICS

YEAR 4

CURRICULUM PLANNING

TOOLKIT



Count in multiples of 6, 7, 9, 25 and 1000


Explain how to work out the 6 times-table from the 3 times-table or the 9 times-table from the 3 times-table.

Know that 9 × 8 = 72 so that 72 ÷ 9 = 8 and deduce 720 ÷ 9.

Explain the relationship between 8 × 7 = 56, 6 × 7 = 42 and 14 × 7 = 98.

Notes:


Find 1000 more or less than a given number


Answer questions such as, what is the missing number in the number sentence and how do you know? 5742 + ? = 9742

Notes:


Count backwards through zero to include negative numbers


Create a sequence that includes the number –5 and then describe the sequence to the class.

Explain how to find the missing numbers in a sequence eg. _ –9, –5, –1, _ and explain the rule.

Answer questions such as, What number can you put in the box to make this statement true? __ < –2

Notes:


Recognise the place value of each digit in a four-digit number (thousands, hundreds,

tens, and ones)


Give the value of a digit in a given number e.g. the 7 in 3 274

Write in figures a given number e.g. four thousand and twenty.

Recognise a number partitioned like this: 4 000 + 200 + 60 + 3 and be able to read and write the number.

Create the biggest and smallest whole number with four digits eg. 3, 0, 6, 5

Find missing numbers in a number sentence e.g. _ +_ = 1249

Notes:


Order and compare numbers beyond 1000


Find numbers that could go in the boxes to make these correct, � + � < 2000, 3000 > � – �

Notes:




Identify, represent and estimate numbers using different representations


Answer questions such as, which of these numbers is closest to the answer of 342 – 119: 200 220 230 250 300

Identify what the digit 7 represents in each of these amounts: £2.70, 7.35m, £0.37, 7.07m

Notes:


Round any number to the nearest 10, 100 or 1000


Explain tips to give someone who is learning how to round numbers to the nearest 10, or 1000.

Answer questions such as, I rounded a number to the nearest 10. The answer is 340. What number could I have started with? Know what to

look for first when you order a set of numbers and know which part of each number to look at to help you.

Notes:


Solve number and practical problems that involve all of the above and with

increasingly large positive numbers


Sort problems into those they would do mentally and those they would do with pencil and paper and explain their decisions. Answer

questions such as, There are 70 children. Each tent can accomodate up to 6 children. What is the smallest number of tents they will need?

The distance to the park is 5 km when rounded to the nearest kilometre. What is the longest/shortest distance it could be? How would you

give somebody instructions to round distances to the nearest kilometre?

Notes:


Read Roman numerals to 100 (I to C) and know that over time, the numeral system

changed to include the concept of zero and place value

This is new content for the primary national curriculum in England. Suggestions for what children should be able to do include;

Know what each letter represents in Roman numerals and be able to convert from Roman numeral to our current system (Arabic) and from

Arabic to Roman e.g. 76 = _ in Roman numerals, CLXIX = _ Arabic numerals.

Know that the current western numeral system is the modified version of the Hindu numeral system developed in India to include the concept

of zero and place value.

Notes:




Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through

varied and frequent practice. They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far.

They connect estimation and rounding numbers to the use of measuring instruments.

Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a

period of time.



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MENTAL IMAGES

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Dice and spinners interactive



Place value charts



Counting stick

Beadstrings

Number lines

Dienes





(Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice


games


reels, matchsticks


PE activities





Knowledge of number and place value permeates many

different aspects of everyday life. The introduction of

Roman Numerals in Year 4 can be developed alongside

knowledge of other number systems throughout history.

Common sources will be clocks, page numbers in books,

production dates on TV programmes and films.

The use of ‘Zero’ within telephone numbers and the start

of the Dewey Decimal library referencing system can be

explored in the classroom. Negative numbers can be

introduced through the contexts of temperature, or bank

accounts in the ‘red’.

When counting in multiples, try to link to ‘everyday’ items

such multiples of six eggs, multiples of 6 players in a six-a-

side football team, 9 players in a baseball team.

Numbers 1000 or more as dates and money.

When teaching rounding or estimating, the context of

numbers of people in an audience or crowd could be used.

Number and place value skills are applied in many other

areas of the mathematics curriculum. Knowledge of four-digit

numbers and decimal numbers links to work in addition and

subtraction.

Place value is also essential when estimating and using

inverse operations to check answers to calculations.

Counting in multiples of 6, 7 and 9 links to the recall of

multiplication and division facts for multiplication tables up to

12 × 12. Other mental multiplication and division work relies

heavily on sound place value and number knowledge.












http://nrich.maths.org/6717&part=



Add and subtract numbers with up to 4 digits using the formal written methods of

columnar addition and subtraction where appropriate

See schools calculation policy


Notes:

Estimate and use inverse operations to check answers to a calculation


Notes:

Solve addition and subtraction two-step problems in contexts, deciding which

operations and methods to use and why. Children should be able to carry out practical tasks such as that represented here in an Australian classroom.

Children were asked to individually run the class market stall. They were told they could use mental strategies or the whiteboard provided to

assist them in their calculations. The customer (their teacher) would come to purchase some items. Each child was asked to solve a

transaction problem involving a single item (calculating change – subtraction) and then a transaction involving two items (adding together

values and then calculating change or two subsequent subtractions). They were also asked to explain their thinking and asked how to give

the change in a different way (representing money values in various ways).

Children should be able to solve problems such as:

I have read 134 of the 512 pages of my book. How many more pages must I read to reach the middle?

There are 8 shelves of books. 6 of the shelves hold 25 books each. 2 of the shelves have 35 books each. How many books

altogether are on the shelves?

I think of a number, subtract 17, and divide by 6. The answer is 20. What was my number?

You start to read a book on Thursday. On Friday you read 10 more pages than on Thursday. You reach page 60. How many pages

did you read on Thursday?


Notes:


http://play.viostream.com/?play=01239ec9-dbf1-4959-8d23-0c8919545f4e



Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics Appendix in this document) or school calculation policy.



connections


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MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings


Empty number lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards


100 squares

Pegs on hanger

Number rhymes


Slider box cards

Dice



Learners will encounter addition and subtraction in many

real life contexts:

When shopping, children will be required to find totals,

calculate change and estimate costs in pounds and pence.

Planning a budget for various projects will involve a great

deal of calculation

Practical tasks such as designing models and packaging,

and calculating perimeters for fencing and borders will all

involve addition and subtraction skills.

When working on addition and subtraction and/or

measurement, there are opportunities to make connections

between them. Examples include:

Measure and calculate the perimeter of a

rectilinear figure (including squares) in

centimetres and metres

Estimate, compare and calculate different

measures, including money in pounds and pence
















Y4: Multiplication and Division Recall multiplication and division facts for multiplication tables up to 12 × 12


Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.

e.g. One orange costs nineteen pence. How much will three oranges cost?

What is twenty-one multiplied by nine?

How many twos are there in four hundred and forty?

Notes:


Use place value, known and derived facts to multiply and divide mentally, including:

multiplying by 0 and 1; dividing by 1; multiplying together three numbers


Pupils practise mental methods and extend this to three-digit numbers to derive facts, for example 200 × 3 = 600 into 600 ÷ 3 = 200.

e.g. Divide thirty-one point five by ten.

Ten times a number is eighty-six. What is the number?

Notes:


Recognise and use factor pairs and commutativity in mental calculations


Pupils write statements about the equality of expressions (e.g. use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4

= 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations e.g. 2 x 6 x 5 =

10 x 6.

e.g. Understand and use when appropriate the principles (but not the names) of the commutative, associative and distributive laws as they

apply to multiplication:

Example of commutative law 8 × 15 = 15 × 8

Example of associative law 6 × 15 = 6 × (5 × 3) = (6 × 5) × 3 = 30 × 3 = 90

Example of distributive law 18 × 5 = (10 + 8) × 5 = (10 × 5) + (8 × 5) = 50 + 40 = 90

Notes:


Multiply two-digit and three-digit numbers by a one-digit number using formal written

layout Notes:


Solve problems involving multiplying and adding, including using the distributive law

to multiply two digit numbers by one digit, integer scaling problems and harder

correspondence problems such as n objects are connected to m objects

Children should be able to: Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should

include correspondence questions such as the numbers of choices of a meal on a menu, or three cakes shared equally between 10 children.

e.g. 185 people go to the school concert. They pay £l.35 each.How much ticket money is collected?

Notes:



Fluency Reasoning Problem Solving Programmes cost 15p each. Selling programmes raises £12.30. How many programmes are sold?


Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.

Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).

Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers (see Mathematics Appendix 1 ).

Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules

of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.

Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a

menu, or three cakes shared equally between 10 children.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings


Hands counting

Straws (bunching)


number lines

100 squares


grid

Counting stick


Loop cards


Cake trays




ITP


Counting – Calculating totals by counting small amounts or

a proportion and then scaling up e.g. standing against a

tree and using your known height to work out ‘How many

of me are equal to the height of the tree?’ or counting

people on one part of a stadium and multiplying to

calculate the total number of spectators.

Money – shopping: adding multiple products of the same

price, adding coins of same value, working out

fraction/percentage discounts and special offers, sharing

bills.

Measurement – Scaling quantities (e.g. recipes) to cater

for more and less people, reading scales and unlabelled

increments on measuring apparatus, calculating area for

carpets, decorating etc., scaling shapes to scale geometric

artwork e.g. How would you make this triangle three times

its size/half its size? Comparing river lengths/building

heights e.g. the River Nile is x times longer than the River

X. The height of Snowdon is (fraction) of the height of

Everest.

Statistics – Reading scales and determining appropriate

scales for different types of graph relating to weather,

temperature, sound etc., Working with proportion, fractions

and percentages using pie charts, comparing data using

ratio, fractions and scaling such as proportion of children

missing breakfast or 1 in 7 children under 10 now has a

mobile phone etc.

Measurement

Convert between different units of measure [for

example, kilometre to metre; hour to minute]

solve problems involving converting from hours to

minutes; minutes to seconds; years to months;

weeks to days.

Fractions

recognise and show, using diagrams, families of

common equivalent fractions

count up and down in hundredths; recognise that

hundredths arise when dividing an object by one

hundred and dividing tenths by ten

recognise and write decimal equivalents to 1/4 ,

1/2 , 3/4

find the effect of dividing a one- or two-digit

number by 10 and 100, identifying the value of

the digits in the answer as ones, tenths and

hundredths















Y4: Fractions (including decimals)

Recognise and show, using diagrams, families of common

equivalent fractions

Recognise that five tenths (5⁄10) or one half is shaded.

Recognise that two eighths (2⁄8) or one quarter (¼) of the set of buttons is ringed

Recognise that one whole is equivalent to two halves, three thirds, four quarters… For example, build

a fraction ‘wall’ using a computer program and then estimate parts.

Recognise patterns in equivalent patterns, such as:

½ = 2⁄4 = 3⁄6 = 4⁄8 = 5⁄10 = 6⁄12 = 7⁄14 And similar patterns for ⅓, ¼, ⅕, ⅙, 1⁄10.

Here is a square.

What fraction of the square is shaded?

Here are five diagrams. Look at each one.

Put a tick (✔︎) on the diagram is exactly ½ of it is shaded. Put a cross (✗) if it

us not.

Notes:


Count up and down in hundredths; recognise that hundredths arise when dividing an

object by one hundred and dividing tenths by ten.

Respond to questions such as:

What does the digit 6 in 3.64 represent? The 4? What is the 4 worth in the number 7.45? The 5?

Write the decimal fraction equivalent to:

two tenths and five hundredths; twenty-nine hundredths; fifteen and nine hundredths.

Continue the count 1.91, 1.92, 1.93, 1.94 ...

Suggest a decimal fraction between 4.1 and 4.2

Know how many 10 pence pieces equal a pound, how many 1 pence pieces equal a pound, how many centimetres make a metre.

Notes:




Solve problems involving increasingly harder fractions to calculate quantities, and

fractions to divide quantities, including non-unit fractions where the answer is a whole

number

What is one-fifth of twenty-five?

Write the missing number to make this correct.

Mary has 20 pet stickers to go on this page.

¼ of them are dog stickers. ½ of them are cat stickers. The rest are rabbit stickers. How many rabbit stickers does

she have?

Match each box to the correct number. One has been done for you.

Notes:


Add and subtract fractions with the same denominator

For example:

½ + ½, ¼ + ¾, ⅜ + ⅝, ⅗ + ⅘ + ⅕, 7⁄10 + 3⁄10 + 5⁄10 + 8⁄10, ¾ - ⅓, 6⁄7- 4⁄7,

9⁄10 + 4⁄10, – 3⁄10

Notes:


Recognise and write decimal equivalents of any number of tenths or hundredths

Recognise that, for example:

0.07 is equivalent to 7⁄100 6.35 is equivalent to 6 35⁄100

Particularly in the contexts of money and measurement

Respond to questions such as:

Which of these decimals is equal to 19⁄100? 1.9 10.19 0.19 19.1 Write each of these as a decimal fraction: 27⁄100 3⁄100 2 33⁄100

Notes:


Recognise and write decimal equivalents to ¼, ½, ¾

Know that, for example

0.5 is equivalent to ½, 0.25 is equivalent to ¼, 0.75 is equivalent to ¾, 0.1 is equivalent to 1⁄10

Particularly in the context of money and measurement.

Notes:


Round decimals with one decimal place to the nearest whole number

Round these to the nearest whole number. For example:

9.7, 25.6, 148.3

Round these lengths to the nearest metre:

1.5m, 6.7m, 4.1m, 8.9m

Round these costs to the nearest £:

£3.27, £12.60, £14.05, £6.50

Notes:



Compare numbers with the same number of decimal places up to two decimal places

Place these decimals on a line from 0 to 2:

0.3, 0.1, 0.9, 0.5, 1.2, 1.9

Which is lighter: 3.5kg or 5.5kg? 3.72kg or 3.27kg? Which is less: £4.50 or £4.05?

Put in order, largest/smallest first: 6.2, 5.7, 4.5, 7.6, 5.2, 99, 1.99, 1.2, 2.1

Convert pounds to pence and vice versa. For example: Write 578p in £.

How many pence is £5.98, £5.60, £7.06, £4.00? Write the total of ten £1 coins and seven 1p coins (£10.07)

Write centimetres in metres. For example, write: 125 cm in metres (1.25 metres)

Notes:


Solve simple measure and money problems involving

fractions and decimals to two decimal places

How much more do the boots cost than the trainers? Rosie buys a pair of trainers and a

pair of sandals. How much change does she get from £50?

A box of four balls costs £2.96. How much does each ball cost? Dean and Alex buy 3 boxes of balls between

them. Dean pays £4.50. How much must Alex pay? KS2 Paper B level 3

A full bucket holds 5½ litres. A full jug holds ½ a litre. How many jugs full of water will fill the bucket?

Harry spent one quarter of his savings on a book. What did the book cost if he saved: £8…£10…£2.40…?

Gran gave me £8 of my £10 birthday money. What fraction of my birthday money did Gran give me?

Max jumped 2.25 metres on his second try at the long jump.

This was 75 centimetres longer than on his first try.

How far in metres did he jump on his first try?

Notes:


Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the

value of the digits in the answer as ones, tenths and hundredths

Notes:




Pupils should connect hundredths to tenths and place value and decimal measure. They extend the use of the number line to connect fractions, numbers and measures. Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths. Pupils make connections between fractions of a length, of a shape and as a representation of one whole or set of quantities. Pupils use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example,6⁄9 = 2⁄3 or 1⁄4 = 2⁄8). Pupils continue to practise adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole. Pupils are taught throughout that decimals and fractions are different ways of expressing numbers and proportions. Pupils’ understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to division of whole number by 10 and later 100. They practise counting using simple fractions and decimals, both forwards and backwards. Pupils learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in several ways, such as on number lines



connections


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Fraction wall

Fraction plates

Fraction strips

Fraction cards

Shapes

Counting stick

Number lines



Fraction videos

Numicon, Cuisenaire



Learners will encounter fractions and decimals in many other aspects of mathematics: Measurements – Children can be asked to find the position 1⁄10 along a metre stick. Where would ¾ be? How many centimetres along the stick is that? Reading scales – When using a tape measure, kitchen scales, a measuring jug. They may be asked to find 1⁄10 of a metre, a kilogram, a litre. Exploring fractions in everyday contexts – how many square pieces make half of this chocolate bar? Data handling – which flavour crisps did ¼ of the children like best? The National Gallery of Art website provides a wonderful resource based on Thiebaud’s ‘Cakes’ picture, and provides some wonderful starting points for fractions work in mathematics.

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum. Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics. (National Curriculum in England Framework Document, September 2013, p9)















http://www.nga.gov/content/ngaweb/education/teachers/lessons-activities/counting-art/thiebaud-elem.html


Y4: Measurement

Convert between different units of measure [for example, kilometre to metre; hour to

minute]

Learn the relationships between familiar units of measurement. They learn that kilo means one thousand to help them remember that there

are 1000 grams in 1 kilogram and 1000 metres in 1 kilometre. They respond to questions such as: A bag of flour weighs 2 kg. How many

grams is this? They suggest suitable units to measure length, weight and capacity; for example, they suggest a metric unit to measure the

length of their book, the weight of a baby, the capacity of a mug. They suggest things that you would measure in kilometres, metres, litres,

kilograms, etc.

Record lengths using decimal notation, for example recording 5 m 62 cm as 5.62 m, or 1 m 60 cm as 1.6 m. They identify the whole-number,

tenths and hundredths parts of numbers presented in decimal notation and relate the whole number, tenths and hundredths parts to metres

and centimetres in length.

Notes:


Measure and calculate the perimeter of a rectilinear figure (including squares) in

centimetres and metres

Measure the edges of a rectangle and then combine these measurements. They realise that by doing this they are calculating its perimeter.

Given the perimeter of a rectangle they investigate what the lengths of its sides could be. They work out the perimeter of irregular shapes

drawn on a centimetre square grid, e.g. using the ITP ‘Area’.

Notes:


Find the area of rectilinear shapes by counting squares

For example, they draw irregular shapes on centimetre square grids, and compare their areas and perimeters.

Notes:




Estimate, compare and calculate different measures, including money in pounds and

pence

Draw on their calculation strategies to solve one- and two-step word problems, including those involving money and measures. They use

rounding to estimate the solution, choose an appropriate method of calculation (mental, mental with jottings, written method) and then check

to see whether their answer seems sensible. They throw a beanbag three times and find the difference between their longest and shortest

throws. After measuring their height, they work out how much taller they would have to grow to be the same height as their teacher. They

solve problems such as:

Dad bought three tins of paint at £5.68 each. How much change does he get from £20?

A family sets off to drive 524 miles. After 267 miles, how much further do they still have to go?

Tins of dog food cost 42p. They are put into packs of 10. How much does one pack of dog food cost? 10 packs?

A can of soup holds 400 ml. How much do 5 cans hold? Each serving is 200 ml. How many cans would I need for servings for 15

people?

I spent £4.63, £3.72 and 86p. How much did I spend altogether?

A string is 6.5 metres long. I cut off 70 cm pieces to tie up some balloons. How many pieces can I cut from the string?

A jug holds 2 litres. A glass holds 250 ml. How many glasses will the jug fill?

Dean saves the same amount of money each month. He saves £149.40 in a year. How much money does he save each month?

Notes:


Read, write and convert time between analogue and digital 12- and 24-hour clocks

Notes:


Solve problems involving converting from hours to minutes; minutes to seconds; years

to months; weeks to days

Solve problems involving units of time, explaining and recording how the problem was solved. For example: Raiza got into the pool at 2:26

pm. She swam until 3 o’clock. How long did she swim? They count on to find the difference between two given times, using a number line or

time line where appropriate and use the 24-hour clock to measure time.

Notes:




Pupils build on their understanding of place value and decimal notation to record metric measures, including money. They use multiplication to convert from larger to smaller units. Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. They relate area to arrays and multiplication.


(Years 1-6)

Cross-curricular and real life connections

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ARTICLES

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PROGRESSION MAPS

REASONING MAPS

Mass/weight:


Equipment: bathroom


Force metres




tapes

Capasity & volume:




Time:

Equipment: Demonstration clock with

geared hands, Analogue clocks,

Digital clocks, Timelines, Timetables

Money:

Coins, notes, money fans, tills

Measuring

scales/Ruler/Thermometer/Measuring

cylinder/Tell time/Area ITPs

Learners will encounter measurement in: Within the science curriculum there are opportunities to connect with measurement, for example, one of the requirements for states of matter is that the children should be taught to identify the part played by evaporation and condensation in the water cycle and associate the rate of evaporation with temperature. This could involve measuring temperatures using a thermometer and tracking the changes over, for example, a morning. The children record the temperature every 40 minutes making a note of the time in 24 hour digital format. Within the design and technology curriculum there will be plenty of opportunities for accurate measuring, particularly of length using different units in the designing and making stages. Within the cooking and nutrition curriculum the children should be taught to prepare and cook a variety of predominantly savoury dishes using a range of cooking techniques. As they work on these practically they will need to measure mass and volume. You could provide them with recipes and ask them to scale them up or down for different numbers of people and then to measure out the correct ingredients. If they require cooking time, the children could make up timetables to show preparation, cooking and clearing up times using 12 or 24 hour digital formats. Within the history curriculum, see, for example:

Roman numbers

The history of our money

The history of length

The history of mass

The history of volume and capacity

The history of time Within the art curriculum, see for example, the work of Kandinsky In real life, measurement is something that we frequently do without even thinking about it. You could ask the children to think about what they have done from waking up in the morning that has involved measuring. They might think of ideas to do with length (distance walking into school), mass (weight of their back pack),capacity and volume (filling their flask with juice), time (leaving home to get to school on time).






















Statutory requirements that are particularly relevant:


recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

order and compare numbers beyond 1000

identify, represent and estimate numbers using different representations

round any number to the nearest 10, 100 or 1000

solve number and practical problems that involve all of the above and with increasingly large positive

numbers

When working on measurement and/or number and place value, there are opportunities to make connections


When converting between different units of measurement children need to know about the place value of

digits. If converting, for example, 1.5km to metres they need to know that 1km is 1000m and that 0.5km is half

of 1000m in order to give an answer of 1500m.

When solving problems involving measures or carrying out practical activities, it would be helpful to give the

children opportunities to order different lengths, masses, capacities and volumes and also to round amounts to

the nearest whole unit, ten, hundred etc. For example,you could ask the children to pick four cards and make a

4 digit number. They pretend their number represents grams and write them in as many different ways as they

can, for example 4563 grams, 4kg 563g, 4.563kg. You could then ask them to round the grams to the nearest

10 (4560g), 100 (4600g) and 1000 (5000g). They could repeat this with metres and millilitres.





recognise and use factor pairs and commutativity in mental calculations

multiply two-digit and three-digit numbers by a one-digit number using formal written layout

When working on measurement and/or multiplication and division, there are opportunities to make


When converting from larger to smaller units the children should use multiplication, for example, 2km would

be multiplied by 1000 to give 2000m. When converting from smaller to larger units division would be involved,

for example, 200ml divided by 1000 would be 0.2l.

When looking at perimeter the children need to explore the algebraic formula of 2(a + b) where a and b are

the dimensions in the same unit. This involves doubling or multiplying by two.

The notes and guidance suggests that the children study area through arrays of squares and discover for

themselves that areas can be found by multiplying the number of rows by the number of columns which is the

same as the length multiplied by the width.

Provide the children with opportunities to solve problems which involve multiplication and division. For

example:

Hammed wants to cover his back yard with grass. His back yard measures 12m by 10m. What

area will he cover?

Ahmed is going to sow grass seed in his garden. It is a rectangular measuring 8m by 4.5m. He

needs to know the perimeter and area so he can buy the grass seed and bricks for the wall he

wants to build around it. What are the perimeter and area of his garden?


Statutory requirements (all are relevant):


add and subtract numbers with up to 4 digits using the formal written methods of columnar addition

and subtraction where appropriate

estimate and use inverse operations to check answers to a calculation

solve addition and subtraction two-step problems in contexts, deciding which operations and

methods to use and why.

When working on measurement and/or addition and subtraction, there are opportunities to make connections


When carrying out activities in measurement, provide opportunities for the children to solve problems that

involve these types of calculation. For example:

Freddie had a length of string which was 1m 75cm. He cut off two pieces, one 28cm and another

75cm and gave them to a friend. How much string did he have left?

Hattie had 2l bottle of juice. She filled three glasses with 250ml of juice in each. How much juice was

left in the bottle?

Amy had saved £575. She bought laptop for £245.50 and a printer for £125. How much of her

saving did she have left?

Mandy left home at 10:30am. She arrived at the shopping centre 40 minutes later. What time did she

get to the shopping centre?

The film started at 17:45. Bobby was 35 minutes early. At what time did he arrive at the cinema?

They should be encouraged to decide which operations and methods to use and why.

Fractions



count up and down in hundredths; recognise that hundredths arise when dividing an object by one

hundred and dividing tenths by ten.

solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide

quantities, including non-unit fractions where the answer is a whole number

add and subtract fractions with the same denominator

recognise and write decimal equivalents of any number of tenths or hundredths

recognise and write decimal equivalents to , ,

find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the

digits in the answer as ones, tenths and hundredths

round decimals with one decimal place to the nearest whole number

compare numbers with the same number of decimal places up to two decimal places

solve simple measure and money problems involving fractions and decimals to two decimal places.

When working on measurement and/or fractions there are opportunities to make connections between them,

for example:

You could encourage the children to explore simple fractions of measurement such as ½, ¼ and ¾ of

different numbers of centimetres, metres, kilometres, litres and kilograms. They could also do this for hours,

perimeters and areas. This would reinforce the concept of finding a fraction by division.



Compare and classify geometric shapes, including quadrilaterals and triangles, based

on their properties and sizes

Pupils should be able to complete this sentence:

All equilateral triangles have …

Notes:


Identify acute and obtuse angles and compare and order angles up to two right angles

by size

Notes:


Identify lines of symmetry in 2-D shapes presented in different orientations

Notes:


Complete a simple symmetric figure with respect to a specific line of symmetry

Notes:





Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium). Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular. Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape.


(Years 1-6)


connections

Making connections to other

topics

NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS




paper

Rulers

Geostrips



Isometric

grids/Symmetry/Fixpoints/Polygon/Calculating

angles ITP

Learners will encounter geometry in:

The world around them – e.g. symmetry on wrapping paper, tiles, letters and digits on labels.

Design Technology – e.g. the use of different triangles in bridge building

Physical Education – e.g. using symmetry to create dance sequences, gymnastic routines

I.C.T – e.g. using programmable robots to create specific shapes or a symmetrical dance sequence.

Art – The NCETM Primary Magazine ‘Art of Mathematics’, features has many different articles where works of art are used as a stimulus for shape work. E.g. Islamic Patterns e.g.https://www.ncetm.org.uk/resources/18030

Making connections to other topics within this year group

Connect work on Geometry with area and perimeter, e.g. calculate the area (by counting squares) and perimeter of given shapes.

Connect work on Geometry with measuring and reading scales, e.g. using rulers and protractors to draw simple shapes accurately.

Connect work on Geometry with co-ordinate positions in the first quadrant, e.g. plot given co-ordinate positions and connect the points – what polygon have you made?

















Describe positions on a 2-D grid as coordinates in the first quadrant

Notes:


Describe movements between positions as translations of a given unit to the left/right

and up/down

Notes:


Plot specified points and draw sides to complete a given polygon

Notes:





Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of coordinates, for example (2, 5), including using coordinate-plotting ICT tools.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Logo

Bee bots

Compass

Square papers

Geo strips

Tracing paper

Co-ordinates ITP

Learners will encounter coordinates in:

Geography, when learning about map referencing and directions.

Learners will encounter translation in:

DT, when designing rooms, planning buildings and construction projects

Art, when looking at patterns and architecture















Y4: Statistics

Interpret and present discrete and continuous data using appropriate graphical

methods, including bar charts and time graphs

Collect data, measuring where necessary. They work with a range of data, such as shoe size and width of shoe across the widest part of the

foot, the number of letters in children’s names, the width of their hand spans, the distance around their neck and wrist, data from nutrition

panels on cereal packets, and so on.

They decide on a suitable question or hypothesis to explore for each data set they work on. For example, ‘We think that…boys have larger

shoes than girls’, ‘…our neck measurements are twice as long as our wrist measurements’, ‘…girls’ names have more letters than boys’

names’ or ‘…children in our class would prefer to come to school by car but they usually have to walk’.

Children consider what data to collect and how to collect it. They collect their data and organise it in a table. They choose a Venn or Carroll

diagram, or a horizontal or vertical pictogram or bar chart to represent the data. Where appropriate, they use the support of an ICT package.

They justify their choice within the group so that they can present it.

They understand that they can join the tops of the bars on the bar-line chart to create a line graph because all the points along the line have

meaning.

Notes:


Solve comparison, sum and difference problems using information presented in bar

charts, pictograms, tables and other graphs.

Undertake one or more of three enquiries:

What vehicles are very likely to pass the school gate between 10:00 am and 11:00 am? Why? What vehicles would definitely not

pass by? Why not? What vehicles would be possible but not very likely? Why? What if it were a different time of day? What if the

weather were different?

Does practice improve estimation skills? Children estimate the lengths of five given lines and record the estimate, measured length

and difference. They repeat the activity with five more lines to see whether their estimation skills have improved after feedback.

What would children in our class most like to change in the school? Children carry out a survey after preliminary research to whittle

down the number of options to a sensible number, e.g. no more than five.

Children identify a hypothesis and decide what data to collect to investigate their hypothesis. They collect the data they need and

decide on a suitable representation. In groups, they consider different possibilities for their representation and explain why they

have made their choice.

In the first enquiry, children use tallies and bar charts. In the second, they use tables and bar charts to compare the two sets of

measurements. In the third, they use a range of tables and charts to show their results, including Venn and Carroll diagrams. They

use ICT where appropriate.

Notes:





Pupils understand and use a greater range of scales in their representations. Pupils begin to relate the graphical representation of data to recording change over time.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Carroll diagrams


Tables

Pictograms

Block graphs

Bar graphs

Multilink towers

Data

Handling/Handygraph/Line

graph/ ITP

Tracing paper

Protractors

Learners will encounter statistics in: Within the science curriculum there are opportunities to connect with statistics, for example, in working scientifically there is a requirement that the children record findings using simple scientific language, drawings, labelled diagrams, keys, bar charts, and tables. In the section on living things they should identify and name a variety of living things (plants and animals) in the local and wider environment, using classification keys to assign them to groups. This can be done using tables or Venn and Carroll diagrams. Within the geography curriculum, the children are expected to describe and understand key aspects of:

physical geography, including: climate zones, biomes and vegetation belts, rivers, mountains, volcanoes and earthquakes, and the water cycle

human geography, including: types of settlement and land use, economic activity including trade links, and the distribution of natural resources including energy, food, minerals and water

Give the children opportunities to gather relevant data and present it in tables, bar charts or pictograms and then analyse their findings.

Addition and subtraction Pupils should be taught to:

add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

estimate and use inverse operations to check answers to a calculation

solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

When working on statistics and/or addition and subtraction, there are opportunities to make connections between them, for example: The requirements for statistics include solving comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. Clearly, solving such problems requires the ability to add and subtract. When covering these concepts you could provide the children with copies of bar charts, pictograms, tables and other graphs and ask them to then make up and solve problems involving addition and subtraction. Multiplication and division Pupils should be taught to:

recall multiplication and division facts for multiplication tables up to 12 × 12

use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

recognise and use factor pairs and commutativity in mental calculations

multiply two-digit and three-digit numbers by a one-digit number using formal written layout

solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

One of the requirements in multiplication and division states that children should be taught to recall multiplication and division facts for multiplication tables up to 12 × 12. You could ask the children to create bar graphs and pictograms with scales going up in step sizes that will help them to practice recalling these facts.














MATHEMATICS

YEAR 5

CURRICULUM PLANNING

TOOLKIT


Y5: Number and place value

Read, write, order and compare numbers to at least 1 000 000 and determine the

value of each digit

Explain what each digit represents in whole numbers and decimals with up to two places and partition, round and order these numbers. What is the value of the 7 in 3 274 105? Write in figures forty thousand and twenty. A number is partitioned like this: 4 000 000 + 200 000 + 60 000 + 300 + 50 + 8 Write the number. Now read it to me. A car costs more than £8600 but less than £9100. Tick the prices that the car might cost. £8569 □ £9090 □ £9130 □ £8999 □

Notes:

Aut 1 Aut 2 Spr 1 Spr 2 Sum 1 Sum 2

Count forwards or backwards in steps of powers of 10 for any given number up to

1 000 000

Count from any given number in powers of 10 and decimal steps extending beyond zero when counting backwards; relate the numbers to their position on a number line. Write the next number in this counting sequence: 110 000, 120 000, 130 000 … Create a sequence that goes backwards and forwards in tens and includes the number 190. Describe your sequence. Here is part of a sequence: 30, 70, 110, □, 190, □. How can you find the missing numbers?

Notes:


Interpret negative numbers in context, count forwards and backwards with positive

and negative whole numbers, including through zero

Count from any given number in whole-number and decimal steps extending beyond zero when counting backwards; relate the numbers to their position on a number line.

Notes:


Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

Explain what each digit represents in whole numbers and decimals with up to two places and partition round and order these numbers and answer questions such as: What is 4773 rounded to the nearest hundred?

Notes:


Solve number problems and practical problems that involve all of the above

Partition decimals using both decimal and fraction notation for example recording 6.38 as 6 + 3⁄10 + 8⁄100 and as 6 + 0.3 + 0.08. They

write a decimal given its parts: e.g. they record the number that is made from 4 wholes 2 tenths and 7 hundredths as 4.27. They apply

their understanding in activities such as:

Find the missing number in 17.82 – □ = 17.22. Play ‘Zap the digit’: In pairs choose a decimal to enter into a calculator e.g. 47.25. Take turns to ‘zap’ (remove) a particular digit using subtraction. For example to ‘zap’ the 2 in 47.25 subtract 0.2 to leave 47.05. The children explain how they work out calculations showing understanding of the place value that underpins written methods.

Notes:




Read Roman numerals to 1000 (M) and recognise years written in Roman numerals Recognise Roman numerals in their historical context Read and write Roman numerals to one thousand

Notes:


Non-Statutory Guidance

Pupils identify the place value in large whole numbers. They continue to use number in context including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They should recognise and describe linear number sequences (for example 3, 3½, 4, 4½ …) including those involving fractions and decimals and find the term-to-term rule in words (for example add ½).

Quick Links Resources (Years 1-6)

Cross-curricular and real life links

NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS



Place value charts



Counting stick

Beadstrings

Number lines

Dienes



(thermometer)


Cuisenaire, unifix, multilink,

straws, (Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice


games


reels, matchsticks

Outdoor score boards and timers

for PE activities





Within the science curriculum there are opportunities to work with number and place value, for example, in the introduction of the Upper Key Stage 2 Programme of Study it states that pupils should select the most appropriate ways to answer science questions using different types of scientific enquiry including observing changes over different periods of time noticing patterns grouping and classifying things carrying out comparative and fair tests and finding things out using a wide range of secondary sources of information. The children could, for example, record changes over periods of time and compare them. You could discuss the differences in the place value of periods of time and the number system. They could record, for example, heights of plants accurately using decimal notation. Within the geography curriculum there are opportunities to connect with number and place value for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and understanding beyond the local area to include the United Kingdom and Europe North and South America. This will include the location and characteristics of a range of the world’s most significant human and physical features. Children could, for example, find and compare distances between countries or cities temperatures lengths of rivers heights of mountains. These comparisons will involve finding differences which involve a secure understanding of place value. See, for example: Weather Environments around the world Mathematics and geography Within the history curriculum there are opportunities to work with number and place value for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should continue to develop a chronologically secure knowledge and understanding of British local and world history establishing clear narratives within and across the periods they study. The children could, when studying the Roman period, focus on their number system and find out how it developed. A Little bit of History in issue 2 of the Primary Magazine has information about this. They could also look at the development of our number system. A Little bit of History in issue 8 of the Primary Magazine has information about this.



















Making connections to other topics Addition and subtraction

add and subtract whole numbers with more than 4 digits including using formal written methods (columnar addition and subtraction)

add and subtract numbers mentally with increasingly large numbers

use rounding to check answers to calculations and determine in the context of a problem levels of accuracy

When working on number and place value and/or addition and subtraction there are opportunities to make connections between them for example: Numbers with decimals are frequently seen in real life, so give the children opportunities to add and subtract these in context. For example, you could give them catalogues or take away menus and ask them to choose two or three items to buy. You could give them a budget and ask them total the prices and find out how much of their budget is left. You could ask the children to measure the lengths of different objects around the classroom and to find their total length. They could then represent these measurements in centimetres and metres. They could then convert them into metre measurements using decimals, for example 3m 24cm would become 3.24m. You could ask them to find out what length they would need to make a longer length that you give them, such as 10m. They could do similar activities for volume and capacity and also mass. Encourage the children to consider whether a mental calculation strategy or a written strategy would be most efficient for their additions and subtractions. They could also make estimates of the totals and differences using rounding. Multiplication and division

multiply numbers up to 4 digits by a one- or two-digit number using a formal written method including long multiplication for two-digit numbers

multiply and divide numbers mentally drawing upon known facts

divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

multiply and divide whole numbers and those involving decimals by 10 100 and 1 000 When working on number and place value and/or multiplication and division there are opportunities to make connections between them, for example: You could make up problems for the children to solve that involve multiplication and division for example: Harris had £38. 96. He shared his money into four equal piles. How much money was in each pile? Naomi was making some fruit juice for a party. She decided each person would need 350ml of juice. If there were 24 people at the party, how many litres of juice does she need to make? Give the children place value grids similar to the one below and a set of digit cards:

1000 100 10 1 . 1/10 1/100

Ask them to make a three digit number, such as 569 and place it in the grid. They can then multiply the number by ten, using the zero as a place holder. They could then divide their number by 10, 100 and 1000 and describe what is happening: the number is becoming 10/100/1000 times smaller the digits are moving to the right.

Fractions (including decimals and percentages)

recognise and use thousandths and relate them to tenths hundredths and decimal equivalents

round decimals with two decimal places to the nearest whole number and to one decimal place

read write order and compare numbers with up to three decimal places

solve problems involving number up to three decimal places When working on number and place value and/or fractions (including decimals and percentages) there are opportunities to make connections between them for example: Using the place value grid suggested above and digit cards, ask the children to make a number that fills the grid. Discuss what each digit is worth. For example, with the number 2315.67 the 2 is in the thousands position so that tells us how many thousands it represents – so the value shown in that column is 2000 the 3 is in the hundreds position so is 300 and so on. When you discuss the 6 and 7 ensure that the children recognise that the 6 is in the tenths position so is worth 6/10 or 0.6 and the 7 is in the hundredths position so is worth 7/100 or 0.07. They could write the numbers they make in words so that they reinforce their place value. They should also model them with structured base 10 apparatus. You could take five examples of the numbers that the children have made in their grids write them on the board and then ask the children to order them in ascending or descending order. Ask problems involving mass, for example: Charlie has three cats. Macy weighs 3kg 250g , Tia weighs 2kg 175g and Elvis weighs 4kg 125g. What would these masses be in kilograms only? In kilograms work out the total mass of the three cats? Georgie was making a cake; she needed 1.6kg of flour 350g of butter and 750g of sugar. What is the total mass of these ingredients? Samir made five jugs of juice. For each he used 2 litres of water and 245ml of cordial. How many litres of liquid did he use altogether. Measurement

convert between different units of metric measure [for example kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]

When working on number and place value and/or measures there are opportunities to make connections between them, for example: Give the children a list of different metric units and ask them to write them in different ways. For example: 3km 50m could also be written as 3050m or 3.05km 2m 10cm could also be written as 210cm or 2.1m 13cm 7mm could also be written as 137mm or 13.7cm 6l 75ml could also be written as 6075ml or 6.075l Using maps the children could work out distances to different places. These are likely to have a scale in centimetres. The children could convert these to kilometres to find the actual distances.



Add and subtract whole numbers with more than 4 digits, including using formal

written methods (columnar addition and subtraction)

Children should be able to use standard written methods for addition and subtraction, e.g. calculate 14 136 + 3258 + 487 or 23 185 – 2078

Use written methods to find missing numbers in addition and subtraction calculations, e.g. 6432 + □ = 8025

Use written methods to add and subtract numbers with different numbers of digits, e.g. Find all the different totals that can be made using

any three of these five numbers: 14 721, 76, 9534, 788, 6

Notes:

Aut 1 Aut 2 pr 1 Spr 2 Sum1 Sum 2

Add and subtract numbers mentally with increasingly large numbers

Children should be able to respond rapidly to oral or written questions, explaining the strategy used, e.g. 750 take away 255, take 400 from

1360, 4500 minus 1050, subtract 3250 from 7600, 1800 less than 3300, 4000 less than 11 580

Derive quickly related facts, e.g. 80 + 50 = 130, 130 – 50 = 80, 800 + 500 = 1300, 1300 – 800 = 500

Derive quickly number pairs that total 100 or pairs of multiples of 50 that total 1000, e.g. 32 + 68 = 100 or 150 + 850 = 1000

Identify and use near doubles, e.g. work out 28 + 26 = 54 by doubling 30 and subtracting first 2, then 4, or by doubling 26 and adding 2

Add or subtract the nearest multiple of 10, 100 or 1000 and adjust, e.g. adding or subtracting 9, 19, 29 ... to/from any two-digit number

Work out mentally by counting up from a smaller to a larger number e.g. 8000 – 2785 is 5 + 10 + 200 + 5000 = 5215

Understand and use language associated with addition and subtraction, e.g. difference, sum, total

Notes:


Use rounding to check answers to calculations and determine, in the context of a

problem, levels of accuracy Children should be able to use rounding to approximate and check e.g. 2593 + 6278 must be more than 2500 + 6200, 2403 – 1998 is about 2400 – 2000

Write approximate answers to calculations, e.g. write an approximate answer for 516 ÷ (15 + 36)

Notes:


Solve addition and subtraction multi-step problems in contexts, deciding which

operations and methods to use and why Children should be able to choose the appropriate operations to solve multi-step problems, decide whether the calculations can be done mentally or using a written method and explain and record how the problem was solved using numbers, signs and symbols. e.g. 13 502 people were at the match last week and there are 2483 more this week, how many more people need to attend to bring the total to the club’s target of 20 000 people?

Identify and obtain the necessary information to solve the problem and determine if there is any important information missing,

e.g. calculating total cost of a holiday for a family, given prices for adults and children and surcharges for particular resorts.

Notes:





Pupils practice using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Appendix 1). They practice mental calculations with increasingly large numbers to aid fluency (e.g. 12 462 – 2 300 = 10 162).


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings


Empty number lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards

Place value cards &

counters

100 squares

Pegs on hanger

Number rhymes

Practical objects linked to

topic

Slider box cards

Dice

Number grid/Number

scales/Number

facts/Difference/Number

line ITPs

Learners will encounter addition and subtraction when focusing on:

Money – when required to add prices, calculate change, add

surcharges or interest, or subtract discounts;

Measurement – when required to add lengths, calculate

remaining distance in a journey, find how much more/less

liquid is needed, add quantities when cooking, calculate

perimeters of regular and irregular shapes, work out time

differences e.g. how many days until Christmas, how many

minutes until break time etc.;

Statistics – comparing and combining sets of data,

interpreting data.

Learners will encounter addition and subtraction in:

Science – when adding and subtracting test measurements;

History – when comparing historical data from different

periods, calculating the duration of monarchs' reign;

Geography – when comparing populations, temperatures

and other data for contrasting regions around the world.














Identify multiples and factors, including finding all factor pairs of a number, and

common factors of 2 numbers

Notes:


Know and use the vocabulary of prime numbers, prime factors and composite (non-

prime) numbers

Notes:


Establish whether a number up to 100 is prime and recall prime numbers up to 19

Use the vocabulary factor, multiple and product. They identify all the factors of a given number; for example, the factors of 20 are 1, 2, 4, 5,

10 and 20. They answer questions such as:

Find some numbers that have a factor of 4 and a factor of 5. What do you notice?

My age is a multiple of 8. Next year my age will be a multiple of 7. How old am I?

They recognise that numbers with only two factors are prime numbers and can apply their knowledge of multiples and tests of divisibility to

identify the prime numbers less than 100. They explain that 73 children can only be organised as 1 group of 73 or 73 groups of 1, whereas

44 children could be organised as 1 group of 44, 2 groups of 22, 4 groups of 11, 11 groups of 4, 22 groups of 2 or 44 groups of 1. They

explore the pattern of primes on a 100-square, explaining why there will never be a prime number in the tenth column and the fourth column

Notes:


Multiply and divide numbers mentally, drawing upon known facts

Rehearse multiplication facts and use these to derive division facts, to find factors of two-digit numbers and to multiply multiples of 10 and

100, e.g. 40 × 50. They use and discuss mental strategies for special cases of harder types of calculations, for example to work out 274 +

96,< 8006 – 2993, 35 × 11, 72 ÷ 3, 50 × 900. They use factors to work out a calculation such as 16 × 6 by thinking of it as 16 × 2 × 3. They

record their methods using diagrams (such as number lines) or jottings and explain their methods to each other. They compare alternative

methods for the same calculation and discuss any merits and disadvantages

Notes:


Multiply numbers up to 4 digits by a one- or two-digit number using a formal written

method, including long multiplication for two-digit numbers

Develop and refine written methods for multiplication. They move from expanded

layouts (such as the grid method) towards a compact layout for HTU × U and TU ×

TU calculations. They suggest what they expect the approximate answer to be

before starting a calculation and use this to check that their answer sounds sensible.

For example, 56 × 27 is approximately 60 × 30 = 1800.

Notes:




Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000 Recall quickly multiplication facts up to 10 × 10 and use them to multiply pairs of multiples of 10 and 100. They should be able to answer problems such as:

The product is 400. At least one of the numbers is a multiple of 10. What two numbers could have been multiplied together? Are there any other possibilities?

Notes:


Recognise and use square numbers and cube numbers, and the notation for squared

(²) and cubed (³) Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10. They should be able to answer problems such as: Tell me how to work out the area of a piece of cardboard with dimensions 30 cm by 30 cm Find two square numbers that total 45

Notes:


Divide numbers up to 4 digits by a one-digit number using the formal written method of

short division and interpret remainders appropriately for the context Extend written methods for division to include HTU ÷ U, including calculations with remainders. They suggest what they expect the approximate answer to be before starting a calculation and use this to check that their answer sounds sensible. They increase the efficiency of the methods that they are using. For example: 196 ÷ 6 is approximately 200 ÷ 5 = 40 3 2 r4 or 4/6 or 2/3

6 196

7

Notes:


Solve problems involving multiplication and division, including using their knowledge

of factors and multiples, squares and cubes

Notes:


Solve problems involving addition, subtraction, multiplication and division and a

combination of these, including understanding the meaning of the equals sign

Notes:


Solve problems involving multiplication and division, including scaling by

simple fractions and problems involving simple rates

Use written methods to solve problems and puzzles such as:

Choose any four numbers from the grid and add them. Find as many ways as possible of making

1000.

Place the digits 0 to 9 to make this calculation correct: ☐☐☐☐ – ☐☐☐ = ☐☐☐.

Two numbers have a total of 1000 and a difference of 246. What are the two numbers?

275 382 81 174

206 117 414 262

483 173 239 138

331 230 325 170

Notes:




Pupils practise and extend their use of the formal written methods of short multiplication and short division (see Mathematics Appendix 1). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.

They use and understand the terms factor, multiple and prime, square and cube numbers.

Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 ÷ 4 = 98⁄4 = 24 r 2 = 24 ½ = 24.5 ≈ 25). Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1,000 in converting between units such as kilometres and metres. Distributivity can be expressed as a(b + c) = ab + ac. They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10). Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example 13 + 24 = 12 + 25; 33 = 5 x ?).


(Years 1-6)


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings


Hands counting

Straws (bunching)


number lines

100 squares

Timestable squares, blank 12 x 12 grid

Counting stick


Loop cards

Arrays: Eggs in boxes, Chocolate, Cake

trays


after division/Multiplication array/Number

grid/Multiplcation grid ITP.

Learners will encounter number and place value in:

Within the geography curriculum there are opportunities to connect with multiplication and division, for example in the

introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and

understanding beyond the local area to include the United Kingdom and Europe, North and South America. This will

include the location and characteristics of a range of the world’s most significant human and physical features. Children

could, for example, find out about the currencies used in a selection of countries. They could then make up a currency

converter using mental calculation strategies and then check using multiplication, for example:

£1= 1.20 Euros

£2 = 2.40 Euros

£3 = 3.60 Euros

£4 = 4.80 Euros

£5 = 6 Euros















Connections within Mathematics

Making connections to other topics within this year group

Fractions (including decimals and percentages)

Requirements include:

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

solve problems involving number up to 3 decimal places

When working on multiplication and division and/or fractions (including decimals and percentages), there are


You could give the children strips of paper and ask them to fold them to show you different proper and mixed

fractions, for example, 5⁄8, 1 3⁄4. Next ask them to multiply these fractions by single digit numbers. They could use the

strips to help them: 1 5⁄8 x 6

1x 6 = 6

5⁄8 x 6 = 30⁄8 or 3 6⁄8

1 5⁄8 x 6 = 6 + 3 6⁄8 = 9 6⁄8 or 9 3⁄4

Numbers with decimals are frequently seen in real life, for example when using money, so give the children

opportunities to multiply these in context. For example, you could give them take-away menus and ask them to find

out how much it would cost to buy four of a meal deal or a particular course. You could give them the total cost of

six of the same dish and ask to work out which dish you chose. You could ask the children problems that involve

multiplying numbers up to 3 decimal places and link to measures, such as:

Jessie had eight lengths of rope. Each was1m 36cm. If he put them side by side what would the total

length be?

Paddy had 12 cartons of orange juice. Each carton contained 0.750l. How much juice did he have

altogether?

Suzie, the baker, was making 14 loaves of bread for the local supermarket. For each loaf she needed

1.275kg of flour. What is the total amount of flour that she needed?

India took part in a sponsored bike ride at her school. She cycled 25 times around the perimeter of the

school playground. The perimeter is 105.34m. How far did she travel?

Measurement

When working on multiplication and division and/or measurement there are opportunities to make


You could give the children opportunities to rehearse multiplying by 10, 100 and1000 by converting, for

example, millimetres to centimetres, centimetres to metres, metres to kilometres. They could then

multiply lengths, masses and capacities of different sizes, for example, 14.75kg by 8. You could then

put these into problem format, for example:

Benji, a party organiser, was going to make a fruit punch. For each guest he needed 0.250ml

of orange juice and 0.250l of mango juice. If there are 25 guests coming to the party, what is

the total amount of juice Benji needs?

You could give the children an approximate equivalence between miles and kilometres, for

example1.6km is approximately 1 mile. Then they multiply this amount to find approximate equivalences

for other miles, for example 5 miles, 8 miles, 10 miles, 14 miles. The children could make a spider

diagram for this and other equivalences.

You could give the children lengths of one side of different regular polygons, for example, pentagon,

octagon, decagon, dodecagon and ask them to find their perimeters by multiplying each length by the

number of sides the polygon has. You could also give the children the lengths of different sized

rectangles and ask them to find their areas, for example, a rectangle 28cm by 12cm. Set problems

involving time and money for the children to use, for example:

Samir spent 45 minutes completing his homework. It took Pete three times as long. How long

did it take Pete to complete his homework?

It took Carol 1 ½ hours to drive from Oxford to London. It took Lorna a third of that time. How

long did it take Lorna to travel to London?

Harry is given £3.75 a week as pocket money. He is saving it to buy a computer game. How

much will he have saved over 8 weeks? What about 12 weeks?

Georgie saved £2.25 of her pocket money each week. How much will she have saved over 9

weeks?

Penny had saved £75 over a period of 12 weeks. She saved an equal amount every week.

How much did she save each week?


Y5: Fractions (including decimals and percentages)

Compare and order fractions whose denominators are all multiples of the same number Children should be able to circle the two fractions that have the same value, or choose which one is the odd one out and justify their decision. 6⁄10,

3⁄5, 18⁄20,

9⁄15 Notes:


Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

Notes:


Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number[for example,2⁄5+4⁄5=6⁄5= 11⁄5] Put the correct symbol, < or >, in each box.

3.03 ☐ 3.3

0.37 ☐ 0.327

Order these numbers: 0.27 0.207 0.027 2.07 2.7 (e.g. ⅖ + ⅘ = 6⁄5 = 1⅕) How many halves in: 1 ½ 3 ½ 9 ½ …? How many quarters in 1 ¼ 2 ¼ 5 ¼ ….?

Notes:


Add and subtract fractions with the same denominator and denominators that are multiples of the same number

Notes:


Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams What is 3⁄10 of: 50, 20, 100…?

What is ⅘ of 50, 35, 100….?

Notes:


Read and write decimal numbers as fractions [for example, 0.71 =71⁄100] What decimal is equal to 25 hundredths? Write the total as a decimal: 4 + 6⁄10 + 2⁄100 = Children partition decimals using both decimal and fraction notation, for example, recording 6.38 as 6 + 3⁄10 + 8⁄100 and as 6 + 0.3 + 0.08.

Notes:







Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents Recognise that 0.007 is equivalent to 7⁄1000 6.305 is equivalent to 6305⁄100

Notes:

Au 1 Aut 2 Spr 1 Spr 2 Sum1 Sum 2

Round decimals with two decimal places to the nearest whole number and to one decimal place

Notes:


Read, write, order and compare numbers with up to three decimal places solve problems involving number up to three decimal places Write these numbers in order of size, starting with the smallest. 1.01, 1.001, 1.101, 0.11 8 tenths add 6 tenths makes 14 tenths, or 1 whole and 4 tenths. The 1 whole is 'carried' into the units column and the 4 tenths is written in the tenths column

Notes:


Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal Write in the missing numbers. 30% of 60 is ☐

30% of ☐ is 60

Shade 10% of this grid. Which is bigger: 65% or ¾? How do you know? What percentage is the same as 7⁄10? Explain how you know? What is 31⁄100 as a percentage? Which is a better mark in a test: 61% , or 30 out of 50? How do you know?

Notes:


Solve problems which require knowing percentage and decimal equivalents of 1⁄2, 1⁄4,1⁄5, 2⁄5 and those fractions with a denominator of a multiple of 10 or 25

Notes:




Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions. They extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions. Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1. Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number. Pupils continue to practise counting forwards and backwards in simple fractions. Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities. Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line. Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems. They mentally add and subtract tenths, and one-digit whole numbers and tenths. They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 ( for example, 0.83 + 0.17 = 1). Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals. Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is 1⁄100, 50% is 50⁄100, 25% is 25⁄100) and relate this to finding ‘fractions of’.

Quick links Practical

Resources


connections

Making connections to other

topics

NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Fraction wall

Fraction plates

Fraction strips

Fraction cards

Shapes

Counting stick

Number lines

Other representations of

fractions: clock faces,

chocolate bars

Fraction videos

Numicon, Cuisenaire



Learners will encounter fractions, decimals and

percentages in:

Measurement – when calculating measures for

recipes, calculating journey times and fuel consumption

Money – working out the result of sales offers,

tips/gratuities on bills, comparing prices

Statistics – interpreting and evaluating data e.g. 19%

of the world’s population lives in China

Fractions, decimals and percentages are used in many

other areas of mathematics.

When converting units of measure, children need a

good understanding of decimals, e.g. converting cm to

m, g to kg etc.

Children should also be required to use fractions and

percentages when interpreting and evaluating data.

Fractions may be used when describing turns.














Y5: Measurement

Convert between different units of metric measure (for example, kilometre and metre;

centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

What is two hundred and seventy six centimetres to the nearest metre?

How many millimetres are in 3 centimetres?

Notes:


Understand and use approximate equivalences between metric units and common

imperial units such as inches, pounds and pints

This bag of sugar weighs 1kg. Approximately how many pounds (lb) of sugar would fit into another empty bag of the

same size as this one? Tick the correct answer.

20lb

14lb

2lb

4lb

Notes:


Measure and calculate the perimeter of composite rectilinear shapes in centimetres

and metres

This shape is made from 4 shaded squares

Calculate the perimeter of the shape

Notes:


Calculate and compare the area of rectangles (including squares), and including using

standard units, square centimetres (cm2) and square metres (m2) and estimate the area

of irregular shapes

Calculate the area of a rectangle which is eleven metres long by 5 metres wide.

Which has the greatest area – a square with sides 6 cm long or a rectangle which is 7 cm long by 5 cm? How much greater is the area?

Notes:


Estimate volume [for example, using 1 cm3 blocks to build cuboids

(including cubes)] and capacity [for example, using water]

Fitting it in is an activity to fill cuboid shapes with multilink cubes. It ends with a ‘create’ challenge that will test

children’s knowledge in this area

Notes:



http://nzmaths.co.nz/resource/fitting-it


Solve problems involving converting between units of time

5 on the clock is a problem that requires children to be able to convert between 12 and 24 hour clocks confidently.

Notes:


Use all four operations to solve problems involving measure [for example, length,

mass, volume, money] using decimal notation, including scaling

A day with Grandpa. Is an engaging problem using imperial units that challenges children's understanding of the concept of area rather than

simply requiring them to follow a rule for finding areas of rectangles. These calculations should also help learners to see the advantages of

the metric system as well as understand it more fully!

Notes:



Pupils use their knowledge of place value and multiplication and division to convert between standard units. Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20 cm. Pupils calculate the area from scale drawings using given measurements. Pupils use all four operations in problems involving time and money, including conversions (for example, days to weeks, expressing the answer as weeks and days).



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Mass/weight:


Equipment: bathroom scales,weighing

scales, balances, Force metres



paper, Trundle wheels, Measuring tapes

Capasity & volume:


containers, spoons, measuring spoons,

buckets, cups

Time:


geared hands, Analogue clocks, Digital

clocks, Timelines, Timetables

Money:


Measuring



Measurement is an area of mathematics that is used constantly in real-life situations. When decorating a room, measurement of area is needed for carpeting the floor, as well as calculating the rolls of wallpaper needed, or litres of paint required. Working with drawings of a room to a specified scale, and determining the measurements of furniture to fit. In Design Technology, children are often required to work to scale, accurately measuring their plans and products as they are developed

Learners will encounter units of measure in many other aspects of their mathematics learning. Word problems lend themselves well to measures, and are a good way of integrating this strand of mathematics with application of calculation skills. Measurement provides a meaningful context for ratio and proportion problems and work with fraction, decimals and percentages.
















Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

These are pictures of 3D shapes. Which 3D shapes are pictured here? Put the

names in the boxes.

Notes:


Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

Look at these angles.

Label each angle acute, obtuse or reflex.

List the 5 angles in order from smallest to

largest.

Notes:


Draw given angles, and measure them in degrees (°)

Measure A accurately. Use a protractor (angle measurer).

Measure accurately the smallest angle in the above shape. Use a protractor (angle measurer).

This diagram is not drawn accurately. Calculate the size of angle m

Notes:




Identify: angles at a point and one whole turn (total 360°) angles at a point on a straight line and ½ a turn (total 180°) other multiples of 90°

PQ is a straight line. Not drawn accurately.

Calculate the size of angle x. Do not use a protractor (angle measurer).

This shape is three-quarters of a circle.

How many degrees is angle x?

In the diagram below, if you were standing at X, facing A, what angle would you

turn through if you turn and face C?

Notes:


Use the properties of rectangles to deduce related facts and find missing lengths and angles

This online activity will challenge children’s knowledge about many different kinds of

quadrilaterals.

Notes:


Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

This online activity from softschools.com asks children to classify polygons. They will

need to draw on their knowledge of sides and angles.

Notes:


http://www.softschools.com/math/geometry/quadrilaterals/

http://www.softschools.com/math/geometry/polygons/regular_and_irregular_polygons/



Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS




paper

Rulers

Geostrips



Isometric


angles ITP

Work on properties of shape can be integrated with work in several other areas of the curriculum. e.g. When working with 2D representations e.g. maps, nets, isometric drawings, plans and elevations When using digital technology e.g. Logo, dynamic geometry to create geometric patterns When looking at art and architecture to identify geometric shapes and properties When using digital cameras to capture geometric shapes and objects in the environment and around school

Geometry- position and direction Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.














Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

Write the co-ordinates of the next triangle in the sequence.

Notes:



Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Logo

Bee bots

Compass

Square papers

Geo strips

Tracing paper

Co-ordinates ITP

Learners will encounter coordinates in Geography when learning about map referencing. Learners will encounter a range of translations in Design Technology when designing rooms, planning buildings and object designs of their own. When focusing on patterns and architecture in Art & Design, translations will be recognised and used

Pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.

Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics. (National Curriculum in England Framework Document, September 2013, p10) Connections within Mathematics














Y5: Statistics

Solve comparison, sum and difference problems using

information presented in a line graph I can find the information in a table or graph to answer a question The table shows the cost of coach tickets to different cities. What is the total cost for a return journey to York for one adult and two children?

Notes:


Complete, read and interpret information in tables, including

timetables

What is the average height of children of different ages?

Are there differences for boys and girls?

This screen shot is from the Interactive Teaching Programme ‘Data Handling’, using the ‘Average Height’ data set.

Notes:



Pupils connect their work on coordinates and scales to their interpretation of time graphs. They begin to decide which representations of data are most appropriate and why.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Carroll diagrams


Tables

Pictograms

Block graphs

Bar graphs

Multilink towers


graph/ ITP

Tracing paper

Protractors

Learners will encounter statistics when comparing data and analysing information. In science, they will be required to represent and interpret data collected in science investigations. In geography, they will be plotting and interpreting data for international and local weather as well as other geographical data for population, land use etc. Statistics are also used in everyday life. E.g. when reading bus timetables and information charts.















MATHEMATICS

YEAR 6

CURRICULUM PLANNING

TOOLKIT



Read, write, order and compare numbers up to 10 000 000 and determine the value of

each digit

Children should be able to determine the steps used in different scales, and so complete activities such as;

Notes:


Round any whole number to a required degree of accuracy

Children should be able to circle the best estimate of the answer to questions such as;

72.34 ÷ 8.91

When given

6 7 8 9 10 11 as possible answers

Children should estimate the position of numbers on a number line. They should suggest which number lies about two-fifths of the way along

a line from 0 to 1000, or a line from 0 to 1. They should be able to justify their decisions.

Notes:


Use negative numbers in context, and calculate intervals across zero

Children should be able to work with negative numbers in a similar way, determining values on a scale and estimating.

Notes:


Solve number problems and practical problems that involve all of the above

Children should be able to use rounding and inverse operations to estimate and check calculations such as;

The temperature inside an aeroplane is 20°C The temperatures outside the aeroplane is -30°C. What is the difference between these

temperatures?

Notes:





Pupils use the whole number system, including saying, reading and writing numbers accurately



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS



Place value charts



Counting stick

Beadstrings

Number lines

Dienes



(thermometer)


Cuisenaire, unifix, multilink,

straws, (Fruitella)

Numicon

Calculators

Money

Dominoes

100 squares

Dice


games


reels, matchsticks

Outdoor score boards and timers

for PE activities





There are lots of opportunities to consider the size and scale of numbers in real life, many of which fit well with other areas of the curriculum. Ordering and understanding population size of different towns, cities, countries and continents gives a useful context for looking at larger numbers. National newspapers and news programmes often provide statistics comparing values of money or other measures. Temperature is often the easiest context through which to teach a good understanding of negative numbers. The ‘In Order’ activity from Nrich requires children to consider and order the temperature, speed, volume and length of time taken for various different ‘real life’ activities

Number – Fractions Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Solve problems which require answers to be rounded to specified degrees of accuracy














Y6: Number - Addition and Subtraction

Use their knowledge of the order of operations to carry out calculations involving the

four operations

Two numbers have a difference of 1.583. One of the numbers is 4.728. What is the other? Is this the only answer?

Notes:



operations and methods to use and why Notes:


Solve problems involving addition, subtraction, multiplication and division

Identify subtractions they can do without writing anything down

Identify why it is possible to solve a calculation mentally, explain the clues they looked for and then solve it

Peter has £10. He buys 3 kg of potatoes at 87p per kg and 750 g of tomatoes at £1.32 per kg. How

much money does he have left?

Each tile is 4 centimetres by 9 centimetres.

Calculate the width and height of the design.

Write down the calculations that you did

Notes:


Use estimation to check answers to calculations and determine, in the context of a

problem, an appropriate degree of accuracy

Identify subtractions they can do without writing anything down

Notes:




Identify why it is possible to solve a calculation mentally, explain the clues they looked for and then solve it

Peter has £10. He buys 3 kg of potatoes at 87p per kg and 750 g of tomatoes at £1.32 per kg. How much money does he have left?

Each tile is 4 centimetres by 9 centimetres.

Calculate the width and height of the design.

Write down the calculations that you did


Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division (see

Mathematics Appendix 1 in this document.

They undertake mental calculations with increasingly large numbers and more complex calculations.

Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency.

Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50 etc., but not to a specified number of significant figures.

Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9.

Common factors can be related to finding equivalent fractions.


(Years 1-6)


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon

Beadstrings


Empty number lines

Dominoes

Counters

Multilink

Dienes

Cuisenaire

Money

Number fans

Digit cards

Place value cards &

counters

100 squares

Pegs on hanger

Number rhymes

Practical objects linked

to topic

Slider box cards

Dice

Learners will encounter addition and subtraction in:

Almost everything! Addition and subtraction are skills used in

many problem solving activities in subjects across the curriculum.

Science

Within the science curriculum there are opportunities to connect

with addition and subtraction, for example in the introduction of

the Upper Key Stage 2 Programme of Study it states that pupils

should select the most appropriate ways to answer science

questions using different types of scientific enquiry, including

observing changes over different periods of time, noticing

patterns, grouping and classifying things, carrying out

comparative and fair tests and finding things out using a wide

range of secondary sources of information. The children could, for

example, interpret graphs and charts and find totals and

differences in pieces of data, including measurement.

Geography

Within the geography curriculum there are opportunities to connect

with addition and subtraction. In the introduction of the Key Stage 2

Programme of Study it states that pupils should extend their

knowledge and understanding beyond the local area to include the

United Kingdom and Europe, North and South America. This will

include the location and characteristics of a range of the world’s

most significant human and physical features. Children could, for

example, find and compare distances between countries or cities,

compare population statistics, temperatures, lengths of rivers,

heights of mountains etc.. See, for example:

Weather

Environments around the world

Mathematics and geography

History

Within the history curriculum, there are opportunities to connect

with addition and subtraction, for example in the introduction of the

Key Stage 2 Programme of Study it states that pupils should
















Number grid/Number

scales/Number

facts/Difference/Number

line ITPs

continue to develop a chronologically secure knowledge and

understanding of British, local and world history, establishing clear

narratives within and across the periods they study. The children

could find differences between the duration of the different periods,

such as the Stone Age and Iron Age or find the lengths of the

reigns of different British monarchs.

The NCETM Primary Magazine provides some useful starting

ideas for linking mathematics with the Romans.





use negative numbers in context, and calculate intervals across zero

round any whole number to a required degree of accuracy

When working on addition and subtraction and/or number and place value there are opportunities to make


Finding temperature increases, decreases and differences, e.g. the temperature one Monday morning in

January was -6.5°. It had risen by 9.5 degrees by lunchtime. What was the temperature at lunchtime?

Rounding numbers to the nearest tenth, one, ten etc. as an approximation of the answer to an addition or

subtraction and also to check the solution, e.g. Bertie scored 2458 points on the computer game. Cindy

scored 3856. How many points did they score altogether? (Rounding provides an approximation – i.e. 2500 +

3900 = 6400. So precise solution can be compared to approximate value for checking. ) How many more

points did Cindy score? (Rounding provides an approximation – i.e. 3900 – 2500 = 1400. So, if precise

answer is not close to 1400 it cannot be correct.)

Measurement

solve problems involving the

calculation and conversion of

units of measure, using decimal

notation up to three decimal

places where appropriate

When working on addition and subtraction

and/or measures there are opportunities to

make connections between them, for

example:

Finding totals and differences of different

measurements, e.g. Kirsty cycled 25.75km,

her brother cycled a further 4.125km. How

far did her brother cycle? How far did they

cycle altogether?

Statistics

interpret and construct pie charts and line graphs and use these to solve problems

When working on addition and subtraction and/or statistics there are opportunities to make connections


Making up and solving problems from a line graph, e.g. How many miles did the lorry driver travel between the

end of the first hour and the end of the 6th hour?

Programme of Study: Algebra

- from Notes and guidance (non-statutory)

pupils should be introduced to the use of symbols and letters to represent variables and unknowns

in mathematical situations that they already understand, such as:

o missing numbers, lengths, coordinates and angles

o generalisations of number patterns and number puzzles (e.g. what two numbers can add

up to)

When working on addition and subtraction and/or algebra there are opportunities to make connections


Solving missing number problems by balancing each side so making use of the idea of equivalence, e.g.

2y-13 = y + 35

(add 13 to both) 2y -13 + 13 = y + 35 + 13

(calculate numerical elements) 2y = y + 48

(subtract y) y = 48

Solving number puzzles, e.g. write down five possible values of a + b in these equations:

a + b = 8.75

a - b = 23 985


Y6: Number - Multiplication and Division

Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the

formal written method of long multiplication

Look at long-multiplication calculations containing errors, identify the errors and determine how they should be corrected.

Solve problems such as:Printing charges for a book are 3p per page and 75p for the cover. I paid £4.35 to get this book printed.

How many pages are there in the book? Write down the calculations that you did. Seeds are £1.45 for a packet. I have £10 to spend

on seeds. What is the greatest number of packets I can buy?

Notes:


Divide numbers up to 4 digits by a two-digit whole number using the formal written

method of long division, and interpret remainders as whole number remainders,

fractions, or by rounding, as appropriate for the context

Every day a machine makes 100 000 paper clips, which go into boxes. A full box has 120 paper clips. How many full boxes can be made

from 100 000 paper clips?

Each paper clip is made from 9.2 centimetres of wire. What is the greatest number of paper clips that can be made from 10 metres of wire?

A DJ has two different sized storage boxes for her CDs. Small boxes hold 15 CDs. Large boxes hold 28 CDs. The DJ has 411 CDs. How

could the DJ pack her CDs?

Notes:


Divide numbers up to 4 digits by a two-digit number using the formal written method of

short division where appropriate, interpreting remainders according to the context

Give the best approximation to work out 4.4 × 18.6 and explain why. Answer questions such as: roughly, what answer do you expect to get?

How did you arrive at that estimate? Do you expect your answer to be greater or less than your estimate? Why?

Notes:


Perform mental calculations, including with mixed operations and large numbers

Use mental strategies to calculate in their heads, using jottings and/or diagrams where appropriate. For example, to calculate 24 × 15, they

multiply 24 × 10 and then halve this to get 24 × 5, adding these two results together. They record their method as (24 × 10) + (24 × 5).

Alternatively, they work out 24 × 5 = 120 (half of 24 × 10), then multiply 120 by 3 to get 360

Notes:




Identify common factors, common multiples and prime numbers

Children should be able to answer questions such as:

How can you use factors to multiply 17 by 12?

Start from a two-digit number with at least six factors, e.g. 72. How many different multiplication and division facts can you make

using what you know about 72? What facts involving decimals can you derive?

What if you started with 7.2? What about 0.72?

Which three prime numbers multiply to make 231?

use their knowledge of the order of operations to carry out calculations involving the four operations

Children should be able to find answers to calculations such as 5.6 ⬜ = 0.7 or 3 × 0.6, drawing on their knowledge of number facts and

understanding of place value. They should be able to approximate, use inverses and apply tests of divisibility to check their results.

Children should know the square numbers up to 12 × 12 and derive the corresponding squares of multiples of 10, for example 80 × 80 =

6400.

Notes:


Use their knowledge of the order of operations to carry out calculations involving the

four operations

Notes:



operations and methods to use and why

Notes:


Solve problems involving addition, subtraction, multiplication and division

Notes:


Use estimation to check answers to calculations and determine, in the context of a

problem, an appropriate degree of accuracy

Notes:




Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division (see Mathematics Appendix 1 in this document). They undertake mental calculations with increasingly large numbers and more complex calculations. Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency. Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50 etc., but not to a specified number of significant figures. Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9. Common factors can be related to finding equivalent fractions.



NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Numicon, Cuisenaire

Beadstrings

Socks on washing

lines

Hands counting

Straws (bunching)

Structured number

lines & empty

number lines

100 squares

Timestable squares,

blank 12 x 12 grid

Counting stick


Loop cards

Arrays: Eggs in

boxes, Chocolate,

Cake trays

Grouping/Number

dials/Remainders

after

division/Multiplication

array/Number

grid/Multiplcation

grid ITP

Learners will encounter multiplication and division in: Art & Design Within the art and design curriculum there are opportunities to connect with multiplication and division, for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should be taught to develop their techniques, including their control and their use of materials, with creativity, experimentation and an increasing awareness of different kinds of art, craft and design. This could include designing and creating life size models of, for example a Barbara Hepworth sculpture or a Van Gogh painting where the children need to find realistic measurements and then scale them down using division. Geography Within the geography curriculum there are opportunities to connect with multiplication and division, for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and understanding beyond the local area to include the United Kingdom and Europe, North and South America. This will include the location and characteristics of a range of the world’s most significant human and physical features. Work on multiplication and division could include converting between miles and kilometres and vice versa when looking at distances between countries or famous locations, making currency converters for pounds sterling and the currency in the country they are investigating. See, for example:

Mathematics and geography

History Within the history curriculum, there are opportunities to connect with multiplication and division, for example in the introduction of the Key Stage 2 Programme of Study it states that ‘in planning to ensure the progression described above through teaching the British, local and world history outlined below, teachers should combine overview and depth studies to help pupils understand both the long arc of development and the complexity of specific aspects of the content’. The history curriculum requires that pupils should ‘compare aspects of life in different periods’, suggesting comparisons between Tudor and Victorian periods, for example. Scale models could be one way of learning about life in different periods. See, for example:

The Tudors

The Victorians

The Ancient Egyptians

The Ancient Greeks




















Fractions

identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

multiply one-digit numbers with up to two decimal places by whole numbers

use written division methods in cases where the answer has up to two decimal places

divide proper fractions by whole numbers [e.g. ⅓ ÷ 2 = ⅙]

multiply simple pairs of proper fractions, writing the answer in its simplest form

When working on multiplication and division and/or fractions there are opportunities to make connections between them, for example: Multiply numbers such as:

245.25 by 10, 100 and 1000

1.35 by 8

¼ x ½ Divide numbers such as:

12 578 by 10, 100 and 1000

237 by 5

⅓ ÷ 2

Ratio and proportion

solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

When working on multiplication and division and/or ratio and proportion there are opportunities to make connections between them, for example: Convert the ingredients in this lasagne recipe for 4 people so that it will serve 12:

350g minced beef

1 onion

1 clove garlic

600g tin of tomatoes

2 tablespoons tomato puree

175g lasagne sheets

Algebra

express missing number problems algebraically

use simple formulae

When working on multiplication and division and/or algebra there are opportunities to make connections between them, for example:

Solve missing number problems, e.g. 6(a + 12) = 144

multiply out the equation: 6a + 72 = 144

balance by -72: 6a + 72 – 72 = 144 – 72

6a = 72

Use known division facts: a = 72 ÷ 6

a = 12

Find perimeters and areas of rectangles using the appropriate formulae, e.g. a square field has sides of 24.75m. What is its perimeter? What is its area?

Measurement

solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

convert between miles and kilometres

When working on multiplication and division and/or measurement there are opportunities to make connections between them by solving problems such as;

1 pint = 0.57 litres, how many litres in 8 pints? How many pints in 12 litres?

Dan was driving between two cities in France. The sign said the distance was 185km. He wanted to know what that was in miles. How can he find out? How many miles is it?

Statistics

calculate and interpret the mean as an average

When working on multiplication and division and/or statistics there are opportunities to make connections between them, for example: Solve problems, e.g. find the mean monthly temperature for Reykjavik, Iceland

Monthly temperatures for Reykjavik

Jan Feb March April May June July Aug Sept Oct Nov Dec

-2°C -1°C 3°C 6°C 10°C 13°C 14°C 14°C 11°C 7°C 5°C -2°C


Y6: Number - fractions (including decimals and percentages)

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Children should be able to recognise that a fraction such as 5⁄20 can be reduced to an equivalent fraction of ¼ by dividing both numerator and

denominator by the same number [cancelling] They should also be familiar with identifying fractions in different units. E.g. what fraction is 20

pence of two pounds? Of four pounds etc…

Notes:


Compare and order fractions, including fractions >1


i] Position fractions on a number line; e.g. mark fractions such as 7⁄5 , 11⁄20 ,

18⁄12 on a number line graduated in tenths

ii] Answer questions such as: What number is half way between 5 ¼ and 5 ½ ?

iii] Which is larger, ⅓ or ⅖? Explain how you know.

Notes:


Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Children should be able to solve practical problems such as;

Here is a chocolate bar.

William eats 3 pieces and Amber eats 2 pieces. What fraction of the chocolate bar remains?

Joe has some pocket money. He spends three-quarters of it. He has fifty pence left. How much pocket money did he

have?

Notes:


Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ × ½ = 1⁄8]


i] Recognise that ¼ of 12, ¼ x 12 and 12 divided by 4 are equivalent

ii] Use cancellation to simplify the product of a fraction and an integer eg ⅕ x 15 = 3 ⅖ x 15 = 2 x ⅕ x 15 = 2x3 = 6

ii] Work out how many ½s in 15, how many ⅖s in 15, how many 2/5s in 1 etc.

Notes:


Divide proper fractions by whole numbers [for example, 1⁄3 ÷ 2 = 1⁄6]


Decide whether they would prefer to share ½ of a pizza with 2 people or ¾ of a pizza with 4 people and explain why.

Notes:


Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3⁄8]


Explain how much pizza each person would get if they divided 4 pizzas between 5 people, as a fraction and a decimal

Notes:




Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

Children should be able to identify the value of each digit in the number 17.036 and multiply and divide this by 10.100 and 1000

Notes:


Multiply one-digit numbers with up to two decimal places by whole numbers

Children should be able to calculate the answer to questions such as;

What is 3.86 multiplied by nine?

Notes:


Use written division methods in cases where the answer has up to two decimal places.

Children should be able to calculate 601 divided by 36, to two decimal places

Notes:


Solve problems which require answers to be rounded to specified degrees of accuracy

Children should be able to solve problems such as;

Four friends win £48,623. The money is to be shared equally between them – how much will each person receive?

107 pupils and teachers need to be taken to the theatre. How many 15-seater minibuses will be required?

How many boxes of 60 nails can be filled from 340 nails?

Notes:


Recall and use equivalences between simple fractions, decimals and percentages including in different contexts

Children should be able to put a ring around the percentage that is equal to three-fifths;

20% 30% 40% 50% 60%

As well as circle the two fractions that are equivalent to 0.6.

6⁄10 1⁄60

60⁄100 1⁄6

Notes:




Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the

denominator of one fraction is a multiple of the other (for example,½ + ⅛ = ⅝ ) and progress to varied and increasingly complex problems. Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle. Pupils use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for example, if ¼ of a length is 36cm, then the whole length is 36 × 4 = 144cm). They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators. Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money. Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication. Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Fraction wall

Fraction plates

Fraction strips

Fraction cards

Shapes

Counting stick

Number lines



Fraction videos

Numicon, Cuisenaire



Learners will encounter fractions in many different real life contexts: When shopping, children can compare prices presented in decimal form. Consider reductions in price when the reduction is given as a fraction (e.g. ‘one third off’) or percentage (‘20% off today’). Sharing the cost of a total bill equally in a restaurant provides a useful context in which to practise estimation of fractions as well as calculating. Fractions skills can be also emphasised when focusing on measurement. Journey times and fuel consumption can be estimated and calculated (e.g. what fraction of the journey do we have remaining?) Measurement of area and perimeter is strongly linked to work with fractions, ratio and proportion; what proportion of the playground needs to be set aside for ball games? When interpreting and evaluating data children will need to use their fraction knowledge. E.g. Half a million people are earning 20% below the minimum wage

Issue 11 of the NCETM Primary Magazine provides wonderful links to the work of artist Mondrian, with a focus on fractions and decimal work.

There are many connections and these need to be

discussed with pupils. They need to see that fractions are

numbers in their own right, and can, thus, be placed on a

number line. They need to understand how fractions are

linked to division – using both sharing and grouping. Also the

link to multiplication and finding factors, and that fractions

express a relationship between 2 groups, e.g. 3 out of these

4, the proportion.
















Y6: Ratio and Proportion

Solve problems involving the relative sizes of two quantities where missing values can

be found by using integer multiplication and division facts

Answer problems such as:

Here is a recipe for pasta sauce.

Pasta sauce

300 g tomatoes

120 g onions

75 g mushrooms

Sam makes the pasta sauce using 900 g of tomatoes. What weight of onions should he use? What weight of mushrooms?

A recipe for 3 portions requires 150 g flour and 120 g sugar. Desi’s solution to a problem says that for 2 portions he needs 80 g

flour and 100 g sugar. What might Desi have done wrong? Work out the correct answer.

This map has a scale of 1 cm to 6 km.

The road from Ridlington to Carborough measured on the map is 6.6 cm long. What is the length of

the road in kilometres?

Notes:


Solve problems involving the calculation of percentages [for example, of measures,

and such as 15% of 360] and use percentages for comparison

Find simple percentages of amounts and compare them. For example:

A class contains 12 boys and 18 girls. What percentage of the class are girls? What percentage are boys?

25% of the apples in a basket are red. The rest are green. There are 21 red apples. How many green apples are there?

Notes:


Solve problems involving similar shapes where the scale factor is known or can be

found

Solve simple problems involving direct proportion by scaling quantities up or down, for example:

Two rulers cost 80 pence. How much do three rulers cost?

Use the vocabulary of ratio and proportion to describe the relationships between two quantities solving problems such as:

Two letters have a total weight of 120 grams. One letter weighs twice as much as the other. Write the weight of the heavier letter.

The distance from A to B is three times as far as from B to C. The distance from A to C is 60 centimetres. Calculate the distance from A to B.

Notes:




Solve problems involving unequal sharing and grouping using knowledge of fractions

and multiples

Relate fractions to multiplication and division (e.g. 6 ÷ 2 = ½ of 6 = 6 × ½), simplify fractions by cancelling common factors, find fractions of

whole-number quantities and solve problems such as:

What fraction is 18 of 12

What fraction is 500ml of 400ml?

What is 14⁄35 in its simplest form? ⅖

What ⅓ × 15? What about 15 × ⅓? How did you work it out?

What is two thirds of 66?

What is three quarters of 500?

Notes:


No statutory guidance

Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (e.g. similar shapes, recipes). Pupils link percentages or 360° to calculating angles of pie charts. Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work.

Pupils solve problems involving unequal quantities e.g. ’for every egg you need three spoonfuls of flour’, ‘⅗ of the class are boys’. These problems are the foundation for later formal approaches to ratio and proportion.


(Years 1-6)


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Stacking counters

Counters

Double sided counters

Learners will encounter ratio and proportion: Within the science curriculum there are opportunities to work with ratio and proportion. For example pupils should select the most appropriate ways to answer science questions using different types of scientific enquiry, including observing changes over different periods of time, noticing patterns, grouping and classifying things, carrying out comparative and fair tests and finding things out using a wide range of secondary sources of information. The children could, for example, construct pie charts or use ratio and proportion to compare groupings and classifications or the results of tests that they carry out. Within the geography curriculum there are opportunities to connect with ratio and proportion, for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and understanding beyond the local area to include the United Kingdom and Europe, North and South America. This will include the location and characteristics of a range of the world’s most significant human and physical features. Children could, for example, find and compare distances between countries or cities, compare population statistics, temperatures, lengths of rivers, heights of mountains. The results of any comparisons could be displayed in a pie chart. See, for example:

Weather

Environments around the world

Mathematics and geography There are also opportunities to work with ratio and proportion, linked to history, for example, ‘pupils should continue to develop a chronologically secure knowledge and understanding of British, local and world history, establishing clear narratives within and across the periods they study. The children could, for example, represent the lengths of the different periods in history and the rules of different British monarchs using pie charts’ (History Programme of Study). This would enable them to make comparisons using proportion as fractions or percentages. See, for example:

The Victorians

The Romans






http://mathstoolkit.wix.com/mathstoolkit#!ratio-and-proportion-/celp













Number – Fractions

use common factors to simplify fractions; use common multiples to express fractions in the same denomination

associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ⅜)

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

When working on ratio and proportion and/or fractions, including decimals and percentages, there are opportunities to make connections between them, for example:

In the same way that fractions describe the relationship between parts of a whole and the whole of which they are a part, proportion also expresses the relationship between parts and wholes. Ratio, on the other hand, describes the relationships between parts. When working with ratio, the whole can be inferred by understanding the total number of parts. In turn, once the total number of parts is known, any number of those parts can be expressed as a fraction or proportion of the whole. It is helpful to work through an example: imagine 10 counters of which 4 are red and 6 are blue. When comparing the red with the blue, we see that there are 4 red for every 6 blue; the ratio is 4:6. This can be simplified to 2:3. Proportion is usually represented as a fraction. Four out of ten counters are red, so, 4/10 are red. Six out of ten counters are blue, so, 6/10 are

blue. These fractions can be simplified to ⅖ and ⅗. You can practise this with the children using counters, interlocking links or cubes or a collection of classroom items, for example, 8 pencils and 4 rubbers. 8⁄12 of the collection are pencils, this fraction can be simplified to ⅔. 4⁄12 are rubbers, this can be simplified to ⅓. Simplifying fractions covers the first objective in the above list.

The fractions made can also be converted to decimals and percentages, for example 0.4 or 40% of the counters are red and 0.6 or 60% of the counters are blue. 0.3 of 30% of the collection are pencils and 0.7 or 70% are rubbers.

Using the ITP Fractions gives opportunities to visually make comparisons between fractions, decimals, ratio and proportion.

Ratio and proportion is another ITP worth exploring with the children. In this ITP you can demonstrate comparisons between different ratios and proportions with volumes of liquids.

Number-Multiplication and division

When working on ratio and proportion and/or multiplication and division there are opportunities to make connections between them, for example:

Scaling an object or an amount down by multiplying by a fraction, for example, if sketching a tree or building in the school’s grounds, the height would need to be scaled down. You could ask the children to make an estimate of the height of the object by walking away from it until, when they bend down they can see its top from between their legs. They put a marker at this point and then measure from the marker to the base of the object. This will give a reasonable estimate of its height because the child will be looking at the top of the tree at an angle of approximately 45 degrees if viewed in this way. Therefore, the height of the tree will be the same as the distance from it. To make a sketch, this measurement needs to be scaled down. For example if it was 10m tall and they wanted to make a scale drawing showing the tree as 1m high, they would need to draw the tree at a scale of 1:10 (or multiply the height of the tree by a scale factor of 1/10).

Children could draw classroom objects to scale. For example, the height of a table measuring 50cm could be scaled down to (multiplied by scale factor) 1/5 to make the table10cm in the drawing.

Statistics

interpret and construct pie charts and line graphs and use these to solve problems

When working on ratio and proportion and/or statistics there are opportunities to make connections between them, for example:

Using the ITP Data Handling is an effective way to explore comparisons using a pie chart. In the example below, the children could estimate the percentages of people of different ages and compare them. They could present the information as proportions using fraction and/or decimals. They could compare data as ratios, for example the ratio of those under 20 to those between 20 and 50 is 1:2.

http://www.nationalstemcentre.org.uk/elibrary/resource/5053/interactive-teaching-programs-2




Y6: Measurement

Solve problems involving the calculation and conversion of units of measure, using

decimal notation up to three decimal places where appropriate

Children should be able to draw a flow chart to help someone else convert between mm, cm, m and km.

They should be able to answer questions such as: approximately how many litres are there in 3 gallons? Give your answer to the nearest

litre.

Notes:


Use, read, write and convert between standard units, converting measurements of

length, mass, volume and time from a smaller unit of measure to a larger unit, and vice

versa, using decimal notation to up to three decimal

places

This scale (not actual size) shows length measurements in centimetres and feet.

Look at the scale. Estimate the number of centimetres that are equal to 2 ½ feet.

Estimate the difference in centimetres between 50 cm and 1 foot.

Notes:


Convert between miles and kilometres

Pupils should know the approximate equivalence between commonly used imperial units and metric units:

e.g. 1 litre is approximately 2 pints (more accurately, 1 ¾ pints)

4.5 litres is approximately 1 gallon or 8 pints

1 kilogram is approximately 2 lb (more accurately, 2.2 lb)

30 grams is approximately 1 oz

8 kilometres is approximately 5 miles

Children should be able to use conversion graphs that show miles/kilometres. They should be able to use it to estimate a distance of 95

miles in kilometres.

Notes:


Recognise that shapes with the same areas can have different perimeters and vice

versa

The perimeter of a square is 72 centimetres.

The square is cut in half to make two identical rectangles.

What is the perimeter of one rectangle?

Notes:




Recognise when it is possible to use the formulae for area and volume of shapes

Children should be able to calculate the perimeters of compound shapes that can be split into rectangles. For example,

Notes:


Calculate the area of parallelograms and triangles

This is a centimetre grid. Draw 3 more lines to make a parallelogram with an area of 10cm2. Use a ruler.

Notes:


Calculate, estimate and compare volume of cubes and cuboids using standard units,

including cubic centimetres (cm3) and cubic metres (m3), and extending to other units

[for example, mm3 and km3] Notes:




Pupils connect conversion (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs. They know approximate conversions and are able to tell if an answer is sensible. Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature. They relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this. Pupils could be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Mass/weight:


Equipment: bathroom


Force metres




tapes

Capasity & volume:




Time:


geared hands, Analogue clocks,

Digital clocks, Timelines, Timetables

Money:


Measuring



In geography, children will learn of other countries around the world, their climate, landscape and traditions. Map work involves the use of scale, and conversion between measurements. Children could convert between pounds Sterling and currencies of these other countries, using formulae or straight line conversion graphs. Calculations of area and perimeter are often used when decorating rooms (for carpet, paint, skirting board etc.) or a garden (circular/square pond area, lawn area, perimeter fencing etc)

Within mathematics, pupils can connect the conversion of units of measurement (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs. They should know approximate conversions and should able to tell if an answer is sensible. When focusing on measuring temperature, pupils should make use of the number line to add and subtract positive and negative integers













Draw 2-D shapes using given dimensions and angles

Children should be able to construct a triangle given two sides and the included angle

Here is a sketch of a triangle. (It is not drawn to scale).

Draw the full size triangle accurately, below. Use an angle measurer (protractor) and a ruler. One line

has been drawn for you.

Notes:


Recognise, describe and build simple 3-D shapes including making nets

Children should be able to identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge

of properties to draw 2-D shapes and identify and draw nets of 3-D shapes

They should be able to respond accurately to questions such as;

‘I am thinking of a 3D shape. It has a square base. It has four other faces which are triangles. What is the name of the 3D shape?’

‘Which of these nets are of square based pyramids? How do you know?

‘Is this a net for an open cube?’ How do you know?

Notes:


Compare and classify geometric shapes based on their properties and sizes and find

unknown angles in any triangles, quadrilaterals, and regular polygons

Children should be able to make and draw shapes with increasing accuracy and knowledge of their properties.

They should be able to carry out activities such as;

‘Give me instructions to get me to draw a rhombus using my ruler and a protractor’

‘On the grid below, use a ruler to draw a pentagon that has three right angles’

Notes:




Illustrate and name parts of circle, including radius, diameter and circumference and

know that the diameter is twice the radius

They should know that:

The circumference is the distance round the circle

The radius is the distance from the centre to the circumference

The diameter is 2 x radius

Notes:


Recognise angles where they meet at a point, are on a straight line, or are vertically

opposite, and find missing angles

Children should be able to estimate angles, use a protractor to measure and draw them, on their

own and in shapes. They should know that the angle sum of a triangle is 180˚, and the sum of

angles around a point is 360˚.

They should be able to use this knowledge to respond accurately to questions such as;

‘There are nine equal angles around a point. What is the size of each angle?’

‘There are a number of equal angles around a point. The size of each angle is 24°. How many

equal angles are there?’

Children should be able to calculate the size of angle ‘y’ in this diagram without using a protractor.

(Not to scale)

Notes:




Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles. Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements. These relationships might be expressed algebraically for example: d = 2 × r ; a = 180 – (b + c).



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS




paper

Rulers

Geostrips



Isometric


angles ITP

Learners will encounter properties of shape in: The world around them – using their ability to recognise and describe 3-D shapes used in building houses, packaging used by supermarkets and storage boxes used in and around the home. Design and Technology – using an ability to draw 2-D shapes using given dimensions and angles to make and construct technology projects. Building simple and more complex 3-D shapes using plastic toy construction materials as an example. Physical Education – e.g. in orienteering, pupils use knowledge of angles to find clues and use an understanding of properties of shapes to solve problems. ICT- use of programming technology to design sequences, using knowledge of angles, to compare and classify geometric shapes based on their properties. Pupils use knowledge of angles to support program writing and building of 3-D models. History – Pyramids and obelisks – using plasticine or modelling equipment to build models and gain an understanding of the faces and angles used in building 3-D shapes used throughout history. Art – the NCETM Primary Magazine provides many useful links for looking at shape within art. Issue 34 provides some useful starting points, using the snail work of Matisse as a stimulus.

When solving practical problems, there are many links to be made between geometry, measures and elements of number and place value. Calculating percentages of angles, e.g. 15% of a circle, of 25% of 360˚ can bring the two mathematical strands together. Shapes of given properties can be translated, rotated and reflected, and positions described on the full 4-quadrant coordinate grid. Measurement skills can be used to define scale factors between similar shapes, and to calculate areas of parallelograms and triangles.















Describe positions on the full coordinate grid (all four

quadrants) Children should be able to answer questions such as; The two shaded squares below are the same size. A is the point (17,8). B is the point (7,-2). What are the co-ordinates of the point C?

Notes:


Draw and translate simple shapes on the coordinate plane, and reflect them in the axes Children should be able to draw a shape with corners at given vertices, and describe the properties of the shape. Can they create the same shape where all of the coordinates will be positive? Negative? They should be able to sketch the reflection of a simple shape in two mirror lines at right angles and find the coordinates of selected points.

Notes:



Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers. Pupils draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. These might be expressed algebraically for example, translating vertex (a, b) to (a - 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.


(Years 1-6)


connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Logo

Bee bots

Compass

Square papers

Geo strips

Tracing paper

Co-ordinates ITP

In geography, learners will encounter coordinates through map work. In Design & Technology, learners may be required to use their knowledge of translation, in particular, scaling up and down. Coordinates and translation may also be used when designing rooms, planning buildings and floor layouts, or when scaling drawings or patterns in Art & Design.

Pupils should make rich connections across mathematical

ideas to develop fluency, mathematical reasoning and

competence in solving increasingly sophisticated problems.

They should also apply their mathematical knowledge to

science and other subjects.














Y6: Statistics Interpret and construct pie charts and line graphs and use these to solve problems

This graph shows the number of people living in a town.

How many people lived in the town in 1985?

In which year was the number of people the same as in 1950?

Find the year when the number of people first went below 20 000.

KS2 2008 Paper A level 5

Class 6 did a survey of the number of trees in a country park. This pie chart shows their results.

Estimate the fraction of trees in the survey that are oak trees. The children counted 60 ash trees.

Use the pie chart to estimate the number of beech trees they counted.

KS2 2006 Paper A level 5

Notes:


Calculate and interpret the mean as an average

From a simple database, children should be able to find the most common score (mode) as well as the mean score for each test.

Children should be able to choose their own sets of data to match given criteria, e.g. find a set of five numbers that have a mean of 5 and a

range of 7.

Notes:





Pupils connect their work on angles, fractions and percentages to the interpretation of pie charts. Pupils both encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects. They should connect conversion from kilometres to miles in measurement to its graphical representation. Pupils know when it is appropriate to find the mean of a data set.



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Carroll diagrams


Tables

Pictograms

Block graphs

Bar graphs

Multilink towers


graph/ ITP

Tracing paper

Protractors

There are many, many examples of ‘real life’ situations where a wealth of data needs to be digested, sorted, presented or interpreted. Websites such as: ‘Stats4Schools’, the content of which is now hosted by the National Stem Centre, has a large number of ‘real’ data sets’ that children could use in other curriculum areas. ‘Census at School’ also provides a vast bank of data resources that can be utilised in the classroom. Geographical data and information based on other regions and countries can provide a good context for statistics work. Measurements and readings recorded in science lessons, e.g. of sound levels, temperature, plant height etc, can all be used as datasets for statistics work in mathematics.

The construction of pie charts will provide an essential link with work on angles and fractions, as well as calculation. The use of conversion graphs when carrying out work on line graphs provides a nice link to converting different units of measure. When carrying out measuring activities in the classroom, it is likely that the mean average will be useful.













Y6: Algebra

Use simple formulae

Children should be able to express a relationship in symbols, and start to use simple formulae. For example:

Use symbols to write a formula for the number of months m in y years.

Write a formula for the cost of c chews at 4p each.

Write a formula for the nth term of this sequence: 3, 6, 9, 12, 15…

The perimeter of a rectangle is 2 × (l + b), where l is the length and b is the breadth of the rectangle.

What is the perimeter if l = 8 cm and b = 5 cm?

The number of bean sticks needed for a row which is m metres long is 2m + 1. How many bean sticks do you need for a row which

is 60 metres long?

Plot the points which show pairs of numbers with a sum of 9.

Notes:


Generate and describe linear number sequences

Children should experience activities such as;

A number sequence is made from counters.

There are 7 counters in the third number.

How many counters in the 6th number? the 20th...?

Write a formula for the number of counters in the nth number in the sequence.

Notes:


Express missing number problems algebraically

Notes:


Find pairs of numbers that satisfy number sentences involving two unknowns

Notes:


Enumerate possibilities of combinations of two variables

Children should be confident to answer questions such as;

Here are five number cards:

A and B stand for two different whole numbers.

The sum of all the numbers on all five cards is 30.

What could be the values of A and B?

Notes:





Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

missing numbers, lengths, coordinates and angles

formulae in mathematics and science

arithmetical rules (e.g. a + b = b + a)

generalisations of number patterns

number puzzles (e.g. what two numbers can add up to)



connections


NRICH OVERVIEW

OVERCOMING BARRIERS

ARTICLES

VIDEOS



MENTAL IMAGES

PROGRESSION MAPS

REASONING MAPS

Balancing scales

Learners will encounter algebra in: Recipes or formulae such as: Child’s dose = Age × Adult dose Age + 12 or F = 9⁄5 C + 32 Working out the reading age of a particular text – e.g. where N is the number of one-syllable words in a passage of 150 words.

FORECAST formula

FOG index

where A = no. of words in passage n = no. of sentences L = no. of words containing 3 or more syllables (excluding the'-ing' and 'ed' endings). More information on reading age formulae, can be found here

Mathematics is an interconnected subject in which pupils

need to be able to move fluently between representations of

mathematical ideas. The programmes of study are, by

necessity, organised into apparently distinct domains, but

pupils should make rich connections across mathematical

ideas to develop fluency, mathematical reasoning and

competence in solving increasingly sophisticated problems.

They should also apply their mathematical knowledge to

science and other subjects.






http://mathstoolkit.wix.com/mathstoolkit#!algebra/c1lyk






http://www.cimt.plymouth.ac.uk/resources/topical/reading/reading.htm

mathematics year 1 curriculum planning …oakwoodlive.net/curriculum/maths/maths - new curriculum...

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