scheme of work for year 6 - st- web viewcontents and the intended use of each section within the...

©Nigel Bufton MATHSEDUCATIONAL LTD

Securing Progress in Mathematics Scheme of

Work for Year 6

Scheme of Work: Mathematics Year 6

Contents and the intended use of each section within the Scheme of WorkEssential Learning in MathematicsThis draws together those key aspects of mathematics pupils need to secure so that they can make good progress over the year and are ready to move onto the work set out in the following year. When planning the year’s work keep these aspects of mathematics in mind. Return to them at regular intervals and provide pupils with the opportunity to refresh and rehearse them through practice, consolidating and deepening their knowledge, skills and understanding.

Problem Solving, Reasoning, CommunicatingThis provides a short summary of the problem solving and reasoning activities pupils should engage in and the communication skills expected of them.

Language and MathematicsThis section emphasises the importance of spoken language in the teaching and learning of mathematics and the need for pupils to acquire a range of appropriate mathematical vocabulary. It highlights and exemplifies five functions language plays in the learning of mathematics.

Learning the Language of MathematicsTwo simple-to-remember principles are identified, that seek to promote the incorporation of language into mathematics planning and teaching.

Key Mathematical VocabularyThis table lists key mathematical vocabulary organised under seven strands of mathematical content which reflect the headings used in the National Curriculum. The table provides a checklist you can refer to when planning. There is some overlap across the year groups to consolidate pupils’ learning.

Learning OutcomesThis table lists the learning outcomes for the year and reflects the National Curriculum Programme of Study. You can select and refer to the learning outcomes, choosing those that will be your focus for a teaching week. This way you can monitor the balance in curriculum coverage over the year.

Assessment Recording SheetThe sheet provides a way of maintaining a termly record of pupils’ attainment and progress in mathematics. The seven headings reflect those in the table of learning outcomes. This is to help you to cross-reference teaching coverage against your assessment of learning, and to identify future learning targets against need. The ‘see-at-a-glace’ profile of progress and attainment can be used to monitor pupils’ progress over time.

Week-by-week PlannerThis sets out weekly teaching programmes, covering 36 teaching weeks. This programme is organised into 6 half terms with 6 teaching weeks within each half term. The weekly teaching programmes offer a guide to support your medium-term and long-term planning. There is sufficient flexibility in the programme to make adjustments to meet changes in lengths of terms. The mathematics for each week is described as bullets. These bullets are not equally weighted and one bullet does not represent a day’s teaching. Use the bullets listed to map out the whole week. Planning based on the weekly teaching programmes should also take account of your day-to-day assessment of pupils’ progress. If more or less time is required to teach a particular aspect of mathematics set out in the programme, review your plans and adjust the coverage of the content in the programme accordingly. It is important that your planning reflects the speed and security of your pupils’ learning. The accompanying notes and examples offer some ideas about how to teach aspects of the content set out in the week. They may inform planning in other weeks too when content is revisited. They are not exhaustive and the resources alluded to in the text are not provided in these documents. The programme reflects the content in the National Curriculum, with the highest proportion of time being devoted to Number.©Nigel Bufton MATHSEDUCATIONAL LTD 2


Essential Learning in Mathematics

Summary of Essential Learning in Year 6 Identify the place value of the digits in large whole numbers and decimal

numbers; round numbers, estimate and approximate to check results; use algebra to represent numbers, evaluate simple formulae and expressions

Recall immediately number facts and the multiplication tables to 12x12 and carry out accurately mental calculations involving all four operations with whole numbers, decimals, fractions, percentages

Use formal written methods of calculation for all four operations; understand and apply order of operations when calculating

Express proportions and relationships between numbers and quantities as a fraction, percentage or ratio; construct, convert between and use equivalents

Measure and draw accurately, convert units to take account of the context and required precision; take and compare reading on different scales; transform shapes and identify conserved properties; calculate missing angles

Organise and analyse data in frequency tables; interpret and construct pie charts and line graphs that relate two variables; describe trends and relationships

Problem Solving, Reasoning, Communicating

Pupils solve multi-step, routine and non-routine problems that involve the four operations. They use estimation to get a sense of the scale of the answer and round answers to a specified degree of accuracy. Pupils express and calculate quantities in given ratios, and use fractions, decimals and percentages to describe and calculate proportions and parts of quantities. They scale equal and unequal quantities up or down and use this to convert between units of measure. Pupils use letters to represent variables, an unknown value and to express relationships in number patterns or between two variables. They evaluate formulae and use them to find areas and volumes.

Pupils reason mathematically. They use known properties of geometric shapes and numbers to sort and classify them and to calculate missing values. They identify the similarities or differences within a set of numbers and shapes, using what they know to deduce related properties. Pupils analyse and interpret information in tables, diagrams and pictures to determine what is important and use this to solve problems and logic puzzles. They use collected data and measurements to determine patterns and relationships and to provide answers to questions along with a justification for their choices and decisions. They infer trends and changes in data over time and use these to predict future results.

Pupils use precise mathematical language to describe their thinking and observations. They interpret quantities and apply solutions to the context of a problem to ensure it is sensible. Pupils describe sequences and proportional parts and explain the difference between an approximate answer expressed as a decimal and an exact answer given as a fraction.

Language and Mathematics©Nigel Bufton MATHSEDUCATIONAL LTD 3


The National Curriculum (Section 6: September 2013 Reference DFE-00180-2013) declares that:“Teachers should develop pupils’ spoken language, reading, writing and vocabulary as integral aspects of the teaching of every subject. Pupils should be taught to speak clearly and convey ideas confidently ... They should learn to justify ideas with reasons; ask questions to check understanding; develop vocabulary and build knowledge; negotiate; evaluate and build on the ideas of others ...They should be taught to give well-structured descriptions and explanations and develop their understanding through speculating, hypothesising and exploring ideas. This will enable them to clarify their thinking as well as organise their ideas ... Teachers should develop pupils’ reading and writing in all subjects to support their acquisition of knowledge ... with accurate spelling and punctuation.” When we think mathematically we may use pictures, diagrams, symbols and words. We communicate our ideas, reasons, solutions and strategies to others using the spoken and written word. We listen to how others explain their methods using mathematical language and read what they have written so we can interpret their ideas and solutions. Language is a fundamental tool of learning and this is as true for learning mathematics as it is for any other subject.Having a good command of the spoken language of mathematics is an essential part of learning, and for developing confidence in mathematics. Children who say little are usually those who are fearful about saying the wrong thing, or giving an incorrect answer. Very often the quiet children are those who may lack knowledge of, or confidence in using the necessary vocabulary to express their ideas and thoughts to themselves and consequently to others.Mathematics has its own vocabulary which children need to acquire and use. They need to be taught how to pronounce, write and spell the mathematical words they are to use, and to know when they apply and to what they apply. Learning the vocabulary and language of mathematics involves: associating objects, measures and events with their names (e.g. a cube, a mixed number, a metre rule, 2016 will be a leap year) stating, repeating and recalling facts aloud, and explaining how they can be used and applied (e.g. a regular quadrilateral is a square, three multiplied by

four is twelve so twelve divided by four is three, seven tenths can be written as zero point seven) describing the relationship between two or more objects, shapes, events or sets (e.g. a diagonal cuts a rectangle into two identical triangles, the number

fifty is double twenty-five, these four lines are all shorter than 15 centimetres, in 20 minutes time it will be 14:35) identifying properties and describing them (e.g. squares have four right-angled corners, negative numbers are less than zero, unit fractions have

numerator one) framing an explanation, reasoning and making deductions (e.g. this triangle cannot be isosceles because its angles are unequal, 3 is a factor of 39 so 39

is not prime but 37 is a prime, if one quarter is £5 then the whole amount is 4 x £5 = £20)

Learning the Language of Mathematics

Learning to use the language of mathematics requires carefully prepared opportunity and continued experience and practice. When planning consider when and how your children will be taught to:

See the words – Hear them – Say them – Use and apply them – Spell them – Record them

It is important that children memorise and manipulate the language of mathematics. When planning consider when and how your children will learn to:

Visualise and manipulate mathematical pictures, diagrams, symbols or words in their heads

Key Mathematical Vocabulary: Year 6©Nigel Bufton MATHSEDUCATIONAL LTD 4


NumberNumber system, powers of ten, place value, units, tens, hundreds, thousands, millions, billions; seven-digit number; decimal point, decimal places, tenths, hundredths, thousandths; round to required degree of accuracy, rounded; estimate, approximate value, is approximately equal to (≈), not equal to (≠); greater than (>), greater than or equal to (≥), less than (<), less than or equal to (≤), negative number; common factor, common multiple; prime number, factors, prime factor, square, cube,

CalculationSum, total, difference, difference between, addition, subtraction; long multiplication, short multiplication; product, scale up, multiple of, multiplier, multiplicand; factor pairs, factor of; long division, short division; quotient, scale up, scale down, divisor of, dividend, remainder; operation, inverse operations, order of operations, mixed operations, priority, brackets, power, index, exponent; commutative operation, associative rule, distributive law, max, min, maximum, minimum

FractionsWhole number, mixed number, unit fraction, proper fraction, improper fraction; equal part, numerator, denominator, common denominator; convert to, simplify, cancel, reduce to, simplest form; equivalent fractions; decimal fraction, three decimal places; per cent, percentage (%); equivalent parts, equivalent numbers, equivalents; fraction as number, fraction as operator

Ratio and proportion

Equal sharing, unequal sharing; one-to-one; two-to-one; one-to-two; relative size; in the ratio; 4:1, four ... for every one ..., 2:3, two ... to every three ...; in the proportion, in proportion to; one ... in every four ... , one quarter of; scale up, scale down, scale factor, scale drawing, similar shapes; size, absolute value, absolute size, relative sizes

AlgebraSymbol, symbolism, notation; general case, generalisation; variable, particular value; arithmetic expression, algebraic expression, term; equivalent expressions; substitute, evaluate an expression, enumerate; variable, combinations of variables; dependent variable, independent variable, formulae; linear sequence, term-to-term rule; equal to, equation, unknown, solution, unique solution, values that satisfy an equation

Measurement

Units of measure, standard units, metric units, imperial units; metre, centimetre, millimetre, kilometre; miles, yards, feet; litre, centilitre, millilitre; gallon, pint; gram, centigram, milligram, kilogram; pound, stone; area, square, square units, m², cm², mm², km²; volume, cube, cubic units, m³, cm³, mm³, km³; degrees Centigrade (ºC), degrees Fahrenheit (ºF), positive temperature, freezing point, negative temperature, below zero; analogue clock, digital clock, 12-hour time, 24-hour time; year, month, day, hour, minute, second; compound units, rates of change, speed, miles per hour, litres per minute, cost per second

Geometry

Dimension, 2-D, 3-D, plane, point, straight line, plane shape, side, corner, angle; right-angled, acute, obtuse, reflex; isosceles, equilateral, scalene, triangle, quadrilaterals, polygon, irregular/regular polygons; tessellation, tessellating shapes; circle, centre, radius, diameter, circumference; perpendicular lines, parallel lines; vertically opposite angles, angles on a line, angles about a point; coordinates, quadrants, axis, axes, vertex, vertices; transform, translate shapes, reflect shapes, line of reflection, mirror line, axis of symmetry; rotate, clockwise, anticlockwise, centre of rotation; cubes, cuboids, pyramids, prisms, polyhedron, polyhedral, nets; edge, vertex, face, side of faces

StatisticsPie chart, sector, size, relative size, proportion, part relative to whole; count, frequency, discrete variable; measure, continuous variable; time graph, changes over time, trends; scatter plot, scatter graph, relationship; line graph, graphical representation, conversion, conversion graph, equivalent values; axes, scale, interval, approximately; average, average value, equal share, mean, middle value, median, most popular value mode; representative value; spread, range, distribution of value, symmetric, skewed

Problem solving,

Reasoning, Communicating

Routine problem, non-routine problem; strategy, representation, picture, diagram, sketch; trial and improvement, systematic; analyse, interpret, construct, convince; collect, organise, order, sort data; identify patterns, establish relationships; if ... then ... ; because; does not apply, is not, as ... is then so is ... , ... is the same as ... , is a scale model of, scale drawing of, scaled up, scaled down; similar to, identical to, congruent to; is different to; conjecture, hypothesise, hypothesis; test, demonstrate, justify, prove, find counter-example; deduce from evidence, deduce results from general properties, deduction, apply general case to particular cases; generalise, generalisation, general case, induce, infer; one-step problem, multi-step problem; represent problem as picture, identify calculations; evaluate outcomes, check results, approximate answer

End-of-Year Learning Objectives for Year 6 Record of coverageA. Number – approximating and place value; Algebra

©Nigel Bufton MATHSEDUCATIONAL LTD 5


A1. Can identify the value of the digits in any whole number and decimal numbers with up to three decimal places

A2. Can round whole and decimal numbers to a required degree of accuracy

A3. Can read negative numbers on scales and work out intervals, including those that cross zero

A4. Can use symbols and letters to represent numbers and relationships in formulae, equations, missing number problems

B. Number - calculation (mental and written)B1. Can recall and use number facts and 12 x 12 tables to calculate mentally, identify common factors and multiples

B2. Can use formal written methods to add and subtract whole and decimal numbers

B3. Can multiply and divide whole and decimal numbers by multiples of 10,100,1000 and by 1- and 2-digit whole numbers

B4. Can use formal written methods to multiply and divide numbers with up to 4 digits by 1- and 2-digit whole numbers

B5. Can represent division as a fraction, express remainders after division as fractions, in decimal form, or round appropriately

B6. Can apply the rules of arithmetic to evaluate expressions including the use of brackets

C. Number - fractions, decimals and percentages; Ratio and proportionC1. Can simplify fractions using common factors, re-write fractions as equivalent fractions

C2. Can compare and order proper, improper and mixed fractions

C3. Can add and subtract fractions by converting to equivalent fractions, multiply pairs of proper fractions

C4. Can multiply simple proper fractions, divide a fraction by a whole number, find a fraction and a percentage of a quantity

C5. Can calculate the whole of a quantity given the value of a fractional or percentage part

C5. Can convert between simple fractions, decimals and percentages and use to calculate proportions

C6. Can interpret and use a ratio or scale factor to increase or decrease quantities

D. MeasurementD1. Can measure accurately, read and convert between the common standard metric units of measure using decimal notation

D2. Can read and convert units of time, give approximate conversions between metric and Imperial units of measure

D3. Can calculate perimeters and areas of 2-D shapes and the volumes of cubes and cuboids using cubic units

E. Geometry – properties of shapes, position and directionE1. Can draw 2-D shapes accurately and find missing angles in triangles, quadrilaterals and regular polygons

E2. Can interpret diagrams of 3-D shapes, build simple 3-D shapes and draw their nets accurately

E3. Can draw and name the parts of a circle, identify and calculate angles between straight lines and about a point

E4. Can plot points and interpret coordinates in all four quadrants; draw, complete, reflect and translate shapes

F. Statistics – interpret pie charts, line and scatter graphs and meanF1. Can interpret information presented graphically and construct pie charts, line and scatter graphs that relate two variables

F2. Can calculate the mean and interpret its use as a representative value for a data set

G. Problem solving, reasoning, communicatingG1. Can solve multi-step problems that involve conversion of units, fractions, ratio, scaling; give answers to required accuracy

G2. Can use known facts to derive properties of number and shape, justify choice of operations when solving problems

G3. Can interpret numbers, shapes, patterns, graphs; use precise mathematical language to explain properties, methods, ideas

Assessment Recording Sheet

Mathematics in Year 6 Autumn term Spring term Summer term



Name:

Class:Key: 6.1 – Working towards expectations 6.2 – Meeting expectations 6.3 – Exceeding expectations

A. Number – approximating and place value; Algebra 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

B. Number - calculation (mental and written) 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

C. Number - fractions, decimals and percentages; Ratio and proportion 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

D. Measurement 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

E. Geometry – properties of shapes, position and direction 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

F. Statistics – interpret pie charts, line and scatter graphs and mean 6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

G. Problem solving, reasoning, communicating

6.1 6.2 6.3 6.1 6.2 6.3 6.1 6.2 6.3

End-of-year assessment of progress and attainment in mathematics Summary report:

Overall end-of-year assessment in mathematics: Working towards Year 6 expectations Meeting Year 6 expectations Exceeding Year 6 expectations

Teacher: Date of final assessment:

Week-by week Planner Year 6Autumn Term (First half term)Week 1 Week 2 Week 3



Number Geometry/Measurement Number/MeasurementMain Teaching: Read write, order, use

place value for whole numbers in tens of millions

Round whole numbers to a given power of 10

Read and record positive and negative numbers on scales and number lines and calculate intervals across 0

Add and subtract mentally 1- and 2-digit numbers with 1 decimal place

Practise formal written methods to add and subtract 4-, 5-digit whole numbers

Solve missing number problems involving one or two numbers

Solve word problems involving negative numbers, and the + and - of whole numbers in the context of money and measures

Notes/examplesIn the number 16 676 360 what is the value of each of the 6 digits? Round it to the nearest 1000...What is the difference in the value of: £20 million and £19 999 000...? The bottom number on my stick is 0, the intervals are in 5s. What number is at the top? If 0 is the top number, what is at the bottom? If 5 is the middle marker. Count in 25s how far up is it to the top? How far is it to the bottom? The intervals are now in 4s; 0 is on this 4th marker, what is the top/bottom number?The table shows in ºC the max and min temperature over 4 days. For each day work out how much the temperature falls? One day the fall was 11 ºC with a min of -16 ºC, what was the max?

Days M T W TMax +3 +4 -3 +5Min -7 -5 -9 0

Main Teaching: Use given information

to draw 2-D shapes Measure the angles

and the lengths of sides in given polygons

Using accurate drawings and measuring, test out and confirm the properties of quadrilaterals

Compare and classify 2-D shapes using their properties

On a coordinate grid with labelled axes, plot coordinates in the 4 quadrants; draw and complete shapes, and identify missing coordinates

By counting squares, work out the areas of simple irregular shapes on grids

Draw rectangles on grids given their area and work out their perimeters

Notes/examplesDraw a kite using the squares in your book for the corners. Draw in the diagonals. Measure lengths and angles and write down any properties you notice. Do the same for other quadrilaterals.Which quadrilaterals can have diagonals that: intersect to form isosceles triangles; bisect each other; are perpendicular? Plot these 2 points: (-3, 1); (5,1). They form one side of a square. What are the coordinates of the 2 other corners? Are other squares possible? The 2 points are now opposite corners of a square what are the coordinates of the other corners? What are the areas of the squares? The points (-1,-1); (-3, 2); (3, 1) are corners of a parallelogram. Draw the parallelograms. What are the coordinates of the missing corners?

Main Teaching: Round whole numbers

to a given power of 10 and decimal numbers to the nearest whole number or to a given place of decimals

Estimate length, weight and capacity then measure to check

Convert mixed units of measure to a decimal and round to the required accuracy

Use common factors to simplify, compare and order fractions

Convert fractions to fractions with a given denominator and generate sets of equivalent fractions

Use diagrams and common multiples to add and subtract fractions

Solve word problems involving equivalent fractions and + and – of simple fractions

Notes/examplesA room is 2m 36cm high. Write that as a decimal. Now round it to whole metres. What is the height to 1 decimal place?

Simplify fractions: 9

24;

1024

How do they help us to

compare: 38

and 512

?

Order the fractions:1124 ;

23 ;

56 ;

1124; 7

12 . Which

fraction is bigger than 34

,

smaller than12? Draw a 3

by 5 rectangular grid. How many squares make up the whole? How many squares make a third/fifth of the whole? Show me two fifths. How many of the squares is that? What

is 25 +

13 ? Why is it

1115?

Use the rectangle to find: 25 -

13 ;

23 -

35 ;

15 +

23 ;

25 +

23 ...

Mental Work: Round numbers to the required degree of accuracy

Mental Work: Visualise and name shapes given their features

Mental Work: Recall and apply multiplication facts to 12x12



Recall and apply multiplication facts to 12x12 Give the complements to 1 of decimal numbers

Identify properties of a given 2-D shape Identify coordinates on straight lines and shapes

Give the complements to 1 of a fraction or decimal Scale fraction up or down; state equivalent fraction

Extension Work: Find pairs of numbers that satisfy a simple equation

with 2 unknowns e.g. 2a+b=6

Extension Work: Describe shapes algebraically e.g. (a, b), (a+4, b),

(a+4, b-3), (a, b-3) a rectangle with sides 4, 3 units

Extension Work: Use simple formulae to convert between metric and

imperial units e.g. pints(P) to litre(L) P=0.568L

Autumn Term (First half term)Week 4 Week 5 Week 6 Statistics/Measurement Number Number Main Teaching: Read and interpret

data from tables, and bar and line charts

Read and label scales with intervals set at different sizes and with starting values other than 0

Find and compare the mean of simple data sets and interpret the value in context of the problem

Interpret and explain the impact on the mean when data in a set is altered

Draw and use conversion graphs to convert values inside and outside the range of the axes on the line graph

Use conversion graphs to solve problems involving metric and imperial units and conversion of currency or temperature

Notes/examplesThe bar chart shows rainfall from Jan to May.

The vertical axis starts at 0 and intervals of 4cm. Read the values for each bar. How much rain fell in these 5 months? A mistake was made: the axis should start at 8cm with intervals of 6cm. What are the monthly figures now? How has the mean monthly rainfall been affected? The line graph is a conversion graph for weight: pounds (lbs) to kg.

Main Teaching: Use and practise

formal written methods to multiply and divide up to 4-digit whole numbers by 1- and 2-digit whole numbers

Describe the impact of changes to digits in a multiplication involving up to 4-digit numbers by 1-digit whole numbers

Identify a remainder in a division of a number close to a known multiple of the divisor

Write remainders as a whole number or as a fraction in its simplest form

Express remainders as decimals with up to 3 decimal places,

Solve word problems involving x and ÷ in context rounding the answer to meet the requirement of the problem’s context

Notes/examplesWork out: 5460 x 7. If the 0 becomes 2. How much bigger is the answer? If the 5 becomes 3 how much smaller? In turn, increase each digit by 1; how does this affect the answer? How does rounding 5460 to the nearest 100 change the answer? What is 6x12? So, is 72 divisible by 12? Yes as 72÷12=6. Is 74 divisible by 12? No, 74 is 2 more than 72 so we know the remainder is 2. Is 68 divisible by 12? No. It is 4 less than 72 so we know the remainder is -4 or +8. Is 306 divisible by 15? What number fact did you use to decide? What is the remainder to 306÷15? What about 290÷15? What’s the remainder for 177÷17; 168÷17; 346÷17? Work out 3520÷16. Give me numbers near to 3520 with remainders 2, 13, 15 when I divide by 16. Find digits to replace the ?s in:127÷6=??R?;34?÷5=6?R3;?7?÷4=?3R3;4??÷7=6?R2

Main Teaching: Read, identify,

record positive and negative numbers on scales; calculate the end numbers of intervals that cross 0

Find estimates to calculations by rounding; explain the impact on the answer

Derive and use alternative mental methods of calculation

Make, describe complete number sequences that are formed by counting in steps of any whole number from any start number

Make and test a generalisation; give reasons why it is sometimes, always or never true

Notes/examplesThe number at the top of my stick is 8. Silently count back in 3s and tell me what number will be at the bottom of my stick. Now count down in 6s from 20 and tell me the bottom number. My bottom number is -15, count up in 5s and tell me the number at the top. How can we find these numbers without counting? For the 10 steps of 3 down from 8: 10x3=30 so we subtract 30 from 8. What is 8-30? We can subtract 8 from 8 to get 0. We still have 22 to subtract. We write: 8-10x3=8-8-22=-22. Fill in the table.

TopNumber Steps Step

sizeBottomNumber

12 8 3: :6 20 -90

To work out 64x5 and 66x5 I used estimates of 300 and 350. As 66x5 is 10 more than 64x5 then 66x5=300+25-5=320 and 66x5=300+25+5=330. Explain my method? Work out: 27x4, 23x4; 56x8, 54x8; and 88x5, 82x5?Don says: “Divide a 4-digit number by a 2-digit number. The answer can be a 2-, 3- or 4-digit number. Is this true or not?



The conversion rate used is 2.2lbs to 1kg.Mark up the scales and use it to convert 90lbs to kg and 30kg to lbs.

Mental Work: Identify points and intervals on scales Carry out mental calculations involving +, -, x, ÷ Round capacities, ml to nearest l; weights g to kg

Mental Work: Recall and apply multiplication facts to 12x12 Recall and apply related division facts Round times to nearest hour, half/quarter hour

Mental Work: Recall and apply multiplication facts to 12x12 Recall and apply related division facts Round times to nearest 10, 5 minutes

Extension Work: Interpret and draw dual bar charts for discrete data

Extension Work: Convert between 24hr, 12hr times using am, pm

Extension Work: Find intervals over a day using 24hr notation

Autumn Term (Second half term)Week 1 Week 2 Week 3 Number Number Geometry/MeasurementMain Teaching: Practise formal

written methods of calculation that include whole and decimal numbers

Read and write whole numbers in words and numerals

Order positive and negative numbers on scales, number lines

Calculate intervals that cross zero

Interpret percentages as fractions and decimals using hundredths, tenths

Calculate 10% of a given quantity and scale up to find percentages that are multiples of 10% up to and beyond 100%

Calculate multiples of

Notes/examplesMy stick starts at 0 and

stops at -10. Where do I put numbers 0, -10 on my stick? What number is in the middle? What numbers are at these arrows? What is the size of the interval between the arrows? My stick now starts at -20 and stops at -30. What number replaces my 0...? What numbers are at the arrows and what is the size of the interval? If we start at -70 stop at -80, what size is this interval? Why is it the same each time? Now my stick starts at 0 but stops at -100. Tell me the interval’s size and the values at the arrows.

Main Teaching: Practise formal


Add and subtract mentally 1- and 2-digit whole numbers; apply to multiples of 10, 100 and 1000

Multiply and divide whole numbers using the multiplication facts to 12x12 and apply to multiples of 10, 100 and 1000

Identify factors and multiples of a given number using the 12x12 table facts

Use simple tests of divisibility; determine single number factors and apply to multiple

Notes/examplesFind digits to replace the ?s in these calculations:

?5?8 + 3?9? = 62726?18 - 37?? = ?573

?7? x 6 = 22?47?2÷?=26?R?

What is 69+34? How did you do this? What can you tell me about 64+39? Work out 460-290; 3300-1900...How do we write 6 squared? Work out all the squares from 0² to 20².Look at the units digits. Can you see a pattern? Can we arrange the units in a cycle? What will the units digit be in 37²? Is 367 a square number? How did you decide? Work out the squares of the 10s to 100. Is 414 square? It could be. What number will we square to get 400? Yes 20.

Main Teaching: Plot coordinates in the

4 quadrants and identify coordinates of given shapes

Identify missing coordinates that will complete shapes

Measure and calculate perimeters of squares, rectangles in cm and m

Calculate the areas of squares, rectangles and triangles in cm² and m²

Estimate the areas of irregular shapes drawn on grids and work out the areas of simple composite rectilinear shapes by counting squares and using enveloping rectangles and triangles

Draw rectangles on

Notes/examples

This triangle is inside a rectangle. What is the area of the triangle if a small square is 5cm by 5cm? Enclose other triangles in rectangles and find their areas. Explain how we can find the area of a triangle if we know the length and perpendicular height of a triangle? Draw irregular shapes on a coordinate grid and find their areas by combining fractional parts and using enveloping rectangles.



10% percentage of 360 and interpret multiples of 100%

Solve problems involving negative numbers and %ages in context

What is 10% of £30? How can we work out 40%? What is 200% of £30? And 240%...A complete turn is 360º. What angle is 10% of a whole turn? And 30%. How many turns in 300%, 450%?

factors Generate the square

numbers up to 20x20 and use patterns and factors to test if a given number could be a square number

If 414 is square it must be 22² or 28² to get the units digit. Work out 22². Is 414 a square number? No. Try 910; 529;1625; 784; 2704?Are 3, 4, 5 factors of 4560? How do you know? So are 12, 20 and 60 factors too?

grids given their perimeters and work out their areas

Recognise that rectangles with a given perimeter can have different areas

This park has a path made of 4 rectangles. Each rectangle is 16m by 4m. What is the area of the path and of the grass inside it?

Mental Work: State %age as fraction and decimal equivalents Work out 10% of given numbers or quantities Work out a whole quantity given a 10% part

Mental Work: Solve missing number problems where there are 1

or 2 unknown numbers involved Identify pairs of numbers with fixed sum/difference

Mental Work: State coordinates of given points on grids Work out area of rectangles given sides, and find

missing side given area and one side inc decimalsExtension Work: Use ICT to explore how a quantity grows over time

when increased or decreased by a fixed %age

Extension Work: Use ICT to explore units digits of cube numbers;

which numbers when cubed end in 3, 9...?

Extension Work: Generate and use algebraic formulae to find the

perimeters and areas of rectangles and triangles

Autumn Term (Second half term)Week 4 Week 5 Week 6 Number/Measurement Measurement/Geometry/Statistics Number/Algebra



Main Teaching: Use common factors

and division to simplify fractions and common multiples to order fractions

Convert a fraction to an equivalent fraction given its denominator and generate sets of equivalent fractions

Recognise that finding a unit fraction involves dividing the quantity by the denominator

Find proper fractions of whole numbers and quantities

Divide proper fractions by a whole number; recognise that this involves multiplying the denominator

Use diagrams and common multiples to add/subtract fractions

Solve word problems involving comparing finding and dividing fractional parts of quantities

Notes/examplesWhat is a fifth of £40? What operation did you use to work this out? Division by 5. We can

write 15

of £40 as £40x15

or £40÷5. What is 25 of

30cm? We divide by 5 to find 1 fifth; two fifths is double that. And 3/5..?

What is 56

x18g;78

of

24cl..?

What fraction of the shape is 10 squares? What is ½÷2 in small squares? Yes 5. We have divided the half by 2 to get ¼ of the shape. What

is 15÷2? It is 2 squares or

110 of the shape. Can

you see a pattern? What is happening to the denominator? Why is it doubled? Is the fraction bigger or smaller? What

is 15÷4;

14 ÷5;

35÷2;

45

÷3..?

What is 12÷

12 ; is

14 ÷

14 ; is

Main Teaching: Know that volume is

measured in cubes; use standard metric units cm³ and m³ and ml and l; know that 1cm³ is equivalent to 1 ml and 1000l = 1m³

Estimate, calculate, compare the volumes of cubes and cuboids

Find rectilinear shapes with the biggest/smallest areas for a given fixed perimeter

Make and test a generalisation; give reasons why it is sometimes, always or never true

Draw and use conversion charts and line graphs to convert gallons and pints to litres

Scale quantities up and down in of 10

Estimate and calculate distances on maps and scale drawing with scale in powers of 10

Notes/examplesWhat shapes are these? How many cubes make up the cuboid? What is the fewest number of cuboids I can use to build a cube? What is the volume of the cube? Kim says: ‘On square grids, shapes with the same area have the same perimeter’. Will says: ‘It’s only true for rectangles’. Lin says: ‘No, it’s only for squares’. Who is right? Pin draws these

2 shapes on her grid.They all agree that the yellow shape has bigger area so it must have a bigger perimeter. Are they right? What other shapes have this perimeter? Which has the smallest area?

Main Teaching: Add and subtract

mentally 2-digit whole numbers and apply to multiples of 10, 100 and 1000

Practise formal written methods of calculation

Identify and describe observed patterns in numbers; make and test a generalisation; give reasons why it is sometimes, always or never true

Apply and explain methods used to solve multi-step problems that involve a number of calculations

Solve missing number problems that involve two unknown values; begin to represent simple problems as an equation

Notes/examplesThis table has 6 columns. Look at the numbers and explain why the even and odd numbers are in separate columns.

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 1

7 18

19 20 21 22 2

3 24

25 : : : : :

Why do the multiples of 5 make diagonal patterns? Describe and explain the patterns formed by other multiples. In the square 10+17=27 and 16+11=27. Does this happen in other squares on the grid? Will it work for all possible squares? Give reasons to support your thinking. Use a 2 by 3 rectangle in place of the square. What do you notice when you add the diagonally opposite numbers? What patterns are there when you subtract or multiply diagonally opposite numbers? Give reasons to support your thinking.



15

÷15

?

Mental Work: Divide fractions by whole numbers in context Solve missing number problems involving 1 or 2

unknown numbers and unknown fractional parts

Mental Work: Convert between units of capacity ml, cl, l Work out perimeter of rectangles given sides, and

find missing side given perimeter and one side

Mental Work: Read/write times on clocks with Roman numerals Add and subtract in context of money and time Convert analogue clock to digital 12, 24hr times

Extension Work: Find improper fractional parts of quantities

Extension Work: Explore the relationship between units of capacity

Extension Work: Explore number patterns on grids with 8...columns

Spring Term (First half term)Week 1 Week 2 Week 3 Number Geometry/Measurement/Algebra Number/Geometry/AlgebraMain Teaching: Practise formal


Apply associative, commutative and distributive rules when carrying out calculations

When adding and subtracting numbers mentally use combinations of numbers that simplify the calculations

Solve problems that require rounding or truncating numbers

Explain when and why you truncate or round up or down

Solve two- or three-step problems that involve all four operations

Represent a problem with a picture to show how

Notes/examplesA cup of tea is 84p. I pay for 6 cups. How many £1 coins will cover the cost of the tea?Eggs are packed into trays of 24 eggs. There are 5582 eggs to be packed, how many full trays of eggs is that? To the nearest kg, what is the weight of 8 frozen packs of vegetables if each weighs 365g? Explain how the answer was rounded in each problem. Why do we always round after a calculation not before?Nabir’s Mum bought tins of beans in packs of 4 at £1.45 per pack and bags of big oranges for 80p a bag of 3. She spent £5.95. How many items did she buy? Did she buy 2 packs of beans? Why not? Draw up lists to help.Paul spends £1.25. He buys 3 pencils and a protractor. How much is a protractor if it costs twice as much as a pencil. A picture may help. Explain how

PencilProtractor

Main Teaching: Measure sides

and angles and draw shapes accurately

Calculate the area of a shape on grids by counting squares and combining parts of squares

Construct and use the formulae to find areas of rectangles, triangles and parallelograms

Name polygons with up to ten sides and the parts of a circle

Practise using a compass to draw circular patterns

Draw 2 points on a circle; draw angles to the centre and to the circumference, measure these; make and test

Notes/examples

What are the areas of the rectangles? What do we multiply together to find the area? What are the areas of the triangles in the red/blue rectangles? What is the area of the yellow parallelogram?

What is the area of the green parallelogram? How did you work this out? What lengths do we use to find the area? Write a formula for finding the area of a parallelogram. Name the 2nd green shape? Find its area; and a formula?

Main Teaching: Know the sum of the

angles on a line, about a point, in a triangle and in a quadrilateral

Identify vertically opposite angles between 2 straight lines and know that they are equal

Calculate missing angles, label missing angles with letters

Know and use the properties of special triangles and quadrilaterals and calculate angles in regular polygons

Estimate the size of angles and measure with a protractor

Identify and notate perpendicular and parallel lines in familiar shapes

Construct and complete simple equations to express relationships

Notes/examplesTwo straight line cross. If one of the 4 angles is 48º, what are the other 3 angles?

Four angles meet at a point. Two angles are 65º; one is a right angle. What is the fourth angle?In a rectangle the angle between a diagonal and a side is 32º. Find all the other angles.This trapezium has two obtuse angles of 118º.

It has been split into 3 identical triangles. What are the 3 angles of the triangle? Are the triangles isosceles?An octagon is regular. What size are its angles?An isosceles triangle has 3 angles p, q and r. Complete the equations: p+q+r = ?; p =180-(?+?); if p = q then r = 2(90-?) Label each angle in a rectangle, rhombus and



the different parts relate to the whole

we can use this picture to work out the cost of 1 pencil.

generalisations about the angles

What is the name of this shape? Find its area by dividing it into triangles.

between angles in polygons

parallelogram and construct equations for their angles.

Mental Work: Add and subtract 3 or more numbers where making

10s and reordering lead to simpler calculations Apply multiplication and division facts for 12x12

Mental Work: Identify parallel, perpendicular lines in shapes Describe, name 2-D shapes and properties Compare, classify 2-D shapes by properties

Mental Work: Calculate missing angles about a point, in triangles Describe, name faces on 3-D shapes and properties Compare, classify 3-D shapes by their properties

Extension Work: Explore the order of operations and use of brackets

Extension Work: Explore the angles of cyclic quadrilaterals

Extension Work: Explore tessellations with triangles and quadrilaterals

Spring Term (First half term)Week 4 Week 5 Week 6 Number Number/Measurement/Algebra NumberMain Teaching: Identify and

interpret rates of change that express an increase or a decrease as an amount in period or unit of time

Given a rate of change, calculate quantities using a written unitary method; scaling down to 1 unit and then up to the required number of units

Convert fractions to fractions with a given denominator

Notes/examplesWhat does mph mean? Yes miles per hour. Give me other examples of rates.Mr Key types 180 words in 6 minutes. How long will he take to type 150 words? We can use a picture.

150 words1 1 1 1 1 1

We divide 150 by 6 to find the words typed in 1min?

150 words1 1 1 1 1 1

30 30 30 30 3

0 30

How many 30s in 150? 150÷30 = 5 minutes. We can record in a table.

Words typed Time in mins

Main Teaching: Describe unequal

sharing as a ratio and calculate quantities shared in a ratio

Scale quantities up and down in a given ratio and work out number of times quantities have been scaled up or down

Solve problems involving ratios set in contexts of measures

Count forwards and backwards in steps of any whole number from any number and from 0 in fractions

Generate, complete

Notes/examplesA cookery book says: the roasting time for a piece of beef depends on its weight and how you want it cooked. It gives the table:

Style of cooking

Per 500g

Plus an extra

Rare 20 mins 20 minsMedium 25 mins 30mins

Well done 30 mins 40mins

For a birthday meal Mrs Lean buys 2.5kg of beef. She likes it well done. For how long must she cook the beef? She wants to eat at 1.30pm, when should she put the beef in the oven? How long would it take to cook the beef so it

Main Teaching: Find common factors

and use to cancel and simplify fractions

Convert between the fractional, decimal and percentage equivalences and use when calculating

Work out mentally and using informal methods, combine multiples of 10%, 5% and 1% to find percentages of quantities

Calculate a percentage using a written unitary method; scaling down

Notes/examplesWhat is 23% of 800cm? We can use 10%, 5% and 1% in a ‘percentage table’.

100% 800cm10% 80cm5% 40cm1% 8cm

20% 160cm3% 24cm

23% 184cm

Can we use fewer calculations? What is 85% of £80? We can scale down to 1% by dividing by 100 and then scale up to 85% by multiplying by 85. We



and generate sets of equivalent fractions

Use diagrams and common multiples to add and subtract proper fractions and mixed numbers

Solve word problems involving the + and – of improper fractions and mixed numbers

180 6180÷6=30 1

150 150÷30=5Mrs Key types 250 words in 5 minutes. How many words will she type in 8 minutes? How long will it take her to type 150 words? Draw a picture to help you. Record working in a table.

Time in mins Words typed

5 2501 250÷5=508 50x8=400

150÷50=3 150

and describe linear number sequences

Describe number sequence using a term-to-term rule in words and symbols

Use simple formulae expressed in a table or words

Interpret an equation with two unknowns and find pairs of numbers that satisfy it

is only medium to rare? Every week Loran has saved £1.50 while Safi has saved £1.20. Over 12 weeks, how much has each saved? Loran now saves £2.20 and Safi £1.60 How long will it take each to save £50? So far they saved £64.60 between them, how long has this taken? How much more has Loran saved than Safi?

to 1% and then up to the required percentage

Work out the whole quantity given a percentage part

Practise and apply formal written methods of calculation, to solve problems that include whole and decimal numbers in context

always cancel as we go. 80 8 4100 10 5 4 x 85 4x17 £68 5 1Is 85% of £60 more than 65% of £80? I find 120% of 400g. Then I find 80% of this the new amount. Do I get back to 400g?Jay says: ‘40% of the time is 30 minutes’. What is the total time?

Mental Work: Recall and apply x, ÷ facts to 12x12 to 10s, 100s... Scale numbers up/down; round decimals answers Work out changes in quantities for simple rates

Mental Work: Multiply 1-digit decimal numbers by whole numbers List prime numbers to 20 and identify prime factors Solve missing number problems involving +,-,x or ÷

Mental Work: Recall and apply x, ÷ facts to 12x12 to 10s, 100s... Decide if a number is a factor/multiple of another Give common %age, decimal, fraction equivalents

Extension Work: Compare speeds in mph; km/hour; metres per sec.

Extension Work: Represent missing number problems algebraically

Extension Work: Explore repeated %age increases or decreases

Spring Term (Second half term)Week 1 Week 2 Week 3Geometry/Measurement Number/Statistics NumberMain Teaching: Calculate areas of

rectilinear shapes, by counting squares

Cut irregular shapes in half; work out the areas to confirm the halves are equal

Use known formula to calculate the areas of rectangles, triangles, isosceles trapeziums and parallelograms

Name and sort the different types of triangles and quadrilaterals by their properties, including reflective symmetry

Notes/examples

How many squares in whole/half the yellow shape? Draw a straight line to cut the shape in half. Use sloping lines like the black line. Explain why the black line cuts the green shape in half? Cut the other shapes in half. Confirm the equal areas.A triangle’s coordinates

Main Teaching: Interpret pie charts;

recognise that a pie chart uses sectors of a circle to illustrate the proportions of a whole expressed as %ages

Know that an angle about a point (360º) represents 100%

Calculate angles about a point for percentages < 100%

Draw pie charts for small data sets to show the relative size of categories

Carry out an

Notes/examplesThe angle around a point is 360º. What is 10% of this angle? What is 5%? And 50%, 45%, 40%...? A pie chart shows the choices of 60 people asked to choose between 3 new flavours of ice cream. The results were: nutty choc 60%, nutty toffee 15%, and nutty nut 25%. Use a table to find the angles of the sectors.

Main Teaching: Practise and apply

formal written methods of calculation with whole and decimal numbers for all four operations

Compare and order proper fractions; use diagrams and common multiples to find the common denominator

Convert and compare improper fractions and mixed numbers

Use diagrams and common multiples to add and subtract

Notes/examples

One row is what fraction of the grid? And one column? Use the grid to work out the answers to: 13 +

13 and

17 +

17 and

13

+ 17

The last sum is 1 row add 1 column. This is 7+3=10 squares out of 21 so the

answer is 1021 . What is

13 -



Find missing angles in triangles, quadrilaterals and regular polygons

Use mathematical language to describe a translation and reflection; understand that only the position of a shape is affected

Identify and plot the position of a shape after a translation or reflection

are: (-4,-6); (-1,-5); (-4,-2) It is translated along 6 units and up 8 units? What are its coordinates? The triangle with coordinates: (-2,-3); (6,-5); (4,-2) is moved to (-2,3); (6,5); (4,2). Describe this move.Now my triangle moves so the top-most corner (apex) is at (0,0). Describe the translation I carry out? Has the shape changed?

experiment that involves collecting data for 2 variables including taking measurements

Draw and interpret scatter plots; identify possible relationships between the 2 variables plotted

Answer and pose questions from data sets

Draw the pie chart and mark on it the number and percentage of people who chose each flavour.

Amir claims: those with smaller wrists have longer hands. Conduct an experiment to see if he is right.

proper fractions and mixed numbers with unequal denominators

Find fractions of quantities, including improper fractions

Find whole quantities given a fractional part

Divide mixed numbers by a whole number by converting to improper fractions

17? It’s 1 row subtract 1

column: 7-3=4 squares.

The answer is 4

21. Work

out: 13

+ 27

; 13

+ 37

; 23

-

37 ;

13 -

27; 4

3 - 57 ; 1

13 +

37 ; 1

13 -

37

The denominator in all answers is 21 the product of the two denominators in the fractions in our calculations. Remember to write mixed numbers as improper fractions.

How do we work out 14

+

15 ;

34 -

25 ; 1

14 +

35 ; 2

14 -

35? What size rectangle?

What common denominator?

Mental Work: Visualise familiar 2-D shapes from their properties Reflect given points in both axes on 4-quadrant grid Find missing angles around point, in 2-D shapes

Mental Work: Read scales and interpret data from graphs/tables State %age of 360º; estimate sectors in pie charts Solve missing number problems involving %ages

Mental Work: Recall and apply x, ÷ facts to 12x12 to 10s, 100s Use division facts to find simple fractional parts +, - mixed numbers with common denominator

Extension Work: Express algebraically translations, and reflections in

the horizontal and vertical axes

Extension Work: Interpret and explore the idea of positive, negative

and zero correlation between two variables

Extension Work: Express common fractions as sums of the unit

fractions alone (Egyptian fractions)

Spring Term (Second half term)Week 4 Week 5 Week 6 Number/Measurement/Algebra Number Number/Measurement


100% 360º10% 36º5% 18º60% 216º25% 90º15% 54º

Check 360º


Main Teaching: Identify, interpret and

produce drawings of 3-D shapes

Calculate, compare and estimate volumes of cuboids in cm³, m³

Convert between standard units of measure, using up to 3 decimal places; carry out calculations where the measures use mixed units

Interpret and make simple scale drawings, including nets of 3-D shapes

Find pairs of numbers for combinations of two variables and solutions to equations with two unknowns

Apply algebraic rules to generate sequences and describe linear sequences algebraically

Represent missing number problems algebraically

Notes/examples

c

a b

This cuboid is drawn on an isometric grid. The lengths of the sides are: a=12m; b=8m; c=10m. What area is each face of the cuboid? How many small cuboids make up the large cuboid? What is the volume of a small cuboid in m³; and the large cuboid? Use isometric paper to draw cubes and cuboids of different sizes and for each work out the volume. Can you find a formula for the volume of cuboids? Choose a scale to use to draw an accurate net of the cuboid. Draw and make nets of simple 3-D shapes.


formal written methods of calculation with whole and decimal numbers for all four operations

Share quantities in a given ratio; increase, decrease quantities while retaining their relative sizes,

Multiply and divide numbers by 10, 100, 1000, give answers with up to 3 decimal places

Use common factors, common multiples to simplify, sort and add and subtract fractions

Add and subtract mixed numbers and decimals that have the same number of decimal places

Solve problems involving calculations with fractions, and decimals; rounding answers to the required accuracy

Notes/examples

How many squares make up ½, ⅜, ⅝, ¼, ¾, ⅛, ⅞ of this grid? Order these fractions, smallest first. What is the common denominator? Fill in this addition table. Remember to write mixed numbers as improper fractions.

+ ½ ¼ .. 1¾ ⅞½¼:1⅛⅞

Fill in this subtraction table.- ½ ¼ .. ⅛ ⅜1½¾:1⅝⅞

What grids and common denominators would we use to help us to add and subtract sixths and quarters; thirds and fifths; ninths and sevenths?

Main Teaching: Convert fractions to

equivalent fractions; simplify and compare

Identify complements to 1, 10, 100 of decimals, fractions or mixed numbers

Use the hierarchy of operation rules to carry out calculations

Use a scale factor to increase/decrease a quantities and to enlarge/shrink lengths

Read, write, represent and compare times, including times on clocks with Roman numerals

Read times and years/dates displayed in Roman numerals; read timetables

Calculate time durations in days, weeks, months, years

Solve problems which involve converting times and calculating time durations and end points of intervals

Notes/examplesGill wrote these fractions:20006000 ;

400500 ;

80200 ;

6001200 ;

240400 ;

250010000

She says the last fraction is the biggest as it has the biggest numerator. Is she right? Explain how you compared the fractions to find the biggest?I caught a train at 14:52. It arrived at 17:18. For how long was I travelling?

Times JourneyHours Mins14:52

16:52 2 0017:00 0 0817:18 0 18Total 2hrs 26mins

The train was1 hr 35 mins late. When should my train have arrived?

LatenessHours Mins

Times17:18

1 00 16:1818 16:0017 15:43

1hr 35mins 3:43pm_+_ - _= 3; _ - _ + _=12_+_ x _= 15; _ - _ x _= 8_+_ ÷ _ = 6; _ - _ ÷ _= 2(_+_)÷ _ = 6; (_ - _)÷_= 2In the number sentences, put in numbers between 1 and 20 to make them true.

Mental Work: Visualise familiar 3-D shapes from their properties Describe and complete linear number sequences Recall and substitute numbers into simple formulae

Mental Work: Use multiplication and division facts to 12x12 Calculate unit fractional parts where answer is exact Recognise prime, square, cube numbers to 100

Mental Work: Read, convert times on analogue and digital clocks Count, state numbers before/after Roman numeral Scale measures up or down to given scale factor

Extension Work: Solve problems that involve interpreting the images

of 3-D shapes; interpret flat-pack instructions

Extension Work: Predict how many prime factors a 2-digit number

might have; check the accuracy of the predictions

Extension Work: Explore how ICT, including calculators apply rules

of arithmetic to evaluate arithmetic expressions



Summer Term (First half term)Week 1 Week 2 Week 3Number/Measurement/Statistics Geometry Number/ MeasurementMain Teaching: Read and interpret

data in tables and bar charts

Interpret percentages shown on a pie chart; work out values each segment represents

Interpret and read axes that have different scales

Construct bar charts to show frequencies, and pie charts to show proportions linked to angles about a point

Read values on line graphs, and describe the change in one variable in relation to changes in the other

Draw line, conversion graphs that relate two variables; use to convert units

Find mean of a data set, interpret the result in context

Solve problems that involve the collection, presentation and analysis of data

Notes/examplesThe average stopping distance for a car depends on its speed. This table gives the stopping distance in feet for speeds in miles per hour (mph). Draw a

Speed Distance10 mph 27 feet15 mph 44 feet20 mph 63 feet25 mph 85 feet30 mph 109 feet40 mph 164 feet50 mph 229 feet60 mph 304 feet70 mph 388 feet

graph of the stopping distances for the speeds. Estimate the stopping distances for 35 mph, 45 mph...How far will it take to stop at 75 mph, 80 mph..? A car skids for 200 feet, at what speed was it going? 1 foot is approximately 305mm; 10 miles is about 16km. Draw 2 conversion graphs to convert feet to metres and miles to km. What is the stopping distance in m for 100km per hour? How far in 20mins at 45mph...?

Main Teaching: Identify and describe

the properties of the sides and angles of 2-D shapes, and of 3-D shapes including their vertices, faces and edges

Estimate, measure and name angles

Draw triangles given information about angles and lengths of sides; mark and label the triangle

Calculate missing angles in triangles

Name parts of circles; draw and measure sectors

Apply scale factors to enlarge and shrink common shapes

Translate and reflect shapes drawn on a coordinate grid and identify line symmetry

Identify and deduce properties of quadrilaterals by manipulating shapes; deduce and use these related facts

Notes/examplesA square, a rectangles and a rhombus. What are their properties? What is the same and different about them?

What can you say about their sides? They all have opposite sides that are equal and parallel. Fold a paper rhombus like this:

What are the fold lines called? Diagonals, lines of symmetry. What do you notice? Adjacent sides and opposite angles are equal. What is the name of the triangle? It’s right angled so the diagonals of the rhombus bisect at right angles. Is this true for any other shapes? What can you find out by folding paper shapes in different ways?


formal written methods of calculation for 4 operations using whole and decimal numbers

Add and subtract mentally and with jottings, whole numbers with 1 or 2 non-zero digits and decimal numbers with 1 or 2 decimal places

Apply knowledge of place value of digits to order whole and decimal numbers, in the context of money, volume/capacity etc

Convert between fractions, decimals and percentages; recall familiar equivalents in context

Express ratio as part to part; calculate parts

Develop strategies to solve routine and non-routine problems that involve ratio and proportion, fractions and percentages

Notes/examplesIf 1st September was a Sunday, what day is Christmas Day? Sunni has £20 and Tas has £48. They are given an equal amount of additional money. Now Tas has twice as much as Sunni. How much money does each end up with?Alice sees a present for her Mum. It is priced at £20, but she gets a 25% reduction. Even so, the seller makes a profit of 20%. What did the present cost the seller?Ali, Bob and Lyn share out stickers. Ali takes two fifths of them. From the rest Lyn takes 2 stickers for every 1 Bob takes. Lyn ends up with 16 stickers, how many stickers were shared out? The school maths club has 42 pupils in it. There are 10% more girls than boys. How many boys are in the club? Money is shared out 3 to 2. Moy has the 3 parts and gets £2.10. How much money was shared out?

Mental Work: Recall number facts and use to calculate mentally Use rates e.g. mph to find distances/time by scaling Make estimates between metric and imperial units

Mental Work: Recall properties and name 2-D and 3-D shapes Calculate missing angles about line or point Estimate angles and name faces on 3-D shapes

Mental Work: Convert given decimals to fractions and %age etc Share quantity in ratio; find part1 given ratio & part2 + and – 10s, 100s, 1000s numbers with 2 digits

Extension Work: Calculate the whole of a quantity given

Extension Work: Draw parallelograms e.g. sides 5, 8cm, angle 55º

Extension Work: Solve non-routine problems involving proportions



Summer Term (First half term)Week 4 Week 5 Week 6Number/Measurement/Statistics Number/Algebra NumberMain Teaching: Interpret data in

tables, bar, pie charts and line graphs

Compare and order positive and negative numbers; calculate intervals that cross zero

Use 12x12 multiplication facts to calculate mentally and with jottings, with whole and decimal numbers, %ages and fractions

Develop strategies to solve routine and non-routine contextualised problems that involve the four operations and working out whole quantities given a fractional part

Notes/examplesMax ºC London New York

Date Jan Jul Jan Jul1 11 21 -3 292 10 23 0 313 9 24 1 334 11 27 -8 295 10 27 -11 236 9 22 0 197 13 22 13 298 12 22 -7 319 14 21 -9 32

10 12 23 -1 30The table shows the max temperatures in ºC in London and New York for the first 10 days in January and July. Work out mean temperatures for the 2 cities in Jan and July. On average, what are the temp differences between the two cities? Draw a bar chart to show these differences in temperature. When, where and what are the greatest and smallest differences in temperature?If ⅔ of a length is 40cm, what is the full length? A jug fills15 200ml glasses. How much liquid is in the jug? A load weighing 1870kg fills 1⅜ lorries. What does 1 hold?

Main Teaching: Practise mental

methods, jottings and formal written methods of calculation with whole, decimal numbers for all four operations; apply to multi-step problems

Calculate parts of quantities using fractions, decimals and percentages

Scale quantities and find missing values in given ratios

Use formulae in words and in algebraic notation to complete and generate sequences

Identify and describe the formula for a sequence using algebraic notation

Solve simple linear equations with one missing value

Find pairs of numbers that satisfy an equation in two unknowns

Notes/examplesa 8 7 .. 2 1 0

3a-2 22

Complete the table. Now extend the numbers for a past zero: -1, -2, -3..? What are the values of a that give us the numbers 34, -35? Change the 3 to 5 and explain the affect this has on the numbers in the table. What is: the value of a if 3a - 2 = 28; the value of b if 5b - 2 = 28?

d 10 9 8 .. 2 1 0

5 7 .. 13

Complete the table. What is the rule for this table? How do we write it using the letter d? Now extend the numbers for d past zero: -1, -2, -3..? What are the values of d that give us the numbers -35, 34? What is the value of a in each of these equations: 9 - a = 6; and 25 - a = 19; 18 - 2a = 12; 20 - 3a = 11; 25 - 5a = 15 and 7 - a = 9; 10 - 2a = 12; 20 - 3a = 32; 25 - 5a = 55?Find possible values of x and y if: x+2y=10 and if:2x-3y=11What two numbers with 2 decimal places will sum to 3?

Main Teaching: Practise mental

methods, jottings and formal written methods of calculation with whole, decimal numbers for all four operations; apply to multi-step problems

Apply the commutative, associate and distributive rules and the hierarchy of brackets and operation to carry out calculations and use complements to simplify calculations

Recall and use number facts to identify factors, multiples, multiply and divide by 10, 100 and 1000, test divisibility

Solve problems that require reasoning, giving an explanation and showing the methods used to find a solution

Notes/examplesUse jottings to work out as quickly as you can:247+371+54+353+46+129;366+557-456+234-99-102;1000-235-58-65-142+100;3x29 - 27x3; 18x8 + 16x6;26÷5 + 14÷5; 81÷7 - 22÷14Explain the strategies and rules you used to do them?Asha is writing out the square number. She says: every even number squared is a multiple of 4; subtract 1 from the odd square numbers they are multiples of 4. Is this true? Explain your reasoning.Hari starts adding the numbers 1 to 10 to their squares. He says: my answers are all even. Will it be true for any number greater than 10? He says: I can see a pattern in the sequence I get but I can’t explain it. Help Hari to explain his pattern? Subtract 1-digit numbers from 3-digit numbers - the answer will always have 3 digits. True or not? Give reasons for your decision

Mental Work: Recall and use multiplication tables to 12x12 Convert between adjacent metric units Calculate with measures that require conversion

Mental Work: Solve missing number problems with 1 or 2 unknowns Extend sequences in units of time Calculate perimeters, areas of compound rectangles

Mental Work: Apply 12x12 facts/distributive rule to mental calcs Give complement of 2-digit numbers to 100s, 1000s Describe sequences; justify why numbers are in/out

Extension Work: Solve non-routine problems involving division

Extension Work: Explore rules for x and ÷ positive/negative numbers

Extension Work: Explore patterns in multiples of 11, 111 and 1111



Summer Term (Second half term) For planning work after the Statutory Assessment PeriodWeek 1 Week 2 Week 3 Mathematics and Music Mathematics and Architecture Mathematics and ArtMain Teaching: Exploration of the use

of mathematics in Music, octaves, scales, time, rhythm, interval, frequency; harmony; clapping; bell ringing; (Mozart, musical dice game length of strings and sound; (Pythagoras, Bach); use of repetition; rounds; cannons; blues; symmetry; frequency, pitch, sine waves; measures; beat, ICT

Focus: Numbers in music,

counting Proportions, fractions

and ratios Relationship between

notes, sounds Repeating patterns Structure and time Interpreting diagrams

and graphs Clap in time, record

counting structures and patterns, analyse a piece of music, make music

Notes/examplesAn important element in music involves being able to count small sequences and place emphases in particular places. Count and clap 1, 2, 3, 4. Repeat this count of 4, but only clap on the counts of 1, 2 and 4. Boys now clap on 2 and 3. Girls clap twice on 1 and 4. In groups make up your own clapping arrangements on the count of 1 to 4 and later you will give the class a performance.A taut string when plucked will make a sound. To make other sounds we shorten the length of the string. Halving the string or dividing it in the ratio 1 to 1 takes the sound up an octave. Using other ratios of lengths on the string provide other harmonious notes. Explore these and other ratios:

1 12 13 1

Main Teaching: Exploration of the use

of mathematics in Architecture, plans, views, orthogonal, isometric, oblique drawings; 1-point, 3-point perspective, focal points, (Alberti, Brunelleschi’s invention), radial lines, instruments; Hindu temples, Cathedrals; Greek, Islamic, Egyptian architecture; bridges; structures, forces

Focus: Draw accurately lines,

angles, shapes Scale measurements

up and down Use properties to

make 2-D images of 3-D shapes

Vertical, horizontal and parallel lines

Horizon and infinity Calculation involving

ratio and proportion Analyse plans of

buildings/structures, present own plans

Notes/examplesWith your arms in front of you lean against a wall so you don’t fall over. Explain what was keeping you up. Were you applying any force? Why didn’t the wall fall down? Draw a picture of the forces involved.

Your arms are pushing the wall and it pushes you back so nothing moves. This is called equilibrium. You are to plan, design, draw and build a bridge from newspaper and string. The bridge must span a 1m gap. It must carry this toy car. How strong is newspaper? Can we make it stronger? Is a tube of paper stronger than a sheet? Look at pictures of buildings and bridges. How is it built? What forces are at work so it stays up? Which bits looks stronger, what parts pull, what pushes what? Are there tests we need to carry out first?

Main Teaching: Exploration of the role

of mathematics in Art, role of shapes, form, perspective (Michelangelo, Giotto Raphael, Botticelli, Titian, Canaletto); use of randomness in paintings (Mondrian); cubism, use of shape in paintings (Nash, Kandinsky, Matisse)

Focus: Lines, points, grids Coordinates Random numbers and

probability Simulation and form Shape and space Use of geometrical

properties to make shapes

2-D and 3-D images Use of symmetry Transformation of

shape, enlargement Analysis of painting,

interpretation and use of shape/space, angles, perspective, replication and transformation

Notes/examplesEarly paintings look flat. Artists wanted to make their paintings have depth so it looked like we could see things in front of and behind others. Durer invented a way of doing this. The method is called perspective. It uses lines radiating from a point.

What does this shape look like? Try to draw cuboids in perspective. Choose a point and draw radiating lines that appear to go towards and away from you. Other artists paint abstract pictures made up of familiar shapes. They use geometry the shapes’ properties to decide where and how to place them. Find out how they did this. Mondrian used random numbers to generate picture. Look him up.

Mental and written knowledge and skills to involve: Counting, clapping in different time intervals Calculations involving time, time scales Calculations involving proportions and fractions Interpreting charts and graphs Identifying, describing patterns and relationships

Mental and written knowledge and skills to involve: Reading measurements and scales Calculations involving measurements, angles Estimation, applying proportion and ratio Interpreting/making drawings and plans Identifying forces, loads, measures of strength

Mental and written knowledge and skills to involve: Identification of shapes and their properties Interpretation of 2-D and 3-D shapes Calculations involving ratio and proportion Calculations involving time intervals Accurate linear measurement and angles


http://en.wikipedia.org/wiki/Titian

http://en.wikipedia.org/wiki/Botticelli

http://en.wikipedia.org/wiki/Raphael

http://en.wikipedia.org/wiki/Michelangelo


Summer Term (Second half term)Week 4 Week 5 Week 6Mathematics and Financial Management Mathematics and Design Mathematics and NatureMain Teaching: Review of a particular

financial matter involving analysis of costs, expenditure, charges, exchanging or borrowing money; commission; interest rates; short/long term loans; repayment of loans; cost of living, personal expenditure; insurance; credit cards; ways of saving on costs; mobile phone charges

Focus: Financial issues Financial planning Income; expenditure Source of money Borrowing money Rate of interest Cost of living Expenditure Tables, graphs Conclusions Group analysis of

costings, financial issues involved, progress reports, final presentation

Notes/examplesMr and Mrs S and their two children are going on holiday to stay with friends in south Spain. They want to stay for exactly 10 nights and can travel both ways on any day of the week. Mrs S asks her children to find the cheapest available flights to Malaga from the nearest airport. She asks them to check on the luggage allowance too and the times they need to get to the airport to catch the flight. She says that while the family are in Spain they will have £250 to spend. She wants them to find how many Euros that is and to explore the cost of food, travel etc in Spain. She wonders what it would cost to borrow £250 or to use a credit card in Spain. She remembers they will need insurance. Carry out a costing of the family holiday.

Main Teaching: Practical design on a

mathematical theme e.g. design/plan use for mathematics of school display, playground, room; mathematical toys or learning equipment; resources to support learning by young or disabled children

Focus: Rationale, purposes Design brief, set out

intended use Projected costs Planned activity Timelines Bid for resources Data collected Measurements, scale

drawing of design Model of design Realisation (where

practical) Group preparation of

design brief and presentation of bid, funding, updates on progress, final models, presentation

Notes/examplesThe school is planning to keep 24 chickens. How much space do chickens need? Given a fixed area how small can we make perimeter length? Plan a suitable space. Explore possible shapes and perimeters. Use practical materials to build models of chicken coops that will provide sufficient space for 24 hens. Make scaled drawings of nets that could be used to build coops. Pose questions on the models of coops to evaluate the designs. How much will each coop cost? Agree on the better designs, and explain the reasons for choices. Write an article for the school newsletter which explores the issues, and the costs of keeping chickens. How much food do they eat? What is the weekly cost of keeping 24 hens? Will selling eggs raise enough money?

Main Teaching: Exploration of use of

mathematics to describe, measure and explain emotions, behaviours, patterns, or growth in nature; Fibonacci sequence; Golden ratios; spirals in shells and fruit, and sunflowers; 3-D spirals, springs; soap bubbles; lattices of triangles, hexagons; bees; population movement; weather patterns

Focus: Description of theme Diagrams/pictures of

phenomenon Role of mathematics Experiments Data collected Analysis, findings Conclusions Group justification for

choices, updates on progress, final presentation with findings, conclusions and hypotheses

Notes/examplesWhat do you understand by the terms ‘needs’ and ‘wants’. Write a definition of each. Explain the types of things you need and want. Record a simple ‘Needs’ and ‘Wants’ chart. Are you a: ‘Want’ or a ‘Need’ type person’? How could we measure ‘wants’ against ‘needs’?Who was Fibonacci? How is his sequence formed? What is the golden ratio? How can we use the term in the sequence to generate it? Draw a rectangle with sides in the golden ratio. Does it look familiar? What spirals occur in nature? Examine sunflowers, strawberries, pineapples, snails, coiled worms, pine cones, roses, other flowers. How can we generate spirals? Wrap a rotating string, with a pencil in the end, around a wide tube. Pythagoras. Spirals from right angled triangles; in rectangles...

Mental and written knowledge and skills to involve: Calculations involving money Calculations involving ratio, percentages Reading, interpreting data, times, figures, rates Use of positive/negative numbers Tables, graphs and charts

Mental and written knowledge and skills to involve: Calculations involving measures Calculations involving scaling and scales Geometrical drawings, angles, circles Estimation and rounding Accurate measuring, precision

Mental and written knowledge and skills to involve: Calculations involving growth, rates of change Calculations involving missing angles Geometrical drawing, angles, spirals Enlargements, tessellations of shapes Accurate measuring, precision


scheme of work for year 6 - st- web viewcontents and the intended use of each section within the...

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