mathematics: number, place value, addition and...

Mathematics:Number, Place Value, Addition and

SubtractionAlex Wedgbury

Mathematics at Brampton Primary School National Curriculum 2014 Lessons The concrete‐pictorial‐abstract (CPA) approach Addition Subtraction Supporting your child at home Questions

Session Outline

Problem solving and reasoning Fluency through varied practice to develop conceptual understanding – less focus on rote learning and memorising procedures

Current education theory – concrete, pictorial, abstract approach; variation

Mathematics at BPS

The national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through

varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately

reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

can solve problems by applying their mathematics to a variety of routine and non‐routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions

National Curriculum 2014

National Curriculum Year 1

Number and Place Value

I can count to and past 100, forwards and backwards starting from any number


I can identify one more and one less, given a starting number


I can find and show numbers using objects and pictures including number lines and use: equal to, more than, less than (fewer), most, least


I can count and read numbers to 100 in numerals


I can count and write numbers to 100 in numerals


I can count in jumps of 2, 5 and 10s


I can read and write numbers from 1 to 20 in numbers


I can read and write numbers from 1 to 20 in words


Addition and Subtraction

I can read and understand number statements using +, ‐ and =


I can write number statements using +, ‐ and =


I can use number bonds up to 20


I can use subtraction facts up to 20


I can add one digit and two digit numbers to 20


I can subtract one digit and two digit numbers to 20


I can answer problems that use addition and subtraction, including missing number problems, using objects and pictures


Chapter 1 – Numbers to 10 Lesson 1 – Counting to 10 To be able to count numbers to 10 accurately ‐ forward and backward. Lesson 2 – Counting Objects to 10 To be able to count similar objects up to 10 with accuracy and fluency. Lesson 3 – Writing to 10 To be able to write all numbers to 10 with numerals and in words; to count only objects of the same name in a group. Lesson 4 – Counting With Zero To be able to understand what zero represents and use it when counting. Lesson 5 – Comparing Objects To be able to compare different sets of objects and say which one has fewer, more or is equal. Lesson 6 – Ordering Numbers To be able to order numbers to 10 and know which number is greater or is lesser in value. Lesson 7 – Comparing Numbers To be able to compare different sets of objects and say which one has fewer, more or is equal. Lesson 8 – Chapter End To practice various concepts that were covered in the chapter, from writing the numbers in words to consolidating the correct value of digits. Chapter 2 – Number Bonds Lesson 1 – Making Number Bonds To understand that a number is made up of other numbers; to understand a number can be made by adding two smaller numbers. Lesson 2 – Making Number Bonds To use number bonds for storytelling. Lesson 3 – Chapter End


Chapter 3 – Addition Within 10 Lesson 1 – Ways to Add To be able to add two different numbers within 10. Pupils will become familar with the different vocabulary associated with addition. Lesson 2 – Add by Counting On To be able to add by counting on from a given number. Lesson 3 – Completing Number Sentences To be able to complete number sentences and to gain an understanding of inverse operations. Lesson 4 – Making Addition Stories To be able to make addition stories using correct vocabulary. Lesson 5 – Solving Picture Problems To be able to solve addition problems through pictures. Lesson 6 – Chapter End Maths journal and reflection of learning throughout the chapter



I can count forward and backwards in jumps of 2, 3 and 5 from 0 and in 10s from any number


I can find the place value of each digit of a number with tens and units


I can find and show numbers using different equipment such as number lines and number squares


I can compare and order numbers from 0 to 100 using < > and =


I can read and write numbers to 100 in numerals


I can read and write numbers to 100 in words


I can use place value and number facts to answer questions



I can solve problems with addition and subtraction including those involving numbers, quantities and measures by using objects or pictures


I can answer simple addition and subtraction questions in my head as well as by writing them down


I can use addition and subtraction facts to 20 quickly and workout similar facts to 100


I can add and subtract a two digit number and a one digit number mentally and when using objects, number lines and pictures


I can add and subtract a two digit number and tens mentally and when using objects, number lines and pictures


I can add and subtract 2 two digit numbers mentally and when using objects, number lines and pictures


I can add and subtract 3 one digit numbers mentally and when using objects, number lines and pictures


I can show that adding 2 numbers can be done in any order but subtraction cannot


I can show that subtraction is the opposite of addition and use this to check my work


Chapter 1 – Numbers to 100 Lesson 1 – Numbers to 100 To count numbers up to 100 using concrete objects: counting up by 1s and 10s. Lesson 2 – Place Value To understand each digit in a number has its own value. Lesson 3 – Comparing Numbers To be able to compare numbers using place value knowledge gained from previous lessons. Lesson 4 – Number Bonds

To be able to split a number into two separate numbers which combine to make the original number: partitioning a number into tens and units.

Lesson 5 – Number Patterns To recognise and describe number patterns that go up and down by 1s, 2s or 10s. Lesson 6 – Number Patterns

To recognise and describe patterns with more complex numbers: in particular 3 and 5.

Mind Workout – Mind Workout To use place value knowledge to think about the effects of each digit in a number.


Chapter 2 – Addition and Subtraction Lesson 1 – Simple Adding

To be able to add a single‐digit number to a 2‐digit number without regrouping the ones.

Lesson 2 – Simple Adding

Simple addition of 10s and ones.


This lesson is a follow on from the previous lesson. In this lesson the units column will consist of one digit being more than 0.


To add with tens and units where the units are both more than 0.

Lesson 5 – Adding with Renaming

To add single‐digit numbers to a double‐digit number resulting in renaming of units.

Lesson 6 – Adding with Renaming

To add two 2‐digit numbers with the sum of units more than or equal to 10. This lesson is the natural next step from the previous lesson.

Lesson 7 – Simple Subtracting

To consider the first steps of subtraction: subtracting units from a 2‐digit number without affecting the 10s column.

Lessons

Concrete – using manipulatives: paper cut‐outs, counters (double sided), plastic objects, kidney beans, base 10, interlinking cubes, ten frames, place value charts, hundred squares and number lines

The CPA Approach

Pictorial – using of pictures: annotations, pictures, dots, lines, shapes

The CPA Approach

Abstract – using numbers and symbols, writing number equations: column methods, algebra, algorithms

The CPA Approach

The concrete‐pictorial‐abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

The CPA Approach

Spend some time on your tables looking through the type of resources your child will be using in class.

The CPA Approach

Counting:

• Stable order principle

• One‐one principle

• Cardinal principle (final value = total amount)

• Order irrelevance principle (can start at any point)

• Abstraction principle (counting anything)

Gelman and Gallistel

Where it all begins…

What does this mean?


equivalent

balance

the same as

equal

The sign does not mean the answer to a calculation!

Addition

Aggregation:combining two amounts Augmentation:

adding on to an amount

6 + 9Both methods rely on

counting, which allows for errors

Addition

Ten frames or similar manipulativesenable addition without continual counting

Addition

+ =

Using straw reinforces the cardinality aspect of number.

Addition

74 3

7 – 3 = 47 – 4 = 33 + 4 = 74 + 3 = 7

ab c

a – b = ca – c = bb + c = ac + b = a

The bar model enables children to develop generalisations.

Addition

Using base 10 equipment helps move children towards the written method for addition.

65 + 77 6 5

+ 7 7

1 4 21 1

Counting on method: 11 + 5, 73 + 4, 209 + 7, 3304 + 5

Making Ten/s method: 7 + 4 , 45 + 15, 197 + 23, 2155 + 15

Part‐Part Whole method: 16 + 15, 27 + 55, 275 + 134, 2356 + 347

Column method: 17 + 32, 28 + 17, 47+64, 197 + 364

Addition

Practice using manipulatives to solve these:

Sammy scored 6 points on a computer game. Sally scored 12 points.How many points did they score altogether?

Nafist planted 18 bulbs in her garden. Yukesh planted 16 in his.How many bulbs did they plant altogether?

Hana flew 65km to her holiday destination. Ben flew 31 to his.How many kilometres did they fly in total?

Subtraction

• 67 - 45

• 67 - 59

• 178 - 99

• 300 - 150

• 468 - 237

• 3241 - 2167

How would you solve these?

Subtraction

This again relies on counting

15 ‐ 9Take away:Removing items from a set

ComparisonReduction

Subtraction

‐ =

Subtraction

82 - 47

7812- 4 7

3 5

Using base 10 equipment helps move children towards the written method for subtraction.

Subtraction

Counting backwards method: 11 ‐ 5, 73 ‐ 4, 209 ‐ 7, 3304 ‐ 5

Part‐Part Whole method: 36 ‐ 15, 77 ‐ 59, 275 ‐ 137

Column method: 97 ‐ 32, 53 + 17, 247 ‐ 168

Practice using manipulatives to solve these:

Sammy scored 56 points on a computer game. Sally scored 8 points.How many more points did Sammy score?

Nafist planted 68 bulbs in her garden. 16 bulbs died.How many bulbs sprouted?

Hana flew 65km to her holiday destination. Ben flew 19 to his.How many more kilometres did Ben fly?

Supporting Your Child at Home

General Play games Involve them in day‐to‐day mathematics Help them learn their number factsHome learning Use concrete resources Draw pictures Talk about the methods they have used

Questions

mathematics: number, place value, addition and...

Documents