Lower School Calculation Briefing.notebook

1

November 27, 2018

Nov 12­13:28

Calculations Briefing Monday 12th November

Objectives

- To understand the school approach to calcuations

- To be able to help pupils in a consistent way

Nov 12­13:28

- Mental strategies - Jottings - Written methods

'Can I do this in my head?''Can I do this in my head using drawing and jottings?''Do I need to use a pencil and paper procedure?'

Lower School Calculation Briefing.notebook

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November 27, 2018

Nov 12­13:28

In order to be able to use written methods successfully children need to be able to:

- Have a secure knowledge of key number facts- Be confident with a variety of mental strategies- Have a secure understanding of place value- Follow a CPA approach to support understanding - Use estimating and inverses- Be aware of the relevant vocabulary for each operation

Nov 12­13:28

Number facts- Numberbonds- x tables (including division facts)

Lower School Calculation Briefing.notebook

3

November 27, 2018

Nov 12­13:28

Mental Strategies

- Using 'friendly numbers' - Related facts- Near doubles

Some examples:

Supported by work in Big Maths

Nov 12­13:28

Place Value

Lower School Calculation Briefing.notebook

4

November 27, 2018

Nov 12­13:28

CPA Approach

- Concrete - Pictorial- Abstract

Base Ten

Nov 12­13:28

In order to be able to use written methods successfully children need to be able to:

- Have a secure knowledge of key number facts- Be confident with a variety of mental strategies- Have a secure understanding of place value- Follow a CPA approach to support understanding - Use estimating and inverses- Be aware of the relevant vocabulary for each operation

Lower School Calculation Briefing.notebook

5

November 27, 2018

Nov 12­13:28

The Number Line

8 + 5 =

Addition +

Nov 12­13:28

Addition +

The empty number line 8 + 5 = 13

48 + 15 = 63

45 + 36 = jumping to or adding a mult of 10

Lower School Calculation Briefing.notebook

6

November 27, 2018

Nov 14­16:50

Using a Hundred Square

Addition +

Nov 12­13:28

Addition +

Partitioning

45 + 36 = 40 + 5

30 + 6

144 + 276 = 100 + 40 + 4

200 + 70 + 6

Lower School Calculation Briefing.notebook

7

November 27, 2018

Nov 12­13:28

Addition + Compact column method

144 + 276 = 1 4 4

2 7 6

Vocabulary: carry 10 or carry 100, NOT carry 1

Extends to bigger numbers- with decimals-different numbers of digits- where misconceptions can arise:

Nov 15­08:26

386 + 20 Add 1350 to 8071

Assessment Questions

'Find the sum of 97 and 4905'

Lower School Calculation Briefing.notebook

8

November 27, 2018

Nov 12­14:29

Subtraction -

The number lineCount backwards But only up to 10

8 - 5 =

Nov 14­16:59

Using a 100 square

Finding the difference

Subtraction -

Lower School Calculation Briefing.notebook

9

November 27, 2018

Nov 12­14:29

Subtraction -The empty number line-Counting up/finding the difference

74 - 27 =

Children will reduce steps as get more secure.

Nov 12­14:29

Subtraction -

754 - 86 =

Compact column subtraction- decomposition

7 5 4

8 6

Use of concrete materials to clarify the process of 'exchanging'

Extends to bigger numbers Misconceptions can arise with different numbers of digits (especially once decimals are involved)

Lower School Calculation Briefing.notebook

10

November 27, 2018

Nov 12­14:29

Children are taught to use a number line and column subtraction right up until Year 6. They should consider which is best for individual questions.

eg 13 - 12.82 3000 - 2807

Nov 15­08:30

Assessment Questions

8423 - 5796

Bob's Bakery makes 150 buns. The bakery sells 125 buns.

Cath's Cake Shop makes 135 buns. The shop sells 98 buns.

How many buns are not sold?

Class 4A bake 566 cakes.

Class 4B bake 472 cakes.

They sell the cakes.

25 cakes are left at the end of the cake sale.

How many cakes are sold altogether?

Lower School Calculation Briefing.notebook

11

November 27, 2018

Nov 12­14:46

Multiplication x

Repeated addition on a number line

Repeated addition is a vital concept

Nov 14­17:03

Using a 100 square

Multiplication x

Lower School Calculation Briefing.notebook

12

November 27, 2018

Nov 12­14:46

Multiplication x

Arraysrecognition of fact families

12 3 = 4 & 12 4 = 3

4 x 3 = 3 x 4

Nov 12­14:46

Multiplication x

The Grid method

34 x 6 =

100 + 80

20 + 4100 + 100 + 4

partition to add back

column to add back

1 8 0

2 4

Lower School Calculation Briefing.notebook

13

November 27, 2018

Nov 12­14:46

Multiplication x

The Grid method with bigger numbers

286 x 9 =

Also extends to bigger numbers, with decimals and different numbers of digits. Place value: adding back often leads to errors.

Nov 15­08:33

Assessment Questions

Multiply 84 by 9

723 x 6bananas 23p each apples 45p each

Fred buys 6 bananas and 2 apples. How much does the fruit cost in total?

Lower School Calculation Briefing.notebook

14

November 27, 2018

Nov 12­14:46

Division ÷

Equal Sharing

Recognition of fact families

12 ÷ 3 = 4 & 12 ÷ 4 = 3

4 x 3 = 3 x 4

Nov 12­14:46

Division ÷

Equal Grouping

4 x 3 = 3 x 4

Recognition of fact families

12 ÷ 3 = 4 & 12 ÷ 4 = 3

4 x 3 = 3 x 4

Lower School Calculation Briefing.notebook

15

November 27, 2018

Nov 12­14:46

Grouping along a number line 12 ÷ 3 =

1 x 3 1 x 3 1 x 3 1 x 3

Division ÷

Nov 12­14:46

Empty number line (including remainders)

81 ÷ 3 = 10 x 3

7 x 310 x 3

137 ÷ 6 =

Division ÷

Lower School Calculation Briefing.notebook

16

November 27, 2018

Nov 15­08:38

Assessment Questions

Divide 132 by 11. 56 cherries are shared equally between 8 children.

Write a division to show how many cherries each child has.

Nov 9­15:02