Lower School Calculation Briefing.notebook
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November 27, 2018
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Calculations Briefing Monday 12th November
Objectives
- To understand the school approach to calcuations
- To be able to help pupils in a consistent way
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- 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
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Number facts- Numberbonds- x tables (including division facts)
Lower School Calculation Briefing.notebook
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November 27, 2018
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Mental Strategies
- Using 'friendly numbers' - Related facts- Near doubles
Some examples:
Supported by work in Big Maths
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Place Value
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November 27, 2018
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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
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November 27, 2018
Nov 1213:28
The Number Line
8 + 5 =
Addition +
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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
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November 27, 2018
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Using a Hundred Square
Addition +
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Addition +
Partitioning
45 + 36 = 40 + 5
30 + 6
144 + 276 = 100 + 40 + 4
200 + 70 + 6
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November 27, 2018
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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'
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November 27, 2018
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Subtraction -
The number lineCount backwards But only up to 10
8 - 5 =
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Using a 100 square
Finding the difference
Subtraction -
Lower School Calculation Briefing.notebook
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November 27, 2018
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Subtraction -The empty number line-Counting up/finding the difference
74 - 27 =
Children will reduce steps as get more secure.
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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)
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November 27, 2018
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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
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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
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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
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November 27, 2018
Nov 1214:46
Multiplication x
Arraysrecognition of fact families
12 3 = 4 & 12 4 = 3
4 x 3 = 3 x 4
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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
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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?
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November 27, 2018
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Division ÷
Equal Sharing
Recognition of fact families
12 ÷ 3 = 4 & 12 ÷ 4 = 3
4 x 3 = 3 x 4
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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
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November 27, 2018
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Grouping along a number line 12 ÷ 3 =
1 x 3 1 x 3 1 x 3 1 x 3
Division ÷
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Empty number line (including remainders)
81 ÷ 3 = 10 x 3
7 x 310 x 3
137 ÷ 6 =
Division ÷
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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.
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