Progression in written calculations

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# Progression in written calculations - PowerPoint PPT Presentation

Progression in written calculations. Tuesday 20 th October. Addition. Practical activities and discussions Finding one more than a number from 1 – 10 Using vocabulary associated with addition Use of a number line Begin to use the + and = sign to record mental calculations

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### Progression in written calculations

Tuesday 20th October

• Practical activities and discussions
• Finding one more than a number from 1 – 10
• Using vocabulary associated with addition
• Use of a number line
• Begin to use the + and = sign to record mental calculations
• Know by heart all number bonds to 10 and within 10
• Use knowledge to know that addition can be done in any order to do mental calculations more efficiently
• Adding 3 single digit number mentally
• Know by heart all number bonds to 20 and within 20
• Use + and = to record mental calculations use a number line to make informal calculations
• Use a number line to make informal jottings
• Use partitioning to reflect mental methods
• 45 +78 = 40 + 70 + 5 + 8
• Vertical format least significant digit first extended to bigger numbers

368

+ 493

11

150

700

861

• Use of a number line to check
• Compact layout, starting to involve carrying

546 472

+ 253 +372

799 844

1

• Extending to decimals
• Compact addition using carrying for Th, H, T, U and decimals
Subtraction
• Practical activities and discussions
• Finding one less than a number from 1 – 10
• Begin to relate subtraction to ‘taking away’
• Use a number line to count on and back
• Begin to understand that subtraction is ‘finding the difference’
• Begin to use the – and = sign to record mental calculation
• Know by heart all subtraction facts to 10
Subtraction
• Know by heart all subtraction facts to 20
• Partition numbers (no crossing boundaries)
• Use informal pencil and paper methods (jottings)
• Use a number line to record complementary addition

eg 84 – 56 =

+4 +20 +4

----------------------------------------------

56 60 80 84

Subtraction
• Vertical expanded method

563 – 241 =

500 + 60 + 3

- 200 + 40 + 1

300 + 20 + 2

• 373 – 125 =

60 13

300 + 70 + 3

- 100 + 20 + 5

200 + 40 + 8

Use of a number line to check

Subtraction
• Compact method – decomposition including larger numbers and decimals

6695

2584 -

4111

6 8

7293

3426 -

3867

Multiplication
• Practical activities to gain experience of doubling
• Become familiar with appropriate language
• Use of arrays
• Know by heart addition doubles to at least 10
• Know by heart x2, x10 multiplication facts
Multiplication
• Understand multiplication as repeated addition
• Know by heart multiplication facts up to x10
• Use a number line to show repeated addition
Multiplication
• Mental methods using partitioning

38 x 7 = ( 30 x 7 ) + ( 8 x 7 ) =

210 + 56 = 266

• Introduce the grid method

38 x 7 = 266

Multiplication
• Extend the grid method to larger numbers

56 x 27 =

Multiplication
• Extend the grid method to even larger numbers and decimals

23.5 x 12 =

• Compact vertical multiplication

38

x 7

266

Division
• Practical activities to gain experience of sharing and to become familiar with the appropriate language
• Understand division as grouping, repeated subtraction or sharing and record informally including calculations with remainder

egHow many 4s in 12?

• How many are left over if I share 13 between 4?
Division
• Use practical informal methods to divide 2 digit numbers.
• Round remainders up and down

eg 14 ÷ 4 =

----------------------------------------------

0 4 8 12 14

Division

Develop and refine written method

eg 98 ÷ 6 =

10 x 6 6 x 6 r2 or 1/3

----------------------------------------------

0 60 96 98

Refine and use efficient written methods using multiples of 10 and remainders

eg 178 ÷ 8 =

20 x 8 2 x 8 r2 or ¼

----------------------------------------------

0 160 176 178

Division

Use a standard written method:

Long division

168

4 ) 672

400 –

272

240 –

32

Compact short division

0 4 7 r 2 or 2/5

5 ) 22337