Calculation PolicyParent’s Evening

Wednesday 22nd January 20147pm

Order of Evening

• Principles of Numicon• Sequence of teaching addition• Sequence of teaching subtraction• Sequence of teaching multiplication• Sequence of teaching division• Time for questions and discussion

Numicon Kits

Firm Foundations (Reception)

Kit 1 (End of Reception, start of Year 1)

Kit 2 (Year 1 and Start of Year 2)

Kit 3 (End of Year 2 and Year 3)

Early Stages

• Counting objects• Counting forwards and backwards• Counting on from a given number• Number games• Counting stories• Counting songs• Real life role play

Writing numerals

• Not formally asked to write numerals until they can order images of number.

• Necessary hand control needed.• Modelling of writing numerals daily.• Making numerals practically.• Making their own number lines.

Beginning to record

Introduced when children can:• Describe verbally what they have made with

Numicon apparatus.• Use signs practically with bodies.• Find numerals and words using cards.• Match signs and number sentences to what

they are describing.

Informal Jottings

• Need to move on to bigger numbers and so it becomes harder to calculate mentally.

• Informal jottings become part of mental strategies.

• May begin independently then should be explained to avoid misconceptions.

• When ready, move onto progression of written calculations.

Addition

Stage 1Partitioning and recombining:

25 + 31 20 +30 = 50 (tens)

5 + 1 = 6 (units)50 + 6 = 56 (recombining)

Introduce the blank number line:25 +31

+10 + 10 + 10 + 1

25 35 45 55 56

Stage 2Continue blank number lines, adding whole

numbers:35 +52

+50 + 2

35 85 87

Move onto larger numbers:

121 +243 +200 +40 +3

121 321 361 364

Begin to use the expanded written method using a horizontal layout:

67 + 24

60 + 720 + 4

80 + 11 = 91

Stage 3

Extending to vertical layout• Once children understand the place value of the

numbers through using the expanded method they should begin to work vertically, and with larger numbers. For example:

264 + 48 264 + 48 12 total of the units 100 total of the tens 200 total of the hundreds 312

•When working with this stage, estimation should always be encouraged first.•This layout should be used for adding amounts of money and decimals.

Stage 4

Progression from the vertical layout to the compact written method

• Continued use of estimation before calculating.

• Carrying should now be shown below the line. For example:

This method should continue to be used for larger numbers, where there is more than one need to carry a number and when adding decimals, including amounts

of money, weight and length.

If the children show any misconceptions at this stage then they should refer back to stage 3.

783 + 135 783 + 135 918 1

Subtraction

Stage 1Begin to understand the use of an empty

number line to count back:32-22

-1 -1 -10 -10

12 13 14 24 34

Stage 2

• Counting on using multiples of 10 on the blank number line:

67-22 +10 +10 +10 +10 +5

22 32 42 52 62 67

Stage 3

Move on to larger numbers using the empty number lines; introduce the concept of the unknown number.

• Counting on or back using partitioning:• 324-113

211 214 224 324

-3 -10 -100

Introduce the concept of the unknown number:

62- = 27

Stage 4

• Expand written methods showing vertical layout with calculations where no exchanging needs to occur.

67-25

60 7-20 5

40 2• Expanded decomposition

Extend to larger numbers using the same method

• When exchanging, it is important to show the children what has actually been exchanged each time. When the children are aware that tens or hundreds are brought across, they can cross numbers out and write the adjusted amount in each column, to make the method more efficient:

Stage 5

• Compact written methods involving decomposition

• Move on to borrowing in a compact method where exchanged numbers are written above the calculation.

• Ensure calculations are worked on where 0 acts as a place holder to teach how to exchange in this situation.

• Extend written methods for subtraction to include decimal numbers with up to 2 decimal places and larger numbers up to 10,000.

• Children should now be able to choose the most efficient and appropriate method for each calculation.

Multiplication

Stage 1

Draw pictures to show equal sets – grouping pictures:

3 x 2 = 3 groups of 2

Stage 2

• Repeated addition on an empty number line:

• 3 x 5 = 3 jumps of 5 +5 +5 +5

0 5 10 15

Stage 3

• Multiplication as an array:

3 x 4 = 3 rows of 4

Stage 4

• Use knowledge of partitioning to multiply:

32 x 3

32 x 3 = (30 x 3) + (2 x 3) = 90 + 6

=96

Stage 5

Develop the extended written method of the grid method for tens and units.

• Partition 2 digit numbers into tens and units and multiply across the grid.

37 x 4

X 30 74 120 28

• When the concept of the grid method is understood, move on to multiply 2 digit numbers by 2 digit numbers.

37 x 23

X 30 720 600 1403 90 21

• Continue the use of this method to multiply 3 digit numbers and decimals.

• Continue to develop the use of estimation throughout the use of multiplication calculations.

Stage 6

Move on to written vertical methods• All vertical methods should be taught

alongside the grid method to ensure understanding. For example:

38X 7 210 (30 x 7 = 210) 56 (8 x 7 = 56) 266

X 30 87 210 56 = 266

• Extend the use of vertical methods for larger calculations.

Stage 7• Extend written methods for multiplication,

encouraging estimation first.• Continue to use the same methods as in stage

6, ensuring the grid method is used alongside vertical methods.

• Begin to develop short multiplication:625 x 6

625 X 6 3750 13

• When appropriate, use the same method moving on to numbers with one decimal place and then extend to two decimal places.

Division

Stage 1

• Draw pictures to show sharing:

9 ÷ 3 = 9 shared between 3

Stage 2

• Repeated subtraction on a number line:

6 ÷ 2 -2 -2 -2

0 2 4 6

Stage 3• Repeated subtraction as chunking.• Subtract chunks of the larger number, such as

multiples of 10. 148 ÷ 4 =

148 -40 (10 x 4) 108 -40 (10 x 4) 68 -40 (10 x 4) 28 -28 (7 x 4) 0

148 ÷ 4 = 10 + 10 + 10 + 7 = 37

Stage 4• Extend written method, encouraging

estimation first.• Move on to using the bus stop method,

recording as long division first. For example:196 ÷ 6

32 remainder 46)196

-60 (10 x 6) 136

-60 (10 x 6) 76

-60 (10 x 6) 16

-12 ( 2 x 6) 4

• This then contracts to the more compact form of repeated subtraction.

196 ÷6

32 remainder 46)196

-180 (30 x 6) 16

-12 ( 2 x 6) 4

Stage 5

• Extend written methods with larger numbers and decimals.

• When children have fully understood the concept of the bus stop method for dividing by one digit, extend to divide by 2 and 3 digits. Then move on to dividing decimals using the same method.