Kellington Primary School Maths Parents’ Workshop 10 th December 2012

Kellington Primary SchoolMaths Parents’ Workshop

10th December 2012

AimsTo explain how we teach your

children +, -, x and ÷.

To give you ideas of how you can help your children at home.

Addition

Laying the foundations……

• Number lines• Practical equipment• Numicon• Multilink cubes• Real life contexts• Number bonds• Patterns

Partitioning……..• Arrow cards• Place value• Partitioning• Recombining

1 2 3 4 5 6 7 8 9 10 11 12 13

6+5=

Use of a 100 square

34+12=

Use of a number line

Beginning to use column addition, step

1…..• Continue to use partitioning• 364+ 34=300+60+4+30+4=300+90+8• Then we recombine it all, to be left

with the answer, 398.

Using column addition, step 2……

• Continue to use partitioning.• 364+54= 364

+ 54 300 110

+ 8 418

Column addition….• The final step, when the children

have a sound grasp of place value & of the whole process…

364+ 54 418

1

Subtraction

Subtraction

3-2=

Taking away practically.

Use of a number line/100 square

12-6=6

1 2 3 4 5 6 7 8 9 10 11 12 13

Written methods for Subtraction

Stage 1: The empty number lineThe empty number line helps to record the steps in mental subtraction. There are several ways to do this:• Counting Back - a calculation like 74 - 27 can be recorded by counting back 27 from 74 to reach 47.

or

• Counting Up - the steps can also be recorded by counting up from the smaller number to find the difference

or


Stage 2: PartitioningSubtraction can be recorded using partitioning to write equivalent calculations that are easier to carry out mentally. For 74 - 27 this involves partitioning the 27 into 20 and 7, then subtracting 20 and 7 in turn. 74 – 27 is the same as 74 – 20 – 7 74 – 20 = 54 54 – 7 = 47


Stage 3: Expanded column method The partitioning stage should be followed by the expanded column method, where tens and units are placed under each other. This is where the concept of ‘borrowing’ is introduced

Example: 74 - 27


Stage 3: Expanded column method It can also be applied to three and four digit numbers. Example: 741 - 367


Stage 3: Expanded column method Depending on the numbers it can get quite complicated and this stage may need a lot of time and perseverance!


Stage 4: Column methodThe expanded method is eventually reduced to:

Multiplication

Multiplication- repeated addition

xxxxx

3x5= (3 groups of 5)

xxxxx

xxxxx

5 + 5 + 5= 15

Times tables• By end of Year 2 children should know

x2,x5,x10 Plus ?????• Practise counting in 2’s, 3’s, 4’s, 5’s,

10’s• Matching pairs (question on one card,

answer on another)2013 By the end of year 4 – all times

tables?

Arrays

Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method.

3 x 55 x 3

Written methods for Multiplication

Stage 1: Mental multiplication using partitioningThis allows the tens and ones to be multiplied separately to form partial products. These are then added to find the total product. Either the tens or the ones can be multiplied first but it is more common to start with the tens. This can look like......

14 3 (10 4) 3(10 3) (4 3) 30 12 42


Stage 2: The Grid MethodThis links directly to the mental method. It is an alternative way of

recording the same steps. It is better to place the number with the most digits in the left-hand column of the grid so that it is easier to add the partial products. For TU x TU, the partial products in each row are added, and then the two sums at the end of each row are added to find the total product


Stage 3: Expanded short multiplicationThe next step is to represent the method in a column format, but showing the working. Attention should be drawn to the links with the grid method above. Children should describe what they do by referring to the actual values of the digits in the columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7 should be stressed. Some children should be able to use this expanded method for TU × U by the end of Year 5.30 8

7210 30 7 210

56 8 7 56266

38 7210

56266


Stage 3: Expanded short multiplicationThe same steps can be used when introducing TU x TU.

1

56 27

1000 50 20 1000120 6 20 120350 50 7 350

42 6 7 421512

1

56 27

1120 56 20 392 56 7

1512


Stage 4: Short multiplicationThe expanded method is eventually reduced to the standard method for short multiplication. The recording is reduced further, with carry digits recorded below the line. If, after practice, children cannot use the compact method without making errors, they should return to the expanded format of stage 3.

5

38 7266

The step here involves adding 210 and 50 mentally with only the 5 in the 50 recorded. This highlights the need for children to be able to add a multiple of 10 to a two-digit or three-digit number mentally before they reach this stage


Stage 5: Long multiplicationThis is applied to TU x TU as follows.

The carry digits in the partial products of 56 × 20 = 120 and 56 × 7 = 392 are usually carried mentally.The aim is for some children to use this long multiplication method for TU × TU by the end of Year 6.1

56 27

1120 56 20 392 56 7

1512


In Year 6, children apply the same steps to multiply HTU x TU

1

286 29

4000 200 20 40001600 80 20 1600

120 6 20 1201800 200 9 1800

720 80 9 720 54 6 9 54

8294

1

286 29

5720 286 20 2574 286 9

8294

Start with the grid method, asking the children to estimate their answer first.

This expanded method is cumbersome, so there is plenty of incentive to move on to a more efficient method.

Children who are already secure with multiplication for TU × U and TU × TU should have little difficulty in using the same method for HTU × TU.

Division ÷

Written methods for Division

Initially division is introduced as ‘sharing’ using real objects or pictures.

Share 10 apples equally between 2 children which eventually becomes 10 ÷ 2 = 5


Stage 1: Mental division using partitioningOne way to work out TU ÷ U mentally is to partition TU into smaller multiples of the divisor, then divide each part separately. Informal recording in Year 4 for 84 ÷ 7 might be:

In this example, using knowledge of multiples, the 84 is partitioned into 70 (most children will be secure with a multiple of 10) plus 14


Stage 1: Mental division using partitioning

or……

and with a remainder

WDIK10 x 420 x 430 x 4etc


Stage 2: Short division of TU ÷ U'Short' division of TU ÷ U can be introduced as a more compact recording of the mental method of partitioning, to children who are confident with multiplication and division facts and whose understanding of partitioning and place value is sound. For most children this will be during Year 5.


Stage 2: 'Expanded' method for TU ÷ U and HTU ÷ UThis method, often referred to as 'chunking', is based on subtracting multiples of the divisor, or 'chunks'. It is useful for reminding children of the link between division and repeated subtraction. However, children need to recognise that chunking is inefficient if too many subtractions have to be carried out.


Stage 3: Refining the 'Expanded' method for HTU ÷ UInitially children subtract several chunks, but with practice they should look for the biggest multiples that they can find to subtract, to reduce the number of steps.Once they understand and can apply the expanded method, children should try the standard method for short division.


Stage 4: Long division for HTU ÷ TUThe next step is to tackle HTU ÷ TU, which for most children will be in Year 6. The layout on the right, which links to chunking, is in essence the 'long division' method. Conventionally the 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second recording.

Thank you and Goodbye!

Documents

Kellington Primary School Maths Parents’ Workshop 10 th December 2012