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Kellington Primary School

Kellington Primary School. Maths Parents’ Workshop 10 th December 2012. Aims. To 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

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Kellington Primary School

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  1. Kellington Primary School Maths Parents’ Workshop 10th December 2012

  2. Aims To explain how we teach your children +, -, x and ÷. To give you ideas of how you can help your children at home.

  3. Addition

  4. Laying the foundations…… • Number lines • Practical equipment • Numicon • Multilink cubes • Real life contexts • Number bonds • Patterns

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

  6. Use of a number line + 6+5= Use of a 100 square 34+12=

  7. 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.

  8. Using column addition, step 2…… • Continue to use partitioning. • 364+54= 364 + 54 300 110 + 8 418

  9. Column addition…. • The final step, when the children have a sound grasp of place value & of the whole process… 364 + 54 418 1

  10. Subtraction -

  11. Subtraction - Taking away practically. 3-2=

  12. Use of a number line/100 square 12-6=6 -

  13. Written methods for Subtraction Stage 1: The empty number line The 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

  14. Written methods for Subtraction Stage 2: Partitioning Subtraction 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

  15. Written methods for Subtraction 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

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

  17. Written methods for Subtraction 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!

  18. Written methods for Subtraction Stage 4: Column method The expanded method is eventually reduced to:

  19. Multiplication x

  20. Multiplication- repeated addition 3x5= (3 groups of 5) xx xx x xx xx x xx xx x x 5 + 5 + 5= 15

  21. 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?

  22. 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 5 5 x 3

  23. Written methods for Multiplication Stage 1: Mental multiplication using partitioning This 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......

  24. Written methods for Multiplication Stage 2: The Grid Method This 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

  25. Written methods for Multiplication Stage 3: Expanded short multiplication The 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.

  26. Written methods for Multiplication Stage 3: Expanded short multiplication The same steps can be used when introducing TU x TU.

  27. Written methods for Multiplication Stage 4: Short multiplication The 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. 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

  28. Written methods for Multiplication Stage 5: Long multiplication This 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.

  29. Written methods for Multiplication In Year 6, children apply the same steps to multiply HTU x TU Start with the grid method, asking the children to estimate their answer first. 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. This expanded method is cumbersome, so there is plenty of incentive to move on to a more efficient method.

  30. Division ÷

  31. 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

  32. Written methods for Division Stage 1: Mental division using partitioning One 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

  33. Written methods for Division Stage 1: Mental division using partitioning or…… and with a remainder

  34. WDIK 10 x 4 20 x 4 30 x 4 etc

  35. Written methods for Division 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.

  36. Written methods for Division Stage 2: 'Expanded' method for TU ÷ U and HTU ÷ U This 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.

  37. Written methods for Division Stage 3: Refining the 'Expanded' method for HTU ÷ U Initially 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.

  38. Written methods for Division Stage 4: Long division for HTU ÷ TU The 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.

  39. Thank you and Goodbye!

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