Mathematical Methods Wallands Community Primary School Information for parents Key Stage 2

Mathematical Methods Addition Subtraction Multiplication Division This booklet is designed to give you information about the main methods for calculating in mathematics that your children are learning in school. The children start by learning mental methods and informal jottings and progress to formal written calculations. Addition Subtraction Multiplication Division

add, addition, plus, total, sum of, more, increase, altogether + Key Words add, addition, plus, total, sum of, more, increase, altogether

Mentally children should add using a count on method. They may imagine an empty number line in their heads, e.g. 85 + 47 = +40 +7 85 125 132 count on… Or they may partition into tens and units adding each separately, e.g. 85 + 47 = 132 80 + 40 = 120 + 7 = 12 120 + 12 = 132

For trickier additions they are more likely to use a column method as shown below: 8 5 + 4 7 1 3 2 1 To help with addition, practise quick recall of number bonds to 10 and adding through multiples of 10, e.g. 18 + 7, 43 + 9 etc

- Subtraction Key Words take away, subtraction, subtract, minus, decrease, difference, less than, leave, left over

Most children find it easier to count on. For subtraction we use an empty number line method as this encourages the children to understand what is happening in the calculation. 85 - 47 = Here is the answer, 3+30+5 = 38 Remember you can re-order the numbers in an addition. Put the biggest number first so 30+5+3 = 38 +30 +3 +5 47 50 80 85 count on… Most children find it easier to count on. When we count on, we are actually finding the difference. Place the lowest number on the left of the number line. How much do you need to count on to get to the larger number? Or, you could do it like this… Here is the answer -7 -40 38 45 85 …count back Some children prefer to count back. Place the highest number on the right of the number line. Count back splitting the number into tens and units.

For trickier subtraction the children will learn a column method For trickier subtraction the children will learn a column method. First they will learn an expanded method where the numbers are split into hundreds, tens and units. 56 – 32 = T U TU 50 + 6 56 - 30 + 2 - 32 20 + 4 24 By teaching the children this expanded method, they are able to understand decomposition of numbers (borrowing) when it comes to more complex subtractions. Decomposition: 754 = 700 + 50 + 4 - 286 200 + 80 + 6 -------- ------------------ 700 + 40 + 14 - 200 + 80 + 6 600 + 140 + 14 - 200 + 80 + 6 ---------------------- 400 + 60 + 8 = 468 Start with the units. 4 – 6 can’t be done! So 700 + 50 + 4 becomes 700 + 40 + 14 Now the units column can be subtracted, work it out and move on to the tens and the hundreds etc.

Don’t forget to line up the hundreds, ten and units carefully! The final stage in subtraction is to use a more compact and efficient method like this: 6 14 7 514 - 2 8 6 4 6 8 Don’t forget to line up the hundreds, ten and units carefully! When children are confident with this type of subtraction, they will work with bigger numbers and decimals in exactly the same way.

x Multiplication Key Word multiplication, multiply by, times, product, multiple, lots of, groups of, product, array When multiplying quick recall of tables is the most important thing. So knowing multiplication and division facts up to 10x10 is vital.

When using repeated addition a number line or informal jottings can be used, e.g. …or children may count up in multiples, e.g. 3 x 5 “3… 6… 9… 12… 15!” …or children may draw an array, e.g. 4 x 2 Grid method multiplication involves partitioning each number into tens and units before multiplying and then adding back together. 12 x 4 = X 10 2 4 10x4 = 40 2x4 = 8 40 + 8 = 48

By setting the final adding part out vertically as in this example, children are able to see how this links to short multiplication. It is very important for children to estimate their answers before starting a calculation! 68 x 7 = X 60 8 4 2 0 + 5 6 4 7 6 7 60x7 =420 7x8 =56 52 x 49 = 2 50 X 40 2 0 0 0 + 4 5 0 8 0 1 8 2 5 4 8 1 40x50 =2000 40x2 =80 9 9x2 =18 50x9 =450 Short multiplication is taught in Year 6. It is a quick method which is particularly useful when multiplying using decimals. Estimate your answer first: 7.92 x 6 = 7.92 is between 7 and 8, but closer to 8. 7 X 6 = 42 8 x 6 = 48 So the answer must be between 42 and 48 but closer to 48. 7. 9 2 x 6 4 7. 5 2 5 1 1 2 5 8 x 3 3 7 7 4 1 2

Division ÷ Key Words divide, division, divided by, divided into, share, group, split into equal groups, count in multiples, repeated subtraction remainder, factor, quotient, divisible by, inverse

Children are encouraged to ask a division as… Children learn about division through practical activity. They need lots of practice sharing out to make groups and counting in multiples. When dividing it is vital that children know their division facts, e.g. 15 ÷ 3 = 5 Children are encouraged to ask a division as… … How many 3’s are there in 15? When using repeated subtraction children use informal jottings to group, e.g. How many 3’s in 15? …or children may count on in multiples like this: …or children may share out into groups like this:

Chunking (division as the inverse of multiplication) After lots of practical work and using known division facts children will move onto the first written method of division – chunking. This method makes use of their multiplication facts, which they should feel fairly secure in by the time they attempt chunking (usually around Year 4). Chunking helps them to see how division is the inverse of multiplication. 91 ÷ 7 = The inverse of this is 7 x ? = 91 Work out how many 7s are in 91 Use multiplication facts that you feel confident with and build up towards your target number. Your target number is 91. This is the number you want to reach by counting up in 7s as you want to find out how many 7s are in 91, which is the same This is the as 91 ÷ 7. It will take too long to count number you up 7,14,21 etc so take a short cut by multiply by using your multiplication facts. 7 x ? = 91 7 x 10 = 70 This is close to 91, but not close enough. 7 x 3 = 21 Can you fit anymore 7s into 91? Add this column to get your answer. This is how many times you multiplied 7 to get 91, which is the same as saying 91 ÷ 7. 7 x 13 = 91 So, 91 ÷ 7 = 13

Bus stop method Chunking is a great method to help children really understand what is happening in division. The bus stop method is a more efficient method once the understanding is there. We always teach chunking first. How many 4s in 7? 1 and 3 left over. 2 1 r 3 ) How many 4s in 8? 2 7 4 8 1 3 r 5 ) 2 7 9 6 How many 7’s are there in 9? How many 7’s are there in 26?