Maths Strategies
Addition and Subtraction
The children will be learning a variety of strategies for solving these types of problems using whole numbers initially, and later on decimals and fractions.
Here’s a quick explanation of what the strategies involve so that you can help your child at home. Hope it’s helpful.
Doubles: e.g. They know 5 + 5 = 10, then 5 + 7 must be another 2 so 5 + 7 = 12 or they know 12 - 6 = 6 so 13 - 6 is just one more, 7.
Using bonds to 10, 20 etc: e.g. 16 + 7 they will say 16 + 4 = 20 and 3 more is 23. Similarly 24 - 9 then 24 - 4 = 20 and then 5 less is 15.
Place value Partitioning: Splitting the problem into tens and ones e.g. 18 + 25 = (10 + 20) + (8 + 5) = 30 + 13 = 43. Similarly 56 - 23 = (56 - 20) - 3 = 36 - 3 = 33.
Rounding and Compensating: using “tidy” numbers to first of all round the number e.g.
39 + 17 can be rounded to 40 + 17 (40 is the “tidy” number) = 57 and then we need to compensate by taking off the extra 1 we added on when rounding, so 57 - 1 = 56. Similarly 42 - 18 we can round to 42 - 20 = 22 and then since we took off 2 too many we’ll compensate by adding it back on, 22 + 2 = 24.
Proportional Adjustment: this uses the fact that 6 + 7 is the same as 5 + 8 by taking 1 off the 6 and adding 1 to the 7. We can use this for trickier problems e.g. 38 + 19 is the same as 37 + 20 = 57. With subtraction we use the fact that 8 - 3 is the same as 7 - 2 (a bit different!) so 43 - 19 is the same as 44 - 20 = 24.
We can also use reversibility which simply means turning a subtraction problem into an addition problem e.g. 51 - 17 we can say 17 + ? = 51 and then use some of the other strategies like partitioning 17 + 3 = 20 and 20 + 31 = 51 so the answer is 3 + 31 = 34.
Working Form: We still teach working form (which is really just partitioning) but only when they have a good grasp of many of the above strategies. It is a lot better that when we teach this method the children fully understand the thinking behind each step.
Multiplication and Division
The children will be learning a variety of strategies for solving these types of problems using whole numbers initially, and later on decimals and fractions.
Here’s a quick explanation of what the strategies involve so that you can help your child at home.
Using known facts: e.g.They know 5 x 7 = 35,then 6 x 7 must be another 7 so 6 x 7 = 42 or they know 4 x 7 = 28 so 8 x 7 is just double that, 56.
Place value Partitioning: Splitting the problem in to tens and ones e.g. 63 x 4 = (60 x 4) + (3 x 4) = 240 + 12 = 252
Rounding and Compensating: using “tidy” numbers to first of all round the number e.g. 39 x 7 can be rounded to 40 x 7 (40 is the “tidy” number) = 280 and then we need to compensate by taking off the extra 7 we added on when rounding, so 280 - 7 = 273.
Proportional Adjustment ( often called doubling and halving, or tripling and thirding): this uses the fact that 4 x 5 is the same as 2 x 10 by halving the 4 and doubling the 5.We can use this for trickier problems e.g. 14 x 17 is the same as 7 x 34 = (7 x 30) + (7 x 4) = 238 ( by partitioning)
We can also use these strategies to solve division problems, bit trickier but essentially the same. Partitioning: e.g. 92 ÷ 4 can be split into (80 ÷ 4) + (12 ÷ 4) = 20 + 3 = 23
Rounding and compensating: e.g. 147 ÷ 3, we know 150 ÷ 3 = 50 so 147 ÷ 3 = 49
Proportional adjustment: e.g. 162 ÷ 18 is the same as 81 ÷ 9 = 9 (halving both numbers)
We can also use reversibility which simply means turning a division problem into a multiplication problem e.g. 192 ÷ 4 we can say 4 x ? = 192 and then use some of the other strategies like partitioning 4 x 40 = 160 and then 4 x 8 = 32 so the answer must be 48.
Basic Facts:These are still extremely important and we expect that children have instant accurate recall of these by the time they finish Year 6, preferably before! A good progression is firstly knowing the 2s 5s and 10s, then the 3s, 4s, 6s and finally the 7s, 8s and 9s.
Knowing families of facts are also beneficial e.g. 3x6=18, 6x3=18, 18÷3=6, 18÷6=3.
Proportions and Ratios
The expectation is that by the end of Year 6 the children will be able to use symmetry and their basic facts to find fractions of sets, shapes and quantities.
e.g. ⅔ of 48, they can use many strategies (⅔ of 30 = 20 and ⅔ of 18 = 12 so 20 + 12 = 32, or ⅓ of 48 = 16 so ⅔ will be 32 or ⅔ of 60 = 40 and ⅔ of 12 = 8 so 40-8=32 or 2 x 48 = 96 and then 96 ÷ 3 = 32 etc.) Similarly we might ask 16 is ⅔ of what?
Children will also be exposed to improper fractions (1½ = 3/2 ), equivalent fractions (⅓ = 2/6), ratios (2:3), and possibly percentages.
Finally, it’s very important that children see fractions in a range of contexts e.g. a fraction of a set of objects, a fraction of a shape, a fraction of a fluid measure, where fractions sit on number lines, a comparison (this piece is half the size of that piece) etc.
Basic Facts
These are still extremely important and we expect that children have instant accurate recall of all addition and subtraction facts to 20 by the time they finish Year 4! (Quite often these get overlooked with the emphasis being on learning the times tables.)
