This week's tasks are based on some simple arithmetic items from a Key Stage 2 SAT test (Paper 1: arithmetic, 2025). We use variants of the items to help children look more closely at the structure of numbers and numerical expressions.
Task 06A: The SAT item here is the first item in the 2025 Paper 1 test and is a simple item about place value: what does the 5 represent? Our variants are sightly more complex in that they also involve seeing how a change in one component of an expression affects other components (as in the Week 02 tasks). So, for example, whereas the missing number in the original item is 500, in Variant 1 it is 1 less than 500, because 40+9 (or 49) in the original item has been changed to 50.
Children might find it quite demanding to invent their own variants for this particular SAT item, but it is worth given children the opportunity, here and in the rest of this week's tasks, if they are willing to do so.
Task 06B: The SAT item here is Q2 from the 2025 Paper 1 test. Children might well use column arithmetic to solve it as this is what they will probably have been taught to do. However, encourage children to work mentally to solve the three variants.
In Variant 1, 15 is added to each term of the given expression 456 – 385. This doesn't change its value. In Variant 2, 55 has been subtracted from each term. Variant 3 involves 'adding on' or 'the shopkeeper's method'.
Task 06C: Here we are not asking children to solve the given SAT item (Q4) but to get some sense of what the answer will look like.
The numbers in the given expression are slightly less than 48 and 52, so their sum is slightly less than 100.
The second number in the given expressions contains three decimal places, with the digit 3 in the third place. The first number only contains two decimal places, so we can think of it as having 0 in the third place. 0 + 3 = 3.
Task 06D: The SAT item here is Q5 from the 2025 Paper 1 test. Here we use the same principle as in Task 06B, that for a subtraction expression A – B, its value does not change if we add (or subtract) the same number to A and to B.
Task 06E: This SAT item is Q6 from the 2025 Paper 1 test. Here we find ways of transforming a division expression without changing its value.
Some children might express the view that these variants don't really make the task any easier. If so, it is worth reiterating that this is not the prime purpose of the task. Rather we are looking at the properties of division. And sometimes such transformations can be quite powerful, as in this example:
