Aaron has $340 and Bala has $220. They each buy the same pair of sneakers. Aaron then has 4 times as much money as Bala. How much did the sneakers cost?
Difference = 340 − 220 = $120
3 units = $120
1 unit = 120 ÷ 3 = $40
Cost of the sneakers = 220 − 40 = $180
The sneakers cost $180.
Ans: $180
Example 2
Jar A has 75 sweets and Jar B has 27 sweets. Mei puts the same number of sweets into each jar. Jar A then has twice as many sweets as Jar B. How many sweets did Mei put into each jar?
Difference = 75 − 27 = 48
1 unit = 48
Sweets put into each jar = 48 − 27 = 21
Mei put 21 sweets into each jar.
Ans: 21
Practice questions with worked solutions
Question 1 is free to try. The other 4 open in the free trial, each with its full working.
How can I help my child recognise P4 unchanged difference questions?
Your child identifies the fixed difference when two quantities increase or decrease by the same amount.
What your child learns here
Your child identifies the fixed difference when two quantities increase or decrease by the same amount. The method applies whole-number operations and mathematical problem solving in the Primary 4 course. It helps your child distinguish a change to both amounts from a transfer, where one amount rises while the other falls.
Recognise an equal change only when both quantities gain the same amount or both lose the same amount, with the direction matching too.
Calculate the difference between the quantities in a state where enough information is known, then carry that difference to the other state.
Connect a fixed difference with a stated times-as-many relationship to determine the value of equal units and recover the required amounts.
Apply the same reasoning to ages as equal numbers of years pass, distinguishing a fixed age gap from a changing age comparison.
Use the before-and-after information to identify the equal amount added or removed when that change is the quantity requested.
Does the answer make sense?
Subtract the smaller amount from the larger before the equal change, then repeat the subtraction afterwards. The two differences must match, even though the combined total changes when both amounts gain or both lose a positive quantity.
How to practise these questions
Intermediate questions develop the unchanged-difference method, while the Challenge question follows equal spending with an equal addition and asks for the new comparison. Your child works with equal spending, equal additions, a future age comparison and equal removals where the total removed is requested. Begin by identifying the difference that survives the change, then use the comparison given for the relevant stage. In the age question, distinguish the age at the future date from the age asked for now. In an equal-removal question, an amount removed from each box is different from the combined amount removed. Ask your child to label that distinction in the final line and to check the before and after differences before accepting the result.
Questions parents ask
Why does the gap stay fixed when both amounts change? Adding the same amount to each quantity extends both by an equal amount, so neither gains on the other. Subtracting an equal amount from both has the same effect on their gap. Your child can verify this by comparing the two differences with subtraction.
Does an age comparison stay the same as children grow older? The difference in their ages stays fixed because the same time passes for both. A statement that one is a certain number of times as old as the other need not remain true. Your child should carry the age difference between dates, then use the comparison given for that date.
How can I distinguish an equal change from a transfer? Ask what happens to each quantity separately. In an equal increase both rise, and in an equal decrease both fall. During a transfer between them, one rises and the other falls. Naming those two actions helps your child decide whether the difference or the total is preserved.
