Before and after, when the difference does not change is in the Primary 5 Four Operations of Whole Numbers chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Lesson video, with the working
The difference stays the same
2 min 35 s
The question shows first; its working is written as the film explains it.
Question 1 of 5 · Intermediate · free to tryThere are 84 pencils in Box A and 36 in Box B. The same number of pencils is…There are 84 pencils in Box A…
There are 84 pencils in Box A and 36 in Box B. The same number of pencils is added to each box. Box A then contains twice as many pencils as Box B. How many pencils were added to each box?
How do you solve difference unchanged questions in P5?
A difference unchanged question adds the same number to two amounts, or takes the same number from both, and the gap between them does not move.
What your child learns here
A difference unchanged question adds the same number to two amounts, or takes the same number from both, and the gap between them does not move. Ages work in the same way, since two people grow older by the same number of years. This page applies the Primary 5 four operations of whole numbers to these problem sums.
Find the difference at the start, before anything is added or taken from the bars.
Keep that difference for the end, because the same change on both bars leaves the gap as it was.
Read the 'times as many' at the end: if one amount is 4 times the other, the gap is 3 units.
Divide the difference by its number of units to find one unit, then compare with the start to find the change.
For ages, the gap between two people is the same in every year, past or future.
Does the answer make sense?
Adding 12 pencils to each box gives 96 in Box A and 48 in Box B. The gap 96 minus 48 is 48, the same as 84 minus 36 at the start, and 96 is twice 48, as the question says. Box B grows from 36 to 48, and 48 minus 36 is the 12 added.
How to practise these questions
Free Question 1 starts with 84 pencils in Box A and 36 in Box B; the same number is added to each box until Box A has twice as many as Box B, and your child finds how many pencils were added. The Intermediate questions train equal spending, equal removing with the total removed asked for, and ages now and in the future. The Challenge question makes two equal changes in a row and asks how many times as much one person has at the end. If your child is stuck, open its worked solution and mark the difference on both bars first.
Questions parents ask
Why does the difference stay the same? Both amounts move by the same number, so whatever is added to one bar is added to the other. The piece of the longer bar that sticks out keeps its length.
Are age questions difference unchanged questions? Yes. Two people grow older by the same number of years, so the gap between their ages never changes. Once the gap is known, the 'times as old' line splits it into units.
Does my child need ratio for these questions? No. The idea returns with ratios in Primary 6, but each question here uses whole numbers and 'times as many', and is solved with a bar model and the four operations.
