Before and after, when the total 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 total stays the same
2 min 16 s
The question shows first; its working is written as the film explains it.
At first, Chloe had 7 marbles for every 3 marbles Marcus had. Chloe then gave Marcus 24 marbles, and they had the same number each. How many marbles did Chloe have at first?
Chloe had 84 marbles at first.
Ans: 84
How to solve it
Draw the units: Chloe has 7 units and Marcus has 3 units.
Add them for the total: 7 units plus 3 units is 10 units.
The marbles only move across, so the total stays 10 units. Shared equally, that is 5 units each.
Find the units that moved: Chloe goes from 7 units to 5, so 7 minus 5 is 2 units, and that is 24 marbles.
Find 1 unit: 24 divided by 2 is 12. Chloe's 7 units are 7 times 12, which is 84 marbles.
The marbles only moved across. So the total is still 10 blue units, before and after. And Chloe's 7 units are 84 marbles.
Practice questions with worked solutions
Question 1 is free to try. The other 4 open in the free trial, each with its full working.
Question 1 of 5 · Intermediate · free to tryTwo boxes contain 315 cards altogether. After 42 cards move from Box A to…Two boxes contain 315 cards…
Two boxes contain 315 cards altogether. After 42 cards move from Box A to Box B, Box B has twice as many cards as Box A. How many cards were in Box B at first?
In a total unchanged question, items move from one person or box to another, and nothing is added or thrown away.
What your child learns here
In a total unchanged question, items move from one person or box to another, and nothing is added or thrown away. This page applies the Primary 5 four operations of whole numbers to these before-and-after problem sums, with a bar model drawn for the end.
Check that nothing is bought, used up or thrown away, so the total before the move equals the total after it.
Draw the bars for the end, where the question links the two amounts with 'times as many', and cut the total into equal units.
Divide the total by the number of units to find one unit.
Undo the move to go back to the start: the giver gets the items back and the receiver loses them.
When one side gives to the other, the gap between them closes by twice the number moved.
Does the answer make sense?
The 315 cards are still 315 after the move. In the end Box B's 210 is twice Box A's 105, and 210 plus 105 is 315. Box B gained 42 cards, so at first it held fewer than 210: 168 cards, leaving 147 in Box A, and 168 plus 147 is 315 again.
How to practise these questions
Free Question 1 has 315 cards in two boxes; after 42 cards move from Box A to Box B, Box B has twice as many as Box A, and your child finds how many cards Box B had at first. The Intermediate questions train using the unchanged total to find one unit, undoing a move, and working out how many must be given so that both have the same number. The Challenge question follows counters through two moves between three trays. If your child is stuck, open its worked solution and redraw the bars for the end before going back to the start.
Questions parents ask
What does total unchanged mean? It means the items only change hands or boxes. No item is bought, used up or thrown away, so the sum of the two amounts is the same before and after.
Is total unchanged a ratio topic? Ratio is taught in Primary 6, where this idea comes back. Every question on this Primary 5 page is written with whole numbers and 'times as many', so the four operations and a bar model are enough.
Why draw the end of the story first? These questions usually link the two amounts only after the move, for example twice as many. Drawing that end gives equal units for the total, and one addition or subtraction then undoes the move.
