The idea in brief. Equal starting holdings mean the final difference is caused entirely by the different changes. Keep the two changes separate. The final difference comes from both of them. In the lesson. In the last lesson, one amount stayed the same while the other changed. Today, we will see how two changes make a difference. When two amounts start equal, only the changes make the difference.
Lesson video, with the working
Equal at first
5 min 28 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Mei and Kavin had equal numbers of shells at first. Mei received 8 shells from another box. Kavin gave 4 shells to a display. Mei then had 3 times as many shells as Kavin. How many shells did each have at first?
Difference now = 8 + 4 = 12
3 units − 1 unit = 2 units
2 units = 12
1 unit = 12 ÷ 2 = 6
Kavin's shells at first = 6 + 4 = 10
Ans: 10 shells
Example 1 of 2
Siti and Bala had equal numbers of shells at first. Siti gave away 5 shells. Bala gave away 13 shells. Then Siti had 3 times as many shells as Bala. How many shells did each have at first?
Difference now = 13 − 5 = 8
3 units − 1 unit = 2 units
2 units = 8
1 unit = 8 ÷ 2 = 4
Bala's shells at first = 4 + 13 = 17
Ans: 17 shells
Example 2 of 2
Ravi and Wei Jie had equal numbers of shells at first. Ravi received 9 shells from another box. Wei Jie gave 3 shells to a display. Ravi then had 4 times as many shells as Wei Jie. How many shells did each have at first?
Difference now = 9 + 3 = 12
4 units − 1 unit = 3 units
3 units = 12
1 unit = 12 ÷ 3 = 4
Wei Jie's shells at first = 4 + 3 = 7
Ans: 7 shells
How to solve it
They had equal amounts at first, so draw two equal bars that end at the same place.
Show each change on its bar. A gain makes the bar grow. A loss marks off the end.
Find the difference now: 8 plus 4 is 12 when one gains and one loses. 13 minus 5 is 8 when both lose.
Mei has 3 units and Kavin has 1. The 2 extra units are 12 shells, so 1 unit is 12 divided by 2, or 6.
Add back what the smaller bar lost to find each amount at first: 6 plus 4 is 10.
When two amounts start equal, only the changes make the difference.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its solution film.
Question 1 of 11 · Basic · free to tryTwo classes had equal numbers of reward cards. Class A received 21 more…Two classes had equal numbers of…
Two classes had equal numbers of reward cards. Class A received 21 more cards and Class B used 9 cards. How many more cards did A have than B afterwards?
This page applies Primary 3 multiplication and division to a before-and-after word problem: two people start with the same amount, each changes by a different amount, and one ends up a number of times the other.
What your child learns here
This page applies Primary 3 multiplication and division to a before-and-after word problem: two people start with the same amount, each changes by a different amount, and one ends up a number of times the other. It builds on the unit bars from the earlier subtopics in this chapter.
Draw two equal bars for the start, then show each change on its own bar.
Work out the gap at the end from the two changes: add them when one gains and one loses, and find their difference when both lose.
Match that gap to units, such as 3 units minus 1 unit making 2 units, and find one unit by division within the tables.
Go back to the starting amount by putting back what was given away or removing what was received.
Does the answer make sense?
Both amounts started equal, so the gap at the end comes only from the two changes: your child adds them when one gains and the other loses, and finds their difference when both lose. Each starting amount must also be larger than anything removed from it, or that box or stall would run out.
How to practise these questions
The Basic questions practise drawing two equal bars and showing each change. The Intermediate questions add a times relationship after the changes, so units must be found from the bars. The Challenge questions give the changes in less direct steps, so your child must track both amounts with care. When an equal-start question is stuck, view its solution film together and try again later from Revision.
Questions parents ask
What does 'equal at first' mean in a word problem? Both people start with the same amount. Because the start is equal, the gap at the end comes only from the different changes, so it can be found without knowing the starting amount.
How do I explain equal at first questions to my P3 child? Start with two equal piles of objects and make the changes in front of your child. Ask how far apart the piles are and where that gap came from. Then draw the same story as two equal bars with the changes marked.
Which P3 skills does this subtopic use? Addition and subtraction to find the gap, and multiplying and dividing within the tables to find one unit, both from the P3 syllabus. The unit bars come from the earlier subtopics in this chapter.
