The idea in brief. A transfer changes both holdings, so the difference changes by twice the transferred amount. Giving one item across changes the difference by two items. In the lesson. In an earlier lesson, the extra part of the longer bar was the difference. Today, we will see why giving shells changes the difference by twice as many. When one person gives shells to the other, the difference changes by twice as many.
Lesson video, with the working
Transfer and difference
5 min 00 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Mei has 30 shells and Kavin has 18 shells. How many shells must Mei give Kavin so they have equal numbers of shells?
Difference = 30 − 18 = 12
Shells Mei gives = 12 ÷ 2 = 6
Ans: 6 shells
Example 1 of 2
Siti has 14 more shells than Bala. Siti gives Bala 5 shells. How many more shells does Siti have than Bala now?
Difference gets smaller by 2 × 5 = 10
Difference now = 14 − 10 = 4
Ans: 4 shells
Example 2 of 2
Ravi has 34 shells. Wei Jie has 20 shells. Ravi gives Wei Jie some shells. Then Ravi has 4 more shells than Wei Jie. How many shells does Ravi give Wei Jie?
Difference at first = 34 − 20 = 14
Difference gets smaller by 14 − 4 = 10
Shells Ravi gives = 10 ÷ 2 = 5
Ans: 5 shells
How to solve it
Find the difference at first: 30 minus 18 is 12.
When one child gives shells to the other, one bar gets shorter and the other longer, so the gap closes from both ends.
So the difference changes by 2 times the number given.
If you know the shells given, multiply by 2: giving 5 shells makes the difference 10 smaller, so 14 minus 10 is 4.
If you know how much the difference changes, divide by 2. To make 30 and 18 equal, 12 divided by 2 is 6 shells.
Check by working out both amounts: 30 minus 6 is 24, and 18 plus 6 is 24.
When one person gives shells to the other, the difference changes by twice as many.
Practice questions with worked solutions
Question 1 is free to try. The other 11 open in the free trial, each with its solution film.
Why do P3 transfer and difference word problems change the gap by twice the amount?
When one person gives some items to another, the total stays the same but the gap between them closes from both ends.
What your child learns here
When one person gives some items to another, the total stays the same but the gap between them closes from both ends. This page applies Primary 3 subtraction, multiplication and division within the tables to these transfer word problems.
Find the difference before any items move.
See that each item given makes one bar 1 shorter and the other 1 longer, so the difference changes by 2.
Multiply the amount given by 2 to find the change in the difference.
Divide a change in the difference by 2 to find how many were given, including when both end up equal.
Recover the receiver's starting amount by subtracting what was given.
Does the answer make sense?
Moving items from A to B leaves the total unchanged and shrinks the gap by twice the number moved, so a new difference must be smaller than the old one. Your child can also check that the amount moved to make two trays or containers equal is half the starting gap, never the whole gap.
How to practise these questions
The Basic questions practise seeing that moving an amount changes the difference by twice that amount. The Intermediate questions add finding how many must move to make two amounts equal or reach a set difference. The Challenge questions combine a transfer with a total or a second change, so the bars must be redrawn. When a transfer question stalls, play its solution film and come back to it later from Revision.
Questions parents ask
Why does the difference change by twice the amount given? The giver's amount goes down and the receiver's goes up by the same number, so the gap closes from both ends. Giving 1 item changes the difference by 2. The lesson film on this page shows this with one bar getting shorter as the other gets longer.
Is internal transfer in the Primary 3 syllabus? The P3 syllabus does not list transfer questions by name. They apply the syllabus skills of subtraction, and of multiplying and dividing within the tables, to a story where items move between two people.
How can I show my P3 child how internal transfer works? Use real objects: two piles of coins or sweets, moved one at a time while your child says the new gap. Seeing the gap shrink by 2 at each move makes the rule easier to trust than hearing it.
