In the lesson (The difference stays the same). And the difference never changed. In the lesson (The difference stays the same). The father is twice as old as the son.
Lesson videos, with the working
Lesson 1
The difference stays the same
2 min 13 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
Aaron has $340. Bala has $220. They each buy the same pair of sneakers. After they pay, Aaron's money to Bala's money is 8 : 3. How much did the sneakers cost?
The sneakers cost $148.
Ans: $148
How to solve it
Draw a bar for each person: Aaron 340 dollars and Bala 220 dollars.
Find the difference before anything happens: 340 minus 220 is 120.
The same price comes off each bar, so both bars get shorter together and the difference stays 120.
After paying, the ratio 8 to 3 means Aaron sticks out by 5 units, and that extra piece is the difference: 5 units is 120.
Find 1 unit: 120 divided by 5 is 24 dollars. Bala keeps 3 units, which is 3 times 24, or 72 dollars.
Bala started with 220, so the sneakers cost 220 minus 72, which is 148 dollars.
Both bars went down together. And the difference never changed.
Lesson 2
The difference stays the same
2 min 30 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
Question 1 of 8 · Basic · free to tryThe number of buttons in Tin A to the number in Tin B was in the ratio 9…The number of buttons in Tin A…
The number of buttons in Tin A to the number in Tin B was in the ratio 9 : 5. After 21 buttons were taken out of each tin, the ratio became 3 : 1. How many buttons were in Tin B at first?
How do you solve constant difference ratio questions in P6?
When the same amount is added to both quantities, or taken from both, the gap between them does not move.
What your child learns here
When the same amount is added to both quantities, or taken from both, the gap between them does not move. Age questions are the classic case. Your child learns to make that gap the same number of units in both ratios before finding 1 unit.
Recognise when both quantities change by the same amount, including the passing of years in age questions.
Rewrite both ratios so the difference has the same number of units.
Use the change in one quantity's units to find the value of 1 unit.
Applies equivalent ratios and missing terms to before-and-after word problems.
Does the answer make sense?
The gap stays fixed, so adding the same amount to both, like years to two ages, must bring the ratio closer to 1 : 1. Taking the same amount from both pushes the ratio further apart, and your child should see that what each loses is less than the smaller starting number.
How to practise these questions
The Basic questions train keeping the difference between two quantities fixed while both change. Intermediate questions apply this to longer before-and-after stories. Challenge questions need the fixed difference matched across two ratios with greater care. When the difference that stays is hard to use, read the written step-by-step solution.
Questions parents ask
Why do age ratio questions use a constant difference? Everyone gets older by the same number of years, so the gap between two people's ages never changes. That fixed gap becomes the same number of units in both ratios.
Is a constant difference question the same as a constant total question? No. In a constant total question something moves from one side to the other. In a constant difference question both sides go up, or both go down, by the same amount, so the first step is deciding which one the story describes.
Which syllabus outcomes does a constant difference question use? It applies equivalent ratios and finding the missing term in a pair of equivalent ratios, outcomes 1.2 and 1.6 of the MOE Primary 6 Ratio sub-strand, to a before-and-after story.
