Before and after, when the difference does not change
P4 unchanged difference questions: recognise equal increases or decreases, track the fixed gap and use it to compare quantities before and after.
Questions in this lesson
Transcript
Aaron has three hundred and forty dollars and Bala has two hundred and twenty dollars. They each buy the same pair of sneakers. Aaron then has 4 times as much money as Bala. How much did the sneakers cost? Try it first. Pause if you like. Draw one bar for Aaron's money, three hundred and forty dollars. Draw a shorter bar for Bala's money, two hundred and twenty dollars. Look at the difference between their bars. Three hundred and forty minus two hundred and twenty is one hundred and twenty. Now they both pay the same price for the sneakers. The same amount comes off the end of each bar. Both bars get shorter by the same amount. So the difference never changes. It is still one hundred and twenty dollars. After paying, Aaron has 4 times as much money as Bala. So Bala's money is 1 unit, and Aaron's money is 4 units. Aaron has 3 more units than Bala. These 3 units are the difference. So 3 units is one hundred and twenty dollars. 1 unit is one hundred and twenty divided by 3, which is 40. So we write 40 dollars in every unit. Bala keeps 1 unit, which is 40 dollars. So Bala paid two hundred and twenty minus 40, which is one hundred and eighty dollars. So the sneakers cost one hundred and eighty dollars.
Jar A has 75 sweets and Jar B has 27 sweets. Mei puts the same number of sweets into each jar. Jar A then has twice as many sweets as Jar B. How many sweets did Mei put into each jar? Try it first. Pause if you like. Draw one bar for Jar A, 75 sweets. Draw a shorter bar for Jar B, 27 sweets. The difference between them is 75 minus 27, which is 48. Now Mei puts the same number of sweets into each jar. Both bars get longer by the same amount. So the difference never changes. It is still 48. Jar A then has twice as many sweets as Jar B. So Jar B is 1 unit, and Jar A is 2 units. Jar A has 1 more unit than Jar B. So 1 unit is the difference, 48. Jar B now has 48 sweets. It had 27 sweets at first. 48 minus 27 is 21. So Mei put 21 sweets into each jar. When both amounts go up or down by the same number, the difference stays the same.