Before and after, when the total does not change
P4 unchanged total questions: follow a transfer between two quantities, identify what stays fixed and use before-and-after information to find amounts.
Questions in this lesson
Transcript
Chloe had 5 times as many marbles as Marcus. Chloe gave Marcus 24 marbles. Then they had the same number of marbles. How many marbles did Chloe have at first? Try it first. Pause if you like. Draw what we know. Marcus has 1 unit. Chloe has 5 times as many, so Chloe has 5 units. Moving marbles from one child to the other does not change the total. Altogether, 5 units plus 1 unit is 6 units. Chloe gives Marcus 24 marbles. Nothing is added, and nothing is thrown away. So the total is still 6 units. In the end, they have the same number of marbles. 6 units divided by 2 is 3 units each. Chloe started with 5 units and ends with 3 units. 5 units minus 3 units is 2 units. So her last 2 units move across to Marcus. Those 2 units are the 24 marbles she gave. So 2 units is 24. 1 unit is 24 divided by 2, which is 12. So we write 12 in every unit. Chloe had 5 units at first. 5 times 12 is 60. Check. Chloe ends with 60 minus 24, which is 36. Marcus ends with 12 plus 24, which is 36. They have the same number each. So Chloe had 60 marbles at first. The marbles only moved across, so the total stayed the same all along.