Before and after, when one quantity does not change
P4 one quantity unchanged problems: use a fixed amount to connect before-and-after comparisons when only the other quantity increases or decreases.
Questions in this lesson
Transcript
At first, there were 6 times as many storybooks as comic books on a shelf. After 18 more comic books were added, there were twice as many storybooks as comic books. How many storybooks are on the shelf? Try it first. Pause if you like. Draw what we know at first. The comic books are 1 unit. The storybooks are 6 times as many, so they are 6 units. Before anything changes, look for the thing that stays the same. Nobody touches the storybooks. So their bar stays exactly as it is. Now the 18 new comic books arrive. They are new, so the new piece is purple. We don't know yet how many units it covers. In the end, there are twice as many storybooks as comic books. So the comic books now reach half of the storybooks bar. Half of 6 units is 3 units. So the comic books are now 3 units. The first unit is the blue one we started with. The purple piece covers the other 2. So 2 units is 18. 1 unit is 18 divided by 2, which is 9. So we write 9 in every unit. The storybooks are 6 units. 6 times 9 is 54. Check. 9 plus 18 is 27 comic books in the end. 2 times 27 is 54, the storybooks. So there are 54 storybooks on the shelf. The storybooks never changed, and that is what made the units match.