Toilet paper is something we don’t think about much, except when it runs out. Then it’s an emergency! But toilet paper is a very cool math object. How long is a whole roll of it? How many times does the paper wrap around? How do they even make toilet paper? Most toilet paper comes from recycled paper. Regular old paper is thrown into water and mushed into a pulp, to wash out ink and dirt. Then rollers smush the pulp into a really thin sheet. Once it dries, the soft paper is rolled onto tubes that are more than 5 feet long, probably longer than you! At the end, they chop that into little rolls. Now let’s see how those squares add up.
Lace up: If you’re counting 5 toilet paper squares, what numbers do you say? Count out loud!
Jog: If you have a pack of 6 toilet paper rolls, and you and your friend roll 2 of them down the hall in a race, how many rolls do you have left?
Sprint: Toilet paper comes in lots of different size packs. If you see packages with 24 rolls, 12 rolls, 48 rolls, and 36 rolls, can you put those numbers in descending order from greatest to least?
Hurdle: If you pull the toilet paper really hard to make it all fly off, and you whip off 40 squares on the 1st pull and 1/2 as many on the 2nd pull, how many squares total do you spin off?
High Jump: If a roll has 240 squares, each 4 inches long, how long is the whole roll in feet? (Hint: 4 inches is a nice neat fraction of 12 inches…)
Pole Vault: If you spin out 20 layers of paper, and the 1st 4 layers have 8 squares each, the next 4 layers have 7 squares each, then 6 squares each, 5 squares each, and finally the last 4 layers have 4 squares each…can you find the shortcut to figure out how many squares you pulled off?
Answers:
Lace up: Count the squares: 1, 2, 3, 4, 5.
Jog: 4 rolls.
Sprint: From greatest to least: 48, 36, 24, 12 rolls!
Hurdle: 60 squares (40+20).
High Jump: 80 feet! (or 960 inches).
Pole Vault: 120 squares. If you don’t feel like adding up all those little numbers, you can see that having 8 squares on a layer and having 4 on another is the same as each layer having 6 squares. Same for 5 squares vs. 7 squares on the same number of layers: it’s the same as having 6 on all of them. So they average out to 6 squares per layer for 20 layers.
