This lesson develops an explanation for the Pop-up Computer result in Lesson 5. First, students predict how the pop-up will fit inside the book when it is closed; then they find out by assembling a pop-up inside a clear folder. The results will probably surprise them (and you)! This information leads to a visual picture of why A + B = C + D.
For each student:
1. When does the pop-up make A + B = C + D?
When you first tape a strip in the book, all you know is the strip length B + C. Lead a discussion about when and how the book decides on the spearate link lengths B & C. See a video illustrating this issue
- Outcome: The book separates B and C and forces A + B = C + D only when it closes.
2. Where does it hide?
To find out why A + B = C + D, we need to know what happens when the book is closed. The Worksheet asks students to predict where the pop-up "hides" when the book is closed. Students should draw their predictions in the middle column. To check their predictions, point out that they can't see inside the book when it's closed -- unless they have x-ray vision, like Superman! To solve this problem, we have invented the See-thru Book, which they can look inside when it's closed. See a video showing how to use the See-thru Book.
3. Discuss the results of the experiment
: Why does the pop-up get pushed over to the right as the book is closed? What is making it go there?
- Outcome: When the left page closes over the right page, it pushes the left page position and fold with it, making them move over to the right.
4. Why does A + B = C + D? Inside the See-thru Book, use markers to label A, B, C, and D. Then compare the distance A + B on one side with the distance C + D on the other side of the book.
See a video showing why A + B = C + D.
- Outcome: When the book is closed, A + B and C + D are on opposite sides of the book and both start and end at the same place, so they are equal.
The Parallel Fold Template
Worksheet: Where Does it Hide?