## Overview

All of the pop-ups we have studied so far produce motion across the gutter, but not along it. Many of the pop-ups in commercially made books and cards can also produce motion along the gutter – up and down if the book is held upright. This unit explores this second type of pop-up mechanism and compares it with the first. Students first sort pop-ups according to the direction of motion. They then explore the differences in construction.

## Materials

For each group:
• Assorted pop-up books and cards, including pop-ups already made by students. These should include both simple and intermediate pop-ups
For each student:
As needed:

## Procedure

1. Dimensions and directions of motion: Distribute sample pop-ups and Post-its and show students how to attach flags along the fold lines. Using these flags, explore the directions that various kinds of pop-ups can move. Then ask the students to sort their pop-ups according to the kinds of motion they can make. If students have difficulty, suggest these two categories: (A) pop-ups that cannot move up-and-down as you hold the book facing you, and (B) those that can. See a video showing how the two kinds of pop-ups can move.
• Outcome: There are three dimensions in space and each one has two directions: back & forth, up & down, and in & out (towards you or away from you). All pop-ups can move back & forth as well as in & out, but only some can also move up & down.
2. How the hinge lines run. Review the names and locations of the four hinge lines. Ask students to look at the pop-ups in each of the two categories. How do the hinge lines run in each case? See  a video comparing the hinge lines in the two types of pop-up, another video on how lines can run in space and on a flat surface and a third video explaining why the two kinds of pop-ups work differently. Provide each student with the "Two Types of Pop-up" Worksheet for them to record their findings.
• Outcome: In Type A pop-ups, which cannot produce up & down motion, all four hinge lines are parallel. This type of pop-up is called a parallel-fold. In Type B pop-ups, which can move up & down as well as in & out and back & forth, all the hinge lines intersect at a point on the gutter. This pop-up is called an angle-fold, because the hine lines come together at an angle. The point where they intersect is called the vertex.

## Troubleshooting

Two common issues occur when students ...