## Overview

The pop-ups we have made so far were attached directly to the book. Pop-up constructions can be more complex than this. This lesson explores “Stair-step” pop-ups, which are pop-ups built onto other pop-ups. Through making stair-step pop-ups and studying their properties, students are introduced to systems concepts and geometric forms.

## Materials

For each student:

## Procedure

1. Systems: Develop systems concepts: input, output, system, and subsystem. Ask students to complete the Inputs, Outputs and Systems Worksheet. See more information about systems.
• Outcome: A system has an input and an output. A pop-up is a system whose input is opening or closing the book, and whose output is the resulting motion of the pop-up.
2. Make a stair-step pop-up: Ask students if they think one pop-up could make another one move. See a video showing how to make a sequence of pop-ups.
3. Stair-step from an edge view: Review how to look at a pop-up from an edge view. Then ask students to look at their stair-step pop-ups from an edge view, in the 3/4-open, 1/2-open and 1/4-open positions. What shapes do they see? They should draw their findings on the Stair-step Pop-up Worksheet.  View a video showing what happens.
• Outcome: From an edge view of a stair-step pop-up, you see similar shapes repeated, from one pop-up to the next. The shapes change from a parallelogram to a rectangle and back to a parallelogram as you open and close the book.
4. System Diagram: At the bottom of the Stair-step Pop-up Worksheet are some prompts leading to a system diagram for the stair-step pop-up. See a video about system diagrams for pop-ups in series and parallel.
• Outcome: The system diagram for a stair-step pop-up shows how the output of one pop-up is the input to the next.

## Troubleshooting

The most common problem is that the pop-ups cling to the book, instead of rising above it, when the book opens or closes. See a video about how to address this problem.