# 3.1: Introduction

**Which Boxes? – Balance-Equality**

**Teacher Notes**

Given a two-pan balance with one pan empty and a weight in the other pan, students determine which boxes from a set of two or three boxes when placed in the empty pan will cause the pans to balance. Since there is an unlimited number of boxes of each type, there is more than one set of boxes that make the pans balance. So, all problems have multiple solutions.

**Solutions**

**Which Boxes? 1**

**Which Boxes? 2**

**Which Boxes? 3**

**Which Boxes? 4**

**(Teacher Page) – You have lots of these boxes.**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain.**

**Which Boxes? 1**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain.**

**Which Boxes? 2**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain.**

**Which Boxes? 3**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain**

**Which Boxes? 4**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain**

**Extras for Experts: Which Boxes? – Balance-Equality**

**Solutions**

**Extra for Experts: Which Boxes? 1**

**Extra for Experts: Which Boxes? 2**

**Extras for Experts: Which Boxes? 1**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain.**

**Extras for Experts: Which Boxes? 2**

**Put boxes in the empty pan.**

**Make the pans balance.**

**Which boxes will you use?**

**Can you use a different set of boxes? Explain.**