# Activity 12C: Using the Moving & Additivity Principles

- Author:
- Trevor Leach, Erika Bratcher

**In this activity, you will use the moving and additivity principles (one or both) to determine the area of the L-shaped region in**

__PART A DIRECTIONS:__

__four__**ways. In each case, you will explain your reasoning and write and evaluate an algebraic expression that fits with the strategy.**

__different__**I have given you a hint on what type of strategy you should apply in each case!**

## Strategy #1: A simple subdividing strategy

## Strategy #1 Explanation

a) Explain your reasoning for Strategy 1. Which principle(s) did you use? b) Write and evaluate an algebraic expression that fits with this strategy. Notice the button on your response box. This button allows you to write mathematical expressions.

## Way #2: A takeaway strategy

## Strategy #2 Explanation

a) Explain your reasoning for Strategy 2. Which principle(s) did you use? b) Write and evaluate an algebraic expression that fits with this strategy. Notice the button on your response box. This button allows you to write mathematical expressions.

## Strategy #3: A move and reattach strategy

## Strategy #3 Explanation

a) Explain your reasoning for Strategy 3. Which principle(s) did you use? b) Write and evaluate an algebraic expression that fits with this strategy. Notice the button on your response box. This button allows you to write mathematical expressions.

## Strategy #4: A combine two copies and take half strategy

## Strategy #4 Explanation

a) Explain your reasoning for Strategy 4. Which principle(s) did you use? b) Write and evaluate an algebraic expression that fits with this strategy. Notice the button on your response box. This button allows you to write mathematical expressions.

**You will use the moving or additivity principles (one or both) to determine the area of the shaded square, which is inside the 2-unit-by-2-unit square, in**

__PART B DIRECTIONS:__**two**different ways. In each case, you will explain your reasoning.

## Way #1

## Way #1 Explanation

Explain your reasoning. What principle(s) did you use? Draw on your diagram and label what is appropriate.

## Way #2

## Way #2 Explanation

Explain your reasoning. What principle(s) did you use? Draw on your diagram and label what is appropriate.