12C: Using the Moving & Additivity Principles

Part A: Directions

In this activity, you will use the moving and additivity principles (one or both) to determine the area of the L-shaped region in four different ways. In each case, you will explain your reasoning and write and evaluate an algebraic expression that fits with the strategy. 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.

Strategy #2: A takeaway strategy (Hint: The polygon tool is very useful)

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.

Part B: Directions

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 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