SWBAT use dissection strategies to find the area of a complex shape and calculate living area per inhabitant. Students will understand the meaning of density as it relates to area.

To Martian colonists living in a confined space for many months, every square foot counts. Students find out just how much.

14 minutes

The warm-up prompt for this lesson asks students to explain how they can find the area of a complex shape, without counting individual unit squares. I ask students to follow our Team Warm-up routine, which involves sharing their responses with the other members of their cooperative learning team. I choose students at random to write the team's chosen response on the board. I encourage them to explain their thinking by showing work, or by writing a bulletized explanation.

I review the team responses with the class. Most will probably involve some sort of dissection strategy. I ask the class which postulate about area measurement a dissection strategy relies on (the Area Addition Postulate).

I display the Agenda and Learning Targets for the lesson and briefly review them with the class. Today, we will use strategies like these to find area and solve a real-world problem.

**Life On Mars**

To motivate the problem, I display the slide which has a link to a National Geographic video (3 minutes) about what life will be like for the first colonists on Mars.

**Video URL**: http://video.nationalgeographic.com/video/mission-mars-sci (accessed August 8, 2014)

15 minutes

I distribute the handout for the activity, one per pair of students. I display the slide as I give instructions. I ask students to work in pairs, so that they will talk about the problem and decide together on how to approach it (**MP1, MP4, MP6, MP7**). The time limit is intended to be short enough that students will need to divide up the work in order to finish in the time limit. As students get to work, I display a digital countdown timer on the front board.

As students are working, I circulate. I offer encouragement, and try to ensure that every student is engaged. If one student is taking the lead, can his or her partner check the computations for accuracy?

My focus is to plan the class discussion on problem-solving strategies that will follow. I use the Strategy Talk Planner to take notes on which students are trying which approach and to decide on a sequence in which to present different strategies.

20 minutes

The **Strategy Talk** is held as a whole class discussion. The object is to share and evaluate different strategies for finding the area of a complex shape (**MP3)**. To encourage student participation and enforce accountable talk, I may use a Math Ball format. I display a slide while giving instructions.

After displaying a student solution using the overhead camera, I ask students to discuss it with their cooperative learning teams (1-2 minutes) before opening the floor for a general discussion.

Questioning Strategies

- How did the students approach the problem as a whole? What was their strategy?
- What are the students doing here? (This helps students who may have trouble reading the work on the slide.)
- Did this strategy give an accurate result?
- Did this strategy give a precise result?
- Could this strategy be used on other problems, or does it only apply here?

It helps to save student solutions from prior sections and have them on hand. They can be used as examples if no one in that section tried a similar strategy.

5 minutes

The prompt asks students to name the postulate about area measurement that they are applying whenever they use a dissection strategy. This reinforces the warm-up problem. The lesson close follows our **individual size-up routine**, and students write their answers in their Learning Journals.

**Homework**

For homework, I assign problems #13-15 of Homework Set 1 for this unit. Problem #13 refers to the proof of the Pythagorean Theorem students analyzed earlier in the week. The second half of the problem is an extension for students who are ready to use algebra in a proof. Problem #14 reviews properties of isosceles triangles and using triangle congruence theorems in a proof. Problem #15 offers additional practice using the Pythagorean Theorem to find the missing side of a triangle.

These problems are not essential for the following lessons, because I may omit this lesson or move it to make the schedule work better (for example, to avoid giving the students the unit quiz on a Monday).