Lesson 13

This activity has two parts: an introduction to the task and individual work time. In the first part, students read the design problem and ask clarifying questions, and then work with a partner or two to look at tent designs and specifications. Then, they work individually to design a tent, create necessary representations of it, calculate its surface area, and estimate of the amount of fabric needed to construct it.

As students work individually, circulate and focus your observations on two main goals:

1. Notice the strategies and mathematical ideas students use to complete the task. Are students:

   • decomposing or rearranging parts of their tent design to find the area? How?
   • drawing a net of their design?
   • labeling their drawings with measurements?
   • calculating area precisely?
   • using formulas they learned in this unit? How?
   • accounting for the areas of all surfaces of their tent design?
   • using square units for area measures?
2. To record the sizes (in terms of numbers of people accommodated) and shapes of individual tent designs. Use this information to arrange students into groups—by tent size—in the next activity.

Collect student work at the end of the session. Arrange for 2–3 students who have tents that accommodate the same number of people but different designs to work together (e.g., two students design tents for three people, but one designed a triangular prism and the other a pentagonal prism). Put their papers together to begin the second session.

Give students 1–2 minutes to read the task statement individually and ask any clarifying questions. At this point, students only need to understand that the tents need to accommodate same-sized sleeping bags and that there is not one right way to design them.

Next, arrange students in groups of 2. Give groups about 15 minutes to look at and discuss potential tent designs, tent specifications, and sleeping bag information. Tell students that the designs are provided for inspiration and reference, but students are not limited to them.

After partner discussions, give each student a copy of the Tent Design Planning Sheet from the blackline master. Give students quiet think time to sketch out their tent design, create necessary drawings, calculate surface area, and justify their estimate. Provide blank paper for students to use to draw their designs and access to their geometry toolkits. (Note that a scale drawing is not an expectation; scale factor is a grade 7 standard.)

Some students may find it challenging to develop and represent a three-dimensional object on paper. Ask them what might help them create or convey their design. Some may find it useful to think in two-dimensional terms and start by drawing a net. Others may wish to build a physical model of their design from paper or other flexible material, or to use a digital drawing tool. Encourage students to consider the tools at their disposal and choose those that would enable them to complete the task (MP5).

After students complete the task, engage students in a whole-class discussion. Ask students: “What were important things you had to think about in your design?”

Collect student work at the end of the session. Tell students they will continue to think about the problem and their proposed solution in the next activity.

Arrange for 2–3 students who have tents that accommodate the same number of people but have different designs to work together (e.g., two students designed tents for three people, but one designed a triangular prism and the other a pentagonal prism). Put their papers together to begin the second session.

This activity gives students a chance to explain and reflect on their work. In groups of 2–3, they share drawings of their tent design, an estimate of the amount of fabric needed, and the justification. They compare their creations with one or more peers. Students discuss not only the amount of fabric required, but also the effects that different designs have on that amount.

Prior to the session, identify 2–3 students who have tents that accommodate the same number of people but different designs (e.g., two students each design a 3-person tent, but one designed a triangular prism and the other a pentagonal prism). Put their papers from Part 1 together.

As students discuss in groups, notice how they reason about and communicate their work. Do they:

• provide justification for their measurements and choices?
• explain clearly their process of calculating surface area?
• see how the type of design affects the amount of fabric?
• compare their tents in terms of the differences in the measurements at the base and the height of tent?

Tell students that they will now reflect on and discuss their tents with another student who designed a tent for the same number of people but in a different way. Arrange students in the predetermined groups of 2–3 and return the presorted sets of papers to them.

Much of the discussion will take place within the groups. Once groups have had an opportunity to share their designs, reconvene as a class. One idea would be to display tent designs that used the most and the least amount of fabric. Also consider asking students to reflect on the following prompts:

• What design choices lead to using less fabric?
• What design choices lead to using more fabric?
• What are some ways that tents designed to accommodate the same number of people could use very different amounts of fabric?
• When calculating the surface area of your tent, what kinds of techniques from this unit did you find useful?