### Summary

In this lesson, students will explore how to find the surface area of prisms and pyramids. Students will discover the general formulas for finding surface area of prisms and pyramids and are introduced to the surface area of spheres and hemispheres. Students will apply what they learn to create a composite model and find the surface area of their model. Lastly, students will also apply their knowledge of surface area to a real-world situation.

### Essential Question(s)

Why would it be useful to find the surface area?

### Snapshot

**Engage**

Students use a modified Quick Write strategy to answer the question "*What would you need to know if you wanted to paint your room?*" through Mentimeter.

**Explore**

Students discover the general formula for finding surface area of prisms and pyramids by analyzing patterns of solids they measure.

**Explain**

Students complete a foldable during class discussion on how to use the formulas for finding the surface area of prisms, pyramids, and other solids.

**Extend**

Students apply what they have learned to create a composite model and find the surface area of their model.

**Evaluate**

Students apply their knowledge of surface area to the real world.

### Materials

Lesson Slides (attached)

Scratching the Surface - Red packet (attached; one per red group; printed front only)

Scratching the Surface - Blue packet (attached; one per blue group; printed front only)

Foldable handout (attached; one per student; printed front/back)

Model Foldable document (attached; for teacher use)

Creating Composites (attached; one per group of 3; printed front only)

Exit Ticket (attached; one half per student; printed front only)

Geometric Solids, at least including: triangular, pentagonal, and hexagonal prisms; triangular, rectangular, pentagonal, and hexagonal pyramids; and cylinder

Nets handout (attached; optional; print front only)

rulers

scientific calculators

glue (or tape)

scissors

paper

### Engage

5 Minute(s)

Introduce the lesson using the attached **Lesson Slides**. Display **slide 3** to share the lesson's essential question with students. Go to **slide 4** to share the lesson's learning objectives. Review each of these with students to the extent you feel necessary.

Go to **slide 5**. Direct students to go to menti.com, enter the generated code, and answer the following question: *What would you need to know if you wanted to paint your room? *Encourage students to write as much as they can using a modified Quick Write strategy. As students enter their responses, display the results for students to see. Have a class discussion about student responses.

### Explore

30 Minute(s)

Display** slide 6 **and direct the students to grab a ruler and pick a solid. Then have students get the paper from the **Scratching the Surface** packet that corresponds with their chosen solid.

Instruct students to identify, measure, and calculate the surface area of their solid.

Display **slide 7**. Direct students to take their materials (handout, solid, and ruler) and find one or more classmates who have the same solid. Instruct students to compare their results and work. Remind them that their answers might differ slightly based on their measurements and rounding. Guide students to compare their work for how they found their surface area regardless of their final results. Students should use their solid and ruler to re-measure if needed.

Display **slide 8**. Direct students to take their materials (handout, solid, and ruler) and go find everyone who has their same type of solid: prism or pyramid.

Show **slide 9** and instruct students to work with their group to find the pattern to make a general formula for the surface area for their solid: prism or pyramid. Direct students to use words to write a formula for the surface area of their type of solid.

### Explain

30 Minute(s)

Show **slide 10** for students to see the connection between their formulas in words to the algebraic formulas. Have students compare what they have on their handout and what they see on the slide.

Give each student a copy of the **Foldable** handout and transition through **slides 11–17**. Use these slides to show students how to prepare their foldable.

Show **slide 18** for students to see what the variables mean in the surface area of a prism formula. Direct students to find an Elbow Partner to fill out the prisms section of the foldable. Have students fill in the blanks on the left and complete the example on the right using the formula they just learned.

After a few minutes, have the class come together to discuss what they wrote and compare results for the surface area of the given prism.

Show **slide 19** for students to see what the variables mean in the surface area of a pyramid formula. Students work with their elbow partner to fill out the pyramids section of the foldable. Have students fill in the blanks on the left and complete the example on the right using the formula they just learned.

After a few minutes, have the class come together to discuss what they wrote and compare results for the surface area of the given pyramid.

Show **slide 20** for students to see what the variable means in the surface area formulas for a sphere and hemisphere. Students work with their elbow partner to fill out the other solids section of the foldable. Have students fill in the blanks on the left and complete the example on the right using the formula they just learned.

After a few minutes, have the class come together to discuss what they wrote and compare results for the surface area of the given solid.

Now direct students to glue their Foldable into their math notebook, if that is a classroom norm.

### Extend

30 Minute(s)

Display **slide 21** and direct students to get into groups of 3 or assign groups. Pass out a piece of blank paper and one copy of the **Creating Composites** handout to each group of students. Instruct students to select one solid per columns 1–4. Tell students to circle their selected solids on their handout and then create a model using their selected solids. Challenge students to also use a solid from the Extra Challenge column in their models.

Show **slide 22** and instruct students to sketch only their model on a blank sheet of paper and find the surface area on the back of their Creating Composites handout.

### Evaluate

10 Minute(s)

Use the Exit Ticket strategy to individually assess what students have learned from the lesson. Go to **slide 23** and pass out the **Exit Ticket** handout to each student. Students are given a scenario of painting a room and are asked to find the area to be painted and the number of gallons of paint needed.

Collect the handout and use responses to see what misconceptions still exist.

### Resources

K20 Center. (n.d.). Bell ringers and exit tickets. Strategies. https://learn.k20center.ou.edu/strategy/125

K20 Center. (n.d.). Quick write. Strategies. https://learn.k20center.ou.edu/strategy/1127

K20 Center. (n.d.). Mentimeter. Tech Tools. https://learn.k20center.ou.edu/tech-tool/645