# 2.5 Surface area of rectangular prisms

## Learning outcomes

Students will understand how to use nets (diagrams) to calculate the surface area of rectangular prisms.

## Teacher preparation

### Time required for lesson

Approximately 55 minutes. Homework time may be needed to complete worksheet.

### Materials needed

- Student handouts:
- Blank graph paper
- Cardboard box factory worksheet (two pages)

- Transparency copy of cardboard box factory worksheet
- Cardboard box factory worksheet answer key
- Various cardboard or paperboard boxes — 10-20 boxes of different sizes, enough for each group of students to have two. (You may bring boxes from home or invite students to brings boxes from home for extra credit prior to beginning the lesson.)
- Rulers
- Overhead projector and pens
- Calculators (optional)

## Pre-activities

Prior to starting this lesson, you will need to cut one of each pair of boxes to form a “net” or flattened version of the box.

## Activities

- Show students the sample boxes. Ask students how companies that make packaging determine how much material they need for each box they make. Lead the students to understand that the box-manufacturing companies must calculate surface area. Ask the students to brainstorm other careers in which people may use surface area in their lines of work. (Answers may include other packaging companies, cabinet makers, construction workers, landscapers, engineers, etc.) Write these careers on the board. (5-10 minutes)
- Put students in small groups. (The number of groups may depend on the number of boxes available. There should be two boxes for each group — one flattened and one in its three-dimensional form.) Give each group a three-dimensional box. (Don’t give them a flattened box yet.) Ask the students what measurements must be known in order to calculate how much material is needed to make a given box. (They should come up with height, width, and length.) Ask the students if there would be an easier way to take the measurements. (This discussion should lead them to say, “A 2-dimensional or flat box pattern.”) (5-10 minutes)
- Give each group a flattened box. Have students draw a “net” representing the box pattern on their graph paper. (One square on the graph paper should equal one inch of the box.) Have the students record the dimensions of each side of the box on the graph paper. (5-10 minutes)
- Have the students calculate the area of each rectangular space they drew, and instruct them to add each area together to find the total surfance area. (5-10 minutes.)
- Independent Practice: Hand out copies of the cardboard box factory worksheet to the students. Have students complete the worksheet using the information they learned in class. (15 minutes)
- Close the lesson with a discussion about jobs that require determining surface area in three dimensions — not just one surface at a time. Examples may include postal workers loading multiple packages in a limited amount of space on a boat heading overseas and grocers stocking shelves with cereal boxes in a limited amount of shelf space.
- As an extra-credit assignment, ask students to answer the following question of the back of their worksheet: What conclusions about surface area can you come up with after having completed this activity/worksheet? (Hint: Think formula!)

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 7

**Goal 1**: Number and Operations - The learner will understand and compute with rational numbers.**Objective 1.02**: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.- Analyze computational strategies.
- Describe the effect of operations on size.
- Estimate the results of computations.
- Judge the reasonableness of solutions.

**Goal 3**: Geometry - The learner will understand and use properties and relationships in geometry.**Objective 3.01**: Using three-dimensional figures:- Identify, describe, and draw from various views (top, side, front, corner).
- Build from various views.
- Describe cross-sectional views.

- Common Core State Standards
- Mathematics (2010)
#### Grade 6

- Geometry
- 6.G.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

#### Grade 7

- 7.G.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

- Geometry