Nets Reveal Surface Area

Overview

In this third lesson of the eight-lesson unit, students connect two-dimensional nets to three-dimensional rectangular prisms. They identify faces, bases, edges, and tabs, then calculate surface area by finding and adding the areas of all exterior faces.

Learning intentions

Students will:

• identify the faces, bases, edges, and tabs of a rectangular-prism net;
• test whether a two-dimensional diagram folds into a rectangular prism;
• calculate the surface area of a rectangular prism using square units;
• explain how a net represents every exterior face of a prism.

Success criteria

• I can label the faces, bases, edges, and tabs on a prism net.
• I can decide whether a net will fold into a rectangular prism and explain why.
• I can calculate the area of each face and add the areas accurately.
• I can include appropriate square units in my answer.

Curriculum links

• Shape and Space — visualize and construct nets of three-dimensional objects.
• Measurement — determine and apply strategies for calculating surface area.
• Mathematical reasoning — make and justify predictions about whether a net forms a prism.
• Communication and representation — label diagrams and explain mathematical thinking using appropriate units.

Lesson structure (30 minutes)

1. 0–4 min · Hook and connection. Display a closed rectangular box and ask, “If the box were opened without tearing or overlapping, what two-dimensional shape would it make?” Open with the hook and lesson question and invite students to sketch a prediction individually before sharing with a partner. Briefly connect to the previous lesson’s work with similar shapes and dimensions.

2. 4–9 min · Direct teach: parts of a net. Use the labelled net and vocabulary slides to show that a net is a two-dimensional arrangement of faces that can fold into a three-dimensional object. Model identifying the two congruent bases, four rectangular side faces, fold edges, exterior edges, and tabs; clarify that tabs help hold a model together but are not part of the prism’s surface area. Students copy a quick labelled net or annotate the teacher’s projected example.

3. 9–14 min · Predict and test. Demonstrate safe handling: carry scissors point-down, cut away from the body, keep materials on a cutting mat, and return scissors when finished. In pairs, students examine the nets on the net-classification and surface-area worksheet, predict which will form a rectangular prism, and justify one prediction using face placement, matching edges, or overlapping faces. Students cut and fold one assigned net, checking whether faces meet correctly and tabs remain outside the solid.

4. 14–20 min · Model surface area. Display the worked rectangular-prism example. Model a prism measuring 6 cm by 4 cm by 3 cm: identify the three pairs of congruent faces, calculate (2(6×4)+2(6×3)+2(4×3)=108\text{ cm}^2), and emphasize that surface area is the total area of the exterior faces, not the volume. Students highlight matching pairs on their net and complete one guided example on the worksheet.

5. 20–27 min · Independent application. Students complete Worksheet 5/6, labelling each face and using square units for each surface-area calculation. Circulate and check that students are counting all six faces once, using dimensions from the net accurately, and not including tabs. Ask selected students to explain how their net shows the two equal bases and four side faces. Early finishers write a second valid net arrangement for the same prism and explain what remains unchanged.

6. 27–30 min · Plenary and exit check. Return to the summary and exit-question slide. Students answer: “A prism has dimensions 5 cm, 2 cm, and 4 cm. What is its surface area, and how do you know all faces were included?” Collect responses or have students show them on mini-whiteboards. Address common errors, especially confusing surface area with volume or counting tabs.

Resources

• the nets and surface-area teaching deck
• the net-classification and surface-area worksheet
• Pre-cut or photocopied rectangular-prism nets
• Cardstock or construction paper
• Scissors
• Cutting mats
• Rulers and pencils
• Glue sticks or tape
• Mini-whiteboards or scrap paper
• Document camera or projector

Assessment

• Listen during pair predictions for correct use of face, base, edge, tab, fold, and overlap.
• Check constructed nets and worksheet responses for accurate labelling, complete face coverage, correct calculations, and square units.
• Use the final problem as an exit ticket; sort responses into secure, developing, and requiring reteaching.

Differentiation

• Provide a partially labelled net, a face-area table, and the prompt “There are ___ pairs of congruent faces” for students needing support.
• Allow students to use colour coding: one colour for each pair of equal faces and a separate mark for tabs.
• For students with fine-motor, visual, or mobility needs, provide pre-cut nets, larger diagrams, a peer cutting partner, or a digital foldable model; read instructions aloud and give extra processing time.
• Support EAL learners with illustrated vocabulary and sentence frames such as “This net works because ___” and “The surface area is ___ square units because ___.”
• Challenge students to compare two different valid nets for the same prism and prove that both produce the same surface area.