Nets: Flat to Solid

Overview

In this third lesson of Similarity to Solid Design, students connect 2-D faces to 3-D solids. They recognise, test, and construct nets for rectangular prisms, triangular prisms, and cylinders, using folding, matching dimensions, and checking for overlaps or gaps.

Learning intentions

Students will:

• recognise nets for rectangular prisms, triangular prisms, and cylinders
• explain how a net folds to form a 3-D solid
• construct and test nets using accurate folds and matching dimensions
• identify why a proposed net is possible or impossible

Success criteria

• I can identify the faces, edges, and vertices of a prism.
• I can name the faces needed for a rectangular prism, triangular prism, or cylinder.
• I can test whether a net folds into a solid without overlaps or gaps.
• I can explain one rule for checking a net.

Curriculum links

• Alberta Mathematics (7–9): connecting concrete experiences to abstract geometric concepts
• Alberta K–9 Mathematics Achievement Indicators: describing and constructing 3-D objects from 2-D representations
• Alberta Mathematics K–12 Scope and Sequence: geometric properties, relationships, and formulas
• Alberta Mathematics (7–9): communicating mathematical reasoning using appropriate symbols, diagrams, and vocabulary

Lesson structure (30 minutes)

1. 0–3 min · Warm-up: inspect a prism. Teacher displays a cereal-box rectangular prism and asks students to name its faces, edges, and vertices, using the hook and retrieval slides to show a clear photograph and labelled diagram. Students discuss with a partner, then identify the numbers of each feature and predict what faces would appear if the box were opened flat.

2. 3–10 min · Mini-lesson: define and model nets. Teacher opens the nets teaching slides and demonstrates that a net is a 3-D solid opened flat; fold lines must create the solid without overlaps or gaps. Students record the DOODLE note: draw cut lines as solid lines and fold lines as dashed lines. Teacher explicitly models the required faces:

• rectangular prism: 6 rectangles
• triangular prism: 2 congruent triangles and 3 rectangles
• cylinder: 2 circles and 1 rectangle, with the rectangle’s length equal to the circumference, (2\pi r) Students identify which edges meet after folding and explain why a cylinder’s rectangle length is not simply its radius or diameter.

3. 10–18 min · Guided practice: cut, fold, and check. Teacher demonstrates safe tool use, then gives each group of four or five cardstock sample nets, scissors, rulers, tape, and a supply-manager role. Students cut and fold the samples while seated, marking pairs of faces or edges that meet. They test each net for required faces, matching shared-edge dimensions, and overlaps or gaps. Teacher circulates and asks: “Which faces become bases?”, “Which edges meet?”, and “What makes this net impossible?” Students revise one sample where needed and prepare one correct net to show.

4. 18–25 min · Independent practice: match and justify. Teacher distributes Worksheet C—Nets Match and directs students to work independently. Students match each net to its solid, identify impossible nets, and write a brief reason using the checks: all required faces are present, shared edges have matching dimensions, and folding creates no overlaps or gaps. Early finishers sketch a second possible net for one prism on the back.

5. 25–27 min · Formative assessment: show and explain. Teacher displays the checking and response slides and asks students to hold up one correct folded or flat net. Selected students explain one fold or one pair of faces that meet. Teacher quickly notes misconceptions, especially missing circular bases, confusing an edge length with a face width, or accepting a net with overlapping faces.

6. 27–30 min · Closure: “fold, don’t guess.” Teacher revisits the plenary rule slide and asks students to record one net-check rule on their worksheet. Students complete the sentence: “A net is possible when…” and share one response before packing away tools safely.

Resources

• the nets lesson slide deck
• Worksheet C—Nets Match
• Cereal-box rectangular prism
• Cardstock sample nets for rectangular prisms, triangular prisms, and cylinders
• Scissors, rulers, tape, and glue sticks or small amounts of liquid glue
• Pencils, coloured pencils, and scrap bins
• One supply-manager role per group
• Optional pre-labelled and dotted-line net templates

Assessment

• During the warm-up and mini-lesson, question students about faces, edges, vertices, congruence, circumference, and which faces meet.
• During group work, observe whether students cut, fold, compare dimensions, and justify a net using the three validity checks.
• Use Worksheet C and the show-and-explain check as evidence. A correct response must include all required faces, no overlapping faces when folded, and matching dimensions at shared edges.

Differentiation

• Support students with dotted fold lines, pre-cut or partly completed templates, pre-labelled faces, visual diagrams, and a partner rehearsal before writing.
• Provide sentence starters: “This net is possible because…”, “These faces meet along…”, and “This net is impossible because…”.
• For EAL learners, pair spoken explanations with labelled diagrams and explicitly model net, face, edge, vertex, congruent, base, and circumference.
• Extend confident students by requiring two different nets for the same prism and a written proof that both fold without overlaps or gaps.
• Safety for all students: scissors point down, cutting happens while seated, tools are passed handle-first, rulers and tools are not swung, and scraps go in bins. The teacher demonstrates before distribution.