Launch: Similar Shapes

Overview

In this first lesson of Similarity to Solid Design, students distinguish similar shapes from shapes that are merely the same size or visually alike. They build on prior work with ratios, proportional reasoning, angles and measurement by identifying corresponding parts and using scale factors.

Learning intentions

Students will:

• identify corresponding sides and angles in similar polygons
• explain that similar shapes have equal corresponding angles and proportional corresponding sides
• calculate and interpret a scale factor
• communicate mathematical reasoning using diagrams, ratios and units

Success criteria

• I can identify matching sides and angles in two shapes.
• I can explain why two shapes are, or are not, similar.
• I can calculate a scale factor using image ÷ original.
• I can use a scale factor to find a missing side.

Curriculum links

• Shape and Space — similarity of two-dimensional shapes
• Number — ratios, proportional reasoning and operations with rational numbers
• Mathematical Processes — problem solving, reasoning, communication and making connections
• Preparation for geometric measurement — surface area, nets and composite objects

Lesson structure (30 minutes)

1. 0–4 min · Warm-up: notice and sketch. Display the opening prompt in the similarity hook and warm-up slide: “Can two shapes have the same shape but different sizes?” Students sketch two similar-looking shapes, circle one pair of corresponding sides and one pair of corresponding angles, then briefly compare with a partner. Invite two students to share different examples and avoid confirming every “similar-looking” shape immediately.

2. 4–12 min · Mini-lesson: define similarity. Use the definition and worked-example slides to establish that similar polygons have equal corresponding angles and proportional corresponding sides. Model triangles with side lengths 3, 4, 5 and 6, 8, 10: match the corresponding sides, show that each image side is twice the original, and record scale factor = image ÷ original = 2. Add the student note: “Same shape, different size!” Emphasize that congruent shapes have the same shape and the same size, while similar shapes may have different sizes. Students annotate a quick diagram and explain the scale factor to a partner.

3. 12–19 min · Guided practice: match and justify. Give each pair a teacher-prepared set of similarity cards showing figures, side lengths and scale factors. Display the matching instructions in the card-sort directions and discussion prompts. Students match each figure to its measurements and scale factor, then justify one match by naming corresponding sides and checking a ratio. Circulate and ask: “How do you know these sides correspond?” and “Does one scale factor work for every pair?”

4. 19–26 min · Similarity Sort. Distribute the Similarity Sort worksheet. Students independently complete the first items, then compare reasoning with a partner; one group of three may work together. They classify pairs as similar or not similar, identify corresponding parts and calculate scale factors. Students should show a ratio or multiplication statement rather than relying on appearance. If finished, they find a missing side using a proportion such as (4:6 = 7:x).

5. 26–28 min · Formative check: misconception check. Show the statement on the misconception-check slide: “Same shape means same size.” Students respond thumbs-up or thumbs-down, then explain their choice to a partner. Reinforce: same shape does not mean same size; similarity requires matching angles and proportional corresponding sides. Address the common mistake of adding side lengths instead of multiplying by the scale factor.

6. 28–30 min · Closure: exit ticket. Display the final prompt in the exit-ticket slide. Students independently define “similar” and solve (4:6 = 7:x), recording the scale-factor reasoning and answer (x = 10). Collect responses to identify students who need support with correspondence, ratios or multiplication before the next lesson.

Resources

• the Similar Shapes lesson deck displayed throughout the lesson
• the Similarity Sort worksheet for independent and paired practice
• Board or projector
• Teacher-prepared similarity matching cards
• Rulers
• Pencils and coloured pencils or highlighters
• Exit-ticket paper or notebooks
• Multiplication tables and a visual scale-factor reminder

Assessment

• During the warm-up and card sort, listen for students correctly naming corresponding sides and angles rather than matching by position alone.
• Check worksheet explanations for both conditions of similarity: equal corresponding angles and proportional corresponding sides.
• Use the exit ticket to assess definition, scale-factor reasoning and the missing-side calculation; sort responses into ready, developing and reteach groups.

Differentiation

• Provide colour-coded corresponding sides and angles on selected cards and worksheet diagrams; allow students to trace or rotate shapes to confirm matches.
• Provide a ratio template, multiplication tables and the prompt “The image is ___ times the original because…” for students needing support.
• Pair students strategically and read the key instructions aloud; use clear diagrams, reduced visual clutter and enlarged print for students with visual, literacy or processing needs.
• For extension, ask students to find a missing side in an unfamiliar similar figure and explain why the same scale factor must apply to every corresponding side.
• Support multilingual learners with a small visual glossary for similar, corresponding, ratio, scale factor, congruent and proportional.