Completing Symmetrical Patterns

Overview

In this second lesson of the three-part unit Mirror Images: Line Symmetry, students revisit the line of symmetry and use it to complete half-finished pictures and patterns. They will reflect each part across a vertical line, compare strategies in small groups, and justify whether their designs are symmetrical.

Learning intentions

• WALT identify a line of symmetry in a picture or pattern.
• WALT reflect shapes and details across a line of symmetry.
• WALT explain how we know a completed design is symmetrical.
• WALT listen to and build on others’ mathematical ideas.

Success criteria

• I can find and describe the line of symmetry.
• I can place each part the same distance from the line on the opposite side.
• I can check that matching parts are the same size and distance from the line.
• I can explain why my completed pattern is, or is not, symmetrical.

Curriculum links

• Mathematics and Statistics — Geometry: recognising and describing symmetry in shapes, pictures and patterns.
• Mathematics and Statistics — Spatial reasoning: using position, direction and distance to reflect visual features.
• Mathsteasers: developing higher-order thinking through challenge, reasoning and justification.
• Te Mātaiaho Mathematics and Statistics: communicating mathematical thinking, comparing strategies and explaining conclusions.

Lesson structure (45 minutes)

1. 0–5 min · Notice and wonder. Open with the hook and mystery pattern showing a half-finished butterfly-like pattern beside a line. Ask, “What might the missing side look like? How could we prove it is fair?” Give quiet think time, then invite partner observations. Students describe what they notice without drawing yet.

2. 5–12 min · Revisit and model. Use the symmetry definition and modelling slides to revisit that a line of symmetry divides a figure into matching halves. Model completing a simple half-picture on the board, thinking aloud: “I find the feature’s distance from the line, move across the line by the same distance, and keep its size and orientation.” Pause deliberately after each step. Students use finger-tracing or mini-whiteboards to show where one missing point should go.

3. 12–15 min · Check the strategy. Display two possible completions using the compare-and-check slide. Ask, “Which one is symmetrical? What evidence do you have?” Wait at least five seconds before taking responses. Students rehearse an explanation with a partner using: “I know it is symmetrical because …” Record useful language such as same distance, matching side, opposite side and line of symmetry.

4. 15–30 min · Group problem solving. Place students in six mixed-ability groups of four and distribute the completing symmetrical patterns worksheet. Groups work through increasingly challenging half-finished designs: simple shapes first, then pictures with several details and finally a repeating pattern. Students should discuss and agree before drawing, with one student explaining, one checking distances, one drawing and one recording the group’s reasoning; rotate roles halfway through. Circulate and ask, “What will you reflect first?”, “How are you keeping the distance equal?”, “What must stay the same?”, and “How could you check without folding?” Allow wait time before prompting further.

5. 30–39 min · Compare strategies. Invite two or three groups to display different completed patterns from the group reasoning and comparison section. Use the discussion prompts and check slide to guide comparison. Students identify similarities and differences in methods, such as counting squares, using a ruler, matching points or mentally folding the picture. Ask, “Does a neat drawing always mean it is symmetrical?” and “Can you find one part that proves your answer?” Groups make one improvement if their design or explanation needs correcting.

6. 39–45 min · Reflect and assess. Show the final prompt on the plenary and exit prompt. Students independently complete: “A design is symmetrical when …” and “One way I checked was …” They then hold up a thumb to show confidence and share one strategy with a partner. Collect worksheets and note students who can reflect accurately, explain distance, or need further support in the final unit lesson.

Resources

• the complete symmetry teaching deck
• the completing symmetrical patterns worksheet
• the Symmetry Mirror Templates
• Whiteboard and markers
• Mini-whiteboards or scrap paper
• Pencils, rulers and coloured pencils
• Six group tables or work areas
• Display space for student work

Assessment

• During modelling, check whether students can identify the line of symmetry and locate a reflected point at the same distance.
• During group work, listen for mathematical explanations rather than simply checking finished drawings. Record students who use distance, position and matching features accurately.
• Use the final written explanation and worksheet evidence to group students for the next lesson: secure, developing or requiring targeted support.

Differentiation

• Support students with the the Symmetry Mirror Templates, enlarged designs, grid paper and a ruler. Begin with one feature at a time and use the sentence starter, “I moved it ___ squares across the line.”
• Pair students strategically and assign clear group roles. Allow students to point, trace or use objects before explaining verbally; provide visual vocabulary cards or gestures for line, across, same distance and matching for EAL learners.
• For students needing additional challenge, ask them to identify and correct a deliberately inaccurate completion, or design a half-pattern that includes a repeated shape and explain how a partner can reflect it.
• Accept drawing, oral explanation or labelled annotations as evidence. Avoid judging symmetry from artistic neatness; focus assessment on position, distance and reasoning.