Designing Symmetrical Patterns

Overview

This is lesson 3 of 3 in the unit Mirror Images: Line Symmetry. Learners apply their understanding of defining, identifying, completing and testing line symmetry by creating an original design, explaining their reasoning and revising their work.

Learning intentions

• WALT define and identify line symmetry.
• WALT create a picture or pattern with a clear line of symmetry.
• WALT test and improve a design using folding or a mirror.
• WALT explain how we know a design is symmetrical.

Success criteria

• I can describe line symmetry as when two parts match exactly on opposite sides of a line.
• I can draw and clearly mark a line of symmetry.
• I can test my design by folding it or using a mirror, then make changes if needed.
• I can explain how my design shows symmetry using mathematical words.

Curriculum links

• Te Mātaiaho Mathematics and Statistics: geometry and spatial reasoning through lines, shapes, position and transformation.
• Te Mātaiaho Mathematics and Statistics: mathematical practices—representing, reasoning, communicating and checking ideas.
• Mathsteasers: higher-order thinking questions that challenge learners and deepen mathematical understanding.
• Learner competencies: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (45 minutes)

1. 0–5 min · Reconnect and hook. Display the opening section of the symmetry design deck and ask, “How could we prove that this picture is symmetrical?” Revisit the definition of line symmetry and briefly review yesterday’s learning about matching sides, mirror lines and reflected parts. Students turn and talk, then share one test they could use.

2. 5–10 min · Model the design process. Use the next slides to model planning a simple symmetrical design on the board: choose a theme, draw a vertical or horizontal line, add one side, reflect the parts on the other side, and label the line. Deliberately include one inaccurate example and ask students to identify and explain the error. Students suggest corrections and use the words symmetrical, line of symmetry, matching, reflect and mirror image.

3. 10–15 min · Plan in small groups. Place learners in six groups of four and distribute the line and shape planning template. Support each group to choose a picture or repeating pattern, such as an animal, plant, koru-inspired spiral, building or geometric design. Students sketch an idea, decide where the line will go and identify shapes or features they will reflect. Circulate and ask, “What must match?” and “How will you check?”

4. 15–30 min · Create and test. Distribute the symmetrical design worksheet and drawing materials. Students create an original picture or pattern, clearly mark the line of symmetry and write a short explanation. They test their design by folding along the line where practical or holding a mirror on the line, then revise any mismatched features. The teacher works with one focus group at a time, checking that students are reflecting position and shape rather than simply copying a pleasing pattern.

5. 30–38 min · Partner explanation. Show the discussion prompts in the symmetry design deck. Students work with a partner from another group and take turns explaining: “My line of symmetry is…”, “I know my design is symmetrical because…”, and “I changed… after testing it.” Partners ask one question and give one specific improvement suggestion. The teacher listens for accurate definitions and reasoning, not just correct-looking drawings.

6. 38–43 min · Gallery walk and feedback. Display designs around the room. Students quietly view several examples and leave oral feedback to a partner using “I notice…” and “I wonder…”. Invite two or three learners to share a design that was revised successfully and explain what the test revealed. Return to the deck for the compare-and-justify prompt.

7. 43–45 min · Reflection and exit check. Use the final slide to ask learners to complete the reflection box on the worksheet: define line symmetry, identify the line in their own design, describe their test and justify whether the final design is symmetrical. Collect worksheets and invite a few students to share one new insight.

Resources

• the symmetry design deck
• the symmetrical design worksheet
• the line and shape planning template
• Plain paper or drawing paper
• Pencils, erasers, coloured pencils and rulers
• Small mirrors or safe handheld mirrors
• Scissors for optional fold-and-check testing
• Board or display space for the gallery walk

Assessment

• During planning and creation, ask individuals to define symmetry, locate the line and predict what should match. Note who can reflect features accurately and who needs prompting.
• Listen during partner explanations for correct use of mathematical language and a justification based on evidence from folding, mirroring or matching parts.
• Use the final worksheet reflection as an exit assessment. Check whether each learner can define, identify, complete, create and justify line symmetry; record a next step for learners who confuse copying with reflection.

Differentiation

• Support learners with a pre-drawn vertical or horizontal line, simple shapes to reflect, a reduced design area and sentence starters: “The line of symmetry is…” and “I know because…”.
• Allow learners who need additional support to work with the teacher or a peer, use a mirror throughout and verbalise each feature before drawing it.
• Provide visual vocabulary on the slides and pair English language learners with a supportive partner; accept labelled drawings and oral explanations alongside written responses.
• Challenge confident learners to create a design with more than one line of symmetry, explain why a near-symmetrical design does not work, or compare vertical and horizontal symmetry.