Discovering Line Symmetry

Overview

In this first lesson of the three-part unit, students explore line symmetry as a shape or picture being divided into two matching mirror-image halves. They build on prior learning about 2D shapes and describing shape features by folding ordinary paper, comparing halves, and explaining how they identify a line of symmetry.

Learning intentions

• WALT describe line symmetry as two matching mirror-image halves.
• WALT investigate shapes, pictures, and patterns to find possible lines of symmetry.
• WALT use mathematical language to explain how we know an object is symmetrical.
• WALT record and mark lines of symmetry accurately.

Success criteria

• I can explain what a line of symmetry is.
• I can test a shape or picture by folding along a proposed line and comparing the two halves, or by carefully matching features visually.
• I can draw or mark a line of symmetry.
• I can explain my thinking using words such as symmetrical, mirror image, matching halves, fold, and line of symmetry.

Curriculum links

• Mathematics and Statistics — Geometry: recognise, describe, and investigate properties of shapes and objects.
• Mathematics and Statistics — spatial reasoning: use visualisation, folding, and mirror images to explore position and shape.
• Mathsteasers: higher-order thinking and challenge through investigation, reasoning, and explanation.
• Te Mātaiaho capabilities: communicating mathematical ideas, making connections, and using mathematical reasoning to justify conclusions.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Teacher displays a butterfly, koru-inspired pattern, and an uneven object in the hook and noticing slides, asking, “If this picture were folded, would both sides match?” Students silently decide, then share observations with a partner. Emphasise that symmetry can be found in nature, designs, and everyday objects, while remaining respectful of cultural designs and avoiding claims that every pattern has symmetry.

2. 5–12 min · Explicit teaching. Teacher models the term line of symmetry: a line that divides a shape or picture into two halves that are matching mirror images. Use a piece of ordinary paper to demonstrate folding exactly along a vertical centre line, pressing the crease, opening it, and comparing whether the two sides are the same size and have matching features. Show a non-example in the same way. For a printed or drawn picture, model careful visual comparison and mark corresponding points. Students use their hands to indicate whether displayed examples are symmetrical and explain why using the sentence stem, “I think it is/is not symmetrical because…”

3. 12–25 min · Small-group investigation. Teacher places students in six groups of four and gives each group pre-cut paper shapes, symmetry picture cards, and plain paper with drawn pictures or shapes. Students fold paper shapes exactly along a proposed line where possible, press the crease, open them, and compare whether the two sides are the same size and have matching features. For printed or drawn pictures, they compare corresponding features carefully and mark corresponding points. They discuss and record: object tested, symmetrical or not, and the position of any line of symmetry. Groups use the roles folder, checker, recorder, and speaker. Teacher rotates between groups, asking, “What did the fold show?”, “Are the two sides the same size and do their features match?”, and “Could there be another line?”

4. 25–33 min · Group reasoning and share-back. Teacher pauses the investigation and invites groups to present one example and one non-example using the investigation discussion slides. Students explain their evidence, point to the line of symmetry, and listen for differences between a shape having one line, more than one line, or no line. Clarify that a line must divide the whole object into matching mirror-image parts; it is not simply any line drawn through the shape.

5. 33–41 min · Independent application. Teacher distributes the line symmetry investigation worksheet and models the first item without giving answers. Students identify whether pictures and shapes are symmetrical, draw possible lines of symmetry, and complete one explanation using mathematical vocabulary. They check suitable paper shapes by folding exactly along the proposed line, pressing the crease, opening them, and comparing the two sides; they check printed or drawn examples through careful visual comparison and by marking corresponding points. Early finishers find a second possible line on a suitable shape and explain how they checked it.

6. 41–45 min · Plenary and exit check. Teacher returns to the definition and plenary slides and asks, “How can we prove that a line is a line of symmetry?” Students complete a quick oral exit response: “A shape is symmetrical when…” and show one finger for one line, two fingers for more than one line, or a closed fist for no line in a final displayed example.

Resources

• the complete symmetry introduction, investigation, and plenary deck
• the line symmetry investigation worksheet
• ordinary paper
• pre-cut paper shapes or printed/drawn pictures and shapes
• pencils
• Coloured pencils or crayons
• Scissors, if students need to cut out paper shapes
• Whiteboard and marker

Assessment

• Listen during partner and group talk for accurate use of mirror image, matching halves, and line of symmetry.
• During group work, observe whether students fold exactly along a proposed line, press the crease, open the paper, and compare the two sides for equal size and matching features; for printed or drawn pictures, check whether they compare features carefully and mark corresponding points.
• Check the worksheet and oral exit response for correct identification, accurately marked lines, and a reason that refers to matching halves.

Differentiation

• Support students with pre-cut, high-contrast shapes; allow them to fold exactly along each proposed line, press the crease, open the shape, and compare the two sides before recording. Use simple printed or drawn pictures for careful visual comparison and marking corresponding points.
• Provide sentence starters: “The line of symmetry is…”, “When I fold it…”, and “The halves match/do not match because…”
• Pair students strategically and assign group roles such as folder, checker, recorder, and speaker so all students participate.
• Extend confident students by asking them to find all possible lines of symmetry in selected shapes and compare shapes with one, two, or several lines. Provide visual vocabulary support and repeated modelling for EAL learners; allow oral explanations, pointing, or drawing before written responses.