Mathematics · Grade 1

Active learning ideas

Symmetry in Shapes

Active learning helps students grasp symmetry because folding paper or drawing lines provides concrete proof of abstract ideas. Hands-on tasks like cutting and folding let children see symmetry in three dimensions before moving to drawings, which builds confidence and accuracy.

• Ontario Curriculum Expectations
• Ontario Curriculum Mathematics 2020: Grade 1, E. Spatial Sense, E1. Geometric and Spatial Reasoning: describe and represent shapes, and compose and decompose two-dimensional shapes and three-dimensional objects.
• Ontario Curriculum Mathematics 2020: Grade 1, E. Spatial Sense, E1.3: identify and describe two-dimensional shapes and three-dimensional objects in everyday life, and sort them by their geometric properties.
• Ontario Curriculum Mathematics 2020: Grade 1, C. Algebra, C1.1: identify and describe repeating elements in patterns of various types.

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 20 min · Pairs

Pairs Activity: Shape Folding Hunt

Provide pairs with sets of 2D shapes cut from paper. Partners fold each shape along possible lines to check for matching halves, then mark lines of symmetry with crayon. Pairs share one symmetrical and one asymmetrical shape with the class.

Explain what makes a shape symmetrical.

Facilitation Tip

During the Shape Folding Hunt, circulate and ask each pair to explain why they chose their fold line, pressing them to use words like ‘match’ and ‘mirror.’

What to look for

Provide students with several shapes, some symmetrical and some not. Ask them to draw the line(s) of symmetry on the symmetrical shapes and write 'no symmetry' on the others. Include a prompt: 'Explain why the square is symmetrical.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 30 min · Small Groups

Small Groups: Mirror Symmetry Stations

Set up stations with handheld mirrors, shapes, and paper. Groups position mirrors along edges of shapes to view reflections, draw what they see, and identify lines of symmetry. Rotate groups every 7 minutes and record findings.

Construct a shape that has at least one line of symmetry.

Facilitation Tip

At the Mirror Symmetry Stations, place a timer visible to all groups to keep rotations brisk and focused.

What to look for

Hold up various paper cut-out shapes. Ask students to give a thumbs up if the shape has a line of symmetry and a thumbs down if it does not. For shapes with symmetry, ask them to demonstrate where the line of symmetry would be with their hands.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 25 min · Whole Class

Whole Class: Symmetry Art Gallery

Display student-drawn shapes on chart paper. As a class, vote on lines of symmetry using string or yarn along potential lines. Discuss matches and create a class mural of symmetrical designs.

Compare shapes that have symmetry to shapes that do not.

Facilitation Tip

For the Symmetry Art Gallery, ask each student to write one sentence on their artwork that names the shape and the number of lines of symmetry it has.

What to look for

Present students with two shapes, one symmetrical (e.g., a heart) and one asymmetrical (e.g., a cloud shape). Ask: 'How are these shapes different? Which one can be folded in half so the two sides match perfectly? What do we call that property?'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 15 min · Individual

Individual: Geoboard Creations

Students use geoboards and rubber bands to build shapes with one line of symmetry. They draw the line on paper and label it. Collect for a symmetry showcase.

Explain what makes a shape symmetrical.

Facilitation Tip

When students use Geoboards, model how to press the pegs firmly so shapes hold their form while they count and trace symmetry lines.

What to look for

Provide students with several shapes, some symmetrical and some not. Ask them to draw the line(s) of symmetry on the symmetrical shapes and write 'no symmetry' on the others. Include a prompt: 'Explain why the square is symmetrical.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teachers should begin with full-body movement: have students stand and fold their own bodies along an imaginary line to feel symmetry physically before touching paper. Avoid rushing to definitions; instead, let students discover mismatches by folding odd shapes so they see firsthand that not every shape is symmetrical. Research shows that students who manipulate materials before drawing lines retain the concept longer, so keep the sequence concrete-to-abstract.

By the end of these activities, students can identify, draw, and explain lines of symmetry in common shapes and tell whether a shape is symmetrical. They will use folding, drawing, and discussion to justify their thinking with evidence from their work.

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Watch Out for These Misconceptions

• During the Shape Folding Hunt, watch for students who assume every shape can be folded in half. Redirect by handing them an L-shape cutout and asking, 'Can you fold this so both sides match perfectly? Try it.'

  After folding, have students place mismatched edges side by side to see the gap, then discuss why some shapes cannot be folded symmetrically.

• During the Mirror Symmetry Stations, watch for students who think a shape is symmetrical if it looks similar after turning. Hand them a mirror and ask, 'Does the reflection match the original exactly, or does it flip?'

  Prompt students to compare the mirror image to the original shape, highlighting that rotation does not create mirror symmetry unless the halves match across a line.

• During the Geoboard Creations, watch for students who draw curved lines as symmetry lines on simple shapes. Provide a heart cutout and have them trace the straight line down the middle with a finger.

  Ask students to fold the heart along their drawn line and observe whether the two halves match exactly; if not, erase and try again.

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Methods used in this brief

• Stations Rotation