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Chapter 9 · Period 1 of 24 · 40 min
Folding to Find: What Is a Line of Symmetry?
Line of Symmetry · Inductive
Watch for students who mark any vertical line through a figure as a line of symmetry without checking whether folding produces exact overlap — a common error. Encourage students to physically fold or trace-and-flip their drawings rather than relying on visual estimation alone.
0–8Open with Figure it Out Q1 (section 9.1 p.219) ("do you see any line of symmetry in the opening figures...."). Students observe flowers, butterflies, rangoli, and pinwheels and share which figures look the same on both sides, surfacing informal understanding of balance and repetition.
8–20Introduce the folding test: teacher demonstrates folding a triangle along a dotted line so both halves overlap exactly — these halves are called mirror halves — and contrasts this with a four-piece puzzle figure that does not overlap when folded. Students state, in their own words, what a line of symmetry means based on this evidence.
20–32Students work on Figure it Out Q2 (section 9.1 p.219) ("for each of five given polygon figures, identify the line(s) of symmetry...."). Each student folds or imagines folding each polygon and records which figures pass the overlap test and where the fold line lies.
32–40Pairs share their answers; class compiles a short list of figures that have a line of symmetry and figures that do not, articulating the formal definition — a line of symmetry cuts a figure into two parts that exactly overlap when folded along that line.
Assessment
Figure it Out Q1, section 9.1 p.219 — Do you see any line of symmetry in the opening figures (flower, butterfly, rangoli, pinwheel)? What about the picture of the cloud?
A line of symmetry divides a figure into two parts. Which of the following best describes what must be true of those two parts?
- A They must be congruent triangles.
- B They must be equal in area but need not have the same shape.
- C They must be mirror images but need not overlap when folded.
- D They must overlap exactly when the figure is folded along that line.
D. They must overlap exactly when the figure is folded along that line.
What each wrong option reveals
- A The student over-restricts the definition to triangular figures, confusing a specific example with the general rule.
- B The student conflates equal area with symmetry, not recognising that shape and orientation must also match.
- C The student partially understands reflection but misses that the overlap test — not just visual mirror-image appearance — is the defining criterion.
Chapter 9 · 24 periods of 40 min
Also saved as 14 periods or 19 periods.
- 2How Many Folds? Discovering Multiple Lines of Symmetry
Figures with more than one line of symmetry - 3Reasoning About Multiple Axes of Symmetry
Figures with more than one line of symmetry - 4Ink Blots and Paper Cuts: Making Symmetric Shapes
Generating shapes having lines of symmetry - 5Punching Holes: Predicting Symmetric Patterns
Generating shapes having lines of symmetry - 6Predict, Cut, and Check: Paper Shapes and Holes
Generating shapes having lines of symmetry - 7Single Cut, Many Shapes: From Folds to Symmetric Holes
Generating shapes having lines of symmetry - 8Completing and Creating: Symmetry on Grids
Generating shapes having lines of symmetry - 9Curved Figures, Completing Halves, and the Symmetry Census
Generating shapes having lines of symmetry - 10Two-Line Symmetry and Dot-Grid Extensions
Generating shapes having lines of symmetry - 11The Windmill Spins: Introducing Rotational Symmetry
Rotational Symmetry - 12Listing Angles: Which Figures Rotate Into Themselves?
Rotational Symmetry - 13Radial Arms and the 360°/n Rule
Rotational Symmetry - 14True or False: Reasoning About Angles of Symmetry
Rotational Symmetry - 15The Circle: Every Angle, Every Diameter
Symmetries of a circle - 16Both Symmetries Together: Drawing Figures That Have Them
Symmetries of a circle - 17Reasoning with the Smallest Angle: Factor Problems
Symmetries of a circle - 18Parliament Building and Real-World Symmetry
Symmetries of a circle - 19Regular Polygons: Counting Lines and Angles of Symmetry
Symmetries of a circle - 20Koch Snowflake and the Ashoka Chakra: Symmetry in Special Figures
Symmetries of a circle - 21Applying Both Symmetry Types to a Wide Range of Figures
Symmetries of a circle - 22Consolidating Rotational Symmetry: From Figures to Generalisations
Symmetries of a circle - 23Extended Practice: Angles, Polygons, and Creative Designs
Symmetries of a circle - 24Four Problems, Two Symmetries: Putting the Chapter to Work
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