PrepShorts · Teaching notes · Class 6 Mathematics · Chapter 9, SymmetryPrepShorts

Chapter 9 · Symmetry

Symmetry as reflection: the fold line acts as a mirror

Teaching notesNCERT9 min

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9 min.

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

What they should be able to do

  • Restate the fold test as a statement about where each point goes
  • Given a square labelled A, B, C, D and a stated line of symmetry, say which corner lands on which
  • Identify the points of a figure that a given reflection leaves where they are
  • Predict the effect of reflecting a labelled square along a diagonal and along each mid-line
  • Use the term reflection symmetry for a figure that has at least one line of symmetry
  • Complete a half-drawn figure on squared paper so that a given line becomes a line of symmetry
  • Complete a figure so that two given lines are both lines of symmetry

Where it usually goes wrong

  • "Reflection turns the figure round." It does not. Each point crosses the line straight over; nothing rotates. Turning is the subject of module m02 and keeping the two apart at this stage is the whole point of section 1.
  • "The image of a point is somewhere near the mirror." It is a specific place: straight across the line, and just as far from it. Section 9 exists to fix that, because the squared-paper exercises are unusable without it.
  • "Every corner moves." A reflection along a diagonal leaves the two corners on that diagonal exactly where they are. Fixed points are not a failure of the reflection; they are part of it.
  • "Reflecting twice gets you somewhere new." Reflecting across the same line twice returns every point to where it started. Worth one beat, because it is what makes the two mirror halves genuinely interchangeable.
  • "Completing a figure means copying it beside itself." On squared paper the copy is flipped, not slid. Counting squares away from the line, in the same row, is the reliable method.
  • "With two mirror lines you draw one extra piece." Q12 needs three: the reflection in each line, and then the reflection of one of those in the other.

Questions to check understanding

  • Given a labelled figure and a stated line of symmetry, say where each labelled point goes
  • Name the points that a given reflection leaves unmoved
  • Complete a half-figure on squared paper across one given line
  • Complete a part-figure across two given lines
  • Add a fixed number of segments to a dot-grid figure so that it acquires a line of symmetry
  • State whether a described figure has reflection symmetry, and give the line
  • Mark the mirror partner of a marked point when the line of symmetry is drawn

Examples worth working on the board

  • The labelled square, §9.1, p.222. A plain square with A at the top left, B at the top right, C at the bottom right and D at the bottom left, and an upright line drawn down the middle. Read off the printed page of p.222: the letters run clockwise from the top left. Every claim in this topic depends on that arrangement, so draw it exactly.
  • The upright reflection, §9.1, p.222. The book works this one out: the two right-hand corners cross to the left and take the places the two left-hand corners held, and the two left-hand corners cross the other way. In the labelling above that is A with B, and D with C.
  • The diagonal reflection, §9.1, p.222. The book asks where A, B, C and D go under a reflection in the diagonal from A to C, and does not answer. Work it: A and C lie on the line, so they stay; B and D exchange places.
  • The flat reflection, §9.1, p.222. Asked on the same page and also left unanswered. Worked: A with D, and B with C.
  • All four at once. Collect the square's four reflections in one table so the student sees that each of them fixes either two corners or none: upright (A–B, D–C), flat (A–D, B–C), diagonal A to C (B–D, A and C fixed), diagonal B to D (A–C, B and D fixed).
  • Q11, §9.1, pp.228–229. Six grids, each with part of a red figure and one blue line; complete each so the blue line becomes a line of symmetry. Part (a) is printed already done, as a model. Parts (c) and (f) carry a printed hint that turning the book helps, because their blue lines run corner to corner.
  • Q12, §9.1, p.229. Six more grids, each with two blue lines. Both must end up as lines of symmetry, so a single starting piece generates three more copies, not one. This is the exercise that shows reflections combining.
  • Q13, §9.1, p.230. Dot-grid figures to be completed with exactly two more segments so that the result has a line of symmetry. Here the student must choose the line as well as the drawing.

Figures to have open

  • The labelled square of p.222 with its upright line. Indispensable, and the letters must sit exactly where the book puts them.
  • The same square with each of its other three lines of symmetry, for sections 6 and 7. Standard schematic.
  • A mirror-partner diagram: point, line, crossing track, partner, with the two distances marked equal. Standard schematic; the book does not print one.
  • Two or three of the Q11 grids and at least one Q12 grid, redrawn from the printed page. Squared paper with a coloured line and a part-figure.

Where this sits in the book

  • NCERT Class 6 Mathematics (Ganita Prakash), Chapter 9 "Symmetry", §9.1 Line of Symmetry — the sub-heading Reflection, pp.221–222
  • §9.1, p.222 — the labelled square, the worked upright reflection, the two unanswered questions, and the bold term reflection symmetry
  • §9.1, pp.228–230 — Figure it Out items Q11, Q12 and Q13
  • Summary, p.241 — the settled statement of line of symmetry

The book

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