Kōkiri Learn

Week 3 of 5

Slide, flip, turn, grow: transformations and symmetry

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Session 1 · SOLVE: Link Ideas

Moving shapes on a grid

  1. 10 minRead 'Moving shapes: transformations and symmetry'. Name the four transformations.
  2. 25 minOn a four-quadrant grid, draw a triangle with corners at whole-number coordinates. Translate it, reflect it in each axis, rotate it 90° and 180° about (0, 0), and enlarge it by scale factor 2 from (0, 0). Record the new coordinates each time.
  3. 10 minLook for the coordinate patterns: what happens to the numbers in a reflection in the y-axis? In a 180° rotation?
  4. 5 minCheck each move with tracing paper or a mirror.

Session 2 · SOLVE: Link Ideas

Reading patterns with respect

  1. 10 minRead 'Tessellations in nature and culture'. Look at the gallery photos of tukutuku and siapo.
  2. 20 minIn groups, study one pattern (tukutuku, tāniko, siapo, Islamic tilework, an Escher print or a honeycomb). Find a translation, a reflection, a rotation and any lines of symmetry. Record the name and meaning of the pattern where the source gives it.
  3. 15 minShare: how did the makers use geometry? What does the pattern mean to the people who made it? Why should we learn from these patterns rather than copy them?
  4. 5 minLink: which transformation will your own design use?

Getting started

Use only translations and reflections in the x-axis to start; add rotation when these are confident.

Stretch

Combine two transformations (for example reflect in the x-axis, then in the y-axis). Which single transformation does the same job?

Checkpoint

Students can perform and describe each transformation on a grid with coordinates and identify line and rotational symmetry in a pattern.

Activities for this week

  • Transformation trail: What happens to coordinates when we reflect, rotate, translate or enlarge a shape?
  • Pattern readers: How do artists of Aotearoa, the Pacific and the world use transformations?

Useful this week