Lesson 3 Workshop: Building Translation Rules

Year 9 60 mins Geometry

Supported route

Coordinates are introduced through a fixed four-step recording routine. The open-inquiry version of Lesson 3 is available for classes that can infer translation rules from longer pattern investigations.

Learning target

Ākonga will move every vertex by the same horizontal and vertical amounts, state the rule, and check that the image remains congruent and keeps its orientation.

The four-step translation card

  1. Name one original vertex and its image.
  2. Count the horizontal movement before the vertical movement.
  3. Apply those two movements to every remaining vertex.
  4. Check side lengths, angles and orientation against the original.

Display one completed card throughout the workshop. Learners may copy its structure, but their coordinates and movement rule must come from the new grid.

Coordinate workshop · 60 minutes

1. Human grid rehearsal · 8 minutes

Mark a simple floor grid. One learner follows a two-part instruction such as “three right, then two up”, while a partner checks the order and direction.

2. Worked example with error · 14 minutes

Model translating a triangle from A(1, 2) to A′(4, 1). Deliberately move one other vertex by a different amount, then use the congruence check to locate and repair the mistake.

3. We do: colour-coded vertices · 14 minutes

Pairs complete two grids in which corresponding vertices share a colour. They fill one four-step card per grid and compare the rule obtained from each vertex pair.

Checkpoint C: all vertex pairs must produce the same movement before a line joins the image.

4. You do: build a border strip · 16 minutes

Starting with a teacher-supplied neutral motif on squared paper, apply one horizontal translation four times. Under the strip, record the rule and one invariant used to check each repeat.

5. Exit repair · 8 minutes

A pre-drawn translation contains one incorrect image vertex. Circle it, plot its correct position, and explain which step on the routine card revealed the error.

Teacher checkpoint notes

Reduce coordinate load: begin in the first quadrant and provide the movement rule; ask learners to focus only on applying it consistently to every vertex.

Make direction visible: use one colour for horizontal arrows and another for vertical arrows until learners no longer reverse the order.

Ready to progress: the learner derives and applies a two-part rule, then catches a mismatched vertex by checking corresponding lengths or orientation.

Curriculum alignment