Lesson 3: Translation Rules

Year 9 60 mins Geometry

Learning Intention

I can describe translations using specific rules and creating repeating border patterns.

Success Criteria

  • I can write a rule for a translation like "3 units right, 2 units down".
  • I can apply a translation rule to move a shape on a grid.
  • I can create a frieze pattern (repeating strip) by translating a base tile.

Lesson Sequence

1. Starter: GPS Directions (10 mins)

On a whiteboard grid, draw a dot at A and a dot at B. "How do I get from A to B?"

Encourage precise language: "Go right 4 squares, then go up 3 squares."

Math Notation (Extension): Introduce vector notation roughly: (4, 3) where first number is horizontal, second vertical.

2. Investigation: The Repeating Strip (25 mins)

Focus on Tukutuku panels often found in meeting houses.

Observation: Look at the Poutama (step) pattern. Is it just one shape sliding upwards?

Activity: Students investigate the "rules" of a border pattern.

  • Take a base 2x2 grid shape.
  • Translate it "2 right, 0 up". Repeat 5 times. What pattern do you get?
  • Translate it "1 right, 1 up". What pattern is that? (Diagonal/Stairs).

3. Design Challenge: Code-a-Pattern (15 mins)

Goal: Write a translation code for a partner.

Student A: Draws a shape and a "destination" shape.

Student B: Writes the rule (e.g., "5 Left, 2 Down").

Student A: Checks if it works.

4. Plenary (10 mins)

Does a translation EVER turn the shape? (No). Does it EVER flip it? (No). The orientation stays exactly the same.