Kōkiri Learn

Week 3 of 5

Test predictions and hunt for where rules break

  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Session 1 · SOLVE: Verify

Does it always work?

  1. 10 minUse your rule to predict step 20 of one pattern. Then build it or count it to check.
  2. 20 minCircles and regions: put 2, 3, 4 and 5 points on a circle and join every pair. Count the regions: 2, 4, 8, 16. Predict the next one.
  3. 15 minDraw 6 points (spaced unevenly) and count carefully. What happened to your prediction? What does this tell you about trusting a pattern?
  4. 5 minWrite: 'Checking cases gives evidence. A proof explains why.'

Session 2 · SOLVE: Verify

Prediction and chance

  1. 10 minPredict: when you roll two dice and add them, which total is most likely? List all 36 outcomes in a grid to find the theoretical probability of a total of 7 (6 out of 36).
  2. 20 minEach pair rolls 30 times and records the totals. Pool the class results to reach 300 or more.
  3. 15 minCompare the pooled experimental probability of 7 with 1/6. Why does the pooled result get closer than any single pair's?
  4. 5 minLink it: our rules predicted exact numbers; chance predicts what happens in the long run.

Session 3 · SOLVE: Verify

Proof with a picture

  1. 15 minPolygon angle sums: split a quadrilateral, pentagon and hexagon into triangles from one corner. How many triangles for n sides? Why?
  2. 15 minProve the triangle angle sum: tear the three corners off a paper triangle and line them up. Then show the same idea with a line parallel to one side.
  3. 15 minWrite the general rule 180(n − 2)° and a justification someone could follow without the drawings.
  4. 5 minCheck: use your rule to find one angle of a regular 12-sided shape.

Getting started

For circles and regions, draw big circles and count regions by shading each one as you count it.

Stretch

Write a picture-proof for why the square numbers go up by the odd numbers (1, 3, 5, 7…).

Checkpoint

Each student has tested one prediction with a new case and can explain why five matching cases are not a proof.

Activities for this week

Useful this week