Kōkiri Learn

Week 2 of 5

Factor fingerprints, powers and roots

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

Session 1 · SOLVE: Organise Information

Factor trees and sausage sizzles

  1. 15 minFactor trees: split 36, 60 and 84 into factors until only primes are left. Every tree for the same number ends with the same primes: its prime 'fingerprint'.
  2. 10 minWrite fingerprints with powers: 36 = 2 × 2 × 3 × 3 = 2² × 3².
  3. 20 minSausage sizzle problem: sausages come in packs of 8 and buns in packs of 12. What is the smallest number of each you can buy with nothing left over? Solve with lists, then with fingerprints (LCM). Then: 24 kapa haka performers and 36 visitors must be split into equal groups with nobody left over. What is the biggest group size (HCF)?
  4. 5 minExit card: find the HCF and LCM of 6 and 9.

Session 2 · SOLVE: Organise Information

Square, cube, power up

  1. 10 minRead 'Powers, roots and the rules of the road' (first half). What does 5² mean? What does √49 mean?
  2. 20 minBuild squares from tiles (1, 4, 9, 16…) and cubes from multilink (1, 8, 27, 64…). Record them in a table with the side length, the power and the root.
  3. 10 minPattern: what is the difference between one square number and the next? Predict the 10th square number without building it.
  4. 10 minDoubling paper: fold a sheet in half again and again. How many layers after 5 folds (2⁵)? After 10? Why can't you keep folding?

Getting started

Use factor pairs from the rectangle table before drawing trees; keep to numbers under 50.

Stretch

Write 360 as a product of primes with powers. Use it to count how many factors 360 has without listing them.

Checkpoint

Each student has a factor tree, a power table and one solved HCF or LCM story problem in their detective notebook.

Activities for this week

Useful this week