TEACHER EDITION

Factors and Multiples — Factors

Grade 7 · Lesson 1 · Dimensions 7A p.2
Math Book 7 · sheet 1
Warm-up — yesterday: Grade 6 — order of operations
Evaluate 4 + 3 × 2².
16

What we are learning

A factor of a number divides it exactly, leaving no remainder. Factors come in PAIRS, which is what makes them findable systematically.

How it is done — keep this beside you

These steps stay on your page while you work. If you get stuck, find the step you are on and read it again before you put your hand up.

1
Find every factor of 24. I will not guess — I will work in pairs.
24
2
1 × 24. Both are factors.
24 1, 24
3
2 × 12.
24 1, 24 1, 2, 12, 24
4
3 × 8. Then 4 × 6.
24 1, 24 1, 2, 12, 24 1, 2, 3, 4, 6, 8, 12, 24
5
5 does not divide 24, and after 4 × 6 the pairs start repeating. Done.
24 1, 24 1, 2, 12, 24 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 8, 12, 24

Practice

I DOteacher builds it, nothing erased
List all the factors of 18.
  1. 1 × 18, 2 × 9, 3 × 6.
  2. 4 and 5 do not divide 18. After 3 × 6 the pairs repeat.
  3. 1, 2, 3, 6, 9, 18
WE DO 1together, on whiteboards
List all the factors of 30.
Work in pairs, starting at 1. Boards up when the pairs meet.
  1. 1×30, 2×15, 3×10, 5×6
  2. 1, 2, 3, 5, 6, 10, 15, 30
WE DO 2together, on whiteboards
List all the factors of 36.
This one has a pair that meets itself. Watch for it.
  1. 1×36, 2×18, 3×12, 4×9, 6×6
  2. 1, 2, 3, 4, 6, 9, 12, 18, 36
YOU DOindependent, from the book
Book 7A p.2 — the Do section, clipped onto the slide
the book page
Ask yourself: “Have the pairs met yet? If they have, I am finished.”
Watch for
36 = 6 × 6 is a square, so 6 is written ONCE. Children list it twice or stop before reaching it. The pairs-meeting test is what tells them when the list is complete — without it they simply stop when they run out of ideas.