TEACHER EDITION
Factors and Multiples — Multiples
Math Book 7 · sheet 2
Warm-up — yesterday: Factors
List all the factors of 12.1, 2, 3, 4, 6, 12
What we are learning
A multiple is what you get by multiplying a number by a whole number. A number has finitely many factors and infinitely many multiples.
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
Factors of 6 — a list that ends.
1, 2, 3, 6
2
Multiples of 6 — start multiplying.
1, 2, 3, 6
6 × 1 = 6
3
6 × 2, 6 × 3.
1, 2, 3, 6
6 × 1 = 6
6, 12, 18
4
It never stops.
1, 2, 3, 6
6 × 1 = 6
6, 12, 18
6, 12, 18, 24, 30, …
5
Factors divide INTO it. Multiples come OUT of it.
1, 2, 3, 6
6 × 1 = 6
6, 12, 18
6, 12, 18, 24, 30, …
factors: finite · multiples: infinite
Practice
I DOteacher builds it, nothing erased
Write the first five multiples of 7.
- 7 × 1, 7 × 2, 7 × 3, 7 × 4, 7 × 5.
- 7, 14, 21, 28, 35
WE DO 1together, on whiteboards
Write the first five multiples of 9.
Multiply, do not keep adding — adding is where errors creep in. Boards up.
- 9, 18, 27, 36, 45
WE DO 2together, on whiteboards
Is 48 a multiple of 6? Is 6 a factor of 48?
Two questions that are really one question.
- 6 × 8 = 48, so yes to both.
- If 6 is a factor of 48, then 48 is a multiple of 6.
YOU DOindependent, from the book
Book 7A p.2 — the Do section, clipped onto the slide
Ask yourself: “Is this number going IN, or coming OUT?”
Watch for
The second WE DO is the whole point of the pair of lessons: factor and multiple are the same relationship named from opposite ends. Do not let the class answer it as two separate questions.
The second WE DO is the whole point of the pair of lessons: factor and multiple are the same relationship named from opposite ends. Do not let the class answer it as two separate questions.