Core activity 4.3: Factors
LB: p24
Resources: Factors photocopy master (CD-ROM). Factor bugs photocopy master (p48). (Optional: Factor spinner photocopy master (CD-ROM).) Set the following challenge:
Vocabulary
“I have 12 small squares. How can I arrange them to make a rectangle?”
Vocabulary factor: a whole number that divides exactly into another number. For example,
Allow learners ‘thinking time’, then take responses. (Possible suggestions: 1 row of 12 squares; 2 rows of 6 squares; 3 rows of 4 squares and so on)
2 × 3 = 6 so 6 ∏ 2 = 3 and 6 ∏ 3 = 2 2 and 3 are factors of 6
Explain that 1, 12, 2, 6, 3 and 4 are factors of 12. If necessary, display the Factors photocopy master to support this statement and explain what is meant by factors. ∑ “What are the factors of 8?” (Answer: 1, 2, 4 and 8) ∑ “What are the factors of 15?” (Answer: 1, 3, 5 and 15)
Unit 1A
4 Multiples, square numbers and factors
factor
Learners who confuse multiples and factors. Ensure that the definitions are clearly displayed in the classroom: ∑ multiples are the product of multiplying a number by a positive whole number ∑ factors are whole numbers that divide exactly into another number. For example, 4 is a factor of 8 but not a multiple of 8. 15 is a multiple of 5 but is not a factor of 5. Example: Factors bug for factors of 24.
1
24
2
12
24 3 4
46
factor
Look out for!
Tell learners that sometimes it is important to find all the factors of a number, so we need to be organised in the way we work. Display the Factor bugs photocopy master and explain it is a way of listing all the factors of a number. “Here is a factor bug. I can write the factors of 24 on its legs. I start at 1 and if it is a factor, I write 1 on a leg on the left and the other factor on the matching right leg.” Demonstrate this as you say it, and Ask: ∑ “What happens if I try to divide 24 by 1?” (Answer: 24, so 1 is a factor) ∑ “What happens if I try to divide 24 by 2?” (Answer: 12, so 2 is a factor) ∑ “What happens if I try to divide 24 by 3?” (Answer: 8, so 3 is a factor) ∑ “What happens if I try to divide 24 by 4?” (Answer: 6, so 4 is a factor) ∑ “What happens if I try to divide 24 by 5?” (Answer: there is a remainder so 5 is not a factor) ∑ “What happens if I divide 24 by 6?” (Answer: the pair of factors 4 and 6 have already been written down) Explain that once you have reached this ‘repeat’ stage you can be sure you have found all the factors. Now write the factors in order: 1, 2, 3, 4, 6, 8, 12, 24.
2×3=6
8 6