Question 1

When do you need a common factor?

Accepted Answer

To split both colours into equal-sized packs with no leftovers, the pack size must divide both totals. (Tempting mistake: The greatest equal packet size for 12 blue beads and 18 red beads is 36.. Why it feels right: I remember finding a common number and use the least common multiple.)

Question 2

If your child says: “The HCF should be 1 because factors are small.”

Accepted Answer

Ask: Do the 2 cm squares also fit both edges? What’s true: Choose the greatest factor shared by the measurements.

Question 3

If your child says: “Only the primes are factors.”

Accepted Answer

Ask: What do the two 2s multiply to? What’s true: Multiplying available primes together also makes factors of the original number.

Question 4

If your child says: “I'll take all three 2s.”

Accepted Answer

Ask: Where is the third 2 in 12? What’s true: A shared factor cannot use more copies than either number contains.

Question 5

If your child says: “6 works because it's the longer strip.”

Accepted Answer

Ask: Can whole 4 cm strips make a 6 cm row? What’s true: A shared multiple must divide exactly by each strip length.

Question 6

If your child says: “Leave out 3 because only 2 is shared.”

Accepted Answer

Ask: Without a 3, how will 6 divide this product? What’s true: Leaving out any required prime prevents one number from dividing the result.

Question 7

If your child says: “The HCF must be smaller than both numbers.”

Accepted Answer

Ask: What prevents 2 from dividing both 2 and 6? What’s true: A number divides itself, so it can be the HCF.

Question 8

If your child says: “The side divisor gives the LCM too.”

Accepted Answer

Ask: Does the side divisor 3 contain enough factors for 6 or 9? What’s true: The LCM also needs both final quotients when they share only 1.

Question 9

If your child says: “Add the HCF and LCM to get the product.”

Accepted Answer

Ask: What operation joins the outside 2 to the bracket? What’s true: For two positive whole numbers, multiplication joins the HCF and LCM into their product.

Finding Common Ground: common misconceptions

The tempting mistake & worked visual

When do you need a common factor?

If your child says… (8 concept checks in this chapter)

Use this chapter three ways

Common misconceptions

How to teach Finding Common Ground →

15 practice questions with answers →

The tempting mistake & worked visual

When do you need a common factor?

If your child says… (8 concept checks in this chapter)

Use this chapter three ways

Common misconceptions

How to teach Finding Common Ground →

15 practice questions with answers →

Cookies