Questions: Multiplication Facts Within 100

Question 1

A student knows that 6 × 8 = 48 but isn't sure about 8 × 6. What mathematical property tells us these must be equal?

• A. The distributive property
• B. The associative property
• C. The commutative property
• D. The identity property

Answer: (C)

The commutative property of multiplication states that the order of factors doesn't change the product: a × b = b × a. So 6 × 8 = 8 × 6 = 48. Students who memorize facts in only one order are not yet trusting this property, which effectively doubles the number of facts they think they need to remember.

Question 2

Any number multiplied by 0 equals 0, and any number multiplied by 1 equals that same number.

• T. True
• F. False

Answer: True

Both are true. The zero property of multiplication says n × 0 = 0 for any n — zero groups of anything is nothing. The identity property says n × 1 = n — one group of n things is just n things. Together these cover the entire ×0 and ×1 rows of the multiplication table, which are often overlooked or confused.

Question 3

Explain in your own words why understanding 'equal groups' helps you learn multiplication facts rather than just memorizing them.

Model answer: Equal groups gives multiplication a meaning: 6 × 7 means 6 groups of 7 objects. This meaning lets you verify facts, reason your way back to forgotten ones, and connect multiplication to real situations — rather than treating facts as arbitrary number pairs to memorize.

Memorization without meaning is fragile — facts learned by rote are easily forgotten and can't be reconstructed when forgotten. If you understand that 6 × 7 means 6 groups of 7, you can reason: 'I know 5 × 7 = 35, so 6 × 7 must be 35 + 7 = 42.' This strategy-based thinking supports fluency even when memory temporarily fails.