Study guide: Compare Multiplicatively and Investigate Factors
Distinguish times-as-many from more, find factors, classify primes, and explain patterns.
Ideas to explain in your own words
- A multiplicative comparison gives several copies of a reference amount.
- A factor divides a whole number with no remainder.
- A prime whole number is greater than one and has exactly two positive factors: one and itself.
- A rule generates a sequence by applying the same change repeatedly.
Useful vocabulary
- factor pair
- Two whole numbers whose product is the target.
- prime
- A whole number greater than one with exactly two positive factors.
Watch your reasoning
- A multiplier does not mean an added difference.
- A divisor leaving a remainder is not a whole-number factor.
- One is neither prime nor composite.
- Do not invent a new rule after seeing only a few terms.
A worked review example
Jo has eight cards. Rae has three times as many, so Rae has 3×8=24. If Rae instead had three more, the result would be eleven. The three repeated eight-card bars show why times-as-many requires multiplication. Underline times as many or more before calculating. A multiplier does not mean an added difference. Draw repeated equal reference bars and label the number of copies.
Make a practice plan
- Distinguish Times as Many from More: Six times as many as seven is 42; six more than seven is 13. Explain the distinction.
- Find Factor Pairs and Their Partners: List factor pairs of 18. Expected: 1×18,2×9,3×6.
- Classify Prime, Composite, and One: Classify 19 and 27. Expected: prime and composite, with 3×9 supporting 27.
- Generate a Pattern and Explain a Feature: Start at five and add six four times. Expected: 11,17,23,29, all odd.