Multiplicatin as a Comparison
What two comparisons does the equation 6 × 5 = 30 show? (Write both verbal comparisons.)
30 is 6 times as many as 5." and "30 is 5 times as many as 6.
Ben has 24 stickers. He shares them equally among 4 friends. How many stickers does each friend get? Write an equation.
24 ÷ 4 = 6 stickers each.
Is 24 a multiple of 6? Explain briefly how you know.
Yes; 6 × 4 = 24.
List the factor pairs of 12.
(1,12), (2,6), (3,4)
Is 2 prime or composite? Explain in one sentence.
2 is prime (only factors 1 and 2).
Write two comparisons that model 28 = 7 × 4
"28 is 7 times as many as 4" and "28 is 4 times as many as 7."
A teacher packs 36 pencils into boxes of 6. How many boxes are needed? Write and solve the equation.
36 ÷ 6 = 6 boxes.
List the first five multiples of 4.
4, 8, 12, 16, 20
Is 18 a factor of 90? Explain and show the factor pair that proves it.
Yes; 18×5=90 → factor pair (18,5)
Is 15 prime or composite? Give its factors.
15 composite; factors 1,3,5,15.
Write a multiplication equation to match this statement: "45 is 9 times as many as what number?" Then explain the two comparisons that equation represents.
Equation: 45 = 9 × 5; comparisons: "45 is 9 times as many as 5" and "45 is 5 times as many as 9."
Sal rides his bike 24 miles on Sunday. That is 3 times as many miles as he rides on Saturday. What is the total number of miles he rides on Saturday and Sunday? Write equations and show work.
Saturday = 24 ÷ 3 = 8; total = 8 + 24 = 32 miles.
Which of these numbers are multiples of 6: 18, 25, 30, 42? Explain your reasoning.
Multiples: 18 (yes), 25 (no), 30 (yes), 42 (yes).
Find all factor pairs of 36. How many factor pairs are there?
(1,36),(2,18),(3,12),(4,9),(6,6) → 5 pairs
Explain how to decide whether 29 is prime or composite. State which it is and why.
29 is prime — not divisible by 2,3,5,7
The product is 72. Give two different multiplication equations that show multiplicative comparisons for 72 using factors 8 and 9. Then write the two verbal comparisons those equations represent.
Equations: 72 = 8 × 9 and 72 = 9 × 8. Verbal: "72 is 8 times as much as 9" and "72 is 9 times as much as 8"
A canoe holds 3 people. There are 28 people (students, teachers, parents). How many canoes are needed? Write an equation using a variable for canoes and explain how you handle any remainder.
Total people 28 ÷ 3 = 9 R1 → need 10 canoes; remainder means one canoe not full.
Given the list 6, 12, 18, 24, 30 — choose all true statements:
(A) They have 4 as a factor.
(B) They have 6 as a factor.
(C) They are factors of 6.
(D) They are multiples of 4.
(E) They are multiples of 6. Explain each choice.
True choices: B and E are true; explain others false (4 is not a factor of 6, etc.).
Determine whether 49 is prime or composite. If composite, list its factor pairs.
49 composite? 49 = 7×7 so composite; factor pair (7,7)
Give three examples of composite numbers between 20 and 40 and list at least one factor pair for each.
Examples: 21 (3×7), 24 (3×8), 30 (5×6) with factor pairs listed.
Create a multiplicative comparison that could be written as 5 × n = 65. Write the equation and both verbal comparisons. Explain why one of the comparisons shows "65 is 5 times as many as n" and the other shows "n is 65 divided by 5 times as many as 13."
Equation: 65 = 5 × 13; comparisons: "65 is 5 times as many as 13" and "13 is 5 as many as 65."
A baker needs 150 cookies packaged in boxes that each hold 8 cookies. She already packed 7 full boxes. How many more full boxes does she need, and how many cookies will be left over? Show equations and interpret remainders.
Need total boxes 150 ÷ 8 = 18 R6. Already 7 boxes → need 11 more full boxes; 6 cookies left over.
Find all multiples of 7 that are less than 100. Then explain how to test whether a number is a multiple of 7 (give one strategy a 4th grader could use).
Multiples of 7 <100: 7,14,21,28,35,42,49,56,63,70,77,84,91,98.
Find all factor pairs for 96. Then explain how knowing factor pairs can help you multiply or divide more quickly.
Factors of 96 pairs: (1,96),(2,48),(3,32),(4,24),(6,16),(8,12)
Describe a quick test to check whether a given two-digit number is definitely composite (give at least two divisibility checks a 4th grader can use), and then apply your test to 91 and explain whether 91 is prime or composite.
Tests: divisibility by 2,3,5,7,11; 91: 7×13 = 91 so composite.