3.PAR.3.1 Multiplication Patterns
Zuri notices that 4 × 3 = 12 and 4 × 4 = 16.
What pattern is happening? Use the pattern to find 4 × 5. Explain.
4 × 3 = 12, 4 × 4 = 16, so the products increase by 4 each time.
Answer: 4 × 5 = 20
Arrington has 3 bags with 5 apples in each.
Draw or describe an array and find the total apples.
3 bags with 5 apples in each means 3 groups of 5.
3 × 5 = 15
Answer: 15 apples
Lyric says 5 × 7 = 7 × 5.
What property is this? Explain.
5 × 7 = 7 × 5 shows the Commutative Property of Multiplication.
Answer: Commutative Property
Is 4 × 6 equal to (4 × 3) + (4 × 3)? Explain.
4 × 6 = 24
(4 × 3) + (4 × 3) = 12 + 12 = 24
Answer: Yes, they are equivalent; both equal 24
Find: 3 × 20
What is 60?
A multiplication chart shows that multiples of 6 increase by the same amount.
What is 6 × 7 if 6 × 6 = 36? Explain the pattern you used.
If 6 × 6 = 36, then one more group of 6 makes 6 × 7 = 42.
Answer: 42
There are 20 cookies shared equally among 4 students.
Write a multiplication and division equation to represent the problem.
20 cookies shared equally among 4 students:
20 ÷ 4 = 5
Related multiplication fact: 4 × 5 = 20
Answer: 20 ÷ 4 = 5 and 4 × 5 = 20
Sumayyah solved 8 × 6 by doing (8 × 5) + (8 × 1).
What property did she use?
8 × 6 = (8 × 5) + (8 × 1) breaks apart 6 into 5 + 1.
Answer: Distributive Property
Is 3 × 8 equal to (3 × 4) + (3 × 4)?
Find both answers.
Yes, both equal 24
Find: 5 × 40
What is 200?
Katia says: “Multiples of 8 are always even.”
Use two examples to prove or disprove her statement.
Yes, Katia is correct.
Examples:
8 × 2 = 16
8 × 5 = 40
Both products are even.
Answer: Her statement is true
A teacher arranges 24 desks into equal rows.
Give TWO different ways to arrange the desks and explain.
24 desks can be arranged in more than one equal way:
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
Answer: Any two valid arrangements, such as 3 rows of 8 and 4 rows of 6
$400
Jashanta’ says 4 × (3 × 2) = (4 × 3) × 2.
Explain if she is correct and name the property.
Yes, Jashanta’ is correct.
4 × (3 × 2) = (4 × 3) × 2
24 = 24
Answer: Associative Property of Multiplication
Chukwu says (5 × 10) + (5 × 2) = 5 × 12.
Is she correct? Explain why.
(5 × 10) + (5 × 2) = 50 + 10 = 60
5 × 12 = 60
Answer: Yes, Chukwu is correct
Find: 7 × 30
Explain using place value.
What is 210?
A pattern shows: 3 × 2 = 6, 3 × 4 = 12, 3 × 6 = 18
What will 3 × 8 equal? Explain how the pattern helped you.
The pattern increases by 6 each time: 6, 12, 18, so next is 24.
Answer: 3 × 8 = 24
Chiteka says 6 × 4 = 24 and 24 ÷ 6 = 4 are related.
Explain how multiplication and division are connected.
Multiplication and division are related because division can undo multiplication.
Since 6 × 4 = 24, then 24 ÷ 6 = 4 and 24 ÷ 4 = 6.
Answer: They are inverse operations
Kerrington solved 9 × 3 by doing (10 × 3) − 3.
Explain what strategy and property she used.
9 × 3 = (10 × 3) − 3
30 − 3 = 27
This uses breaking apart 9 as 10 − 1.
Answer: Distributive Property with a compensation strategy
Which is equal to 8 × 6?
A. (8 × 3) + (8 × 3)
B. (6 × 6)
Explain your choice
What is A. (8 × 3) + (8 × 3)?
A store packs pencils in boxes of 50.
How many pencils are in 8 boxes? Explain your thinking.
8 boxes of 50 pencils:
8 × 50 = 400
Answer: 400 pencils
McKenna notices that multiples of 5 always end in 0 or 5.
Use this pattern to determine if 5 × 13 will end in 0 or 5. Explain your thinking
Multiples of 5 always end in 0 or 5.
5 × 13 = 65, so it ends in 5.
Answer: 65, ending in 5
A classroom has 36 books. They are placed into equal groups.
List all possible equal groupings and explain how you know.
Possible equal groupings for 36:
1 × 36
2 × 18
3 × 12
4 × 9
6 × 6
Also the related turn-around facts.
Answer: Valid equal groupings include 1, 2, 3, 4, 6, 9, 12, 18, 36
A student says 8 × 6 = (8 × 3) + (8 × 3).
Is this true? Explain.
Yes, true
Write an equivalent expression for 9 × 5 using addition.
What is 9 + 9 + 9 + 9 + 9 = 45?
Compare 9 × 40 and 4 × 90.
Which is greater? Explain using place value or patterns.
9 × 40 = 360
4 × 90 = 360
Answer: They are equal