4.1 Factors and Multiples
Unit Goals
- Students apply understanding of multiplication and area to work with factors and multiples.
Section A Goals
- Determine if a number is prime or composite.
- Explain what it means to be a factor or a multiple of a whole number.
- Relate the side lengths and area of a rectangle to factors and multiples.
Section B Goals
- Apply multiplication fluency within 100 and the relationship between multiplication and division to find factor pairs and multiples.
Section A: Understand Factors and Multiples
Problem 1
Pre-unit
Practicing Standards: 3.MD.C.7.a
Find the area of each rectangle. Explain your reasoning.
Solution
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Problem 2
Pre-unit
Practicing Standards: 3.MD.C.7
On the grid, draw a rectangle whose area is represented by each expression.
- \(3 \times 5\)
- \(4 \times 8\)
Solution
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Problem 3
Tyler wants to build a rectangle with an area of 20 square units using square tiles.
- Can Tyler build a rectangle with a width of 4 units? Explain or show your reasoning.
- Can Tyler build a rectangle with a width of 6 units? Explain or show your reasoning.
Solution
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Problem 4
List the possible side lengths of rectangles with an area of 32 square units. Explain or show how you know your list is complete.
Solution
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Problem 5
List the factor pairs of each number. Is each number prime or composite? Explain or show your reasoning.
- 37
- 27
- 77
Solution
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Problem 6
-
Calculate the area of each rectangle.
- How did you use multiplication facts to calculate the areas?
Solution
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Problem 7
Exploration
-
You want to arrange all of the students in your class in equal rows.
- How many rows can you have? How many students would be in each row?
- What if you add the teacher to the arrangement? How would your rows change?
-
Find some objects at home (such as silverware, stuffed animals, cards from a game) and decide how many rows you can arrange them in and how many objects are in each row.
Solution
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Problem 8
Exploration
What is the largest prime number you can find? Explain or show why it is a prime number.
Solution
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Section B: Find Factor Pairs and Multiples
Problem 1
Pens are sold in packages of 5 and also in packages of 6.
- Jada wants to buy 60 pens for her class. Which packages of pens and how many should Jada buy if she doesn't want any extras? Explain or show your reasoning.
- Han wants to buy 55 pens for his class. Which packages of pens and how many should Han buy? Explain or show your reasoning.
Solution
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Problem 2
- Find the factor pairs of 36.
- How many factors does 36 have?
- List the factors of 15.
Solution
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Problem 3
Select all numbers that are multiples of 8.
Solution
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Problem 4
Exploration
- List the multiples of 2 up through 30.
- List the multiples of 3 up through 30.
- What do you notice about the numbers in the two lists?
Solution
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Problem 5
Exploration
Which number(s) from 1 to 100 have the largest number of factors? Explain or show how you know.
Solution
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