Section A: Practice Problems Understand Factors and Multiples

Section Summary

Details

In this section, we used our understanding of the area of rectangles to learn about factors, multiples, factor pairs, prime numbers, and composite numbers.

If we know the side length of a rectangle, we can find the areas that the rectangle could have. For instance, a rectangle with a side length of 3 could have an area of 3, 6, 9, 12, 15, or other numbers that result from multiplying of a whole number and 3. We call these numbers multiples of 3.

If we know the area of a rectangle, we can find the side lengths that it could have. For example, a rectangle with an area of 24 square units can have side lengths of 1 and 24, 2 and 12, 3 and 8, or 4 and 6. We call these possible pairs of side lengths the factor pairs of 24.

4 rectangles.

We also learned that a number that has only one factor pair—1 and the number itself—is called a prime number. For instance, 5 is prime because its only factor pair is 1 and 5.

A number that has two or more factor pairs is a composite number. For instance, 15 is composite because its factor pairs are 1 and 15, and 3 and 5.

Problem 1 (Pre-Unit)

Find the area of each rectangle. Explain your reasoning.

  1.  

    Area diagram. 3 rows of 6.

  2.  

    Diagram. Rectangle partially partitioned to show 4 rows of 7 same sized squares.

Problem 2 (Pre-Unit)

On the grid, draw a rectangle whose area is represented by each expression.

blank grid of 12 by 12.

Problem 3 (Lesson 1)

Tyler wants to build a rectangle with an area of 20 square units using square tiles.

  1. Can Tyler build a rectangle with a width of 4 units? Explain or show your reasoning.

  2. Can Tyler build a rectangle with a width of 6 units? Explain or show your reasoning.

Problem 4 (Lesson 2)

List the possible side lengths of rectangles with an area of 32 square units. Explain or show how you know your list is complete.

Problem 5 (Lesson 3)

List the factor pairs of each number. Is each number prime or composite? Explain or show your reasoning.

  1. 37

  2. 27

  3. 77

Problem 6 (Lesson 4)

  1. Calculate the area of each rectangle.

    Grid with 4 rectangles labeled A, B, C, D.

  2. How did you use multiplication facts to calculate the areas?

Problem 7 (Exploration)

You want to arrange all of the students in your class in equal rows.

  1. How many rows can you have? How many students would be in each row?

  2. What if you add the teacher to the arrangement? How would your rows change?

  3. 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.

Problem 8 (Exploration)

What is the largest prime number you can find? Explain or show why it is a prime number.