The purpose of this activity is for students to notice and use the structure in multiplication expressions to represent the area of rectangles. Students estimate products to see if they are greater than or less than a given amount to solve a problem. Remind students they can draw a diagram if it is helpful.

• “What are some whole-number side lengths that would work for Priya’s garden?”
• Draw a diagram to represent a set of side lengths. “How does this diagram represent an area of 36 square feet?”

• Ask previously selected students to share how they know that two of the expressions will have values a little bit less than 36. (I know that  and is a little less than 4. I know that and is a little less than 3.)

In the previous activity, students reasoned about the value of each product by thinking about the decomposition of the mixed number factor, and how close the mixed number is to the nearest whole number. The purpose of this activity is for students to reason about the value of products by rounding either the whole number or mixed number factors and multiplying.

When students try to make a product close to 20 using the given digits, they will rely on number sense. They may need to experiment and refine their choices and strategy after finding the value of the product (MP1).

• Ask selected students to share.
• Consider asking:
  • “What strategies did you use to determine the just right product?” (I rounded the mixed number to a whole number based on the size of the fraction and multiplied.)
  • “In the third problem, is your product more, less, or equal to 20? How do you know?”