The purpose of this activity is for students to make a reasonable estimate for a given product. In addition to estimating the product, students also decide whether the estimate is too large or too small. In the Activity Synthesis, students consider how far their estimate is from the actual product. In the next activity, students will evaluate the expressions, using a strategy of their choice.

Students choose between several different possible estimates and justify their choice before they calculate the product (MP3).

• Invite students to share their estimates for the product and their reasoning.
• “Why do you think is a good estimate?” (18 is close to 20 and 149 is very close to 150, and I know .)
• “Is the value of greater than or less than ? How do you know?” (Less, because 18 is less than 20 and 149 is less than 150.)
• “Can you estimate how much less?” (About 300, because I added 2 to 18 to get 20 and is about 300.)
• Display the sentence “ is about .”
• “In the next activity, we’ll check to see how good our estimate is.”

The purpose of this activity is for students to multiply a three-digit number by a two-digit number, using a strategy that makes sense to them. The expressions are scaffolded so that students can use one calculation to help with the next, particularly when they look for the final product, which is .

Students may:

• Draw diagrams to help visualize the calculations.
• Use a form of partial products and the distributive property.
• Round 49 to 50 or 149 to 150, and then compensate.

This activity encourages students to compare the strategy they used with the strategies that their classmates used, and to discuss the similarities and differences. The intent of this activity is not to create a list of strategies for students to choose from. Instead, students have an opportunity to think about how the properties of operations and place-value understanding were used in each strategy.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• 5–7 minutes: Gallery Walk
• “What is the same and what is different between the approaches used to find the values of the expressions?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Invite students to share their diagrams.
• Highlight at least one diagram, or use the diagram from the student solutions. “How does the diagram help keep track of the calculations?” (For , I know I need to find and , and then add them.)