The purpose of this activity is for students to estimate whole-number products in the context of volume. In the next activity, students will calculate the least and greatest volumes within the range recommended for each type of bird. The estimates here may or may not fall within the range, depending on the numbers students pick. When making reasoned estimates, there is always some compromise between accuracy and using the most friendly numbers. During the Activity Synthesis, students explain the different strategies they use to make reasonable estimates, with calculations that they can perform as simply as possible, often mentally (MP3).

Students may need a quick reminder of how to find the volume of a rectangular prism. If needed, remind students that the volume of a rectangular prism is the product of the length, the width, and the height, or alternatively, the product of the area of a base and the height for that base.

• “How did you estimate the volume of a house for a wood duck?” (I know is 180 and I multiplied by 10 since that just adds a zero. I also used , but I multiplied by 20 since that is between 10 and 24. I got cubic inches.)
• “How did you estimate the volume of a house for a red-headed woodpecker?” (I found that the area of the floor is 36 square inches. I multiplied this by 10 to get 360 and by 20 to get 720, and then I picked a number in between, 500 cubic inches. I found the area of the floor was 36 square inches and I rounded that to 40 since it is a nicer number, and then I found , which is 480.)
• “Which numbers are the friendliest for estimating products? Why?”(10 is the friendliest because I can use place value. Multiples of 10, like 20, are also friendly, as I can multiply by 10 and then double.)

The purpose of this activity is for students to find the range of recommended volumes for the birdhouses introduced in the first activity. This means finding the value of the products of three numbers. Students will be able to choose which two factors to multiply first and may do so strategically so they can find the value mentally. Monitor for students who change their strategy, based on the numbers they are multiplying. Also monitor for students who are using the standard algorithm to multiply three-digit numbers by two-digit numbers.

When students interpret the meanings of the products they find in the volume context, they reason abstractly and quantitatively (MP2).

• “How did you find the recommended volumes of the bluebird house?” (I knew and . I used an algorithm to find . I knew and and then doubled that to get .)
• “How did you find the recommended volumes for the wood duck?” (The smallest volume is so I used place value to find the volume of 1,800 cubic inches. For the biggest volume, I multiplied 10 by , which I found with the standard algorithm.)