# Lesson 9

The Birds

## Warm-up: Notice and Wonder: For the Birds (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that the shape of a birdhouse can be modeled by a rectangular prism, which will be useful when students solve problems about the volume of birdhouses in a later activity. While students may notice and wonder many things about the photograph, the shape of the birdhouse is the important discussion point.

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How would you describe the shape of the birdhouse?” (It looks like the sides are rectangles. It could be a rectangular prism.)

## Activity 1: Home is Where the Bird Lives (15 minutes)

### Narrative

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 smallest and largest 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 tension between accuracy and using the most friendly numbers. During the 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, width, and height, or alternatively, the product of the area of a base and the height for that base.

### Launch

• “What do you notice and wonder about the table?” (There are different kinds of birds listed. There are side lengths for the floor but the height is a range. What do the numbers mean? Do smaller birds have smaller houses?)
• 1 minute: quiet think time
• Share and record student responses.
• If needed, display images of different kinds of birds.

### Activity

• 2 minutes: quiet think time
• 5 minutes: partner work time
• Monitor for students who consider friendly numbers to use for the height and also for estimating the product of the area of the floor and the height.

### Student Facing

Different types of birds use different types of houses. The table gives you the recommended side lengths for birdhouses of various species.
type of bird side lengths of floor height volume estimate
chickadee 4 in by 4 in 6 to 10 in
wood duck 10 in by 18 in 10 to 24 in
barn owl 10 in by 18 in 15 to 18 in
red-headed woodpecker 6 in by 6 in 12 to 15 in
bluebird 5 in by 5 in 6 to 12 in
swallow 6 in by 6 in 6 to 8 in
Estimate a possible volume for each birdhouse. Be prepared to explain your reasoning.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How did you estimate the volume of a house for a wood duck?”
• I know $$10 \times 18$$ is 180 and I multiplied by 10 since that just adds a zero.
• I also used $$10 \times 18 = 180$$ but multiplied by 20 since that is between 10 and 24. I got $$3,600$$ 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 picked a number in between, 500 cubic inches.
• I found the area of the floor was 36 square inches. I rounded that to 40 since it is a nicer number and then found $$40 \times 12$$ 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.)

## Activity 2: What is the Volume? (20 minutes)

### Narrative

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 products of 3 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 meaning of the products they find in the volume context, they reason abstractly and quantitatively (MP2).

MLR1 Stronger and Clearer Each Time. Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to “What is the possible range of volumes for each type of birdhouse?”. Invite listeners to ask questions, to press for details, and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.
Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for determining the possible range of volumes for each type of birdhouse before they begin.
Supports accessibility for: Organization, Conceptual Processing, Language

### Launch

• Groups of 2
• “You are now going to find the full range of recommended volumes for each of the birdhouses.”

### Activity

• 5 minutes: individual work time
• 5 minutes: partner work time
• Monitor for students who use different strategies including:
• mental calculations for smaller products
• place value understanding when multiplying by 10
• the standard algorithm

### Student Facing

Use the criteria from the table to determine the recommended range of volumes for each type of birdhouse.
type of bird side lengths of floor height range of volume
chickadee 4 in by 4 in 6 to 10 in
wood duck 10 in by 18 in 10 to 24 in
barn owl 10 in by 18 in 15 to 18 in
red-headed woodpecker 6 in by 6 in 12 to 15 in
bluebird 5 in by 5 in 6 to 12 in
swallow 6 in by 6 in 6 to 8 in

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How did you find the recommended volumes of the bluebird house?”
• I knew $$5 \times 5 = 25$$ and $$25\times 6 = 150$$. I used an algorithm to find $$25 \times 12$$.
• I knew $$5 \times 6 = 30$$ and $$30 \times 5 = 150$$ and then doubled that to get $$5 \times 5 \times 12$$.
• “How did you find the recommended volumes for the wood duck?”
• The smallest one is $$10 \times 10 \times 18$$ so I used place value to find the volume of 1,800.
• The biggest one I multiplied 10 by $$18 \times 24$$, which I found with the standard algorithm.

## Lesson Synthesis

### Lesson Synthesis

“Today we used different strategies to solve multiplication problems.”
“When is it most helpful to use the standard algorithm for multiplication?” (I like to use it when the numbers are complicated. I always like to use it because it's reliable and I know how it works.)

“Take a minute to think about which of these problems you would use the standard algorithm to solve. Then share your strategy with your partner.”

$$45 \times 6$$
$$20 \times 200$$
$$143 \times 67$$
$$125 \times 9$$

“Different problems call for different strategies, and we each might choose a different way to solve each of these problems. We could use the standard algorithm to solve all these problems, but we don’t have to.”

## Cool-down: On Screech (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

In this unit we found products of a three-digit number and a two-digit number. We first

represented the products with diagrams that help us break down the product by place value.

This diagram breaks up the product $$412 \times 32$$ by place value. If we find and add up all of the partial products, we will get the product of $$412 \times 32$$.

Then we learned a new algorithm to multiply numbers, the standard algorithm for multiplication.

We can see the partial products are organized in a different way. 824 represents the partial product for $$2 \times 412$$ and 12,360 represents the partial product for $$30 \times 412$$.

We noticed that sometimes we need to compose a new unit when we use the standard algorithm, and we represent that unit with notation. Sometimes, we may have to compose more than one new unit.

The 1 above the 1 in 216 represents the ten from the product $$3 \times 6$$ and the 2 represents 2 hundreds from the product $$40 \times 6$$.