Lesson 9

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.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿Cómo describirían la forma de la casa de pájaros?” // “How would you describe the shape of the birdhouse?” (It looks like the sides are rectangles. It could be a rectangular prism.)

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.

• Display table from task.
• “Observen la tabla. ¿Qué observan? ¿Qué se preguntan?” // “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.

• 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.

• “¿Cómo estimaron el volumen de una casa para un pato joyuyo?” // “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.
• “¿Cómo estimaron el volumen de una casa para un carpintero pelirrojo?” // “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.
• “¿Cuáles números son los más amigables para estimar productos? ¿Por qué?” // “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 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).

• Groups of 2
• “Ahora van a encontrar el rango completo de volúmenes recomendados de cada una de las casas para pájaros” // “You are now going to find the full range of recommended volumes for each of the birdhouses.”

• 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

• “¿Cómo encontraron los volúmenes recomendados de la casa para un azulejo?” // “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 \(5 \times 5 \times 12\).
• “¿Cómo encontraron los volúmenes recomendados de la casa para un pato joyuyo?” // “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.