Unit 1, Lesson 6
Expressions for Volume (Parts 1 and 2)
Grade 5
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This Warm-up is the start of Part 1.
The purpose of this True or False? is for students to demonstrate the strategies and understandings they have for determining the equivalence of numerical expressions. These understandings help students deepen their understanding of the properties of operations and are helpful as students interpret expressions for volume. In this activity, students have an opportunity to notice and make use of structure (MP7) when they use the properties of operations to determine equivalence, without having to calculate.
This is the first time students experience the True or False? routine in grade 5. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.
Decide if each statement is true or false. Be prepared to explain your reasoning.
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Card Sort
To Copy (from Blackline Masters)
Card Sort Match the Expression Cards
To Gather
Connecting cubes
The purpose of this activity is for students to interpret expressions that represent the volume of a rectangular prism. This matching task gives students opportunities to analyze rectangular prisms and expressions closely and make connections between the structure in rectangular prisms and the symbols in their related expressions (MP2, MP7). If there is time and you would like to add student movement, have students make a poster to display the sorted cards. Students can walk around and add additional expressions to other posters to represent the volume of the prism.
Your teacher will give you a set of cards.
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The purpose of this activity is for students to compare and contrast two different ways to calculate the volume of a rectangular prism: multiplying the area of the base and its corresponding height, and multiplying all three side lengths. Students see that both strategies result in the same volume. It is a convention to consider a prism’s base the face on which it rests, however when calculating the volume of a rectangular prism, any face of the prism can be considered the base, as long it is multiplied by the corresponding height. Similarly, when calculating the volume of a rectangular prism, any edge can be considered the length, the width, or the height.
Work with your partner to complete the tables. One partner completes Table 1 and the other completes Table 2.
| length (units) | width (units) | height (units) | volume (cubic units) |
|
|---|---|---|---|---|
| Prism A | ||||
| Prism B |
| area of the base (square units) | height (units) | volume (cubic units) |
|
|---|---|---|---|
| Prism A | |||
| Prism B |
Optional
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Your teacher will assign you and your partner 2 prisms.
For each of your assigned prisms:
Give your expressions to your partner.
Which expression does not represent the volume of the prism in cubic units? How do you know?
What other expressions represent the volume of the prism in cubic units?
Notice and Wonder
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This Warm-up is the start of Part 2.
The purpose of this Notice and Wonder is to elicit the idea that all whole numbers (except 1) are either prime or composite, which will be useful when students express numbers as products of prime factors in a later activity. While students may notice and wonder many things about this chart, reviewing the definitions of prime and composite numbers from grade 4 and the fact that the number 1 is neither prime nor composite are the most important discussion points.
What do you notice? What do you wonder?
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At the end of Part 1:
Display Prism 1 from Activity 1:
“What expressions could we write to represent the volume of this prism in cubic units?”
For each expression, ask students to explain how it represents the volume of the prism. As students explain, record expressions on a poster for all to see. Use parentheses to show which factors represent the area of a base and which factor represents the corresponding height. If not mentioned by students, display and discuss these expressions.
Math Community
After the Cool-down, ask students to individually reflect on the following question: “Which norm did you feel was most important in your work today, and why?” Students can write their responses on the bottom of their Cool-down, on a separate sheet of paper, or in a math journal.
Tell students that as their math community works together over the course of the year, the group will continually add to and revise its “Doing Math” and “Norms” actions and expectations.
At the end of Part 2:
“Today we wrote expressions and equations to represent products and volumes using only prime factors. We discovered that we can represent composite numbers as products using only prime factors. What were some strategies you used to find the prime factors of a number?” (Decompose it into factors, then figure out if the factors are prime. Break up any composite factors into smaller and smaller factors until all the factors are prime. With even numbers, use 2 as a factor as many times as possible, then look for other prime factors.)
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If students choose an expression that doesn't represent the volume of the prism, consider asking:
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If students write numbers that don't correspond to the height for a given base, consider asking,
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If students identify only side lengths that include at least one composite number, consider asking:
Express each number as a product using only factors that are prime numbers.
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Building Toward
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to access Cool-down.