Unit 1, Lesson 6
Expressions for Volume (Parts 1 and 2)
Grade 5
Preparation
Lesson Narrative
Note: The material in this lesson is intended to be covered over two instructional days. Part 1 refers to the first day of instruction, and Part 2 refers to the second day.
In a previous lesson, students learned to find the volume of a rectangular prism by multiplying the number of cubes in a base layer by the number of layers. They connected this understanding to the multiplication of the length, the width, and the height to find the volume of a rectangular prism. They also used a two-dimensional representation of a base and its corresponding height to find the volume of a rectangular prism.
In Part 1 of this lesson, students write and interpret numerical expressions that represent the volumes of rectangular prisms. Students use what they know about rectangular prisms to reason whether or not an expression represents the volume of a rectangular prism.
In grade 4, students learned about prime and composite numbers. In Part 2 of this lesson, students combine and extend those skills and concepts. Students find different side lengths for prisms with the same volume. They use the side lengths to write expressions that represent the volume, and they identify which of those expressions use only prime factors. Then students determine if given volumes for rectangular prisms can be created using only prime factor side lengths. Lastly, they practice expressing different numbers as products of prime factors.
During the next lesson, "Cubic Units of Measure," students will describe which standard cubic unit they would use to measure the volumes of objects that are shaped like rectangular prisms. Consider which objects students see on a regular basis in their communities that are shaped like rectangular prisms and bring pictures of those objects to show students during the next lesson. If possible, consider going on a prism scavenger hunt around the community before the next lesson.
Math Community
Tell students they will reflect on their identified norms at the end of this lesson.
- Engagement
- MLR8
- Compare and contrast (orally) different ways of determining the volume of a rectangular prism.
- Comprehend (in spoken and written language) that the “length, the width, and the height” of a rectangular prism refer to the side lengths of the prism.
- Generate equations to represent the volume of rectangular prisms using the formula $V = l \times w \times h$.
- Match (orally) rectangular prisms and expressions that represent the same volume. Generate expressions that represent the volume of a rectangular prism.
- Represent (in writing) a whole number between 2 and 50 as a product of prime factors.
Required Materials
Activity 1
Activity 4
Activity 5
Required Preparation
- Create a set of cards from the blackline master for each group of 2 students.
- Have connecting cubes available for students who need them.
- Each group of 2 needs at least 30 connecting cubes.
Teacher Reflection Questions
After Part 1:
As students matched expressions to images of prisms today, what evidence did you see that they are building on their understanding of the structure of rectangular prisms?
After Part 2:
Which math ideas from today’s lesson did students grapple with most? Did this surprise you, or was this what you expected?