Guided Lessons

# Various Volumes Solution

Strengthen your students' understanding of cubic units and volume! They'll solve a realistic problem and explain key ideas about volume. Use this lesson on its own or use it as support for the lesson Volume and a Building.
This lesson can be used as a pre-lesson for theVolume and a BuildingLesson plan.

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This lesson can be used as a pre-lesson for theVolume and a BuildingLesson plan.

Students will be able to use the formula V = l × w × h to find the volume of rectangular prisms in real-world situations.

##### Language

Students will be able to solve a real-word problem about volume and explain their answer using peer support.

(3 minutes)
• Show a box of any size and ask students to think about all the books that may fit into the box. Allow them to share their ideas aloud with the class and choose books.
• Integrate some of the vocabulary words relating to volume (e.g., "length," "width," "height") as you model restating their answers.
• Have a volunteer check the guesses by trying to put the books into the box. Emphasize that they added volume to the box with each book they added to show that volume is additive.
• Explain that today they'll learn about why they should know the volume of boxes and how it will help them with packaging.
(5 minutes)
• Provide a real-world scenario that requires students to consider the volume of rectangular prisms and whether objects will fit into a box. For example, tell the students, "The United States Post Office has flat-rate boxes that will ship heavy books for a flat price, but the books have to fit within the volume of the box. I don't have the box yet, but I know the dimensions of the box are 12in × 12in × 6in. I do have 4 books of varying dimensions that I can measure. Will you help me see if the books will fit?"
• Distribute the vocabulary cards and have students choral read the meanings with you.
• Direct students to create a rectangular prism using themselves as the sides to demonstrate the words Width, Length, Height. Have two sets of three students stand shoulder to shoulder to represent the length and two sets of two students stand shoulder to shoulder to represent the width.
• Emphasize that the length is the longer measure of an object from front-to-back (or three students long) and the width is the shorter measure of an object side-to-side (or two students long). The height is how tall the students are. Students should imagine all participants are the same height.
(12 minutes)
• Model finding the volume of one of the books using the volume formula V = l × w × hAnd ask students to copy your teacher marking onto their vocabulary cards. Have a student recount the steps you used to find the volume of the book and write the steps on the board:
1. Find the length, width, and height of the rectangular prism.
2. Multiply the length by the width.
3. Multiply that product by the height.
4. Label the volume, adding the unit of measurement cubed.
• Separate students into partnerships and ask them to find the volume of a book. Then, have them each explain to their partner how they determined the volume of the book. Encourage students to use their vocabulary cards to remind them of the key vocabulary terms in their explanations. Provide sentence frames such as:
• "First, I ____, and then I ____."
• "After I ____, I then ____."
• Monitor their conversations and choose a student to share the processes aloud. Write down some of their explanations on the board.
(10 minutes)
• Allow each group to share the volume of the book with the class and call on one person from the group to share how they got the answer.
• Ask the whole class to consider if the books, given their volumes, will fit into the flat-rate box. Lead them to determine they need to add up the volumes of the books, but then also consider whether the length and widths (i.e., area) of the books themselves will fit into the box. At least one book should not be able to fit given its length.
• List the volumes for all the books from the different groups on the board. Separate students into different groups of 4 to find the total volume of all the books they can fit into the box. Give students the chance to check their answers by putting the books into the large flat-rate box.
• Tell students they will have to explain each step they used to solve the problem of the day (i.e., "Will the 4–6 books fit into the large flat-rate box?") Explain that you will call on a random person to give an explanation so they should make sure each group member can give an explanation by helping each other. Possible reasons for the books to fit or not fit can include the volume, length, width, or number of books.
• Provide the following sentence frames they can use in addition to the other sentence frames from the board: "I know ____Fit because ____," and "Another reason I know ____Fit is because ____."

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all their conversations.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Provide reference materials in their L1 to assist in their vocabulary word acquisition.
• Have them only explain one step of the process instead of multiple steps.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Allow them to find the measurements of the books and then calculate the volume.
• Encourage them to explain their process for finding the volume to the class to model a clear explanation.
(7 minutes)
• Allow students to talk about the steps they used to solve the problem in groups and then tell them to restate their answers in partners.
• Choose 1–3 students to share their explanations aloud with the class.
• Use the Formative Assessment: Peer Persuasion Checklist worksheet to evaluate their responses. Use that information to help highlight strengths and improvements in their reasoning or explanations.
(3 minutes)
• Write down two example responses you observed during the assessment or group work on the board. Ask students to compare the explanations and critique them. Encourage them to consider the vocabulary and clarity of the examples. (Tip: choose an exemplary example and an example that needs improvement.)
• Emphasize that understanding volume will help when they consider more irregular shapes, like roller skates or helmets, and whether they will fit into particular boxes.