# Filling and Measuring

Lesson 13 of 19

## Objective: SWBAT: • Define volume. • Use a fractional unit cube to find the volume of rectangular prisms and cubes. • Use a formula to find the volume of rectangular prisms and cubes including fractional edges.

## Big Idea: What’s the volume of the sugar in this container? How would you solve this problem? Students apply their knowledge of volume to answer more complex problems.

*50 minutes*

#### Do Now

*7 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to review their strategies for filling a rectangular prism. Some students may multiply the length by the width by the height to determine how many cubes it will take. Other students may figure out the number of cubes in one layer and multiply that by the height of the box. I also want students to review how to multiply with fractions. A common mistake is for students to multiply the whole numbers together and then add on the fraction. Some students may create improper fractions to multiply. Other students may use the box method and multiply 6 by 4 and ¾ by 4 and then add the products together.

I ask students what strategies they are thinking about to answer the questions. I call on students share what they think and why. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others.**

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#### Problem

*3 min*

I read over the question. Students participate in a **Think Write Pair Share. **I chose not to include the measurements so that students will focus on the *process *of solving this problem. Some students may share that you can figure out the height of the sugar and multiply it by the length and width to find the volume of the sugar. Other students may share that you can find the total volume of the container and then subtract the volume of the empty space. Students are engaging in **MP2: Reason abstractly and quantitatively.**

#### Resources

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#### Fractional Unit Cubes

*7 min*

We fill in the notes together. I read over the problem. I give students a few minutes to write down their own strategy. I walk around and monitor student progress. Some students may find the volume of the smaller cube and then multiply it by 27 to find the volume of the larger cube. Other students may use the unit cube to find the dimensions of the larger cube and then multiply. Other students may find the volume of one layer and then multiply that volume by 3. Students are engaging in **MP6: Attend to precision**.

I call on 2-3 students who used different strategies to come up and show and explain their work. I tell students that they are responsible for copying at least one strategy that is different than how they solved the problem.

#### Resources

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#### Practice

*18 min*

**Notes:**

- Before this lesson, I use the ticket to gos from the previous lesson to
**Create Homogeneous Groups.** - I give each group a
**Group Work Rubric.** - I
**Post a Key**for these problems around the room.

We go over directions and expectations. I inform students that they should start with Practice B. If they struggle with the first question, they should go back and start with Practice B. My goal is that students complete Practice B. As students work I walk around to monitor student progress and behavior. Students are engaging in **MP6: Attend to precision.**

If students are struggling, I may ask them one or more of the following questions:

- What do you know? What are you trying to figure out?
- Make an estimate for your answer.
- What strategies do you have for finding volume?
- Does your answer make sense?

When students complete their work, they raise their hands. I quickly scan their work. If they are on track, I send them to check with the key. If there are problems, I tell students what they need to revise. If students successfully complete a practice set they can move onto the next set. If they complete Practice C they can move onto the challenge problems.

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#### Closure and Ticket to Go

*15 min*

For the **Closure**, I have students turn to the sugar problem that now has measurements. Students participate in a **Think Write Pair Share. **If students get stuck, I encourage them to flip back to their notes on this problem from the beginning of the lesson. I call on students to share their answer and explain their thinking. Students are engaging in **MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, **and** MP3: Construct viable arguments and critique the reasoning of others**.

I pass out** **the **Ticket to Go** and the **Homework.**

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Hi Andrea!

I love your lessons! They are very well designed and help students develop every one of the mathematical practices. I'd like to know, is there an answer key anywhere? Thanks

| 4 days ago | Reply

Hi Andrea!

I love your lessons! They are very well designed and help students develop every one of the mathematical practices. I'd like to know, is there an answer key anywhere? Thanks

| 4 days ago | Reply

Hi Andrea!

I love your lessons! They are very well designed and help students develop every one of the mathematical practices. I'd like to know, is there an answer key anywhere? Thanks

| 4 days ago | Reply

Hi Andrea!

Hi Andrea!

*expand comments*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Unit 7 Pretest
- LESSON 2: Perimeter vs. Area
- LESSON 3: Area of Triangles
- LESSON 4: Area of Composite Shapes
- LESSON 5: Exploring Circumference
- LESSON 6: Area vs. Circumference
- LESSON 7: Area, Perimeter, and Circumference
- LESSON 8: Classifying 3D Figures
- LESSON 9: 3D Figures and Nets
- LESSON 10: Nets and Surface Area
- LESSON 11: Show What You Know About Perimeter, Area, and Surface Area
- LESSON 12: Unit Cubes and Volume
- LESSON 13: Filling and Measuring
- LESSON 14: Designing Boxes
- LESSON 15: Geometry Jeopardy
- LESSON 16: Unit Closure
- LESSON 17: Unit Test
- LESSON 18: Quadrilaterals and the Coordinate Plane
- LESSON 19: Covering and Filling: Surface Area and Volume of Rectangular Prisms