Unit Cubes and Volume

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Objective

SWBAT: â¢ Define volume. â¢ Use a unit cube to find the volume of rectangular prisms and cubes. â¢ Use a formula to find the volume of rectangular prisms and cubes.

Big Idea

What is volume? How many unit cubes would it take to fill this box? Students work to develop formulas for finding the area of rectangular prisms and cubes.

Do Now

7 minutes

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 the difference between surface area and area.  I want students to recognize that area is covering a two-dimensional figure while surface area is covering a three-dimensional figure.  I also want students to start using their spatial reasoning to determine the number of cubes that make up a figure.  Some students may struggle to count the cubes that they cannot see.  Other students may count the faces of the cubes without realizing that some cubes have multiple exposed faces.  If students struggle, I encourage them to think about the solid as a number of layers.

I ask students what strategies they are thinking about to answer the questions.  I call on students to share what they think and why.  If there is disagreement, build the first cube out of connecting cubes.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

How many cubes will it take to fill up the box?

8 minutes

Notes:

• For this lesson I have collected 12 open boxes that can be filled with unit cubes.  I use place value cubes and wooden cubes depending on the size of the box.  I only give students a few unit cubes, not enough to fill a complete layer of the box.
• If you don’t have boxes, you can use inch grid paper to create boxes.  Here are some examples. I show students that we can create a net for the rectangular prism.  Some students struggle to use the three labeled dimensions to label the other sides of the net.  I explain that each rectangular prism is composed of three matching faces.  Two faces that fold together to make one edge must share the same measurement.

I explain the task to the students and review expectations.  I pass out materials.  As students work I walk around to monitor student progress and behavior.  Students are engaging in MP5: Use appropriate tools strategically, MP6: Attend to precision, and MP8: Look for and express regularity in repeated reasoning.

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

• How many unit cubes do you have?
• How many unit cubes would it take to fill the bottom of the box?  How do you know?
• Is there another way to find the number of unit cubes it would take to fill the box?

If students complete the problem and explain their thinking on their paper I may ask them:

• How many unit cubes would it take to fill half of the box?
• How many unit cubes would it take fill 1/3 of the box?
• Another box takes up 75% of the space of your box.  How many cubes would it take to fill it?

Volume

8 minutes

We fill in the notes and complete the examples together.  I want students to look for patterns when finding the volume of the boxes.  Some students may notice that if you multiply the length, width, and height the result is the total number of cubes it takes to fill the box.  Other students may notice that if you multiply the number of cubes it takes to fill the bottom of the box by the height the result is the total number of unit cubes that it takes to fill the box.  I push students to see whether these ideas work for each of the different boxes.  Students are engaging in MP8: Look for and express regularity in repeated reasoning.

Guided Practice

5 minutes

We work on these questions together.  I ask students, “How can we apply the work we just did to answer these questions?”  I call students up to the front to show their ideas and explain their thinking under the document camera.

Practice

12 minutes

Note:

• I Post a Key for these problems around the room.

We go over directions and expectations.  As students work I walk around to monitor student progress and behavior.  Students are engaging in MP6: Attend to precision and MP8: Look for and make sense of repeated reasoning.

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?