How Many Cubes? «The Toy Factory »

Guiding Questions What is the relationship between the standard units of measure for area and volume? How does a change in the side of a shape affect the volume of the shape? How can two different shapes have the same volume?

Packaging Factory You have all just become employees at a packaging factory. Your company makes cardboard boxes of different shapes and sizes for packing and shipping products. One product you package is little toy figures. Each toy figure is the same size and is packaged in a little cube. You often need to ship more than one toy figure at a time, so you pack the cubes in larger shipping boxes. We’re going to work on determining how many cubes will fit in a shipping box and decide whether there’s a way that we can figure this out without actually counting each cube.

Here’s an example of a box that we could use to ship our toys. In this lesson, we are going to pretend that these unifix cubes are our toys and that these paper grid boxes are our shipping boxes. You’re going to work with a partner over the next couple of days. Let’s choose our partners from the hat...\..\..\..\Desktop\The Hat.lnk..\..\..\..\Desktop\The Hat.lnk Find a place to work with your partner and you will need the following supplies: grid paper, scissors, unifix cubes, pencil.

Now, let’s work together to make a box that is 4 x 3 x 2 and the rectangular prism that would fit inside it.

Now that we’ve practiced making one, it’s your turn. You will be working on Student Activity Book pg It has 6 problems to solve to find the number of cubes that fit in a box. We’ll use these cubes as the unit of measure to find the volume of the box.

For each problem you will: Determine how many cubes fit in the pictured box without building the box and write the first answer in the blank. Draw the box pattern on grid paper, cut it out, fold it, and tape the edges to make the box. Fill the box with cubes to check your first answer, then write the actual number of cubes that fit in the box. Think about how close your first answer was to the actual count before going on to the next problem.

Packaging Factory By now, everyone’s had a chance to work on most of the box patterns. Think about how you found the number of cubes that fit in the box before you built each one. We will be using this activity for our bulletin board in the hallway so really think through your writing and make sure it makes sense. On an index card: Describe a way to find how many cubes will fit in a rectangular box without building the box and filling it with cubes. Your method should work for any box, whether you start with a box pattern, a picture of the box, or a description of the box in words.

As you listen to your classmates explaining their strategies, your job is to think about what they’re saying and to see whether your strategy is similar or different. Remember that the strategy you present should work for any box, so try not to use specific numbers in your explanation. Strategies we came up with:

Now – let’s see if you can use your strategy to find the number of cubes in a box that you don’t build or have a pattern to look at. Find the number of cubes that fit in a box that is 20 units by 10 units on the bottom and 12 units high. How can you convince the rest of the class that your answer is correct? Put T32 on Elmo after a few minutes as a hint.

Pulling it all together You just gave me some really great strategies for finding out how much a box will hold. Let’s tie it all together. What is volume? Is there a formula we could write that would always work for finding volume?

Which of the following would require finding the volume? A.Determining the length of wallpaper border needed to go around the ceiling of a room B.Determining the amount of felt needed to cover the bottom of a jewelry box C.Determining how many 1-inch blocks fill a shoebox

Which of the following would be an appropriate unit for volume? A.Square cm. B.Cubic cm. C.Cm.

Jayne has a trunk that is shaped like a rectangular prism. It is 4 ft. long, 2 ft. wide, and 3 ft. tall. What is the number of cubic feet in her trunk? A.11 cu. ft. B.24 cu. ft. C.9 cu. ft. D.12 cu. ft.

How Many Cubes? «The Toy Factory » Day 2

Guiding Questions What is the relationship between the standard units of measure for area and volume? How does a change in the side of a shape affect the volume of the shape? How can two different shapes have the same volume?

Monday, we spent some time in class creating boxes and coming up with ways to figure out how many units would fit inside it. Let’s talk for a minute about the dimensions of 3 dimensional shapes If we wanted to describe the dimensions of this prism, what three numbers would we use? What do the numbers represent? We could write it 3 x 4 x 2 – in this situation (when describing dimensions) the x doesn’t mean to multiply – it means « by »

For the purposes of the activities we are working on this week, the order of the numbers isn’t really important. What is important is that you know what each of the numbers represents. Work with your partner on this: The packaging factory wants us to build a box that holds twice as many cubes as a 2 x 3 x 5 box. See how many boxes you can find that will hold twice as many cubes. Be sure to list the dimensions in your journal.

What are the dimensions of the boxes you found that will hold twice as many cubes as the 2 x 3 x 5 box? What do you notice about these dimensions? Talk to your partner about it.

Back at the Packaging Factory We are back to being employees at the packaging factory. We’re going to make boxes to ship different quantities of these five packages. Before, our “package” was only one cube, but now the “packages” have more than one cube. Here are my examples.

Your job is to determine how many of each package will fit in a box before it is made. For now, you will put only one kind of package in the box. For example, first you’ll find how many of Package A will fit in the box. Then you’ll find how many of package B will fit in the box, and so on. The Student Activity Book page 15 is similar to what you’ve been doing. First, you’ll try to determine the number of each package that will fit in the box, before you build. Then you’ll build the package(s) to see whether you are correct. Do them one at a time. That way, you’ll get better at finding accurate answers without building boxes.

I know that not everyone is finished with pg. 15 yet, but let’s stop to discuss. Who will explain a strategy for finding how many of Package A fit in the box? Your explanation should include describing your thinking and showing the materials you worked with. You need to convince everyone that your strategy is a valid strategy and be able to justify your thinking.