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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now a smaller box: 5 long, 2 wide, 2 tall. What formula do we use? Let's put in the numbers: V = 5 × 2 × 2. What is 5 × 2? We got 10. Now multiply 10 × 2. What is the volume? Yes, V = 20 cubic units. Don't forget the cubic units! Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartTo find the area of a composite figure, you first…

   1. Abreak it into basic shapes you know
   2. Bmeasure around the outside
   3. Cmultiply all the side lengths
   4. Dfind the longest side

   How do you know?
3. 3

   Warm restartA figure is a 6 by 4 rectangle with a 2 by 3 rectangle attached. What is the total area?

   1. A30 square units
   2. B24 square units
   3. C15 square units
   4. D144 square units

   How do you know?
4. 4

   Warm restartA 10 by 8 rectangular garden has a 3 by 3 square patio cut out of it. What area is left?

   1. A71 square units
   2. B89 square units
   3. C80 square units
   4. D62 square units

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the volume of the large box?

   1. A7,776 in³
   2. B4,752 in³
   3. C3,024 in³
   4. D60 in³

   Why is that the answer?
2. 6

   Think it throughWhat is the volume of the medium box?

   1. A2,520 in³
   2. B3,024 in³
   3. C3,240 in³
   4. D4,752 in³

   How do you know? Give a second reason as well.
3. 7

   Think it throughHow many more cubic inches does the large box hold?

   1. A4,752 in³
   2. B10,800 in³
   3. C1,728 in³
   4. D3,024 in³

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelContainer C holds the most (96 in³) and Container B holds the least (50 in³). What do you notice about the dimensions that make one volume larger than another?

Use the words

Fill each blank with a word from the bank.

• The number of unit cubes inside a prism, found with V = l × w × h, is the ___.
• The amount of space inside a three-dimensional solid is its ___.
• A solid with six rectangular faces, like a box, is a ___.
• The unit used to measure volume, like cubic centimeters, is ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box.
2. 10

   Say moreContainer C is 8 × 3 × 4 and Container B is 5 × 5 × 2. How did you count or multiply the unit cubes to find each volume, and which holds more?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Two time capsule containers sit side by side. Capsule A is 4 in long, 3 in wide, and 8 in tall. Capsule B is 6 in long, 6 in wide, and 6 in tall. A classmate says Capsule A must hold more because it looks taller.

   Show your work

Last check

These two come from Lesson 5.4. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A rectangular prism has l = 11 in, w = 5 in, h = 4 in. What is the volume?

   1. A220 in³
   2. B55 in³
   3. C220 in²
   4. D200 in³

   Explain your choice.
2. 13

   From Lesson 5.4Explain your thinking — A composite figure is made of a 9 ft x 7 ft rectangle and a 3 ft x 4 ft rectangle joined together. What is the total area?

   1. A75 sq ft
   2. B63 sq ft
   3. C12 sq ft
   4. D75 ft

   How do you know?
3. 14

   From Lesson 5.4What will the carpet cost?

   1. A$580
   2. B$116
   3. C$300
   4. D$1,160

   How do you know?

Be honest — this tells your teacher what to do next