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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: 4 long, 3 wide, 2 tall. How many pairs of faces does it have? Top and bottom: 4 × 3 = 12, times 2 = 24. Front and back: 4 × 2 = 8, times 2 = 16. Left and right: 3 × 2 = 6, times 2 = 12. Now add 24 + 16 + 12. What is the surface area? Yes, SA = 52 in². Remember to use square units. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the volume of a rectangular prism with l = 4 in, w = 3 in, h = 5 in?

   1. A12 in³
   2. B60 in²
   3. C24 in³
   4. D60 in³

   How do you know?
3. 3

   Warm restartA box has a base area of 12 square cm and a height of 3 cm. What is its volume?

   1. A36 cm³
   2. B15 cm³
   3. C4 cm³
   4. D36 cm²

   How do you know?
4. 4

   Warm restartA box has a volume of 36 cm³. Its length is 6 cm and width is 3 cm. What is the height?

   1. A6 cm
   2. B3 cm
   3. C12 cm
   4. D2 cm

   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 surface area of the box?

   1. A568 in²
   2. B840 in²
   3. C284 in²
   4. D280 in²

   Why is that the answer?
2. 6

   Think it throughWhy is each face pair multiplied by 2?

   1. AA rectangular box has two identical faces of each size
   2. BBecause you always double in geometry
   3. CBecause there are 2 sheets of paper
   4. DTo convert to square inches

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

   Think it throughHow many sheets of wrapping paper do you need?

   1. A1
   2. B2
   3. C3
   4. D568

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

   Back to the modelThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

Use the words

Fill each blank with a word from the bank.

• The total area of every face, found by adding the faces in a net, is the ___.
• The total area of all the faces of a solid is its ___.
• A flat pattern that folds up into a solid is a ___.
• A flat surface of a solid figure is a ___.

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 Surface Area Using Nets is finding the area of only one face from each of the 3 matching pairs and forgetting to double it, instead of counting all 6 faces.
2. 10

   Say moreFor the box l = 8, w = 5, h = 3, you found three face pairs. How did you use the net to organize the faces into pairs, and which pair had the largest area?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Yuzuki is making paper replicas of the Pyramids of Giza for a social studies project. She has flat sheets of paper and needs to know how much paper each pyramid will take.

   Show your work

Last check

These two come from Lesson 5.5. 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 = 9 in, w = 5 in, h = 3 in. What is the surface area?

   1. A174 in²
   2. B135 in²
   3. C174 in³
   4. D87 in²

   Explain your choice.
2. 13

   From Lesson 5.5Explain 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

   How do you know?
3. 14

   From Lesson 5.5How 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

   How do you know?

Be honest — this tells your teacher what to do next