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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: A box is 4 in long, 3 in wide, and 2 in tall. Use its net to find its surface area. Find the area of each pair of faces. (2 × 12 = 24, 2 × 8 = 16, 2 × 6 = 12) Add the pairs. What is the surface area? (24 + 16 + 12 = 52 square inches) Why do we multiply each face area by 2? (Each face has a matching face on the opposite side. Top matches bottom, front matches back, left matches right.)

   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. B24 in³
   3. C60 in²
   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. A4 cm³
   2. B15 cm³
   3. C36 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. A2 cm
   2. B3 cm
   3. C6 cm
   4. D12 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. A280 in²
   2. B284 in²
   3. C568 in²
   4. D840 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 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 ___.
• A flat shape with length and width but no thickness 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 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. A87 in²
   2. B135 in²
   3. C174 in²
   4. D174 in³

   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. A55 in³
   2. B200 in³
   3. C220 in³
   4. D220 in²

   How do you know?
3. 14

   From Lesson 5.5How many more cubic inches does the large box hold?

   1. A1,728 in³
   2. B3,024 in³
   3. C4,752 in³
   4. D10,800 in³

   How do you know?

Be honest — this tells your teacher what to do next