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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 try a box that is 4 long, 2 wide, and 0.5 tall. Let's do it the base-area way. What is the base, 4 × 2? The base area is B = 8. Picture that base sitting on the table — that is one layer. Now stack the base up the height: V = B × h = 8 × 0.5 (that means half of 8). What is the volume? Yes, V = 4 cubic units. Check it the other way: 4 × 2 × 0.5 = 4. Same answer, because B × h already used the length and width. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA regular hexagon splits into 6 identical triangles, each with an area of 8 square cm. What is the area of the hexagon?

   1. A48 square cm
   2. B14 square cm
   3. C8 square cm
   4. D48 cm

   How do you know?
3. 3

   Warm restartA regular pentagon is decomposed into triangles from its centre. How many triangles are there?

   1. A5
   2. B3
   3. C6
   4. D10

   How do you know?
4. 4

   Warm restartA regular octagon has an area of 96 square inches and splits into 8 identical triangles. What is the area of one triangle?

   1. A12 square inches
   2. B8 square inches
   3. C768 square inches
   4. D24 square inches

   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 tank's volume?

   1. A4,608 in³
   2. B4,806 in³
   3. C576 in³
   4. D52 in³

   Why is that the answer?
2. 6

   Think it throughAbout how many gallons does the tank hold?

   1. Aabout 20
   2. Babout 2
   3. Cabout 200
   4. Dabout 231

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

   Think it throughWhy divide by 231 instead of multiplying?

   1. ABecause you are finding how many 231-in³ gallons fit inside the tank
   2. BBecause dividing always makes numbers smaller
   3. CBecause 231 is bigger than 24
   4. DBecause gallons are bigger than inches

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

   Back to the modelCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

Use the words

Fill each blank with a word from the bank.

• The space inside a rectangular 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 is a ___.
• The unit used to measure volume 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 of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal.
2. 10

   Say moreCapsule A (2 × 1.5 × 1) and Capsule B (3 × 1 × 1) both have a volume of 3 ft³. How did your multiplication produce the same volume from different dimensions?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A classmate asks whether a cube is always a rectangular prism. This prism is built from small cubes that are each ½ inch on every edge.

   Show your work

Last check

These two come from Lesson 5.9. 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 = 7 ft, w = 2 ft, h = 3 ft. What is the volume?

   1. A42 ft³
   2. B24 ft³
   3. C42 ft²
   4. D12 ft³

   Explain your choice.
2. 13

   From Lesson 5.9Explain your thinking — A regular pentagon is decomposed into 5 triangles from its center. Each triangle has a base of 7 inches and a height of 4.8 inches. What is the total area of the pentagon?

   1. A84 sq in
   2. B16.8 sq in
   3. C168 sq in
   4. D84 in

   How do you know?
3. 14

   From Lesson 5.9What will the flooring cost?

   1. A$360
   2. B$120
   3. C$45
   4. D$960

   How do you know?

Be honest — this tells your teacher what to do next