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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 parallelogram has a base of 5 cm and a height of 4 cm. Find its area. Multiply the base by the height. What is the area? (5 × 4 = 20 square centimeters) Why does base × height work for a parallelogram? (Cut the triangle off one end and move it to the other end. You get a 5 cm by 4 cm rectangle.) Why can't you multiply the base by the slanted side? (The slanted side is longer than the height. The area would come out too big.)

   Show your work
2. 2

   Warm restartA bus travels 45 miles each hour. Which equation gives the distance d after h hours?

   1. Ad = 45h
   2. Bd = 45 + h
   3. Cd = h ÷ 45
   4. Dd = 45 − h

   How do you know?
3. 3

   Warm restartUsing d = 45h, how far does the bus travel in 6 hours?

   1. A7.5 miles
   2. B45 miles
   3. C51 miles
   4. D270 miles

   How do you know?
4. 4

   Warm restartA table shows x = 1, 2, 3 with y = 6, 12, 18. Which equation fits?

   1. Ay = x + 5
   2. By = 6x
   3. Cy = x + 6
   4. Dy = 6 + x

   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 area of the parallelogram courtyard?

   1. A28 sq ft
   2. B56 sq ft
   3. C90 sq ft
   4. D180 sq ft

   Why is that the answer?
2. 6

   Think it throughHow many tiles does the architect need?

   1. A45
   2. B90
   3. C180
   4. D360

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

   Think it throughWhy use the height instead of the slanted side length?

   1. ABecause the slanted side is always longer
   2. BBecause parallelograms have no height
   3. CBecause the base is on the bottom
   4. DBecause area needs the perpendicular distance between the two bases

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

   Back to the modelIf you cut a triangle from one side of the parallelogram and move it to the other side, what shape do you get? How does this help you find the area?

Use the words

Fill each blank with a word from the bank.

• The leaning side of a parallelogram, which is NOT the height, is the ___.
• A quadrilateral with two pairs of parallel sides is a ___.
• Two sides that stay the same distance apart and never meet are ___.
• The side of a parallelogram you measure the height from at a 90° angle is the ___.

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: The most common mistake in Area of Parallelograms is multiplying the base by the slanted side instead of the perpendicular height.
2. 10

   Say moreOn the grid you cut a triangle off one end of the parallelogram and slid it to the other side. What shape did you make, and why does that prove the area is base x height?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The Dockland building in Hamburg, Germany, is built in the shape of a parallelogram leaning over the water.

   Show your work

Last check

These two come from Lesson 4.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A parallelogram has a base of 13 inches and a height of 5 inches. What is its area?

   1. A18 sq in
   2. B36 sq in
   3. C65 sq in
   4. D65 in

   Explain your choice.
2. 13

   From Lesson 4.5Explain your thinking — A sweater's sale price is $42, which is 60% of the original price. What was the original price?

   1. A$25.20, because 0.6 × 42 = 25.20
   2. B$60, because the percent is 60
   3. C$70, because 42 ÷ 0.6 = 70
   4. D$102, because 42 + 60 = 102

   How do you know?
3. 14

   From Lesson 4.5If the percent given is less than 100%, the whole must be…

   1. ASmaller than the part
   2. BLarger than the part
   3. CEqual to the part
   4. DImpossible to find

   How do you know?

Be honest — this tells your teacher what to do next