Section A Practice Problems

Problem 1

  1. Which shapes are hexagons? ____________________

    6 different shapes labeled A to F.

  2. Draw a quadrilateral and label it Q. Draw a pentagon and label it P.

    Grid.

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Solution
  1. A, D, F
  2. Sample response:

Shapes on grid.

Problem 2

<span>Diagram. Rectangle partially partitioned to show 3 rows of 6 same-sized squares.</span>

  1. Finish covering the rectangle with equal-size squares.
  2. Write an addition equation showing how many small squares there are in the rectangle.
  3. Write a multiplication equation showing how many small squares there are in the rectangle.
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Solution
  1. Students finish covering the rectangle with 18 small squares.
  2. Sample responses: 6+6+6=186 + 6+ 6 =18 or 3+3+3+3+3+3=183+3+3+3+3+3=18
  3. Sample responses: 3×6=183 \times 6 = 18 or 6×3=186 \times 3 = 18

Problem 3

What is the area of the figure?

Diagram. 6 sides. Top length, unknown units. Down 4 units, right 4 units, down unknown units, left 10 units, up 9 units.

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Solution
74 square units. Sample response: There is a 10 unit by 9 unit rectangle with area 90 square units and then a 4 unit by 4 unit square has been removed and that's 16 square units, 90−16=7490 - 16 = 74.

Problem 4

Find the length of each rectangle.


  1. Ruler measuring a rectangle in centimeters, starting at 0 centimeters.

  2. Ruler measuring a rectangle in centimeters, starting at 8 centimeters.

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Solution
  1. 13 centimeters
  2. 9 centimeters. Sample response: 17−8=917 - 8 = 9

Problem 5

Six different shapes labeled A to F.

  1. Which shapes have 5 angles? ____________________

  2. Which shapes have all equal side lengths? ____________________

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Solution
  1. D, F
  2. A, B, E, F

Problem 6

6 triangles labeled A to F.

  1. Which triangles have 1 right angle? ____________________

  2. Which triangles have 2 equal side lengths? ____________________

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Solution
  1. D, F
  2. B, C, E

Problem 7

One of these quadrilaterals is Diego’s mystery quadrilateral.

4 quadrilaterals labeled A to D.

List some questions you would ask to identify Diego’s mystery quadrilateral. How would the answers help you figure out which quadrilateral it is?

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Solution

Sample responses:

  1. Does the shape have 4 equal sides?
  2. Does it have 4 sides that join like in a square?
  3. Does it have 2 pairs of equal sides?

If 1 and 2 are yes, the mystery quadrilateral is D. If 1 is yes and 2 is no, it’s A. If 1 and 2 are no and 3 is yes, it’s B. If 1, 2, and 3 are no, it’s C. 

Problem 8

Select all of the quadrilaterals that are rectangles.

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Solution
A,B,E

Problem 9

 
Dot grid.

  1. Draw a quadrilateral that is not a rhombus and label it A. Explain why your shape is not a rhombus.
  2. Draw a quadrilateral that is not a rectangle and label it B. Explain why your shape is not a rectangle.

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Solution

Sample response:

Figures on dot grid.

  1. Its sides are not all the same length, so it is not a rhombus.
  2. The sides don’t join like in a square, so it is not a rectangle.

Problem 10

Find 1 of each of the following shapes in the image.

  1. a triangle with a right angle
  2. a triangle with 3 equal sides
  3. a rhombus
  4. a rectangle
  5. a square

<p>Diagram with tiling.</p>

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Solution
Sample responses:
  1. Each individual shape in the design is a right triangle.
  2. If I put together a blue and green triangle, I get a triangle with 3 equal sides.
  3. 4 of the triangles together make a rhombus.
  4. Groups of 6 triangles make a rectangle.
  5. There are no squares. (Students may measure the rectangles in the image to verify this, or reason about whether extending the pattern would eventually lead to a square.)

Problem 11

Do any of the triangles have:

  1. 1 right angle?
  2. 2 equal sides?
  3. 3 equal sides?

<p>A 6-equidissection of a square.</p>

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Solution
  1. Yes. Sample response: The yellow one on the bottom right.
  2. Yes. Sample response: The yellow one in the top right.
  3. No