Shapes and Data Displays: practice solutions, Grade 3 – download the PDF

1 Name that quadrilateral ★★★

1. A square: equal sides and right angles.
2. A rectangle: it has right angles, but its sides are not all equal.
3. A rhombus: its sides are equal but it has no right angle.

2 Find the quadrilaterals ★★★

A quadrilateral has exactly 4 sides. The rectangle, the rhombus, the square and the trapezoid have 4 sides. The triangle (3), the pentagon (5) and the hexagon (6) do not.

There are 4 quadrilaterals.

3 Sandwich fourths ★★★

1. The sandwich has 4 equal parts, so each piece is one fourth, written \(\dfrac{1}{4}\).
2. Her brother eats 3 pieces of 4 equal pieces: \(\dfrac{3}{4}\) of the sandwich.

4 Favorite sports picture graph ★★★

1. Soccer has 3 circles. \(3 \times 4 = 12\) votes.
2. Tennis has only 1 circle (4 votes), so tennis got the fewest.
3. \(12 - 4 = 8\). Soccer got 8 more votes.

5 Measure the crayon ★★★

The crayon starts at 0 and ends 3 small marks after the 1 inch mark. Each small mark is \(\dfrac{1}{4}\) inch.

The crayon is \(1\dfrac{3}{4}\) inches long.

6 Bean line plot ★★★

1. \(2 + 3 + 4 + 1 = 10\) beans.
2. There are 4 X marks at 1 inch and 1 at \(1\dfrac{1}{4}\) inches: \(4 + 1 = 5\) beans.
3. The last X is above \(1\dfrac{1}{4}\), so the longest length is \(1\dfrac{1}{4}\) inches.

7 True or false? ★★★

1. True. A square has 4 right angles.
2. False. A rectangle that is 5 cm by 2 cm is not a square.
3. True. A square has 4 equal sides.
4. False. A slanted rhombus has no right angles.

8 A rhombus with 5 cm sides ★★★

1. All 4 sides are equal, so it is a rhombus.
2. \(5 + 5 + 5 + 5 = 20\). The perimeter is 20 cm.
3. No. A square needs 4 right angles, and this shape has none.

9 Garden rectangle ★★★

1. In a rectangle, opposite sides are equal: the two long sides are 9 feet and the two short sides are 4 feet.
2. \(9 + 4 + 9 + 4 = 26\). The distance around is 26 feet.

10 Sorting by attributes ★★★

4 right angles: P and Q.

4 equal sides: P and R.

Neither: S. The square P is in both groups.

11 Pizza sixths ★★★

1. Each piece is \(\dfrac{1}{6}\).
2. Two pieces: \(\dfrac{2}{6}\).
3. \(6 - 2 = 4\) pieces are left: \(\dfrac{4}{6}\).

12 Are these thirds? ★★★

He is not right. The parts have different widths, so they are not equal. Thirds must be 3 equal parts. The rectangle must be cut so that A, B and C have the same width.

13 Boxes recycled ★★★

1. The tallest bar is Tuesday, with 50 boxes.
2. \(30 + 50 + 20 + 40 + 10 = 150\) boxes.
3. Wednesday has 20. Twice 20 is 40, which is Thursday.

14 Fruit stand picture graph ★★★

A half circle stands for 2 fruits.

• Apples: \(14 = 4 + 4 + 4 + 2\), so 3 circles and 1 half circle.
• Pears: \(6 = 4 + 2\), so 1 circle and 1 half circle.
• Plums: \(10 = 4 + 4 + 2\), so 2 circles and 1 half circle.

15 Two ribbons ★★★

The red ribbon is \(2\dfrac{1}{4}\) inches, which is 9 quarter inches. The blue ribbon is 7 quarter inches.

\(9 - 7 = 2\) quarter inches, and 2 quarters is \(\dfrac{1}{2}\) inch. The red ribbon is \(\dfrac{1}{2}\) inch longer.

16 Pencil line plot ★★★

1. \(\dfrac{1}{2}\) inch: 2 pencils. \(\dfrac{3}{4}\) inch: 1 pencil. 1 inch: 3 pencils. \(1\dfrac{1}{2}\) inches: 2 pencils. Total \(2+1+3+2 = 8\), which matches.
2. 3 X marks above 1.
3. Lengths less than 1 inch are \(\dfrac{1}{2}\) (2 pencils) and \(\dfrac{3}{4}\) (1 pencil): \(2 + 1 = 3\) pencils.

17 Reading a scaled bar graph ★★★

1. \(7 \times 5 = 35\). The Tigers have 35.
2. The Hawks bar is on the 4th line: \(4 \times 5 = 20\). The Hawks have 20.
3. \(55 \div 5 = 11\), so it is the 11th line.

18 Rhombus or square? ★★★

The shape has 4 equal sides, but its corners are slanted. It is a rhombus, not a square. So 4 equal sides is not enough.

A square also needs 4 right angles.

19 Mystery shapes ★★★

1. All angles are right angles, so it is a rectangle. The sides are not all equal, so it is a rectangle that is not a square.
2. Equal sides and no right angles: a rhombus. Perimeter: \(4 \times 6 = 24\) inches.

20 Two ways to cut a square ★★★

1. Yes. Both squares are cut into 4 equal parts, so each shaded part is \(\dfrac{1}{4}\). The parts have different shapes but the same size.
2. The area of the square is \(8 \times 8 = 64\) square inches. \(64 \div 4 = 16\), so each shaded part has an area of 16 square inches.

21 Hiking trails ★★★

1. \(35 + 20 + 15 + 40 = 110\) hikers.
2. \(40 - 15 = 25\) more hikers.
3. \(15 + 10 = 25\), and \(25 = 10 + 10 + 5\). Draw 2 circles and 1 half circle.

22 Leaf collection ★★★

1. \(1 + 3 + 5 + 3 + 2 = 14\) leaves.
2. Longer than \(1\dfrac{1}{2}\): \(1\dfrac{3}{4}\) (3 leaves) and 2 (2 leaves), so \(3 + 2 = 5\) leaves.
3. The longest leaf is 2 inches and the shortest is 1 inch. \(2 - 1 = 1\). The difference is 1 inch.