Shapes, Arrays and Equal Parts: practice solutions, Grade 2 – download the PDF

1 Name the polygon ★★★

The number of sides gives the name.

1. 3 sides: a triangle.
2. 5 sides: a pentagon.
3. 4 sides: a quadrilateral.
4. 6 sides: a hexagon.

2 Count sides and vertices ★★★

Count the dots to count the vertices: there are 6. A polygon has as many sides as vertices, so there are also 6 sides. The shape is a hexagon.

3 Facts about a cube ★★★

A cube has 6 faces, 12 edges and 8 vertices. Each face is a square.

4 Rows and columns ★★★

There are 5 rows and 4 columns. Each row has 4 stickers, so \(4 + 4 + 4 + 4 + 4 = 20\). There are 20 stickers.

5 Cut a sandwich ★★★

Each part is a half. Two halves make the whole sandwich, so the answer is 2.

6 Name the shaded part ★★★

The circle has 4 equal parts and 1 is shaded. The shaded part is one fourth (a quarter).

7 True or false? ★★★

1. True. A square has 4 sides.
2. False. A triangle has 3 sides, so it has 3 vertices.
3. False. A circle has no straight sides, so it is not a polygon.

8 Cookies on a tray ★★★

By rows there are 3 rows of 5: \(5 + 5 + 5 = 15\). By columns there are 5 columns of 3: \(3 + 3 + 3 + 3 + 3 = 15\). The tray has 15 cookies.

9 A growing garden ★★★

Now there are 4 rows of 4 plants. \(4 + 4 + 4 + 4 = 16\). There are 16 plants. Check: \(12 + 4 = 16\).

10 Squares in a rectangle ★★★

There are 3 rows and 4 columns. Rows: \(4 + 4 + 4 = 12\). There are 12 squares.

11 Two friends share cornbread ★★★

The pieces from a cut down the middle are rectangles, and those from corner to corner are triangles, so the shapes differ. In each case the 2 pieces are the same size, so each piece is still one half. Equal shares do not need the same shape.

12 Name the shaded fraction ★★★

The circle has 3 equal parts, so each part is a third. Three thirds make the whole circle.

13 Shape riddles ★★★

1. A square.
2. A hexagon.
3. A triangle. Three vertices mean three sides.

14 Equal or not? ★★★

The left rectangle has 2 parts of the same size, so these are halves. The right rectangle has 2 parts of different sizes, so these are not halves. Maya is right about the left rectangle only.

15 Two cubes ★★★

One cube has 6 faces, so \(6 + 6 = 12\) square faces. One cube has 12 edges, so \(12 + 12 = 24\) edges. One cube has 8 vertices, so \(8 + 8 = 16\) vertices.

16 Riddle with numbers ★★★

1. A quadrilateral has 4 sides, and \(4 + 2 = 6\). I am a hexagon.
2. A hexagon has 6 sides, and \(6 - 1 = 5\). I am a pentagon.
3. \(6 + 5 = 11\) sides in all.

17 The baker and her trays ★★★

First, \(5 + 5 + 5 + 5 + 5 = 25\). Then \(25 - 7 = 18\) muffins left. Three equal rows of 6 make \(6 + 6 + 6 = 18\), so yes, with 6 muffins in each row.

18 Shading half and a fourth ★★★

1. \(5 + 5 + 5 + 5 = 20\) squares.
2. Half of 20 is 10, because \(10 + 10 = 20\). Shade 10 squares.
3. Four equal groups of 5 make 20, so one fourth is 5 squares (one row).

19 Halves of different wholes ★★★

No, Ben is not right. Both are halves, but the wholes are different sizes. Half of a big pizza is more pizza than half of a small pizza. To compare fractions, the wholes must be the same size.

20 Which is smaller? ★★★

The fourth is smaller. The circle with fourths is cut into 4 equal parts, and the circle with halves into only 2. More equal parts means each part is smaller, so a fourth is smaller than a half.

21 Build an array ★★★

By rows: \(5 + 5 + 5 = 15\). By columns: \(3 + 3 + 3 + 3 + 3 = 15\). Adding 2 rows makes 5 rows of 5: \(5 + 5 + 5 + 5 + 5 = 25\). The rug has 25 squares.