Shape and space · Ages 9–10

Cutting up and putting together worksheet

Part of: Quadrilaterals, tiling and the eight directions

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Shape and space · Ages 9–10

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Cutting the shape along the lines in the picture, how many pieces do you get?
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2.How many squares 1 cm a side make one big square 4 cm a side?
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3.A regular 6-sided shape is cut along lines from its centre. How many triangles do you get?
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4.How many squares 1 cm a side make one big square 5 cm a side?
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5.A regular 7-sided shape is cut along lines from its centre. How many triangles do you get?
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6.Small equilateral triangles 1 cm a side make one big equilateral triangle 8 cm a side. How many small triangles does it take?
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7.Small equilateral triangles 1 cm a side make one big equilateral triangle 5 cm a side. How many small triangles does it take?
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8.Cutting the shape along the lines in the picture, what shape is each piece?
- A. A pentagon
- B. A triangle
- C. A hexagon
- D. A four-sided shape
Choose the right answer
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9.Two equilateral triangles with sides of 8 cm are put together along a whole side. What shape do they make?
- A. A square
- B. A rectangle
- C. A trapezium
- D. A rhombus
Choose the right answer
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10.Drawing every diagonal from one corner of a regular 10-sided shape cuts it into 7 triangles.
True or false?
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11.Drawing every diagonal from one corner of a regular 4-sided shape cuts it into 4 triangles.
True or false?
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12.Two equilateral triangles with sides of 5 cm are put together along a whole side. What shape do they make?
- A. A rhombus
- B. A rectangle
- C. A square
- D. A trapezium
Choose the right answer
Answer:

13.Tsz-hin has 23 equal equilateral-triangle cards. Every 6 make a regular hexagon. At most how many hexagons can Tsz-hin make?
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14.Square tiles 10 cm a side cover a rectangular floor 50 cm by 60 cm. How many tiles does it take?
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15.Ka-lok cuts a rectangular cake into 6 rows of 6 equal rectangles. How many pieces is that?
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16.Square tiles 20 cm a side cover a rectangular floor 40 cm by 140 cm. How many tiles does it take?
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17.Chi-keung cuts a rectangular cake into 4 rows of 4 equal rectangles. How many pieces is that?
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18.May has 34 equal equilateral-triangle cards. Every 6 make a regular hexagon. At most how many hexagons can May make?
Working:
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Show the answers and working

Cutting up and putting together worksheet: Answers and working

1. 4 pieces
Count the pieces one by one along the lines, marking each so you don't count it twice.
There are 3 cut lines, and each one adds a piece: 1 + 3 = 4 pieces. Counting them one by one gives 4 too.
2. 16 squares
Each row holds 4 small squares. Think how many rows you need.
4 in a row and 4 rows: 4 × 4 = 16.
3. 6 triangles
The centre is joined to every corner. Think how many triangles each side gets.
The centre joins every corner, so each side gets a triangle: 6.
4. 25 squares
Each row holds 5 small squares. Think how many rows you need.
5 in a row and 5 rows: 5 × 5 = 25.
5. 7 triangles
The centre is joined to every corner. Think how many triangles each side gets.
The centre joins every corner, so each side gets a triangle: 7.
6. 64 triangles
Count row by row from the top: 1 in the first row, 3 in the second… and there are 8 rows.
Row by row from the top: 1, 3, 5, …; 8 rows make 8 × 8 = 64.
7. 25 triangles
Count row by row from the top: 1 in the first row, 3 in the second… and there are 5 rows.
Row by row from the top: 1, 3, 5, …; 5 rows make 5 × 5 = 25.

8. B. A triangle
Look at one piece first and count its sides.
Count each piece's sides: every piece has 3.
9. D. A rhombus
An equilateral triangle's sides are all 8 cm. Once they are joined, count the new shape's sides and their lengths.
The four-sided shape has four sides of 8 cm: a rhombus.
10. False
From one corner there are 2 fewer triangles than sides. Work out how many a 10-sided shape gives, then compare with 7.
From one corner there are 2 fewer triangles than sides: 10 − 2 = 8.
11. False
From one corner there are 2 fewer triangles than sides. Work out how many a 4-sided shape gives, then compare with 4.
From one corner there are 2 fewer triangles than sides: 4 − 2 = 2.
12. A. A rhombus
An equilateral triangle's sides are all 5 cm. Once they are joined, count the new shape's sides and their lengths.
The four-sided shape has four sides of 5 cm: a rhombus.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 3 hexagons
Every 6 make one. How many 6s are there in 23? Leftovers too few for a whole hexagon don't count.
23 ÷ 6 gives 3; what's left isn't enough for another.
14. 30 tiles
First work out how many tiles fit along the length, 50 ÷ 10; then do the same for the width.
50 ÷ 10 = 5 along and 60 ÷ 10 = 6 across: 5 × 6 = 30.
15. 36 pieces
The cake makes 6 rows of 6 each. Multiplying is quicker than counting.
6 rows of 6: 6 × 6 = 36.
16. 14 tiles
First work out how many tiles fit along the length, 40 ÷ 20; then do the same for the width.
40 ÷ 20 = 2 along and 140 ÷ 20 = 7 across: 2 × 7 = 14.
17. 16 pieces
The cake makes 4 rows of 4 each. Multiplying is quicker than counting.
4 rows of 4: 4 × 4 = 16.
18. 5 hexagons
Every 6 make one. How many 6s are there in 34? Leftovers too few for a whole hexagon don't count.
34 ÷ 6 gives 5; what's left isn't enough for another.

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