Shapes & Patterns

14 Grade 3 Mathematics questions on Shapes & Patterns, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   3 marks

   A rectangle has perimeter 28 cm. Its length is 9 cm. Find its width.

   (3 marks)

   Marking scheme

   The perimeter of a rectangle is $2(l+w)$, so $2(9+w)=28$. (1)

   Divide both sides by $2$: $9+w=14$. (1)

   Subtract $9$: $w=5$. Check: $2(9+5)=28$ cm. (1)

   Final answer: the width is $5$ cm.

2. Question 2

   1 mark

   How many edges does a cuboid have?

   (1 mark)

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3. Question 3

   1 mark

   Look at the pattern: $2,4,6,8,\square$. What number completes the pattern?

   A. $10$

   B. $9$

   C. $7$

   D. $12$

   (1 mark)

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4. Question 4

   1 mark

   Draw and continue the pattern: ○ □ △ ○ □ △ ○ ___

   (1 mark)

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5. Question 5

   2 marks

   Find the perimeter of a square with side 5 cm.

   (2 marks)

   Marking scheme

   All four sides of a square are equal, so the perimeter is $4\times$ side. (1)

   $4\times 5=20$. (1)

   Final answer: $20$ cm.

6. Question 6

   1 mark

   How many vertices (corners) does a triangular pyramid have?

   (1 mark)

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7. Question 7

   1 mark

   Name a 3D shape that looks like a ball.

   (1 mark)

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8. Question 8

   1 mark

   What is the next number in the pattern: 3, 6, 9, 12, ___?

   (1 mark)

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9. Question 9

   2 marks

   Find the area of a square with side 6 cm.

   (2 marks)

   Marking scheme

   The area of a square is side $\times$ side, because the square is covered by rows of unit squares. (1)

   $6\times 6=36$. (1)

   Final answer: $36$ cm${}^2$.

10. Question 10

    2 marks

    A triangle has $3$ sides and a rectangle has $4$ sides. How many sides do the two shapes have altogether?

    (2 marks)

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11. Question 11

    1 mark

    How many faces does a cube have?

    (1 mark)

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12. Question 12

    1 mark

    Name a 2D shape that has 3 sides.

    (1 mark)

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13. Question 13

    1 mark

    How many sides does a hexagon have?

    (1 mark)

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14. Question 14

    2 marks

    A rectangle has a length of 8 cm and a width of 3 cm. Find its perimeter.

    (2 marks)

    Marking scheme

    The perimeter is the distance all the way round. A rectangle has two lengths and two widths, so $P=2(l+w)$. (1)

    $2(8+3)=2\times 11=22$. (1)

    Final answer: $22$ cm.

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