MATH FOR KIDS
I. Number-Sum Puzzles
1. Three numbers A, B and C satisfy:
A + B = 16
A + C = 13
B + C = 11
Find A, B and C. Hint: Add all three equations first.
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2. Three numbers P, Q and R satisfy:
P + Q = 21
P + R = 17
Q + R = 14
Find P, Q and R.
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3. Challenge: Four numbers A, B, C and D satisfy:
A + B = 6
B + C = 9
C + D = 12
D + A = 9
Find two different sets of values for A, B, C and D. How come there are no fixed results?
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II. Volume
1. Find the volume of a rectangular prism with length 12 cm, width 5 cm and height 7 cm.
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2. A rectangular prism has a volume of 480 cm³. Its length is 12 cm and its width is 8 cm. Find its height.
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3. A cube has side length 4 cm.
a) Find its volume.
b) A similar cube has side length 8 cm. Find its volume.
c) How many times larger is the second cube's volume?
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III. Similar 3D Shapes
For similar 3D shapes: Volume scale factor = (length scale factor)³
1. A small cube has side length 2 cm. A larger similar cube has every length 3 times as large. How many times
as large is its volume?
2. A small ball and a large ball are similar. The large ball has 5 times the diameter of the small ball. How many
times as large is its volume?
3. A model penguin is enlarged so that every length is 10 times as large. How many times as large is the
volume of the enlarged penguin?
Year 6 Mathematics Homework
4. A model has been enlarged and its volume becomes 64 times the original volume. How many times longer is
each corresponding length?
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5. A similar 3D object has half the corresponding length of the original object. What fraction of the original
volume does it have?
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IV. Think Deeply
A cube is easy to understand: if every side becomes 10 times as long, we can imagine 10 × 10 × 10 = 1000
small cubes filling the large cube.
But suppose the shape is a sphere, pyramid, animal or another irregular 3D shape. Explain why enlarging every
dimension by a factor of 10 should still make the volume 1000 times as large.
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Review questions
V. Change Side, Change Sign
Solve each equation. Show your working.
1. x + 7 = 15
2. x - 6 = 13
3. 3x = 27
4. 4x - 5 = 19
5. 5x + 7 = 32
6. 7x - 11 = 38
VI. Variables on Both Sides
Move all the x terms to one side and all the numbers to the other side.
1. 2x - 4 = x + 7
2. 3x - 5 = x + 13
3. 5x + 2 = 2x + 23
4. 6x - 9 = 3x + 15
5. 4x + 12 = 7x - 9
6. 18 - 2x = x + 6