Same Rule, Every Time

Mathematics · Mathematical Thinking · ages 9-10

Name ______________________ Date ____________

Use the 100 trick: 100 x 12 divided by 4 equals 25 x 12. What is 100 x 12?
Answer: ______________
What comes next in this pattern: 1/2, 2/4, 3/6, ...?
- 4/7
- 4/8
- 5/8
To find 10% of a number, what do you do?
- Divide by 10
- Multiply by 10
- Divide by 5
Which two steps give the same answer as multiplying by 25?
- ×100, then ÷4
- ×4, then ÷100
- ÷4, then ×10
A sequence rule is: multiply the position by 3 and add 1. What is the 4th term?
Answer: ______________
10% of 60 is 6. What is 30% of 60?
Answer: ______________
Why does multiply by 100 then divide by 4 equal multiply by 25?
- Because 100 divided by 4 is 25
- Because 100 plus 4 is 104
- Because 25 goes into 100 twice
- Because 4 times 25 is 200
Priya finds 35% by adding 10% + 10% + 10% + 5%. She says 35% splits into chunks of 10% and 5% this way. Is she right?
Circle one: True False
A sequence starts at 2 and adds 4 each time. Which rule finds the 20th term without listing every number?
- 2 + (4×20)
- 4 + (2×19)
- 2 + (4×19)
Which calculation gives 25 x 16?
- 100 x 16 divided by 4
- 16 x 100 divided by 2
- 25 + 16 times 4
- 25 x 8 divided by 2

Answer key

For grown-ups. Fold this page away before handing over the rest.

1200 · 100 x 12 = 1200.
4/8 · If the top keeps adding 1 and the bottom keeps adding 2, the next pair is 4 on top and 8 on the bottom, so 4/8.
Divide by 10 · 10% means 10 out of every 100, which is the same as dividing by 10.
×100, then ÷4 · 100 ÷ 4 equals 25, so ×100 then ÷4 has the same effect as ×25.
13 · 3 x 4 + 1 = 13.
18 · 3 lots of 6 is 18.
Because 100 divided by 4 is 25 · 100 divided by 4 is exactly 25.
True · Priya is right: the chunks sum exactly to 35%.
2 + (4×19) · The 20th term is 19 steps after the start, so multiply the step by 19 and add the start: 2 + (4×19) = 78.
100 x 16 divided by 4 · 100 x 16 divided by 4 equals 25 x 16.