Finding the Rule Behind the Facts

Mathematics · Mathematical Thinking · ages 8-9

Name ______________________ Date ____________

A fraction equals 1/2 and its bottom number is 8. What is its top number?
Answer: ______________
Which fraction equals 1/2?
- 5/10
- 4/10
- 5/9
- 4/9
If 7 × 3 = 21, what is 7 × 30?
- 210
- 630
- 70
In the fraction 4/8, the numerator (4) is half of the denominator (8), so 4/8 equals 1/2.
Circle one: True False
Work out 6 × 9 by splitting 9 into 5 + 4, using 6 × 5 = 30 and 6 × 4 = 24.
Answer: ______________
Which fraction is NOT equal to 1/2?
- 7/14
- 5/12
- 8/16
What is 7 × 200?
- 1400
- 140
- 14000
- 14
Ben splits 9 into 5 + 4 to find 6 × 9 and says the same split trick works for other hard table facts. Is Ben right?
Circle one: True False
Since 4×5=20 and 5000 is 1000 times bigger than 5, what is 4×5000?
- 200
- 2000
- 20000
If 7 × 2 = 14, what is 7 × 2000?
Answer: ______________

Answer key

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

4 · The top is 4 because half of 8 is 4.
5/10 · 5/10 equals 1/2 because 5 is half of 10.
210 · 30 is ten times 3, so 21 becomes 210.
True · 4 is half of 8, so the rule holds and 4/8 is the same amount as 1/2.
54 · 6 × 9 = 54 because 30 + 24 = 54.
5/12 · 5/12 is not one half because half of 12 is 6. The other two fractions have a numerator that is half the denominator.
1400 · 200 is 100 times 2, so 14 becomes 1400.
True · Ben is right. Split one factor into known parts, multiply each part, and add them. This strategy works for many facts.
20000 · If one number gets 1000 times bigger, the answer does too: 20 becomes 20,000.
14000 · 2000 is 1000 times 2, so 14 grows to 14000.