Bigger or Smaller?
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Bigger or Smaller? Number Factory
Bigger or Smaller? is a maths game that asks students to predict the direction of multiplication and division with fractions and decimals, without calculating. A number goes into a glass machine as a box, and the machine's screen shows an operation, such as × 3/4 or ÷ 1/2. The student decides: when the number comes out, will it be bigger, smaller or the same?
What is it for?
For years, students think “multiplying makes bigger, dividing makes smaller”. With fractions and decimals, this rule misleads: 12 × 3/4 = 9 gets smaller, and 12 ÷ 1/2 = 24 gets bigger. The game practises:
- Predicting the direction of the result before calculating
- Checking whether the number in the operation is bigger or smaller than 1
- Seeing that multiplying by 3/4 means “split into 4 pieces and take 3 of them”
- Discovering that division works in the same machine: ÷ 3/2 does the same job as × 2/3
How to play
- Choose your machine. In the See-through machine you can see inside; in the Closed machine the inside is hidden and the questions are harder.
- Choose your shift. There are four shifts, each a little harder.
- Look at the operation. The box goes into the machine and the screen shows the operation.
- Make your prediction. Tap Gets smaller, Stays the same or Gets bigger. On a phone, swiping right means “bigger” and swiping left means “smaller”.
- Watch the machine. The box is cut into equal pieces. If the number gets bigger, new pieces are added; if it gets smaller, extra pieces are taken away. A dashed line shows the box's old size.
A correct prediction scores points; if you are fast and get several right in a row, you also earn a bonus. If you get stuck, Hint shows the number in the operation on a line marked 0, 1 and 2. Every shift has 10 questions, and at the end you see your stars, your score and your record.
The shifts
| Shift | What's in it? |
|---|---|
| 1. Multiplying Belt | Whole number × fraction |
| 2. Fraction Workshop | Fraction × fraction |
| 3. Division Press | Dividing by a fraction and by a whole number |
| 4. Mixed Shift | Multiplication, division and decimals |
What happens after a mistake?
Mistakes teach too. The game says “Not this time” and shows why straight away. For example, a student who says “bigger” when multiplying by 3/4 sees: “Multiplying doesn't always make bigger! Multiplying by a number less than 1 means taking part of the number.” A wrong answer does not cost points.
Who is it for?
- Designed for students in grades 6 and 7; it can also be used at the end of grade 5.
- Works on computers, tablets and phones.
- No sign-up, no account and no internet connection needed. No personal data is collected.
- Playable in Turkish, English, Spanish and French.
Teachers and parents who want to know the research behind the game can read Does Multiplying Always Make Bigger? in the “For teachers” section.