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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Searching for Mean(ing)

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Age 11 to 16

Challenge Level

*Searching for Mean(ing) printable sheet*

*If you have not used the Cuisenaire Environment before, you might find it helpful to look at the instructions and video before trying this problem.*

Imagine you have a large supply of 3kg and 8kg weights.

Can you see how the picture below can be used to explain why two 3kg weights and three 8kg weights have a mean weight of 6kg?

**Can you find other combinations of 3kg and 8kg weights whose mean weight is a whole number of kg?**

What's the smallest possible mean?

What's the largest?

**Can you make all the whole numbers in between?**

*You may wish to use the interactive Cuisenaire environment below.*

Now explore some different pairs of weights (for example 2kg and 7kg).

**Which whole numbers is it possible to have as the mean weight?**

What do you notice about your results?

Can you use what you notice to find the combination of 17kg and 57kg weights that have a mean weight of 44kg......of 52kg.......of 21kg.....?

Explain an efficient way of doing this.

Can you explain why your method works?

Click here for a poster of this problem.