### Bat Wings

Three students had collected some data on the wingspan of some bats. Unfortunately, each student had lost one measurement. Can you find the missing information?

### A Mean Tetrahedron

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

### Pairs

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.

# Searching for Mean(ing)

##### Stage: 3 Challenge Level:

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

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?
What's the largest?

Can you make all the whole numbers in between?

What if you have a different pair of weights (for example 2kg and 7kg)?
Which whole numbers is it possible to have as the mean weight now?

Try other different pairs of weights.

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.