### 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.

# Archery

### Why do this problem?

This problem offers a good opportunity to gather and compare data to create and test hypotheses and decide how much data is needed to be able to reasonably justify your conclusions.
The problem should also generate much discussion in the classroom:

### Possible approach

Use the interactivity - aiming the bow and shooting. Ask two or three students to come up in turn and have 10 attempts.
Who scores most?
Do they have any strategies?
Why is it not enough to line up with the bull's eye? What might be affecting what is happening?

Once some ideas have been seeded set the students the task of finding a strategy for achieving a high score. Ask them to make a note of things they notice or decisions they make.

Students will need to justify their conclusions so teachers could use the problem to challenge students to provide convincing evidence.

### Key questions

How do I decide which way to adjust the sight?
How many goes should I have on each setting so that I can compare meaningful results?
If I score 10 followed by 10 with my first two arrows, does that mean I have the ideal setting?

### Possible extension

Comparing different sets of data from the same setting - can the students draw any conclusions about the average scores and spread for each set?

### Possible support

Suggest that the students aim for the bulls eye and discuss the number of attempts that might make results "meaningful".