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### Why do this problem?

This activity offers an opportunity to combine skills from mathematics and science. Students are required to make estimates, understand and calculate with units, think about orders of magnitude, and find information to draw conclusions.

This problem highlights the fact that in science it is rather hard to calculate anything without making some sort of assumptions. Good science will clearly state and be aware of these assumptions; bad science will ignore them.

### Possible approach

Hand out

this worksheet with all sets of quantities, and give students a few minutes on their own or in pairs to rank them in order of magnitude. Reassure students that at this stage, they do not need to perform any written calculations and it doesn't matter if they are unsure of their rankings.

*Alternatively, hand out these different sets of quantities to different groups: Area, Distance, Mass, Number,
Speed, Time, Volume.*

Next, give each group two sets of quantities to work on in more detail, so that each set is looked at by at least two groups.

"Your task is to come up with a rank order for the quantities you have been given, together with a convincing presentation of evidence to justify your order."

Allow students access to reference materials, measuring equipment, and anything else that might be useful, and give them plenty of time for research and experiment. This could be part of a homework task.

Once they have finished, take each set of quantities and invite the different groups to present their rankings and reasoning. Ask the rest of the class to judge the different presentations on the strength of the evidence they have offered for their rankings.

### Key questions

What is precisely stated and what is not precisely stated?

Can you give quick, sensible lower and upper bounds on the quantities before calculating?

Is a detailed calculation necessary for all of the parts of the problem?

What can be resolved by experiment? By measurement? By looking something up?

### Possible extension

Ask students to produce definite upper and lower bounds for the quantities. The ordering is only guaranteed when the intervals do not overlap.

### Possible support

Reassure students that there are often no exact values (so no "wrong" answers), and their task is simply to find some evidence to convince others of the rankings. Encourage them to experiment, and offer some guidance on how to search for suitable data.

In Order has quantities to rank using simpler scientific contexts.