Place your orders
Problem
Place Your Orders printable worksheet
Have a look at the sets of four quantities below. Can you rank them in order from smallest to largest?
To help you to decide on your rankings, you may need to find extra information or carry out some experiments.
Can you provide convincing evidence of your final rankings?
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Number of 
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Distance 
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Time 
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Speed 
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Mass 
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Area 
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Volume of water 
Perhaps you might like to make 4 ranked quantities of your own to challenge a friend.
For more advanced science, see Approximately Certain.
Getting Started
What extra information might you need to find out?
For some questions, you may need to be more accurate in your estimations than others to arrange the list in order of magnitude.
Student Solutions
We received many solutions to this problem, including carefully considered solutions from Patrick from Otterbourne School, the Math Club from DMCS in Canada, Siannah from Ricards Lodge School, members of the Pythagorean Club at All Saints Dagenham School, and from Kartik and Mustafa from Wilson's School.
Many of you pointed out that the rankings depended on estimates and that different contexts and assumptions might lead to different conclusions (e.g. the size of the bath, the flow of water from a shower, how well the pet rat is looked after, the size of the classroom, the pace at which a leisurely walker travels...).
Bearing this in mind, here is a suggested ranking with the evidence that was provided:
Time
That a pet rat lives 23 years
For all of the red blood cells in your body to be replaced....10 times 3 years
Between two football world cups 4 years
For light to reach us from the nearest star other than the sun 4.2 years
Distance
You can hop in 5 seconds 8 metres
The distance from the penalty spot to the goal on a football field 11 metres
From the top of a 6 storey building to the ground 18 metres
A car can drive on 1$cm^{3}$ of fuel 20 metres
Speed
Of the fastest sprinter in the world 10m/s
Of a bus going past the school (30mph = 13.4m/s)
Of a racehorse running at maximum speed 15m/s
Of the fastest cyclist in an Olympic cycle sprint race 19m/s
Mass
Of enough potatoes to make chips to feed everyone in the school for a week. (1000kg for 1000 students)
Of a million cubic centimetres of water 1000kg
Of a standard family car 1500kg
Of a team of international male rugby players (15 players) 1500kg
Volume of water
used in a 10 minute shower 90 litres
used in 5 dishwasher cycles 100 litres
in a halffilled bath 100 litres
used to flush the toilet 20 times 120 litres (modern toilet)
Number of
Steps when walking at a leisurely pace for 1 hour 8000
Mars bars with the same total weight as your whole class 20000 (for a class of 30 students weighing about 40kg each)
Stitches in a handknitted jumper 75000
People at a cup final in a large stadium 80000
Area
Of the sheets of paper in a ream (500 sheets) of A4. 30m$^2$
Covered by 5 litres of paint 50m$^2$
Of the floor of the classroom 60m$^2$
Of fabric needed to make school uniforms for the whole class will depend on the size of the class, the width of the fabric and the design of the uniform!
Teachers' Resources
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.
Possible approach
This printable worksheet may be useful: Place Your Orders.
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, you could use the Number of... category to look at together as a class, and then hand out this worksheet with Distance, Time and Speed, and/or this worksheet with Mass, Area and Volume.
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?
What can be resolved by experiment? By measurement? By looking something up?
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.
Possible extension