In Order
Can you rank these quantities in order? You may need to find out
extra information or perform some experiments to justify your
rankings.
Age
7 to 11
Challenge level
Problem
Have a look at the sets of four quantities below.
Can you rank them in order from smallest to largest? To help you decide, you may need to find extra information or carry out some experiments.
Can you convince us that your order is right?
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Temperature
Of a kettle of boiling water
Of the centre of the sun
On a thermometer when you are quite well
Of the water in a school pond
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Speed
Of a rocket going up on bonfire night
Of a train
Of a ladybird walking along a leaf
Of a ball being thrown to your friend
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Time
Taken for a puddle of water to evaporate on a hot day
Taken for frogspawn to grow into a frog
Taken to walk across the playground
Taken for the moon to orbit the earth
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Sound
Of a clap of thunder
Of a teacher blowing a whistle
Of a tap running
Of a recorder being played by a friend
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Getting Started
How could you estimate each of the quantities?
What extra information might you need to find out?
What extra information might you need to find out?
Student Solutions
Thank you to those of you who sent solutions to this problem. Unfortunately, though, not many of you explained how you knew the order in which to put the quantities.
Katie from Hymers College Junior School took us through the first set of quantities:
First of all I am going to tackle the temperature question.First you look at what to rank
*Of a kettle of boiling water
*Of the centre of the sun
*On a thermometer when you are
quite well
*Of the water in a school
pond
Then you think about the ones that you know the temperature.
So it is clear that the sun is the hottest. So now tick that off the list.
Then you think, well our school pond is quite deep and therefore quite cold. So compared to the rest of the list the pond is the coldest so now you can check that off the list.
Now you are left with the two middle answers. Everybody knows that water boils at $100^\circ$ and your body temperature is around $38^\circ$. From this research you now know that the kettle of boiling water is the second hottest. Now you can tick that off the list.
Finally you are left with the last one to tick off the list, the temperature of the thermometer when you are quite well.
So now they are all ticked off the list you can put them into their final order which is:
1. Of the centre of the sun.
2. Of a kettle of boiling water.
3. On a thermometer when you are quite well.
4. Of the school pond.
Katie then ordered the speed, time and sound quantities:
Speed:1. Of a rocket going up on bonfire night
2. Of a train
3. Of a ball being thrown to your friend
4. Of a ladybird walking along a leaf
Time
1. Taken for frogspawn to grow into a frog
2. Taken for the moon to orbit the earth
3. Taken for a puddle of water to evaporate on a hot day
4. Taken to walk across the playground
Sound
1. Of a clap of thunder
2. Of a teacher blowing a whistle
3. Of a tap running
4. Of a recorder being played by a friend
The last one and the whistle depend on how hard they blow. For number 4, the friend is a controlled recorder player and for number 2, the teacher is having a bad day so is very loud.
Thank you, Katie. I like the way you've given us more information about the sound quantities. Someone from Ricards Lodge who didn't give their name, gave a different answer to the sound part of the problem:
For the sound category the loudest sound is a clap of thunder,
then it's a teacher blowing a whistle, next it's your friend
playing a recorder, and finally the quietest sound is a tap
running.
To find this out I knew thunder would be the
loudest.
Then I tested whether a recorder was louder than a tap,
and it was, so then I tested whether a recorder was louder
than a whistle, but it wasn't and that is how I got my order.
Your results may be different depending on your equipment. But
these are the results I got.
It's interesting that there is a differing opinion about these sound quantities. However, it is great that Katie and the pupil from Ricards Lodge have both explained their own reasoning. Well done! I wonder what you think?
Teachers' Resources
In Order
Have a look at the sets of four quantities below.
Can you rank them in order from smallest to largest? To help you decide, you may need to find extra information or carry out some experiments.
Can you convince us that your order is right?
| Image
|
Temperature
Of a kettle of boiling water
Of the centre of the sun
On a thermometer when you are quite well
Of the water in a school pond
|
| Image
|
Speed
Of a rocket going up on bonfire night
Of a train
Of a ladybird walking along a leaf
Of a ball being thrown to your friend
|
| Image
|
Time
Taken for a puddle of water to evaporate on a hot day
Taken for frogspawn to grow into a frog
Taken to walk across the playground
Taken for the moon to orbit the earth
|
| Image
|
Sound
Of a clap of thunder
Of a teacher blowing a whistle
Of a tap running
Of a recorder being played by a friend
|
Why do this problem?
This activity offers an opportunity to combine skills from mathematics and science. Learners are required to make estimates, understand and use appropriate units, 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
Give each pair of children a copy of this sheet which has all the quantities on it. Invite the pupils to try and rank the quantities but at this stage, make it clear that it doesn't matter if they are unsure. You may like to have a brief discussion about their thoughts.
Then, organise pairs into small groups and allocate two of the sets of quantities (i.e. two from temperature, speed, time and sound) to each group. The aim now is for each group to come up with an order for the quantities they have been given, together with a convincing presentation of evidence to justify their order. Allow pupils access to reference materials, measuring equipment, and
anything else that might be useful, and give them plenty of time for research and experiment.
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 and the assumptions they have made. There might not be just one 'right' answer.
Key questions
What is stated precisely and what details are missing?
Do you have an idea of what order they might go in?
What could you do to find out how hot/how fast/how long/how loud that is?