Order, Order!
Can you place these quantities in order from smallest to largest?
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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Time
Taken to travel to school
For mustard and cress to grow from seeds
Taken to eat a biscuit
Between your 6th and 7th birthdays

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Distance
You could jump up in the air
You can kick a football
You can run in half a minute
Length of a bug

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Mass
Of a blownup balloon
Of a bar of chocolate
Of a loaf of bread
Of your teacher

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?
Daisy from Ricards Lodge has given us lots of details to explain how she ordered the quantities. Are you convinced by what Daisy says?
Time: (shortest to longest)
Eat a biscuit  I think that to eat a normal sized circular biscuit takes roughly $30$ seconds to eat at a usual pace!
Taken to travel to school  The journey from my house to school takes $40$ minutes and this is quite a common length of time for the journey amongst my classmates.
Taken for mustard and cress to grow from seeds  in a suitable climate this process should take no longer than three days.
The period between your 6th and 7th birthday  this is $365$ days, (unless your birthday is on a leap year) a whole year, clearly the longest amount of time on this list.
Distance: (shortest to longest)
Length of a ladybird  they grow up to approximately $4$mm.
How high you can jump in the air  This really depends on your height but it is very likely to still be measured in cm; which is why I put it second on the list.
How far you can kick a football  Amateur footballers can kick a ball up to $50$m, definitely a longer distance than the last measurement.
How far can you run in $30$ seconds  In my age group, it is possible to run $200$m in under half a minute, considerably longer than the length you can kick a ball.
Mass: (lightest to heaviest)
A balloon  I estimate that the mass of a balloon is about a gram as it is practically all gas which has a very minimal mass.
Bar of chocolate  A usual bar of chocolate (measuring roughly $20$cm) weighs between $50$g and $60$g.
Loaf of bread  A loaf of shopbought presliced bread weighs $800$g.
Teacher  The average weight of a woman in the UK is $65$kg and for men, $72$kg. This makes it the heaviest measurement in the list.
Let us know if you have any comments about Daisy's estimations.
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. This idea is likely to come up informally as the children talk to each other, and you can draw attention to examples that they themselves bring up.
Possible approach
Give each pair or group of children a copy of these cards. Each card has one of the statements on it along with a picture. The picture will help those who cannot read so well remember the content. Invite the pupils to put the four time cards in front of them to
start with and ask them to order the cards in their pairs/groups. At this stage, make it clear that it doesn't matter if they are unsure. Have a brief discussion about their thoughts and then have a go at the distance and mass statements in a similar way.
Then, allocate one of the sets of cards (i.e. time, distance or mass) to each pair or group. The aim now is for each pair/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.
Key questions
Do you have an idea of what order they might go in?
What could you do to find out how long/how far/how heavy that is?