Order, order!

Can you place these quantities in order from smallest to largest?

Age

5 to 11

Challenge level

Primary

Measurement

Comparing and Estimating

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

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?

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

Distance

You could jump up in the air

You can kick a football

You can run in half a minute

Length of a bug

Mass

Of a blown-up balloon

Of a bar of chocolate

Of a loaf of bread

Of your teacher

Teachers' Resources

Order, Order!

Image	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
Image	Distance You could jump up in the air You can kick a football You can run in half a minute Length of a ladybird
Image	Mass Of a blown-up balloon Of a bar of chocolate Of a loaf of bread Of your teacher

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?

Possible extension

Some children might like to have a go at a similar problem In Order, which demands more clarity about the assumptions they are making.

Possible support

Reassure learners 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 order. Encourage them to experiment, and offer some guidance on how to search for suitable data.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners