Middle primary

The data you need to collect with your class is described on the Core Activities page.

Lead-up ideas

Estimate: how many times do you think your foot length will fit into your height?

According to the ancient Roman architect, Vitruvius: a 'palm' is the width of four fingers; a 'foot' is four palms; a 'cubit' is six palms; and a man's height is four cubits.

• How many foot lengths did Vitruvius think a person’s height would be? Do you think this might be true? How could you test this idea?

If you wanted to describe how big your feet are, what characteristics could you use (e.g. length, width, area, sneaker size…)?

Discuss the national Reach for the Stars activity - students all over Australia are going to measure and share some information about the size of our feet and how tall we are. (What information do we need to collect? How could we make the measurements? What would be the best way? How will we record our data?)

Some other measurement ideas to talk about:

• Ways of measuring (formal and informal, examples of units, specific tasks using various units, measuring the same object using different units).
• Relationship between unit size and number of units (if you use smaller units then you need more of them).
• Usefulness of standard forms of measurement.
• Importance of accuracy in different circumstances.
• The idea of “average”

Collecting and recording the data

Encourage students to suggest, discuss and choose possible methods for collecting the required data. (Some ideas are provided below, but you need not be constrained by these). Consider issues of accuracy and consistency (how to deal with shoes, hair etc.). Would all methods give the same result? Which are “better”? Why is accuracy in measurement important?

Each child could make a concrete representation of his or her height and foot length using paper streamers or cutout figures.

Foot sizes

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  Children could design and make boxes or other devices which allow them to classify the size of their right foot according to the Reach for the Stars Foot Size Scale.
• Alternatively, use one of the resources provided here:
  • a series of 'box' patterns (for Foot Sizes A to J)
  • a collection of labelled linear measures (for Foot Sizes A to M)

Heights

Remember that students' height data will need to be grouped according to their gender and "Foot Size" classification.

• Measure each individual's height, then record all the measurements in groups ("Boys with Foot Size G", "Girls with Foot Size H" etc.) on a large chart or in workbooks. Add the heights in each group as an individual or class activity. Measurement methods might include:
  • Mark a line on the wall for the height of each student (and label appropriately), then measure the heights of the lines;
  • Take turns to stand next to a ruler or measuring tape on the wall; or
  • If students made streamers or cutouts, measure the length of each.

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  Alternatively, students could first group themselves according to gender and "Foot Size".
  • If they made streamers or cutouts, tape these together and use a tape measure or trundle wheel to determine the total length for each group.
  • Line up head to toe along the ground and measure the total length of the line with a tape measure or trundle wheel.
• Recognise that adding together the individual height measurements is the same process as measuring all the heights lined up end-to-end.

Display your data

Create a wall display in the classroom or corridor

• using your cutouts or streamers
• showing each child's own data (perhaps using this footprint template)
• with graphs created from your data (e.g.: distribution of foot sizes, heights grouped by "Foot Size" etc.)

Investigating

How many times does your foot length fit into your height? (See the junior primary page for some ideas). Display your class data (talking about the shape of a graph showing each person's height:foot length ratio might be interesting).

Is Vitruvius' conjecture true for you? Is it true for others in your group/class? Are the answers different for people who are bigger/smaller or older/younger than you?

Does the tallest person have the biggest feet? Do taller people always have bigger feet? Could you use your data to predict who might have left a particular footprint?

As a group: develop, explain and test strategies for ordering yourselves according to foot length. After you have done this, are you also lined up in order of height?

Do boys have bigger feet than girls? (Is the person with the biggest feet in our group a boy? Among the five people with the smallest feet are there more boys or girls? How else can we look at the question?)

In how many different ways can you group your data (e.g. by age groups, gender, Year level...)?

What is the difference between your height and (the height of the tallest person in the group? the height of the teacher?)

Invite some parents/teachers/other special visitors in to your class to be measured and compare your results with theirs.

What other questions might you ask?

A hands-on approach to the concept of “average” – make a piece of string for each person; join them together, then fold the total length enough times that there is one length of string for each person in the group.

Can you compare your data with those of another class (or classes)? How could you do this? (use graphs, tables; compare spread of foot sizes, spread of heights, height:foot length ratios) [Teacher note: it might be interesting to look for the idea that height and foot size distribution will vary in older and younger classes, but does the relationship between foot length and height?].

Investigate the national data (available on Tuesday 11 September) and compare the findings with those of your class.

More activity ideas for middle primary school