Stepping Out

Purpose

In this unit students find out the length of their pace when walking and running, and compare these with the paces of others

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Specific Learning Outcomes
• make estimates of lengths between approximately 50cm and 1.5m (lengths of strides)
• measure lengths in metres and centimeters
• convert between metres and centimeters
Description of Mathematics

In this unit the students use tape measures to measure lengths in centimeters, in metres and decimal parts of a metre. Students can use calculators for dividing lengths.

Required Resource Materials

tape measures

calculators

pedometers (optional)

Activity

Session 1

Finding the length of one’s pace.

1. Ask students (while remaining seated) to estimate the length of their pace. Ask for suggestions as to how we could find the length of our normal walking pace.
2. In pairs, have all the students measure the length of their walking pace in two ways:

First method: Measure out ten metres. One student walks ten metres while the other counts the number of paces, expressing the last part-pace as a decimal, for example ‘about 14.5 paces’. Divide 10 metres by the number of paces, and record the result in two ways: for example ‘0.69 metres, 69 centimetres.’

Second method: Walk 10 paces, and measure and record the distance walked (‘Should we start/finish measuring at heel or toe of your foot?’). Divide this distance by 10.Record the result in two ways: for example ‘I walked 6.92 metres; each pace 0.69 metres, 69 centimetres.’

These data could be entered in a table:

 Length of pace (m) Length of pace (cm) 10 metres 14.5 paces 0.69m 64cm 10 paces 6.29 metres 0.69m 69cm

Comment: I estimated my pace would be about 80cm. It was shorter, only about 69 cm. Both my measurements were the same.

1. Discuss the different results and the methods used.
Were your two results similar or very different?
Were your estimates quite accurate or not?
Which method do they think is better and why?

Session 2

1. Repeat the activity from session 1 but this time running, not walking.
2. Estimate first. Record the results in the same way, and compare walking and running paces and their estimates.
3. If time allows, repeat the activity, running 20 paces and 20 metres. Compare pace lengths over 10 and 20 metres.

Session 3

1. Do taller students have longer paces?
2. In pairs measure each other’s height and enter all heights and pace lengths on a class chart.
3. Pairs of students now draw a scatter graph of heights and pace lengths of students in their class and write a comment explaining what the graph shows.

1. Is there a link between height and pace length.   Could they use this graph to predict the pace lengths of younger/shorter and older/taller students?

Session 4

1. Collect data about the pace lengths of other students, adults or animals, depending what resources are available. The following possibilities could provide rich tasks:

• Mark out ten metres and ask one or two teachers, parents or other available adults to walk the distance while the class first estimates then counts paces and calculates the length of pace.

• Students can bring data (height and pace length over 10 metres) from their parents, family or friends and graph and compare these.

• Students may be able to find the pace length of their pet cat or dog: counting paces will not be easy!

• If pedometers are available students could investigate using one.
• Video from students or from the internet may be able to provide examples of athletes running over 100 metres or other distances. If the video can be slowed down, paces can be counted and the athlete’s pace length calculated and marked out in the classroom. Students are likely to be surprised how far out their estimates will be. Videos may also be available of horses running over a set distance, of swimmers (count number of strokes and calculate length between strokes), or videos of pets taken and shown in slow motion.

Session 5

After a class discussion of results, students can write up a detailed account of what they have found out during the week and suggestions for further investigations. These could be used to direct further lines of inquiry or could be displayed to show other classes or parents.