The unit explores relationships between the hand length, width, span of a person and their height and other body measurements. By using the hand print of a giant, students are able to use relationship between hand size and body size the find out how big the giant is.
- Measure accurately using centimetres and millimetres.
- Organise and record data, in tables and graphs.
- Interpret trends and identify number relationships.
- Apply mathematical knowledge to practical problem solving.
In this statistical project students investigate the relationship between two variables: hand size and height. They collect a set of data for the investigation by taking measurements from a sample of people, then create dot plots to explore potential relationships. They interpret their data displays to identify the relationship between hand size and height, and communicate their findings to their classmates, considering the limitations of their results.
Because the project involves collecting measurement data, it provides plenty of opportunities for students to practice measuring and recording length accurately. It also develops students’ understanding of the relationship between measurement units: metres, centimetres and millimetres.
The learning opportunities in this unit can differentiated by providing additional workshops to scaffold students’ work. Possible workshops include:
- measuring accurately in centimetres and millimetres
- use of Excel
- interpretation of dot plots
- converting between metres, centimetres and millimetres.
The identity of the giant can be adapted. Work together with students to brainstorm who the giant might be, drawing on, for example, New Zealand myths and legends, picture book characters, or animated movie characters.
- Rulers: 30 cm, 1m, tape measures
- Access to Excel or similar
- Giant hand print (photocopy of teacher's enlarged to fill an A3 page)
- Construction material
- People of varying ages
Before working on this unit, students should have engaged in practical measurement exercises where they measured items of varying length using metres, centimetres and millimetres. They should also know the relationship between metres, centimetres and millimetres.
In this session we introduce the problem and start collecting data.
- Show the students a photocopy of the giant’s hand. Ask the question:
We know the length, width and span of the giant’s hand… can we determine their height?
- Discuss the possible relationship between their hand size and their body height.
- Gather information to investigate the possible relationships.
- Get them to suggest that it might be worth measuring and recording: body height, hand length, hand width, hand span.
- Discuss the size of the sample needed to provide reliable information.
- Discuss range of ages (junior, middle, adolescent, adult) and gender (male, female) as variables.
- Get the students to measure themselves and a partner and collect the data on a spreadsheet. You could share data with other classes to get a larger sample of people.
- The students could also gather more data from their family and whānau. This would give a greater range of ages and heights.
In this session we create scatter plots of the relationship between height and hand measurements.
What relationship are we trying to determine? (Relationship between height and hand size.)
How can we determine whether there is a relationship between the various pieces of information we have gathered?
How best could we show that relationship?
- Show the students how to set up a scatter plot. Get them to plot some data manually as well as using Excel as this will give them a better idea of how the computer generates scales for the axes.
- Develop scatter plots for each of the following: height versus hand width, height versus hand length, and height versus hand span.
- Discuss the appearance of the graphs.
Are there any apparent patterns or relationships?
Using the information on the graph can you predict a person’s height or hand size?
What relationships are you identifying? A person is (?) times their hand length, or their hand width is one-tenth of their height?
Which hand measure is the best predictor of height? Why?
Can you use this information to work out the giant’s height?
- You may like to discuss the amount of variance and the range within which the relationships fall. This gives an opportunity to discuss lines of best fit and apply them to constructing the giant.
- Explore whether the prediction will be different if you know that the giant is young or old, male or female. Excel allows you to sort the data in ascending or descending order and draw a scatter plot of only the junior children, or males, etc… if you want.
In this session we create a silhouette of the giant.
- Discuss possible relationships between other body parts.
- Determine a list of body parts to be measured.
Will the giant be 2-dimensional or 3-dimensional?
- Can we use a simple length measurement to predict the size of other parts of the giant? For example: head length/width, foot to hip length, shoulder width, foot length, arm length, waist circumference, head circumference, or thigh/calf circumference.
- Record measurements on a spreadsheet.
- Use scatter plots to investigate relationships between measurements to determine the size and proportion of the giant.
- Make a 2-dimensional silhouette of the giant using newspaper or butcher's paper. Look up the tallest known man and woman and compare your giant to these people.
In this session we discuss the accuracy of our findings.
How accurate is your information?
Using only a hand print, what other measurements can you predict?
How accurate were your predictions?
- Discuss how a small change in the length of hand measurement makes a big difference to the predicted height.
- Ask: Should we measure the hand length in centimetres or millimetres if we’re going to use it to predict the giant’s height? Why?
- For several people use the relationship you have established for hand length and height. Measure their hand lengths in both centimetres and millimetres and use both measurements to predict their height. Does the accuracy of the hand length measure give a better prediction of height?
- Ask: If we used thumb length as the predictor for height would it be more or less accurate than hand length? Why?
- Get the students to investigate these questions in small groups and report back their results.
In this session students are challenged to investigate other things we might be able to find out about the giant from their hand print.
Students will have many ideas about this such as:
- How many steps will the giant take to walk from your house to school?
- How long will it take them?
- What size would the giant’s house be?
- How much would the giant eat each day?
- What would their food bill be for a week?
- How big would the giant have been when they were a baby?
- How many balls of wool would you need to knit the giant a jersey?