AO elaboration and other teaching resources [2]

AO elaboration and other teaching resources [3]

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

Although we use a variety of mathematical skills in this unit it is essentially a project that relies heavily on Statistics. Throughout we will be measuring and recording length; exploring the relationship between metres, centimetres and millimetres; organising data; presenting and interpreting graphs; identifying number relationships; and applying number relationships. All of this is aimed to collect data that will enable us to suggest the height of a giant given their handprint. Like all such investigations it is important to have a good idea of what data should be collected, how much data is needed, and what the limitations of the collecting mechanism are.

#### Prior experiences

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.

#### Session 1

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 his 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 use other classes to get a larger sample of people.
- The students could gather more data from their family and whanau. This would give a greater range of ages and heights.

#### Session 2

In this session we create scatterplots of the relationship between height and hand measurements.

- Discuss:

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? - Encourage suggestions: Create a scatterplot graph. This can be done easily on Excel. Show the students how to set up a scatterplot graph. Get them to plot some samples manually on their own number plane as this will give them a better idea of how the computer generates scales for the axes.
- Develop scatterplots 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 his/her hand length, or his/her hand width is one-tenth of his/her 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 scatterplot of only the junior children, or males, etc. if you want.

#### Session 3

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 scattergraphs 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 Guinness Book of Records to compare your giant with the tallest known man and woman.

#### Session 4

In this session we discuss the accuracy of our findings.

- Discuss:
*How accurate is your information?**Using a hand print only of a known person can you predict their other measurements?*(*Check this)**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.

#### Session 5

In this session students are challenged to investigate other things we might be able to find out about the giant from his 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 him/her?
- What size would the giant’s house be?
- How much would the giant eat each day?
- What would his/her food bill be for a week?
- How big would the giant have been when he/she was a baby?
- How many balls of wool would you need to knit the giant a jersey?

Family and Whanau,

This week in maths we are investigating a mystery. A giant has left a handprint and we are using the measurement of the handprint to work out how big other parts of his body are. To do this we need to collect some measurements from other people for comparisons. Please allow your child to measure your hand, height, and a few other parts of your body. They will add this information to our class spreadsheet. Ask them to let you know what we find out by the end of the week and explain to you how we figured this out.