Are You Square?

Introduction

If you are asked "Are You Square?" what would your answer be?  How could you find out using a mathematical way?  What measurements should you take?  Either investigate this your own or look at the following prompts:

1. Measure your height (h)

2. Measure your arm span (s) (the length from left-hand finger tip to right-hand finger tip)

   • How do we ensure accuracy/ precision?

3. Enter your results in a class Google Sheet (here is an example of one done in a previous Year 8 class).

4. Create a scatter graph to see how spans and heights compare (here is a video showing you how to do it on Google Sheet).

   • Which variable is x and which is y?

   • Is it necessary for the axes to start at 0?  Why or why not?  If so where would all the data be clustered?

   • What’s a reasonable scale?  

   • Why is it important to use the same measurement scale for both Height and Arm Span?

5. How do we find out about the correlation?

   • Calculate the mean/ median height (h).

     • Draw a vertical line on the scatter graph at this value of h.

   • Calculate the mean/ median arm span (s)?

     • Draw a horizontal line on the scatter graph at this value of s.

   • The scatter graph is now divided into 4 quadrants. 

     • How would you describe the correlation if most of the data points are located in Quadrants 1 and 3?

     • How would you describe the correlation if most of the data points are located in Quadrants 2 and 4?

     • How would you describe the correlation if there is an even number of data points in each of the four quadrants?

   • Where are most of the data points located?  What does that tell you about the correlation/relationship between height and arm-span? Are they related?  

Further Questions

1. What are some other comparative measures we could take?

   • Distance around head

   • Length of smallest finger

   • Hand span

   • Length from wrist to elbow

2. What are some things we could consider?

   • The most “average” person in the class

   • The range

   • The most frequent measurements

   • Whether approximate ratios exist between pairs of measures

3. How could we extend the investigation?

   • Boys vs Girls?

Further Practice

Some of the essential skills introduced in this lesson are "correlation" and "scatter graph".  The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.  Watch any video and/or go through any online lesson as you see fit.  

Transum

• Cartoon Scatter Graph - place the cartoon characters on the scatter graph according to their height and age.

• Plotting Scatter Graphs - plot scatter graphs from data representing a number of different everyday situations.

• Correlation - arrange the given statements in groups to show the type of correlation they have.

Desmos

• Robots: What a Point in a Scatter Plot Means - you will interpret points in a scatter plot within a context and add points to a scatter plot given information about an individual in the population. What is happening for a particular individual? What is happening at a global level for the entire population?

• Dapper Cats - do you see a set of data points as a single thing that can be analyzed or just a bunch of disconnected point? What connections are there between the scatter plot and the line?

• Fit Fights - can you place a line on the scatter plot and trying to max out a meter that measures the goodness of the fit?

Extension

1. Click here to learn more about how to calculate correlation step by step.  Here is another way of calculating the correlation coefficient on Google Sheet.

1. • How do you interpret this number?

   • What would the number be for a positive correlation?

   • What would the number be for a negative correlation?

   • What would the number be for no correlation?

   • What would the number be for a strong correlation?

   • What would the number be for a weak correlation?

   • Try this guess the correlation game.

2. Does that mean that height is caused by arm-span?  Or arm-span is caused by height?  Or both?  Or neither?

3. Do you think you could predict a person’s height by measuring their arm-span?  Why or why not?  Are We Square?

   • If so, what would the arm-span of someone with a height of 150cm be?

What would the height of someone with an arm-span of 150cm be? This is not required at this level!

Here and here are some extra tasks from Don Steward.  Last lesson's task is one of these examples!

Here are a few more recommended by Mr Barton.