# Core Maths Taster Session

Welcome to the Core Maths Taster Session!

We're really looking forward to meeting you in person next year! At this point of the year we would normally invite you to visit our department for Taster Day so that you could get to know some of us and learn about the courses we have on offer. In place of this, we've put together a lesson below which we'd like you to work your way through. We hope you enjoy it!

Please follow the instructions and videos below:

# Introduction

What is Core Maths? What are we going to look at today?

Watch this short clip to find out!

## Activity 1: Critical Analysis

Critical Analysis is a key component of the Core Maths course!

One component of critical analysis is being able to spot misleading information.

In particular, being able to spot why and how graphs are misleading is a key skill.

Graphs can be misleading in a few ways including:

A distorted vertical or horizontal scale (I.e. one or both axes are wrong somehow, maybe they doesn’t start at 0 or they skips numbers, etc.)

The graph is mislabeled

Data is left out

Let's look at some examples!

### Graph 1: Chevy

Have a look at this graph. Can you spot how it might be misleading? How should it be improved?

Check out or hint if you get stuck! Then take a look at the video solution below.

### Hint

Take a look at the y-axis... Can you see how it might be misleading?

### Graph 2: Job Loss

Have a look at this graph. Can you spot how it might be misleading? How should it be improved?

Check out or hint if you get stuck! Then take a look at the video solution below.

### Hint

Take a look at the x-axis... Can you see how it might be misleading?

### Graph 3: The Times

Have a look at this graph. Can you spot how it might be misleading? How should it be improved?

Check out or hint if you get stuck! Then take a look at the video solution below.

### Hint

Take a look at the graph on the right... Can you see how it might be misleading?

### Graph 4: Unemployment Rate

Have a look at this graph. Can you spot how it might be misleading? How should it be improved?

Check out or hint if you get stuck! Then take a look at the video solution below.

### Hint

Take a look at the scale... Are all the points plotted correctly?

## Activity 2: Correlation and Causation

So we know that Graphs can be misleading. How else can we be misled by statistics?

One common issue is when people confuse Correlation with Causation.

*Correlation is roughly defined as the statistical relationship between two variables. It doesn’t mean that one thing is causing another, just that the two are related somehow. Often there are other factors that can explain why two variables have a strong correlation.*

Let's look at some examples!

### Example 1: Ice Cream and Drownings

This graph appears to show a strong positive correlation between ice cream sales and drownings.

Does that mean that buying ice cream causes drownings?

### Hint

Is there a third factor you can think of that is related to both drownings and ice cream sales?

### Example 2: Marriage and Life Expectancy

This statement is often quoted in magazines and newspapers. Data shows that married people, and married men in particular, are more likely to live longer than single people.

Does marriage really make men live longer?

Can you spot the misconception here?

### Hint

What factors contribute to whether or not someone gets married?

### Example 3: Nightlights and Glasses

This is a pretty scary statement if you're a parent who usually leaves a night light on!

Does leaving the light on really cause damage to the eyesight of children?

Can you spot the misconception here?

### Hint

What factors contribute to whether or not someone needs glasses? Can you think of a friend or family member with glasses? Do their parents or grandparents have glasses?

## Activity 3: Fermi Estimation

Watch this short video explaining the concept of Fermi Estimation - a key unit in Core Maths!

### Example 1:

See if you can work out an estimate for this problem.

When you're ready, watch the video solution below for one possible answer!

### Example 2:

See if you can work out an estimate for this problem. What things will you need to know and what assumptions will you make?

When you're ready, watch the video solution below for one possible answer!

This video is not really something we study in Core Maths but provides a really neat application of maths to suggest how to distribute a vaccine.

## Conclusion

We hope you've enjoyed this short introduction to Core Maths!

You might be wondering about what else you might learn about in Core Maths.

We also cover topics like:

Numerical and Graphical Statistics:

Sampling, graphs and charts, comparing data

Finance:

Calculate your income tax, national insurance and student loans payments.

Compare bank accounts and loans to get the best deal

Normal Distribution & Confidence Intervals

Modelling real-world situations with the normal probability distribution

Making decisions based on statistical confidence

And so much more!