The Sheaf Valley Maths Trail is a short walk starting outside Sheffield City College on Granville Road, along the footpath to Sheffield Station and the steel blade sculpture, behind the station to the steel steps and the amphitheatre, up the hill to the Cholera Monument and then back to college via Clay Wood. Along the way you will answer questions on many different aspects of mathematics. It is suitable for school groups, college students studying Functional Skills, home schoolers and their parents or anyone who would like to have a go!

Download the student booklet here. It is best printed as a booklet.

There are also a teachers booklet and a powerpoint which I will send to you on request. Email graham@mathswithgraham.org.uk to request these. Please let me know who you are planning to use it with.

Topics touched on on the trail include

**Number**

Counting

Multiplication

Fractions

Time calculations

Reading a timetable

Calculating journey cost

Speed Distance Time calculations

**Shape and Space**

Measuring length

Estimating length and weight

Symmetry (Line and Rotational)

3 dimensional shape

Angles

Circle calculations

Volume of a cuboid

Area of irregular shapes

**Data Handling**

Averages

Feel free to adapt the trail by missing out some questions and adding others to make it suitable for your students/pupils.

Split your group into teams of 3 or 4 people. Make sure less able students are paired with more able students. Each team will need a DIY tape measure, a large ball of string, a large protractor, a pencil and a calculator. You need to work out the logistics of ensuring there is someone to help at the various stopping points.

Tell your students to stay together, look after each other and take extra care when crossing roads. If this is a school/college outing you will need to fill in a risk assessment.

There are lots of different methods to do long multiplication. This activity helps you perfect one- the grid method. It also tests you on your car knowledge! Grid multiplication for car lovers!

In this exercise you will need to read the information from an Amey press release about the massive Streets Ahead contract. You will then use your skills to answer the questions. You can download a worksheet or use the interactive version here.

Here is a great phone app that will help you with your arithmetic so you don’t need to be afraid when you are faced with that non-calculator exam. It’s called Maths Tricks and shows you lots of short cuts to performing calculations and gives you endless practice to improve your speed and accuracy. Best of all it’s free!

https://play.google.com/store/apps/details?id=com.dexterltd.maths.tricks_lite

You can find it on Google Play. I am recommending this because it is good, not because I have any connection to the app.

I have just discovered the quiz site Sporcle. Here is a multiplication game to get us started! You have to be really quick at typing as well as arithmetic!

Have a go at this worksheet to find all the Prime Numbers less than 100.

Now try this much bigger Sieve to find all the Prime Numbers less than 400! Start by clicking on 2 and all the multiples of 2 will be removed. Then click on 3 to remove the multiples of 3 and continue clicking on the prime numbers until you are only left with red prime numbers.

Also take a look at this video

Ask your teacher (or somebody else) to

1. Write down your house number.

2. Double it.

3. Add the number of days in a week.

4. Multiply by 50.

5. Add your age.

6. Subtract the number of days in a year. (not a leap year)

7. Add 15

The answer is your teachers house number and their age!

Can you explain why this works?

Many people on a low income are not able to open a bank account. If they need to borrow money they can be offered loans with massive rates of interest. This exercise looks at how to calculate interest rates and compares different ways of borrowing money.

The video mentions two businesses in particular. Wonga.com and Quick Quid both charge interest rates in excess of 2000%. Do you know of higher rates of interest? Please comment below to name and shame the loan sharks!

The same exercise is here in worksheet format.

The Joseph Rowntree Foundation research into the minimum income standards for the UK. The Minimum Income Standard for the UK shows how much money people need, so that they can buy things that members of the public think that everyone in the UK should be able to afford.

- Figures are based on public views about a minimum standard that nobody should fall below.
- It does not show you what you require to meet all your individual needs, and is
**not suitable**for use as a personal budgeting tool.

By entering a few details about your circumstances you can compare your income with the MIS, and see how this is made up. For instance my children are now all grown up and have left home, so I live with my wife. When I have entered details about my rent/mortgage. gas/electric/water bills etc it tells me the minimum income I require is £23,099. They break this down into how much I need for food, alcohol. council tax, clothing etc. It makes very interesting reading!

The picture shows the results for a single person.

Go to http://www.minimumincome.org.uk/ and enter your details to see what it suggests for your household.

Try this exercise to find out about a single persons minimum income. It will also help you to calculate percentages.

How do you work out how much electricity something uses?

This exercise will help you understand “units” of electricity and help you work out how much electricity different things use.

There is a worksheet version of the activity or an interactive version.

Download, print and cut out the triangles. Work with a friend to try and match all the questions with the correct answers and make a shape

Download, print and cut out the triangles. Work with a friend to try and match all the questions with the correct answers and make a shape.