Here is a complete lesson with 18 activities and some exam questions at the end to see if you have understood.

This puzzle has become very popular on social media. Why not share it on your page and see if your friends can get it right?

Here is the solution.

#### howmanytriangles

The solution to the “How many triangles?” puzzle.

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

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.

Be systematic! What sort of numbers are important to help you solve this problem?

How many triangles are in this shape? (A Transum starter)

When you are absolutely sure you have counted them all, click here and press the yellow button to see if you are right.

Download, print and cut out the triangles. Work with a friend to try and match all the questions with the correct answer. Ideal for Esol students learning to count in English.

Counnting Entry 1 Jigsaw

The Tower of Hanoi is one of the most famous mathematical puzzles. See if you can work out how to do it with 3, 4, 5, 6 and 7 discs.  Then see if you can do it using the minimum number of moves.

Lots of my ESOL students still get confused with some numbers. Seventy becomes 17 rather than 70 and sixteen is sometimes written as 60 rather than 16. Try this matching quiz to see if you can get them right.