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# Train your mind

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# With MathFitness you can do it!

Have you ever thought of training your mind in a fun, interesting way, and maybe learn something new? The MathFitness project has been active since 2006; its goal is to promote mathematics through play, interactivity, and informal teaching methods. Come visit us at our gym: a “personal trainer” will suggest problems and games and will help you work out how to solve them yourself. Or you can keep up with all our activities (so you can show them to your students) by signing up to our website for free. It’s all in your hands! You will also be able to decide what to do, by choosing between experiments, riddles, magic tricks, brain teasers, logic puzzles, everyday math, and much more… Go check out our activities

If you want to know more, you can browse our activities by searching for specific subjects, or by checking our collections and paths you can follow to go on your own little mathematical adventure. These activities make up our many bundles. There’s something for everyone, including schools. To keep up to date with new developments, subscribe to our Newsletter and follow us on social networks.

### The project

MathFitness was born in 2005 with the goal of designing, organizing, and creating didactic, recreational, and formative activities and to spread the creative dissemination of mathematics. If you are interested, you can learn more about the project, see our collaborations, our portfolio, and the awards we have received.

### A network of gyms

Our strength comes through sharing. MathFitness contains activities in many different subjects, which are then spread through math gyms, as well as little gyms in every school. Are you interested? Check out how you can open your own gym. It’s very simple!

### Our bundles

Throughout the years, we have designed many different bundles of activities to satisfy every demand. We have activities we designed ourselves as well as the ability to organize events. If you’re interested, go check out our bundles.

### Schools

Many activities were designed following direct requests from teachers, and many others were meant to follow the national curriculum. Informal teaching methods are now officially accepted as a possible way to complement formal lessons. Go check out our page dedicated to schools.

### The gym

The mathematical gym is a space with many shelves full of games, common objects, and our special interactive exhibits. With these, you can train your mind, learn to solve problem, learn theorems (or relearn them after a long time) in new and different ways, and see what math really is good for. Most importantly of all, you can learn what math truly is, and how it can help your life, as well as the lives of your children and grandchildren in the future. Go learn more, or see where you can find our math gyms to see if there is one near you. And if there isn’t, you can open one yourself. It’s easy!

### The school gym

A school can permanently dedicate a classroom to the gym and MateFitness will provide the teaching materials necessary to set up the activities that are suitable for the age of the students, as well as the training to use them, as well as tips and tricks to follow. Apart from our initial training courses (and you may want to attend more than one over time to follow developments), opening a gym inside a school is completely free. You can find existing school gyms, or maybe learn more about them, and then see how you can open one yourself.

### The traveling gym (a kit so you can train anywhere)

With this option, it is possible to have access to all of our interactive recreational activities without setting up a permanent space to house them. Materials, contents, and information from the website can be used  for events, festivals, school visits. It is by definition flexible, adaptable to different necessities and contexts. You can learn more or find how you can get one.

# Example activities

• Activity 1
• Activity 2
• Activity 3
• Activity 4
• Solution 1
• Solution 2
• Solution 3
• Solution 4

Everyone know that a football (or a soccer ball if you’re American) is made with 32 pieces of leather, of which 12 are regular pentagons and 20 are regular hexagons, all with the same side length.

The 32 pieces are then stitched together. Each seam joins together the sides of two pieces of leather, which may have similar or different shapes.

How many seams are there in a football (or soccer ball)?

Two father and two sons went fishing. They caught a total of 9 fish between them. When the time came to share their catch, each person got 3 fish.

How is this possible?

Additional information:

• there were no cats around;
• they did share 9 fish;
• there were no fish inside other fish.

A classic riddle that may help you learn something about math.

A brick weighs one kilogram plus half a brick.

How much does a brick weigh?

Esther finds a classic Greek book in her immense library. She likes it so much that every day she reads twice as many pages as she has read before.

After twenty days, she has read the entire book. (Which is impressive, as it was quite a brick!)

On which day did Esther reach the halfway point?

The pieces of leather have a total of 12 x 5 + 20 x 6 = 180 sides. Since each seam joins two sides together, there are 180 : 2 = 90 seams.

In geometry, an Archimedean solid is a convex polyhedron composed of two or more types of regular polygons that meet in identical vertices. The classic football is a truncated icosahedron, which is a polyhedron formed by 12 pentagons and 20 hexagons. It can be obtained by cutting an icosahedron.

The solution is simple but hard to think of at first. This is one of the many activities that allow you to train your problem solving.

There were three people: a boy, his father, and his grandfather. Two of them are father and two are sons.

Again, the solution is simple, but it’s only obvious once you know it. Reaching it for the first time isn’t always easy (but it’s fun and it can make you feel accomplished once you do). But once you’ve seen similar problems enough times, you’ll learn the way of thinking that allows you to solve them.

The answer is 2 kg.

You can reach it by thinking logically, or you can do the math yourself by using some algebra (which is part but not all of mathematics).

With a simple reasoning, we can say that is a brick weight “1 kg plus half a brick”, then we can imagine a brick divided into equal halves: one half obviously weighs half a brick, and the other weighs 1 kg. You can see that if half a brick weighs 1 kg, then a whole brick must weigh 2 kg.

With algebra, we can set up an equation to solve the problem. “Translating” the text, and calling our brick “b“, we obtain:

$1b=1kg + \frac{1}{2} b$

We can then solve for b:

$1b-\frac{1}{2} m=1kg+\frac{1}{2}b-\frac{1}{2}b$
$\frac{1}{2}b=1kg$
$b=2kg$

Clearly Esther will reach the halfway point on the 19th days, since on the 20th the number of pages she has read doubles, and she reaches the end.

This is another example of a solution that doesn’t immediately come to mind. The math behind this sort of riddle is simple, just fractions and powers of two. It’s natural to try the calculations, even though the solution can be reach through a little lateral thinking. This too is an important part of mathematics.

MathFitness is one of the projects that are changing  the world.

(Google, 2012 –  awarded a priza of \$100,000)

What a marvellous idea, and so well presented.
Seeing the joy on the faces of so many children…
You can tell it’s working!

(Roger Penrose)

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