Shoe size Math trick explained >> Did you know that your shoes can tell your age?

Guest Blogger: @enyinda14

Shoe Size Math Trick

How often do students ask their history instructors “when am I going to use what I’ve learned?” NEVER. How often do students ask their math instructors “when am I ever going to use this?” ALL THE TIME. Why is this the case? Because most students don’t find mathematics fascinating. They don’t get as excited about fractions and equations as they may about the War of 1812.  There are quite a few exercises and examples that prove math to be a fascinating subject. I recently found one such problem via @magicalmaths. It stated:

“Did you know that your shoe size can tell you your age!”
1)      Take your shoe size (no half sizes, round up)
2)      Multiply by it 5
3)      Add 50
4)      Multiply by 20
5)      Add 1017
6)      Subtract the year you were born
The first digit(s) are your shoe size and the last two digits are your age! Its shoe magic!

shoes size math trick

Shoe size math trick revealed

I reviewed it and figured out how it was constructed and why it works. It is a very clever algebra problem, one I wish I had thought of myself, but I didn’t. So I created a similar one:

1)      Take your shoe size (no half sizes, round up)
2)      Add 20 to it
3)      Multiply by 50
4)      Add 7
5)      Multiply by 2
6)      Subtract the year you were born
Alas, the first digit(s) are your shoe size and the last two digits are your age!

I like this one a little better because it does not give away the year with adding 1014. We can create an infinite number of this kind of “magic”. It is a great exercise that can be used to introduce students to algebra. It will peak their interest in the subject. Here is how this works.

1)      “Take your shoe size.” I do not know your shoe size. In typical mathematics fashion, we let x be the shoe size.
2)      “Multiply by it 5” gives us 5x
3)      “Add 50” is 5x + 50
4)      “Multiply by 20” is 20(5x + 50) = 100x + 1000
5)      “Add 1017” is 100x + 2017
6)      “Subtract the year you were born” gives us 100x + 2017 – (your birth year)

At this point, the problem clears up. We see that 2017 minus your birth year will give us your age (unless your birthday is later in the year). Next, when we multiply a whole number (except 0) by 100, we get that number with two zeros at the end. For instance, 5(100) = 500. So, 100x will put your shoe size first and the last two digits will be reserved for your age (as figured out earlier).

This magical shoe size math problem can be modified in various ways. For instance, instead of shoe size, ask for their favorite number. That choice is typically a whole number. Try this with students new to algebra and let them see the power of x.

Categorised as: Algebra | Algebra | Facebook | G Post | Lesson plenary | Lesson starters | Mathematics | Share A Maths Starter | Sharing Starter | Twitter


  1. lydiah says:

    it amazing how you played with numbers, u hated algebra with passion, I wish I was introduced to it in same stile,I couldn’t have scored that grade I got

  2. Frank Kniebel says:

    1014 is incorrect on the calculating your birth year! My calculations shows I am 64. I am 65 and soon to be 66!

  3. suzanne says:

    The shoe trick did not work with me.

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