Pythagoras and the Knotted Rope

Pythagoras fun for kids 2

Now we’ve switched to a full-time living maths approach, we’re actually making time to play with some of the wonderful resources we’ve had on our shelves for years.

What’s Your Angle, Pythagoras?

Pythagoras for kidsOn Friday we read What’s Your Angle, Pythagoras, a picture book which tells the story of how the young Pythagoras learns how to make a right-angled triangle using knotted rope, and discovers how to calculate the length of its hypotenuse using square tiles.

Obviously the book is mostly fictional, and it takes some historical liberties – the boy Pythagoras visits Alexandria, for instance, several hundred years before the city was built! – but these are discussed at the back of the book in a way that made my kids laugh and was a handy review of Ancient Greece and Alexander the Great.

How to make a right-angled triangle using rope

In the book, the young Pythagoras notices what happens when buildings are constructed with less-than-accurate right-angles. On a trip to Alexandria with his father, he learns how the Egyptians use knotted rope to overcome this problem.

We tried it out for ourselves. We tied eleven knots at equal distance along our rope before joining the ends in a final knot, so that we ended up with twelve short lengths of rope between each knot.

Pythagoras knotted rope living maths

Then we used our rope to make different shaped triangles. We counted how many lengths of rope were on each side of each triangle.

To make a right-angled triangle, we found that we needed the sides to be 3 lengths, 4 lengths and 5 lengths of rope respectively.

Pythagoras for kids

(Top Tip: Take care to make the knots evenly spaced. C(9)’s rope worked perfectly for making right-angled triangles, whereas the one I helped J(8) make didn’t, oops!)

Using Lego to demonstrate the Pythagoras Theorem

While playing with floor tiles, the young Pythagoras in the story discovers that if he makes a square along each side of a right-angled triangle, the square on the longest side uses the same number of tiles as the other two sides’ squares put together.

We tried this for ourselves with 2×2 Lego bricks.

drawing a right-angled triangle
C(9) measured 3, 4 and 5 Lego bricks and drew a triangle with sides those lengths
lego proof of Pythagoras Theorem
1 side is 3 Lego bricks long …


lego proof of Pythagoras Theorem
another side is 4 Lego bricks long


lego proof of Pythagoras Theorem
Completing the squares


9 bricks + 16 bricks = 25 bricks

Pythagoras uses what he has learned to work out how long a ladder is needed to reach the top of a wall. He also helps his father calculate the sailing distance to Rhodes. Β Β Both excellent demonstrations of the usefulness of maths!

lego proof of Pythagoras Theorem
C(9) annotated her Lego diagram to show the Pythagoras Theorem

I would never have thought to teach my kids the Pythagoras Theorem at the ages they are (8 and 9) – all we did was read a picture book. But that living book inspired us to play, and before we knew it we were formulating mathematical proofs. Β Another living maths success!


I’m appreciatively linking up here:

Homeschool Review at Hammock Tracks

Collage Friday at Homegrown Learners

Weekly Wrap-Up at Weird Unsocialized Homeschoolers

Math Monday Blog Hop – Math & Children’s Literature


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19 thoughts on “Pythagoras and the Knotted Rope

  1. Isn’t it so much more interesting to teach maths this way? I can see that your children are loving it. Finding mathematical proofs this way is certainly more inspiring and less painful than the traditional way. πŸ™‚

    1. We’re all loving it! I think that might be the very best thing about homeschooling – rediscovering amazing things that seemed so dull at school!

    1. Thanks, Phyllis. Yes I’d been thinking it would be fun since we got the Pythagoras book a couple of years ago.

  2. What great resources. I love all the hands on things. I so miss Keilee being young enough to do things like this. You are always doing the most creative, fun things! Kei got an app about knot tying but quickly grew frustrated with it. What a beautiful fun way to teach Math. πŸ™‚

    1. Thank you Karen! It’s so sweet of you to stop by with your encouraging words, especially as Keilee is that much older than my two. As I said on your blog, I love reading what Keilee is up to – so inspiring for the future!

  3. We used this book last year and had great fun with it. I didn’t knot a rope though! My children missed out there!!

    1. It’s a fab book, isn’t it? I must admit my rope knotting was rather poor – must practise! πŸ˜€

  4. YOu know, I couldn’t quite decide where to pin this, my math board or my Creation to Christ board……

  5. Would you be willing to interview you concerning this new approach to math? I would love to feature your responses in this Friday’s Homeschool Review. Thanks for linking up and I look forward to hearing from you.

    1. Thanks for hosting the link up, Savannah. I’d love to talk more about our maths approach, we’re really enjoying it.

  6. What a fun book! We’re headed to Greece this fall and I have been looking for some fun living math books. I think my boys will have a lot of fun with it. Thanks!

  7. Fantastic ideas πŸ™‚ were doing it right now! I was so excited when book arrived yesterday and kids loved knotted rope and story. We’re just using Lego idea now πŸ™‚

    1. Hi Harriet, I’m so pleased you’re doing it too! Did you have fun with the Lego? Thanks so much for taking the time to write πŸ™‚ Lucinda

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