Hula Hoop Maze (patterns)

Buy Hula Hoops of four colors for your age 5-8 math class! Spread a bunch of them out on the floor in this hexagonal arrangement. For children aged 6+ give them one of the paper Hula Hoop Mazes found in the pdf below. The hard objective is to randomly choose two of the four colors and then try to get from the left to the right. Here I have chosen yellow and black and failed.

The colors chosen in the pdf and this slide show are good for color blind children.

The easy objective is to try to get from the bottom to the top. Here we have succeeded with red and blue. We have succeeded both in the hard objective of going from the left to the right – and in the easy objective of going from the bottom to the top.

Try this as a class. Choose any two colors. Try the left to right challenge.

Do not go to the next slide till you have tried this.

Here we have succeeded with yellow and red.

Here we have succeeded with yellow and black.

You can also find five hula hoop colors and arrange them in a square grid. In this case you still only choose two colors, but you may move diagonally.

The pdf below has six of these puzzles.

Why can I be so sure that no more than half of the mazes on the hexagonal grid can be solved? The total number of mazes equals the six going from left to right and the six going from bottom to top.

For the square grid – I could say something similar, but I’d need to include mazes that choose three colors in which you could not move diagonally along with the mazes I’ve already described.

Older students may also use these mazes as a backdrop to introduce some combinatorics like “5 choose 2.”

Hula Hoop Mazes of Hong Kong

(MathPickle, 2017)

Last week I worked with the elementary school children at the Chinese International School in Hong Kong. What a joy! And what an unexpected joy when we discovered some newly polished Hula Hoops 😉 It was time to get creative with some colorful mazes.

Here are eighteen of them to download.

The images below show our first attempts at making this maze. A regular hexagonal pattern is better!

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. Try pairing up elementary students and getting older students to work in threes.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Use the right tools!

Students should use the right tools: 0-99 wall charts, graph paper, mathigon.org. etc.

MP6 Be precise!

Students learn to communicate using precise terminology. Students should not only use the precise terms of others but invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist! 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?

(http://www.corestandards.org/Math/Practice/)

Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.