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Shared Factors – A Quadratics Puzzle

I shared this shared factors puzzle on twitter recently, but I thought I should share it on my blog as well.

Shared Factors Quadratics Puzzle by mathequalslove

Shared Factors Puzzle

Each side of the square shares a factor with each of its neighboring sides. Determine the missing values that make this statement true.

Shared Factors - A Quadratics Puzzle

This would be a great task for including in a polynomials or quadratics unit. I look forward to seeing how others incorporate it into their classrooms.

Adaptation by John Golden

John Golden brilliantly suggested that this problem could be reframed using an area model. I love the box method for polynomials, so I found this approach to be really satisfying.

Tweet by John Golden with Adaptation of Shared Factors Puzzle.
Image Source: https://twitter.com/mathhombre/status/1340128289558556674

If you like this approach, check out John Golden’s Geogebra adaptation.

John Golden Geogebra Adaptation of Shared Factors Puzzle.

Puzzle Solutions

I intentionally do not make answers to the printable puzzles and math activities I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, as fun activities in their workplace, or as a birthday party escape room.

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

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