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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

ANsWer key link

Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.

Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.

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, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!

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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