Pumphrey's Math

Patterns, everywhere

Seven Squares – The Essence of Mathematics


This post is my attempt at being part of the ExploringtheMathTwitterBlogosphere community.

This week (or last weeks) challenge is to post your favorite rich/open ended math task.

Without doubt mine is nrich’s Seven Square’s problem. To my mind, this captures the essence of what mathematics is all about: Patterns. I love starting my Algebra 2 course with this to give them a sense of why we do the Math.

In class I will give each group a set of toothpicks. Some use them, others go straight to the drawing but all seem to get into it at their level/pace straight away. It’s amazing what comes up from students of all abilities.

A great extension to this is Dan Meyer’s toothpick activity. There is no end to shapes that students can investigate. It is one of those ideas that is great for all ability levels and really does help when you are dealing with the content skills throughout the course. I find that I refer back to this lesson, often.


Author: PumphreysMath

A British Math(s) Teacher now living in Indianapolis, USA, aiming to show my students how questions are often more important than answers. Presenter of the MathEd Out Podcast and contributor for the Guardian Teacher Network.

4 thoughts on “Seven Squares – The Essence of Mathematics

  1. Whoa great post! I had never seen the Nrich activity (cool stuff!) and sequencing it with Dan Meyer’s toothpicks looks like a great idea. I teach 6th & 7th graders and feel like both problems could work well with those grade levels also. What do you think having done them both before? I’ve used Fawn’s http://www.visualpatterns.org/ with them a bunch and they seem to dig them. “Patterns, everywhere” is right!

  2. Great problem! Thanks, I will try it with my seventh graders.

  3. I ran across the nrich problems at some point, but your post is a great reminder to bookmark this great resource! Welcome to MTBoS. I look forward to reading more from you-can already tell I will appreciate your style of teaching and what you share.

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