This was the title of my presentation at the NCTM Annual Conference a few years ago.  Since then, I have had the opportunity to share these tasks with other teachers, and I hope you find them helpful.

Why are these visual tasks important?  For years we have understood the importance of using representations to help students understand concepts.  We’ll discuss this in future posts, but consider the recent emphasis on the CRA (Concrete-Representational-Abstract) model.  All students need to conceptually understand mathematical concepts, but I would argue we do not need to sacrifice critical thinking and reasoning for conceptual understanding; we can have both!  The following are just a couple of ways to represent algebraic thinking visually while also incorporating critical thinking.  I have personally used these materials in grades 2-8.  In elementary, these materials were used with gifted and high-achieving elementary students.

Elementary students use these as mathematical logic puzzles, and in middle school, I used these to introduce writing equations and solving systems of equations.

Puzzles similar to the picture above use a series of balances.  They are similar to Balance Benders and Weight Logic.   (Balance Benders is the example with a series of scales; it is wonderful for introducing systems of equations.)

Venn diagram puzzles use logic to introduce writing equations using variables.  For a more detailed free sample and explanation, visit the store.

I also love Hands-on-Equations.  Students on all levels think these are so fun!  When teaching middle school, my students asked me for more!  (If you have taught middle school, you will know this is high praise!)  All students love a challenge!

Students should be able to solve these without using ‘guess and check’ at all!  In future posts, I plan to share examples of how we teach using each of these resources, along with questioning tips to help students develop strategies for each type.

Visit my resources page for links to purchase these and other materials that promote both critical thinking and algebraic reasoning!