Weight Logic Algebraic Thinking Problems

By: Mary Kienstra on: February 14, 2015  in: algebra, Engagement, Math


Weight Logic by Marcy Cook

Elementary students access algebraic thinking using different formats and problems. I’ve found the greatest resource for teaching my students algebraic thinking is to practice weekly with Weight Logic algebra problems from Marcy Cook Math.  These problems encourage algebraic thinking in a very friendly way – using balances and pieces of fruit!

Marcy Cook Math products develop students’ number sense by engaging students in interesting problems.  Her products use different formats to enrich and extend math thinking in ways that worksheets and texts do not.  Although I’ve used many of the Marcy Cook Math products, I think Weight Logic is my favorite!

Wt log

Marcy Cook Weight Logic Problem

Our weekly routine involves  students viewing the weight logic problem on the screen and solving it on their own.  Then they show how they solved each balance and how they found the weight of each type of fruit.  They explain their strategies and comment on each other’s ideas.  This discussion is rich as they describe algebraic concepts and different strategies for solving.  Lastly, my students convert the representations on the balances to traditional algebra equations using symbols to replace the pieces of fruit.  With this last step they are moving from the concrete to the abstract, deepening their understanding and building their confidence.

After my students have mastered Marcy Cook’s Weight Logic problems, I realized the next step in the progression could be replacing the pictures of fruit with algebra symbols.  I created a series of algebra logic problems using Marcy Cook’s ideas with A for apple, B for banana, and C for orange (citrus).  My students easily understand that these new problems require the same kinds of algebraic thinking to solve.  They have moved another step closer to the abstract thinking required to solve algebra problems as they are essentially solving 3 unknowns in 3 equations.

Weight Logic problems using algebra symbols and decimal operations

Weight Logic problems using algebra symbols and decimal operations

To make these even more challenging, I added decimal points to Marcy Cook’s original problems.  Now my students are using their knowledge of operating with decimals to solve these weight logic algebra problems.  Since I have provided scaffolding along the way, students are more than ready to solve these problems.

My students are confident solving many different kinds of problems that require algebraic thinking.  I showed them problems that they had solved in 3rd or 4th grade using guess and check.  Now they can solve those by putting them into the balance format and solving them using the Weight Logic thinking.  I feel like now they are well on their way to the abstract thinking they will need for solving algebra problems.




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