Monday, 2 November 2015

Math Tip Monday - Operations & Algebraic Reasoning

Algebra is about recognizing the relationships that exist among qualities and operations.  These relationships are a good springboard for the symbols that algebraic expressions represent.  Students at a very young age can explore algebraic relationships.  Here are a few tips to get you started:

1) Explore Properties & Relationships using Manipulatives

When multiplying, students can use the commutative property of  a X b = b X a.  Before introducing the equation, students may explore this with tiles while creating various arrays.  For example, start with 24 counters.  How can 24 be represented in two different ways?

Experimenting with manipulatives such as tiles or counters will lead to understanding and representing the operations with a formula.  Another way to do this is with balance scales.  This can happen as early as Kindergarten.

Choose linking cubes for this activity.  Start with 10.  You can add 5 and 5 on one side and then 3 and 7 on the other.  Will they balance out?  You can generate various situations using the number 10.  From the visual representation, students can then see that 5 + 5 = 3 + 7.  You can even place these equations at a math station and have the students explore them.  5 + 5 = a + 7.  

2) Algebraic Reasoning Becomes Functional Thinking

Working with visual patterns allows young students to see the relationships between numbers.  This can be accomplished through math read alouds.  One of my "go to" read alouds is Two of Everything.

This story is a great way to talk about functions and function machines. Working with a function machine allows students to select input numbers that are then transformed by a particular rule to generate output numbers (in this case doubling numbers). This task engages them in thinking about the relationship that holds true for all input–output pairs.

Older students connect visual representations with symbolic representations, allowing them to explore the properties of functions (example, table of values, graphs....).  Younger students can create an input-output chart.  

Thanks to Theresa's Teaching Tidbits and K's Classroom Kreations for hosting this Math Tip Monday! 


  1. I really like that idea about using a balance scale. It's so visual and really gets the point across about equal values on opposites sides of that equal sign. I use foam tiles all the time to teach math. We used them to learn multiplication. It was fun turning an array on its side and showing the Commutative Property of Multiplication.

    1. Thanks for your feedback. Great idea for using this during multiplication! Thanks for sharing.

  2. I agree with Dad and the Boys....using a balance scale is a wonderful way to demonstrate/explore equality.

    1. Thank you! It works well with many grade levels. Your feedback is appreciated.