Our story of playing with big mathematical ideas — and resources to help your family enjoy learning math together

activities to help kids learn the basics of algebra using cotton balls and a DIY balance scale

If you can lay a strong foundation in math for young children and lead them to discover how things work, keeping the learning environment stress-free and enjoyable, I believe this will give kids the best chance to entirely by-pass math anxiety and succeed in higher levels of math and science as they grow.

I have not yet started any specific curriculum with my own kids for homeschooling, (the boys are 2 and 4 years old) but we’ve been doing a lot of fun little math activities. I’ll be posting them in my Math Monday series, so stay posted if you’d like to hear more.

I taught high school math for 6 years, so I’m ever-ready and eager to teach math to my preschooler sons ;). During my Masters in Teaching program, I learned a lot about the foundation of math and ways to teach fundamental concepts that extend throughout the entire field of mathematics. One such overarching concept is Equality.


20170309_093202Things (numbers, variables, expressions) on either side of an equal sign are the same. If kids can really understand this idea, they won’t stumble when they get to Algebra and have to start solving for x. If they can grasp the big ideas behind simple concepts like Equality, they’ll be much more fluent with higher level math concepts.

I wanted to practice introducing these ideas to my (then) 3 year old. I found some things we had at home and made up a very simplistic balance beam. Using egg carton pieces, a paper clip flattened out, and a toilet paper tube shaped into a triangular prism, I asked N to try to make it balance (stay level) using different amounts of cotton balls on each side.

I put one cotton ball on one side and asked him to try to make it balance. He placed one on the other side and we watched the paper clip “flatten out” as the two sides balanced. We did this with 2 and 3 cotton balls per side so he could visually get the idea that in order to balance the scale you have to have the same amount on both sides.

Solving a mystery:

20170309_093555Then I told him it was time to be a detective.  I put a secret number of cotton balls on one side and then I taped a napkin piece over it. He had to guess how many were hiding on the left side. At first he was desperate to untape the napkin to count how many there were, (I was glad to see that at least he was intrigued by the question 😉 ) but pretty quickly he figured out that he could solve the mystery by putting cotton balls on the other side and seeing how many it took to balance. Then he was excited to untape the left side to see if he guessed correctly.

Preschooler solving for x like a boss! 🙂

At a later point I’ll revisit this with him and show him how to translate our experiment into the language of math by writing equations to match each step. I know there are math manipulatives available that can escalate this whole idea to a much richer learning experience, and at some point we’ll probably find and use those. For now though it’s fun to just play with ideas and see what we can learn and what questions we can ask about what we see, rather than just following a curriculum guide that lays out all the questions, steps and answers for us. There may be a time for that later … and I have a pretty good feeling that the RightStart Mathematics program is going to be great for this kind of learning. I’ll update this blog once we make more headway on that front.

Download your own Algebraic Reasoning Activity Pack

Edited to add: I later went back and created an 16 page parent guide with interactive activities for kids based on these activities.

You can see the product and full detail here

Brief overview

preview of activity based lesson pack on algebraic reasoning for Pre-K - 6th grade

If you are a teacher, tutor, or homeschooling parent looking for an engaging way to introduce your students to the foundations of Algebraic thinking, I believe that you will find this resource very helpful. Based on my experience teaching high school Algebra and homeschooling my own children, I have created this activity based lesson pack to help you take your students through the amazing journey of thinking abstractly, reasoning mathematically, and communicating effectively while exploring hands-on activities (with candy!). I have scaffolded the lessons so that students of any age can complete and understand the lessons; younger students can explore ideas tangibly and intuitively while older students will see connections to other math concepts and will learn to confidently manipulate equations to solve for a single variable based on a strong visual and concrete understanding.

Introduction to the Mathematical Property of Equality

One of the core “pillar concepts” in math is Equality. In the early grades, the equals sign is used to represent the answer to a problem. Extending the idea further, however, the equals sign comes to mean that both sides of the equation are balanced; therefore, whatever mathematical operation is done to one side must be done to the other side. Although this may seem like a basic idea, I’ve noticed in my 6 years of teaching Algebra that many students work their way through years of math without truly understanding this concept. This lack of a solid foundation then becomes a handicap to them as they advance into Algebra and higher levels of math.

The activities laid out here can be started with beginning learners (as young as 5) but the extension activities can be used with students up through Algebra. The sooner that students are introduced to these concepts, the stronger their foundation will be in math, and the faster they can progress through the following modules, lessons, and extension activities.

Preview Pages

Here are 3 preview pages of the complete unit:

preview of activity based lesson pack on algebraic reasoning for Pre-K - 6th grade


preview of activity based lesson pack on algebraic reasoning for Pre-K - 6th grade


preview of activity based lesson pack on algebraic reasoning for Pre-K - 6th grade

Click here to get your copy and to see several free and less-than-a-dollar math journal activity pages. I hope these resources help your kids enjoy learning math!



Other Math Monday posts:

Teaching and Learning Products

To see my series of activity-based lesson packs and other learning resources (Pre-K – 12th grade), visit my store at: https://www.teacherspayteachers.com/Store/Sandra-Balisky

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