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  • Writer's pictureolivershearman

Demystifying Algebra: Puzzles, Practice and Patience

Break down algebraic concepts with relatable examples and step-by-step explanations, making math more accessible and engaging.

We know as mathematics teachers that algebra is a difficult topic, once grasped it can be a bit like a bike. It is hard to forget and easy to pick up once again, however like riding a bike it is not easy to develop an understanding in the first place. Because of this initial hurdle of effort many students never truly embrace the simple and useful practices of algebra.

So, how can we engage students in algebra and its useful applications?

The first point I would argue is engaging students in WHY we learn algebra in the first place. While they might not understand it, showing them an advanced problem they could not solve without algebra might be a useful hook to engage them in learning the topic. Particularly if you can link it to a real world word problem as well.

Learning algebra is useful because it helps understanding calculus and statistics, two key skills for modeling and financial related applications which occur in many job fields. Algebra can help develop logical thinking skills and the patience and practice for step by step use of instructions and knowledge to solve a problem using a set of learned rules.

Algebra can help students in their science studies, often as they go up the scientific learning ladder, they will need more mathematical skills - including algebra. In chemistry it is both relevant and important for stoichiometry. For physics we use it all the time for formula rearrangement and for biological studies, particularly for example in population growth and decay. These examples highlight the necessity of algebra to study yet another subject and indicate it is a key foundational skill.

So now we know the why, but HOW do we teach and engage otherwise disconnected students? Well I thought of that too.

The beginnings are easy enough, I like to use baskets / buckets with a set number of items and show students what they can and can't do with algebra. It helps them grasp that x (or any other letter) is just an unknown number. For instance 3x + 2x = 5x is good, but 3x + 2x = x^2 is not so good. Seeing this with baskets helps deal with misconceptions.

Another one that is great for beginners is visualizing using scales (balances) to help students see how they need both sides of the equation to match. The classic internet items that make you solve pictorial representations of simultaneous equations are also good. This is where three unknown numbers are represented by some icons or graphics and students are given three equations and asked to solve. See the below for an example I made for young students on this. I use this as part of my math menu items I sell (link here). Some of my icons are shown here from my solve it template in Grade 3 math multiplication menu.

Another method would be through slowly levelling up their abilities and skills through a level based framework. So each skill comes one after the other with explanations and questions in an order that makes sense. I have such a framework you might consider purchasing here (link here).

One site I really love using to help students with algebra is Not that I am a spokesperson for them, they just do really good content and for free if you are an educator! You can even add your class for free as well. It's great for reading, interactive elements and stories. It has a great mix of images, words, problems and accurate explanations too. I highly recommend it.

Image source:

This links to the concept of word problems and similarly stories or even riddles. Finding or making up relevant word problems and little stories that make or have an algebra problem is greatly engaging. One rhyme I made up for my students is pirate themed - so I do a pirate accent and chant - "aarrghh - in between the number and the letter lies the buried treasure… and don’t forget it ya salt-licked seadogs". This is in reference to the fact that there is a multiply between a coefficient and a pronumeral. Ie: X marks the spot! Rather than treating it as this abstract mathematics concept, students can instead visualize algebra as a way to solve real world problems like optimization for more advanced students for example. Image source:

Given all of the above, there are plenty of ways to get students up to speed with their algebraic comprehension and I hope this article has supported and maybe even inspired you. Algebra is a great tool of mathematics and one that has paved the way for so much more beyond and incredible abstract and logical thinking in equal measures.

Thanks for reading.

Cheers and stay curious

Oliver - The Teaching Astrophysicist


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