Algebraic Expressions Activities for Middle School Math

Algebraic expressions can be translated, just like any other language. When middle school math students learn how to translate algebraic expressions correctly, they begin to see algebra as the language it is and more than just a random set of rules. In this post, there are a few algebraic expressions activities to help middle school math students practice translating algebraic expressions into numbers and symbols, along with some research supporting a varied approach to teaching math.

Teaching algorithms, keywords and procedures in math has become so taboo over the last 10 or so years. We want students to build a strong conceptual understanding of the math they are learning, and push toward this goal by modeling math through hands-on manipulatives, drawings, word problems and partner work.

But two things can be true at the same time. While it's so important to teach math with the goal of deep understanding, it's true that math is a translatable language with well-developed procedures. There are distinct words in English that mean multiply, equals, add, subtract, less than, is less than, and so on. We can teach math conceptually and also that it is a decodable language.

A mix of conceptual and procedural math helps ensure we're reaching as many students as possible. Some students immediately need to know the why. They learn best through pattern blocks, algebra tiles, pictures and proofs. Other students thrive on the how. They want to know the procedure and take comfort in that structure. For a lot of these kids, the why comes through the how.

As stated more recently on The Science of Math website: "Conceptual knowledge supports procedural knowledge AND procedural knowledge supports conceptual knowledge. They should be taught together!" 

I've seen it stated that executive function in kids with ADHD can take 30% longer to develop, and while this specific claim has not yet been fully explored and peer-reviewed, there is data to support the brains of students with ADHD taking longer to develop:

"In youth with attention deficit hyperactivity disorder (ADHD), the brain matures in a normal pattern but is delayed three years in some regions, on average, compared to youth without the disorder, an imaging study by researchers at the National Institutes of Health’s (NIH) National Institute of Mental Health (NIMH) has revealed. The delay in ADHD was most prominent in regions at the front of the brain’s outer mantle (cortex), important for the ability to control thinking, attention and planning. Otherwise, both groups showed a similar back-to-front wave of brain maturation with different areas peaking in thickness at different times." - Brain Matures a Few Years Late in ADHD, But Follows Normal Pattern, National Institute of Mental Health, November 2007

Does this mean that kids with ADHD can't learn math conceptually? Absolutely not. But we can be aware of a real reason not all kids will understand the why of fraction division in 5th grade, for example. For now, we can teach them the why, mix in the how, and know that the why may need a little longer to sink in.

Here's an example of an algebraic sentence and an algebraic expression that are almost identical:

The word is tells us we have a sentence. Is on its own translates to =. When followed by less than we get an inequality that can be solved. Without is, we have an algebraic expression that can be translated but not solved. It's important to teach students that math symbols can be translated into English words, and vice versa.

Below are a few algebraic expressions activities to help students practice translating and evaluating algebraic expressions.

Algebraic expressions activities

Translating algebraic expressions escape room

This engaging, self-grading translating algebraic expressions escape room asks students to translate algebraic expressions, equations and inequalities from word form to numbers and symbols. Questions are grouped 4 per puzzle, resulting in five 4-letter codes that will unlock all 5 locks. The activity is no-prep in digital form and low-prep in its printable PDF form.

Evaluating algebraic expressions escape room

For evaluating practice, the printable version of this evaluating algebraic expressions escape room comes with five printable PDF puzzles and a student answer sheet. A self-grading digital version is also included if you'd like no prep. Students evaluate 20 expressions by substituting in given values, then type or write the correct 4-letter code.

Language of math poster

This language of math poster developed over a few years and my students and I encountered new keywords while translating expressions in algebra. It comes as a small handout for student notebooks, a 2-page printable classroom wall poster, and has a link inside to a blog post with directions for making an even larger poster, if needed.

Algebraic expressions error analysis activity

Error analysis is a nice way for students to show what they know through finding mistakes. This algebraic expressions error analysis activity gives students practice "plugging back in" to check their work. On each card are three evaluated expressions with one solved incorrectly. Students identify the "lie" and correct it on their answer sheet.

Algebraic expressions math pennant activity

This algebraic expressions math pennant activity mixes student work with math classroom décor. Students' final pennants make a nice bulletin board display of student work. Students translate algebraic expressions into numbers and symbols, then evaluate. Students can then color their pennants before hanging to display.

Quadratic keywords poster

Later in high school when students are learning to solve quadratic word problems, they'll need to recognize when problems are asking for an x-intercept, y-intercept or maximum/minimum value. This is the quadratic word problems poster students get to help them identify what they are being asked to find.

Numberless quadratics activity

We then complete a numberless quadratics activity to really focus on the wording of the problems to zero in what they're asking us to find.

Browse all algebraic expressions activities

All this is to say, we can skip the tricks while keeping some of the time-tested procedures to build our kids' conceptual understanding and love of math. We can teach students that math is translatable.

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