Parts of an Expression + Evaluating Expressions


Students typically enter 7th grade with a pretty good understanding of the different parts of an expression. I like to spend the beginning of the class providing a quick refresher of some common vocabulary words including algebraic expression, variable expression, term, variable, coefficient + constant. Many of these words show up in future lessons, so I want to make sure I spend at least a few minutes going over them before I move into evaluating expressions.

Evaluating expressions is pretty straight forward, so there isn't much "discussion" that occurs... it's mainly just providing students with example problems so they can practice, practice, practice. There are usually four main points I try to hit when practicing evaluating expressions:

1) ab means, a • b, so if a = 3 and b = 4 it is 3 • 4, not just 34.

2) When you square a negative number, your answer will be positive. We can blame rotten calculators (or the misuse of calculators) for this common misconception. Let's say the problem is a^2 + b and a = -3 and b = 5. Students need to remember -3 • -3 = POSITIVE 9, not negative. If students type -3^2 into their calculators without parentheses they will get a negative answer, not a positive.

3) Plugging a negative into a negative value, such as -a + b when a = -3 and b = 4. Students have to remember the negative sign actually represents -1, so -a is really -1 • a not just -a. The problem should become -1 • -3 + 4, so it is 3 + 4 = 7.

4) Any problem with negative values and subtraction signs. Initially, this seems to be the biggest struggle for my students. I try to provide plenty of problems where students will be plugging in negative values (or multiplying by negative values) and then subtracting.


I use a set of digital notes to teach this concept. The first slide is just an introduction to a lot of the common vocabulary terms associated with expressions. The next slide involves two practice problems where students will plug in various values to get a final answer. I complete this slide together as a group. The final slide includes an activity where students will solve 6 practice problem and then click and drag them in descending order.

Activity #1 - Only Positive Values

When I taught 6th grade math, I had created an activity on evaluating expressions with positive values only. Sometimes I like to start with this activity, especially when I have a group of students who are struggling with negative values. This way, students still get practice on the concept and don't get completely overwhelmed with the negative numbers. Students will solve the problems provided. Once they successfully complete the problem, they get a piece of the puzzle. In the end, they can put the pieces together and see that their puzzle says, This activity is available, for free, in my TpT store. Click the picture to download.

Activity #2 - Positive + Negative Values

The second, and most common, activity I like to use in my class is a mystery food thief over evaluating expressions. Before they begin, I always like to have students make a "hypothesis" on who committed the crime, what they stole, where they stole it from and what time it was stolen. This initial step always keeps my students invested in the activity right up until the end. Students then answer 12 problems. Their answers will give them a clue about the crime. In the end, only one suspect, food, location and time remains. This activity is digital, but you could print out the questions if needed. Click on the image to check it out.