Writing and Evaluating Algebraic Expressions

When learning algebra in school, children come across many word problems. Some are simple and concise, whereas others are complex and may even resemble a short story. To solve such word problems, kids must first create algebraic expressions out of word problems.

This is referred to as evaluating and writing algebraic expressions.

Teachers and homeschooling parents can support their students in solving such algebra problems in various ways, which we’ll look at in the following article. Read on to learn more.

What Is Writing and Evaluating Algebraic Expressions?

For starters, ask children whether they remember the definition of an algebraic expression. Most likely, some of them will reply that an algebraic expression is a mathematical expression that consists of constants, variables, and operations (such as addition, subtraction, multiplication, etc.).

Provide an example, such as 5x-2 is an algebraic expression, as it contains two constants (the number 5 and 2 which don’t change), a variable (the letter x, which can change), and an operation (subtraction).

Then point out that algebraic expressions are not always provided in a straightforward way as the above example, but may come in the form of word problems. Explain that when algebra problems come as word problems, we must translate these words into algebraic expressions.

The process of translating written words into algebraic expressions is called writing algebraic expressions, whereas the process of substituting a number for each variable and doing the operation is called evaluating algebraic expressions.

How to Teach Evaluating and Writing Algebraic Expressions

Bell-Work Activity

Start with a brief preparatory activity to review previously learned concepts with children. You can create a simple bell-work activity that contains several math problems to help children go through concepts that writing and evaluating algebraic expressions builds on.

This includes math problems on recognizing whether an expression is an algebraic expression, recognizing what a variable is, practicing the order of operations, differentiating between algebraic expressions and numerical expressions, etc.

Writing Algebraic Expressions

After you’ve defined what writing algebraic expressions means, it’s time to move on to the actual process of writing algebraic expressions out of word problems. First, highlight some common phrases to which students should be attentive.

These include:

Addition: sum, more than, increased by…

Subtraction: less than, decreased by, taken from, minus…

Multiplication: times, multiplied by, product…

Division: divided by, divided into…

For an overview of more common phrases in word problems, you could try using some visually stimulating materials. For example, you can draw a chart in different colors for each operation and the phrases associated with it.

Then, you can provide some practical examples. For instance, explain how you’d write an algebraic expression for the following word expression:

The sum of 6 multiplied by z and 8 multiplied by y

You can start by encouraging students to first identify the phrases indicating operations. You may even encourage them to use a highlighter. Explain that in this case, there is one addition (‘sum of’) and then two multiplications (‘multiplied by’).

In other words, we can translate the identified operations into 6 x z + 8 x y or 6z + 8y.

Encourage children to be attentive to commas in verbal expressions, as this will help them group the terms properly. In lack of commas, you can even break down a word expression to explain this more visually, for example:

The sum of

(6 multiplied by z)

AND

(8 multiplied by y)

Evaluating Algebraic Expressions

Once children are comfortable with writing algebraic expressions, demonstrate how to evaluate such expressions. Explain that since we know that evaluating algebraic expressions entails substituting a number for each variable and performing the operations while keeping in mind the order of operations, we can easily find the value of the algebraic expression.

Provide an example, starting with an easier problem, such as:

Evaluate the following expression when z = 2 and y = 3.

6 x z + 2 x y

Explain that by substituting a number for each variable, we’ll get:

6 x 2 + 2 x 3

Then ask children whether multiplication or addition comes first according to the order of operations. After someone explains that multiplication is performed first and only then addition, you can proceed to solve the equation, i.e:

6 x 2 = 12;

2 x 3 = 6

12 + 6 = 18

Now you can gradually proceed with more difficult examples, such as:

Evaluate this expression when a = 3 and b = 5

3a² – (2a + b)

Again, point out that by substituting a number for each variable, we’ll get:

3 x 3² – (2 x 3 + 5)

Remind students that exponentiation comes first and then multiplication, as well as that multiplication should be performed before addition and subtraction, that is:

3 x 9 – (6 + 5) =

27 – 11 = 16

Writing and Evaluating Algebraic Expressions Games

Online Game

There’s nothing more engaging for children than incorporating technology in your lesson.

Use an online game, such as the second game by IXL listed here, and have children practice writing and evaluating algebraic expressions.

The game is usually played individually, so you’ll need to make sure there’s a suitable technical device for each student. The game contains several math questions with multiple answers on writing and evaluating algebraic expressions.

In the end, their progress is tracked through a ‘smart score’ out of 100. By answering questions correctly, students can reach ‘excellence’ or conquer the ‘Challenge Zone’ and thus achieve mastery.

‘Do You Have?’ Game

To play the ‘do you have?’ game in your classroom, you’ll need to prepare two sets of cards. One set of cards contains the verbal expressions and the other set of cards contains the corresponding algebraic expressions.

For example, let’s say that you include this verbal expression in the first set of cards:

‘Represent the total number of calories in 𝒙 peanuts and 𝒚 potato chips if each peanut contains 5 calories and each potato chip contains 10 calories.’

In the second set of cards, you’ll have to make sure you have a corresponding algebraic expression, or:

5x + 10y

It’s advisable to have the back of one set of cards in one color (ex: purple) and the other set of cards in another color (ex: yellow). This way, you’ll avoid the game taking too much time.

Now launch the game!

Tell children you’re going to play a game to practice writing algebraic expressions.
Hand out one card per student.
Explain the rules of the game. Students should not reveal the card they have to others, they should only show the color of the card so that the other students know whether to approach them.
The students that received a card with a verbal expression, i.e. a purple card, should translate the words into an algebraic expression, such as 5x + 10y, depending on the specific word expression.
They then approach the students with a yellow card, one by one, and ask each student with a yellow card ‘do you have 5x + 10y?’ (or any other algebraic expression that corresponds to their word expression).
The first that finds their corresponding algebraic expression, comes in first, the second comes in second, etc.

Before You Leave…

If you liked these resources and info, we have a whole lesson that goes into evaluating and writing algebraic expressions in depth. So make sure to check out our worksheets and resources on teaching rounding multi-digit whole numbers. These are all pdf files, so you’ll be able to print them out easily:

To get the Editable versions of these files, join us in the Math Teacher Coach community!

1-4 Assignment (Doc – Members Only)
1-4 Bell Work (Doc – Members Only)
1-4 Exit Quiz (Doc – Members Only)
1-4 Guided Notes SE (Doc – Members Only)
1-4 Guided Notes TE (Doc – Members Only)
1-4 Lesson Plan (Doc – Members Only)
1-4 Online Activities (Doc – Members Only)
1-4 Slide Show (Doc – Members Only)

This article is based on:

Unit 1 – Algebraic Expressions and Integers

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