Evaluating Algebraic Expressions

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SWBAT evaluate algebraic expressions.

Big Idea

How can we use order of operations to evaluate expressions?

Do Now

10 minutes

Previously, students learned how to translate algebraic expressions.  The Do Now Problems are a review of this concept.  Students will have about 5 minutes to work on the following problems.

 Do Now:

Write an algebraic expression for each.

1) The product of four and a number

2) Nine less than a number

3) One half of a number

4) The difference between eight and a number

5) Three times a number less two

I will call students to the board to present their answers.  They will have to explain which operation they used and why.  For problem 2, students often forget to reverse the order when "less than" is used.  Problem 5 may present some difficulty for students because it involves more than one operation.  I will remind students to look for and underline key words that indicate an operation.


Mini Lesson

15 minutes

The focus of this lesson will be evaluation expressions.  As we work on the first example, students will develop the steps.

Ex. 1 - Evaluate 9 + a2 for a = 6

What do we call 9 + a?

Students should recognize that it's an expression.

What does evaluate mean?  What word do you (almost) see in evaluate?

Students may notice that evaluate contains the word value.  I will share that evaluate means that we need to find the value of the expression.

How can we find the value for this expression?

Many students will recognize that we are given a value for the variable, a, that we can use.

If we substitute 6 for a, what should we do next, since there is both an exponent and addition?

Students should make the connection that the order of operations should be applied at this point.

We will work through a few more examples, so students can realize that expressions can be evaluated with fractions, decimals, and more than one variable.

Ex. 2 - Evaluate 6x + 12 for x = 1/3

It is important for students to be mindful when evaluating expressions with multiplication.

If I replace x with 1/3, should I rewrite the expressions as 61/3 + 12 ? 

Most students will recognize that 61/3 is not the same as 6 times 1/3 .

What should we do to make the operation clear?

Students need to indicate the operation with a multiplication sign.

Ex. 3 - Evaluate 4a + 2b + 9 for a = 2 and b = 3

Ex. 4 - Evaluate 8.1x - 3.2 for x = 2.4

Independent Practice

10 minutes

Following the lesson, students will have the opportunity to independently practice evaluating expressions.  Students should follow the steps that they've developed.

As students work on the problems, I will circulate throughout the room focusing on students who had difficulty with the order of operations lesson.  

* It may be helpful to group together the students who had difficulty with the order of operations lesson.

Independent Practice

1)  4z - 5 for z = 4

2)  2a + 5 for a = 3

3)  6(n - 4) for n = 9

4)  2(3y - 2) for y = 2

5)  52 - b2 for b = 7

6)  x3 - 7 for x = 5

7)  3h + 2 for h = 3

8)  2x2 for x = 3

9)  4a + a/c for a = 8 and c = 2


After 15 minutes, I will give each group a problem to present.  Groups will be given a whiteboard and marker in which to show their work on.  Groups will have a few minutes to agree on their work and answer and then they will present to the class.  If students should disagree or have questions, we will discuss the problem as a class.

Exit Ticket

5 minutes

To assess students' understanding of the lesson and verify that there are not any misconceptions, I will give students an exit ticket to complete.  

Exit Ticket

Evaluate 2x + 6y - 3 for x = 5 and y = ½ 

When checking the exit tickets, I will be looking for incorrect answers caused by using the order of operations incorrectly and multiplication errors.

I will use the results to clarify any misconceptions in the following lesson and also for student groupings.