Evaluating Expressions

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SWBAT write and evaluate numerical expressions when the variable is in multiple positions in an equation.

Big Idea

This lesson is part of laying the foundation for algebraic thinking, including an understanding that cracking the code can be fun! Students view an algebraic expression as a challenging code to make sense of.

Warm Up

7 minutes

The warm-up is designed to get students thinking mathematically.  In my classroom the warm up is something to tackle, but not become frustrated with. This is posted where students see it - daily - as they enter the class each day.  Students are asked to spend at least “3 quiet minutes” working independently and then they may choose to turn and talk to a friend about their strategies. 

This warm- up activity is called I wonder...

Today students begin to generate a list of questions about our school.  The questions must have a math component, but students are reminded that math is part of almost anything - they just have to find it. Before students begin, I remind them that math questions about our school can include time, money, people, area and perimeter, etc.  To make sure every student is included, I call on a few students to share examples of questions that come to mind. 

Then I give the students 3 quiet minutes to list their thoughts.  After 3 minutes they share their thinking with a neighbor, and we have a few share out to the group.  These lists will remain in the students math journals.  They can revisit these questions on their own.  I will come back to these questions as an assigned "I wonder warm-up" within the next few days.


5 minutes

A numerical expression with variables can be intimidating.  Helping students see the fun in the challenge is important.  I start this lesson with a conversation that gets students interested in what we will learn about today, and also helps them appreciate the challenge.  I want my students to know that hard math is fun math.  

Let's talk about codes for a few minutes.  What is a code?  Do any of you know or use any codes? Who else uses codes?  

I explain to students that mathematicians use codes all the time.  Algebraic expressions are an example of one of these codes. Students use a resource to look up the meaning of algebraic expression choosing from their text book, other math text books, or use the dictionary.  I ask a few to share the definition they find, then we create one to use as a class.  "An algebraic expression is an expression that has at least one variable".   I ask the students to write up an example of an algebraic expression on a scrap of paper and share with those around them.  

I put a few examples of my own expressions on the board and ask the student to give it a thumbs up if it is an algebraic expression and a thumbs down if not.  I start with simple expressions like 3 - c and then get more complex.  Adding in examples with more than one operation.  Finally, I challenge them with 10b.  This triggers yesterdays discussion about representing multiplication when there is a variable. 

One student creates a complex expression - (a + 9) x (d +16) - so I ask him to write it on the board.  This is a tough code to crack.  So we break it down into pieces together.  Before we do, I explain that today we are going to practice writing and interpreting more expressions.  

Remember, you will have to be a detective and look for math clues to change "math talk" into English and English into "math talk". 

Guided Practice

20 minutes

As a class, we play the game Algebraic Expressions Millionaire, from Math-Play.  I start with a think-a-loud to model how to use what you know about math to find clues to crack the code.  

The first step of cracking a code is not finding out the value of the variable.  First, you must use all the clues you know to understand what the expression means.  This game will help us practice finding clues to help us understand the meaning of different expressions.  

I use a gradual release approach to completing this game.  After modeling solving a few algebraic expressions, have students work in their partner groups and take turns answering each question. Simply saying the answer is not enough, each student is expected to explain their approach and survey the class before clicking the answer.


• This is an appropriate time to review the properties of addition and multiplication.

Now You Try It

20 minutes

Students work with their color group (color groups are homogeneous by ability) to write and interpret algebraic expressions. 

I set the expectation before they begin. "While you are working, I am going to be coming around and listening to your discussions. You and your partners should be talking about the clues that you can find, before you write the algebraic expression. These are going to be a bit tougher than the game, because you do not have multiple choices... so use your group members for support."

When we work in color groups, I know each group will have different needs during this lesson.  I circulate around the room and add challenges and supports as needed.  There are 4 color groups. These groups are fluid, they are reassigned periodically based on topic, concept and student performance. 

1 - These students need more support.  I start with them, to help make sense of the directions and also to facilitate the discussion around the first question. Today, I stay with this group for the first 3 questions to ensure the discussion is math based.

2 and 3 - These groups are able to answer the questions based on the directions, but need support in organizing their thinking about the clues that help them solve the problem.  

4 - This group needs an additional challenge. I encourage them to extend their understanding by writing their own phrases to create a round of "Numerical Expressions Millionaire", this time writing the algebraic expression and providing choices using English phrases.

Group Share

5 minutes

I bring the students back to their own seats for a group share.  I typically ask the same question.  "Did any group have an interesting mathematical argument, discussion, or discovery?"

At this time, one student from each group shares their experience to help bring the class back as a whole.  We answer any questions and clarify any misunderstanding.  If students make a mistake and learn from it, we share this too.

Today's group share focuses on one group who had a mathematical argument about one of their problems.  The question asked them to write the algebraic expression for 5 less than the product of 6 and 3.

Sometimes, the English language can be a barrier to understanding the math.

Ticket Out

5 minutes

I close with an assessment to test where everyone is at, after this lesson. Students independently solve the following problem that is posted on the board.  

Write an expression to show:

1/2 of 10 more than the number of wheels on w 18 - wheelers.