# Evaluating Expressions

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## Objective

SWBAT evaluate expressions at specific values of their variables using substitution in the conventional order

#### Big Idea

The value of an algebraic expression can be found by replacing the variables with given numbers and applying the order of operations to simplify the expression.

## Think About It

7 minutes

Students work in partners on the Think About It problems (TAB). Here, they are substituting in a value of n for different expressions.

For problems a and b, I have students respond chorally, in whisper voices.  I expect the majority of students to get these two problems pretty easily.

For problem c, I tell them that our (imaginary) friend BoBo thinks the value is 124.  I ask for someone to explain what mistake BoBo made.  Students know that 12n means 12 times the number n from previous lessons.  I have the student who explained this to the class call on another student to share the value of 12n, when n =4.

Finally, I frame the lesson by letting students know today we’ll be evaluating more complex expressions using everything we know about expressions and order of operations.

## Intro to New Material

15 minutes

The Intro to New Material (INM) starts with an example:

Evaluate 2x + 8 if x=4

What does 2x mean?      (twice some number x)

What is the 2 called?       (the coefficient)

I model how to solve, without the help of students:

• Re-write the expression 2x + 8.
• Wherever you see x, replace or substitute it with 4 in a parentheses.
• I ask students to turn and talk for 30 seconds about why I put the 4 in parentheses (so that it is clear we mean 2*4, so that we don’t think it means 24)
• Finish simplifying by using order of operations: I ask students to list out the order of operations that we follow, and create a quick visual on the  board to represent grouping symbols, exponents, multiplication/division, and subtraction/addition

2x + 8

2(4) + 8

8 + 8

16

For Example 2, we’re given an equation to use to evaluate a situation.  I have a student read the problem out loud as the class annotates the problem.  This includes drawing and labeling a triangle to help us make sense of the problem.

My students are familiar with the formula to find the area of a triangle, so I quickly have them share out to remind each other of the meaning of each variable.  Then, I ask them what our units should be when we are done (square feet).

We go through the same steps I used for Example 1 – rewrite the equation, substitute in for the variables, using parenthesis, and then evaluate.

This problem is a great one to apply the commutative property of multiplication.  Rather than find half of 5, we can multiply 5 and 6, and then find half (or, find half of 6 and then multiply by 5).

Finally, we look at one more example together that is more complex. 3n2 – 4 + 2I ask students what is more complex about this problem (the exponents).

We’re still going to follow the same steps.  First, rewrite the expression.  Then, substitute a 3 in every place we see an n.

3(3)2 – 4 + 22

What comes first in order of operations? (grouping symbols).  Do we have any of those? (nope) So what’s next? (exponents)  We evaluate the exponents, which leaves us with:

3(9) – 4 + 4

Now what do we do?  (multiply three by 9)  That leaves us with:

27 – 4 + 4

What’s left? (subtraction and addition, which we perform from left to right, like we’re reading a sentence)

What do you think happens when we subtract 4 and then add 4? (we end up right back to 27) Let’s test it, to be sure.

27 – 4 + 4

23 + 4

27

Students complete two quick problems on their own, and then check their own work against my exemplars, which I put under the document camera.

Finally, we fill in the steps that we’ve used.  Students come up with the words in the blanks. I post the Visual Anchor for the class after they’ve filled in the blanks, so they can reference it once they’ve started to work without my help.

## Partner Practice and CFU

15 minutes

Students work in pairs for 10 minutes on the Partner Practice set.

As they are working, I am circulating and checking:

• Are students rewriting the expression
• Are students using parentheses around the substituted value?
• Are students using the correct order of operations?
• Are students including units, for the formula problems?

I ask partners:

• What did you do first here?
• Where did you put in ___ (value of the variable)?
• What was your first step, when evaluating this expression? What did you do second?

After 10 minutes of work time, I pull a popscicle stick to get a student work sample for the document camera.  The student walks through how (s)he completed the task. During the explanation I ask the same questions that I asked of partners as I circulated.

Students then work independently on the final CFU problem. If students have not seen the formula d = rate * time before, take the time to discuss what each variable stands for.  After a minute of work time, I have students flash me their answers by holding up their papers.

## Independent Practice

15 minutes

Students work on their own on the Independent Practice problems.

As I circulate, I am particularly focused on making sure students are not making the error of representing 6n as 64 when n = 64.

I’m also focused on the order of operations, especially when there is both a coefficient and an exponent with the variable (like 4n3)

## Closing and Exit Ticket

8 minutes

Before students begin work on their exit tickets, I ask them to evaluate my work on problem 8, where h = 5.1. I intentionally make a mistake with my multiplication of 3 and 5.1 (I write the product as 15.1, instead of 15.3). I provide several students with the opportunity to consider my work and explain if it is correct or incorrect.

After our discussion, students work on their Exit Tickets.