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# Evaluating Expressions

Lesson 7 of 12

## 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.

*60 minutes*

#### Think About It

*7 min*

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.

#### Resources

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#### Intro to New Material

*15 min*

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. **3n ^{2} – 4 + 2^{2 }**I 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 + 2^{2}

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.

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#### Partner Practice and CFU

*15 min*

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.

#### Resources

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#### Independent Practice

*15 min*

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 4n^{3})

#### Resources

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#### Closing and Exit Ticket

*8 min*

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.

#### Resources

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Order of Operations
- LESSON 2: Order of Operations with Grouping Symbols
- LESSON 3: Writing Numeric Expressions
- LESSON 4: Writing Algebraic Expressions
- LESSON 5: Algebraic Expressions and the Real-World
- LESSON 6: Multi-Step Expressions and the Real World
- LESSON 7: Evaluating Expressions
- LESSON 8: Writing and Evaluating Expressions
- LESSON 9: Identifying Equivalent Expressions
- LESSON 10: Combining Like Terms
- LESSON 11: Applying the Distributive Property
- LESSON 12: Applying the Properties