##
* *Reflection: Grappling with Complexity
PRE-ALGEBRA: Evaluating Expressions - Section 5: Closure

Students did very well with this pre-algebra lesson. All students were able to evaluate the expressions with a great degree of accuracy. Because students were able to get the "input-output" idea, I knew that we would be able to proceed into the remainder of the functions unit without any more pre-algebra work.

Despite the work completed in the "do now" portion of the lesson, I did notice that students were still having difficulty with a negative number squared. When I prompted several students on their thinking, I determined that they had used a calculator and had typed -1^2. This gave them an answer of -1. This led to a discussion with the entire class where the students came up with a way to use the calculator to get an accurate answer (-1)^2 (with parenthesis).

The work on the ticket out was encouraging because many students were able to show or describe their thinking on the "Noella" problem. This is challenging because the question is written in such a way that students could rationalize that both expressions are saying the same thing. However, the students were able to use the order of operations to see that while a fraction line does mean division, writing the expression in these two different ways were not actually equivalent.

(Note: At the beginning of the next class, I asked students to think about how they could re-write the second expression so that it would have the same answer as the first expression. After they had an opportunity to think, we put up the second student's response so that they could connect to this way of thinking).

*Grappling with Complexity: Closure Reflection*

# PRE-ALGEBRA: Evaluating Expressions

Lesson 1 of 18

## Objective: SWBAT evaluate an algebraic expression by substituting in one or more values for variables. SWBAT show that they understand order of operations when evaluating expressions.

#### Do Now

*5 min*

Slide 3: Students can determine if the expressions have the same values individually. Then have them share their results with their partner. I will call on one pair to share out about why the two expressions have the same value (this expression was chosen for two reasons 1) students often mistake 8^2 as sixteen and 2) students often forget that a negative number squared must equal a positive value. This pair of expressions aims to build some understanding around these two points). Once one group has shared, I like to look to one or two other pairs to build on what the initial group has said.

#### Resources

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#### Opening

*5 min*

Slide 4: Have students evaluate the expression on their own without discussing it with their partners. I then call on students to give the answer(s) and I record them on the board. Typically, there will be several answers from the class due to the fact that students are not using the order of operations properly. After making a list of all the answers that the class gives (I do not give any indication as to which one is correct) I ask the class if they see a problem with what just happened? I ask them to think about this for 30 seconds on their own and then I have them **share their thoughts with their partner** as I walk around to hear what the partnerships are thinking. When we share out with the whole class usually a student will say that “we got different answers.”

This is a start, but we want to guide the conversation towards the understanding that we cannot all simplify the same expression and get multiple answers. I explain to students that arithmetic is guided by a set of rules that indicate that things need to be done in a certain order.

Slide 5: Students have all seen this many times and I just put it up as a reminder and then we go back to slide 3. I give students a second opportunity to simplify the expression again with their partner.

When students were sharing the answers, I made note of the groups that arrived at the correct solution of 23. I let one of these groups share from their seat or come up to the board to explain the proper order in which to simplify the expression.

#### Resources

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Slide 7: While substituting and evaluating expressions should not be new for students, it is important to review this skill as it will help to lay the foundation for evaluating functions in this unit. I put these exercises on the board and let students work on them in their partnerships without any instruction. Students will then have the opportunity to put their answers on the board or under the document camera to explain their work and ensure that the remainder of the class is in agreement of how to simplify the expressions.

#### Resources

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#### Closure

*10 min*

Slide 8: In this **ticket out** students are working with their partner to discuss an error analysis question where a student made a mistake. Students should work with their partner to write what the mistake was and how to fix it, showing the correct solution as a results.

Slide 9: This final question requires students to critique the reasoning of another student (**MP3**) and explain why they are correct or incorrect. As a scaffold, if students are having some difficulty with this question I will encourage them to evaluate both expressions first in order to determine if they are equivalent or not. Since this lesson takes place in the beginning of the year, I take some extra time to show what a good explanation might look like for this question using student work. The most important thing is that students are citing mathematics directly from the problem to make their case.

*e.g. Noella is incorrect in her thinking. While she is correct that a fraction line does mean division, when a fraction is written vertically as in the first expression it is implied to evaluate the top (10 times 15) and bottom (5 times 3) of the fraction first. When the expression is written horizontally as in the second expression, order of operations would dictate that we do 15 divided by 5 first.*

#### Resources

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###### Evaluating Expressions

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- LESSON 1: PRE-ALGEBRA: Evaluating Expressions
- LESSON 2: Defining Functions Recursively
- LESSON 3: Tower Task: Exploring Explicit Formulas
- LESSON 4: Function Notation
- LESSON 5: Understanding Domain and Range
- LESSON 6: Multiple Representation of Functions
- LESSON 7: Piecewise and Step Functions
- LESSON 8: Mirror Task: Understanding Equivalent Functions
- LESSON 9: Modeling with Functions
- LESSON 10: Functions Practice and Assessment
- LESSON 11: Introduction to Piecewise Functions: Dance-a-Thon Question
- LESSON 12: More with Piecewise Functions
- LESSON 13: Evaluating Functions Day 2
- LESSON 14: Transformation of Functions Day 1
- LESSON 15: Transformation of Functions Day 2
- LESSON 16: Transformations "How To" Guide
- LESSON 17: Functions Review Assignment
- LESSON 18: Functions Unit Assessment