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* *Reflection: Debate
Evaluating Functions Day 2 - Section 1: Open

Sometimes it is difficult to pose a question that students can debate using mathematical language. Because mathematics often yields right and wrong answers, students are often not ready to debate the accuracy of an explanation. However, debating also means justifying your thoughts which is a mathematical practice that successful mathematicians exhibit.

Today's opening question was great for creating the environment for a debate. The non-verbal cue revealed that the class was about 60%:40% on the correct value of f(2). The majority of students said the output value should be 4. But the remainder of the students either thought that there was no output value or that the output value was 3. I was able to keep from tipping my hand to show (either verbally or non-verbally) what the answer should be. I let the students make arguments and counter-arguments until they came to the conclusion that the solution should be 4. There was some significant time spent processing the debate (which I did somewhat anticipate), but it was time well spent for the opportunity for students to engage in mathematical practices (MP3).

A fear for some teachers when debates arise is that while you have 4-5 students discussing an idea or a solution publicly, the other students are "opting-out." I used a turn and talk at the end of the discussion to get all students in the class talking about what was said and why the solution came out to be f(2) = 4. This strategy appeared to work well.

*Opening-reflection*

*Debate: Opening-reflection*

# Evaluating Functions Day 2

Lesson 13 of 18

## Objective: SWBAT evaluate a function from an equation and a graph. SWBAT determine the domain and range of a function.

#### Open

*10 min*

Students should work with their partner on each slide of the evaluating_functions_2_opening activity. On the first slide, students are using a graph to evaluate a function for two given input values. As students are working, move around the room to monitor student progress. The evaluation of **f(-1)** should be fairly straight forward for students. This question will give you a sense of whether or not students understand the basics of evaluating functions. Evaluating **f(2)** will require students to make sense of both the graph and the open and closed circles (MP1)(MP2).

When you bring the class together to share out use a non_verbal to see how each pair of students is thinking (students can hold up a certain number of fingers to show the output value). Challenge students to explain their solution to question #2. Also, don't tell students whether or not they are correct at first. Let students argue their ideas with other members of the class (MP3).

In the second slide students should determine the domain of the same piecewise function. Students will need to address whether or not the "jump" in the graph affects the domain. Let students discuss this with a partner first and then open up a whole class discussion. Help guide the discussion back to the domain being all of the input values for the function. Since all of the x-values between -6 and 7 (including 2) yield an output value the domain of function f is [-6,7].

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#### Independent Practice

*20 min*

Students should work with partners on evaluate_functions_2_practice. This worksheet provides students some time to practice and apply what they have been learning in previous classes.

As students are working, there are some things that you will want to watch out for as a teacher:

1) In Question #1f and Question #1h watch for students who are writing 31 and 2 respectively for their solutions. This is a common mistakes that students will make. Rather than solving for x, they are substituting the f(x) value for x in the equation.

2) In Question #2e, ensure that students have 3 solutions. The question is saying to find the x values where the function has an output of 2. There are three places on the graph where this happens (MP2).

3) In question #3, students will often write that the range is [-4,1]. Make sure that they realize that the range is a list of all possible output values.

4) In question #4, students will make the connection between evaluating a function and the graph that a function represents (MP4). Ensure that when students are squaring their negative values they are doing so correctly.

5) Ensure that students are correctly graphing the output values at x=4.

#### Resources

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#### Closure

*10 min*

Give students sufficient time to work on the functions_representations exit ticket. Now that students have had some time to practice with a classmate, you can evaluate their understanding of the concepts. Questions 1-3 test students mastery of the concepts and skills worked on during the independent practice. Question #4 requires students to identify the domain for a square root function (MP1 and MP2) and explain their reasoning (MP3).

#### Resources

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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