Identifying and Evaluating Functions Lesson Plan


Ever wondered how to teach identifying functions and evaluating functions in an engaging way to your 8th grade students?

In this lesson plan, students will learn about functions and their real-life applications. Through artistic, interactive guided notes, check for understanding, a doodle & color by number activity, and a maze worksheet, students will gain a comprehensive understanding of identifying and evaluating functions.

The lesson culminates with a real-life example that explores how functions are used in practical situations.

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Identifying & Evaluating Function Guided Notes with Doodles Sketch Notes 8.F.A.1

Identifying & Evaluating Function Guided Notes with Doodles Sketch Notes 8.F.A.1


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Learning Objectives

After this lesson, students will be able to:

  • Identify functions from tables, graphs, mapping diagrams, and set notations

  • Understand the concept of inputs and outputs in a function

  • Evaluate functions by substituting values into the function

  • Explain how functions are used to model real-life situations


Before this lesson, students should be familiar with:

  • Basic operations with integers (addition, subtraction, multiplication, and division)

  • Basic understanding of plotting ordered pairs and coordinate planes

  • Understanding of order of operations (when substituting) to simplify numerical expressions


Key Vocabulary

  • Identifying functions

  • Inputs

  • Outputs

  • Domain

  • Range

  • Tables

  • Graphs

  • Vertical line test

  • Mapping diagrams

  • Set notations

  • Evaluating functions

  • Substitution



As a hook, ask students why it is important to understand and identify functions. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce & define functions, inputs, and ouputs (as well as domain and range). Explain to students that a function is a special type of relationship where each input has exactly one output. Students will fill in the notes that include a function machine. Walk through the key points of identifying functions set notation, mapping diagrams, and tables. Show them how to determine if a table represents a function by checking if each input has a unique output. Emphasize the importance of looking at both the inputs and outputs to make this determination. Do the same for all the representations.

Use the second page of the guided notes to introduce identifying functions from graphs using the vertical line test. Explain to students that if a vertical line can be drawn and only intersects the graph at one point at a time, then the graph represents a function. You can alternatively model the vertical line by moving a pencil across the graph. Show them examples of graphs that are functions and graphs that are not functions and have them sketch their own examples on the guided notes (top of page 2). Guide the students through the process of applying the vertical line test to determine if a graph is a function.

Use the third page of the guided notes to introduce evaluating functions through substitution. Model the first few example and then have students complete the rest on page 3 of the guided notes.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.


Have students practice identifying and evaluating functions using the maze (page 4) and color by number activity (page 5). Walk around to answer student questions. You can assign it as homework for the remainder of the class.

Real-Life Application

Using the last page of the guided notes, bring the class back together and introduce the concept of real-world applications of identifying and evaluating functions. Students will read the passage about real life applications of functions and reflect on the bottom section with their own examples.

Explain that functions are used in various fields and industries to analyze data, make predictions, and solve problems.

You can use the following examples to illustrate the real-life applications of functions:

  1. Finance - Explain how functions are used in finance to calculate compound interest. Students can learn how to evaluate functions to determine the amount of money they will have in their savings account based on the initial deposit, interest rate, and time.

  2. Engineering - Talk about how engineers use functions to model and analyze various physical systems. For example, they might use functions to determine the trajectory of a projectile, the flow rate of fluids through pipes, or the efficiency of a mechanical system.

  3. Medicine - Explain how functions are utilized in medical research and patient care. Functions can be used to model the spread of diseases, analyze medical imaging data, or predict the effectiveness of a treatment based on patient characteristics.

  4. Technology - Show how functions are essential in computer programming and software development. Functions are used to write algorithms, create simulations, and solve complex computational problems.

Students will also complete the self-assessment (circle the set of 3 emojis) to indicate how confident they felt about today's lesson (page 5 of guided notes).

Refer to the FAQ section for more ideas on how to teach the real-life applications of identifying and evaluating functions. Encourage students to think critically and brainstorm other examples of how functions are used in the real world.


Additional Self-Checking Digital Practice

If you’re looking for digital practice for identifying and evaluating functions, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here's a Pixel Art activity to explore:


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