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Identifying & Evaluating Function Guided Notes with Doodles Sketch Notes 8.F.A.1
$4.25
Overview
- Standard: CCSS 8.F.A.1
- Unit: 8th Grade → Unit 4: Functions
- Grade: 8th Grade
Get the Lesson Materials
Identifying & Evaluating Function Guided Notes with Doodles Sketch Notes 8.F.A.1
$4.25
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
Prerequisites
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
Materials
- Pencils
- Colored pencils or markers
- Identifying & Evaluating Function Guided Notes
Key Vocabulary
- Identifying functions
- Inputs
- Outputs
- Domain
- Range
- Tables
- Graphs
- Vertical line test
- Mapping diagrams
- Set notations
- Evaluating functions
- Substitution
Procedure
Introduction
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.
Practice
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:
- 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.
- 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.
- 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.
- 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.
Extensions
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:
FAQs
A function is a mathematical relationship between two sets of numbers, where each input (x-value) corresponds to exactly one output (y-value).
To identify a function from a table, check if each input (x-value) has a unique corresponding output (y-value). If there are any repeated inputs with different outputs, then it is not a function.
The vertical line test is a way to determine if a graph represents a function. If any vertical line drawn on the graph passes through more than one point, then the graph does not represent a function.
To identify a function from a mapping diagram, check if each input (from the domain) is paired with exactly one output (from the range). If there are any inputs with multiple outputs, then it is not a function.
In set notation, a function is identified by ensuring that each input (element in the domain set) has only one output (element in the range set). If there are any inputs with multiple outputs, then it is not a function.
To evaluate a function, substitute the given input (x-value) into the function equation and calculate the output (y-value). This process helps determine the value of the function at a specific point.
Sure! Let's say we have the function f(x) = 2x + 3. To evaluate f(4), we substitute 4 in place of x in the function equation: f(4) = 2(4) + 3 = 8 + 3 = 11. Therefore, f(4) evaluates to 11.
Guided notes and doodles are great ways to engage students in the learning process. Here's how you can integrate them into your lessons:
- Provide students with structured notes that guide their learning process.
- Encourage students to personalize their notes through doodles and visual representations.
- Use guided questions to foster student understanding and check for comprehension.
- Allow students to use their notes as references during problem-solving activities.
This resource provides guided notes and practice worksheets for teaching identifying and evaluating functions. Here are some ideas on how you can use it:
- Begin by using the guided notes to introduce the concept of functions, including various methods of identification.
- Guide students through examples and discussions to reinforce their understanding.
- Use the practice worksheets to provide hands-on practice in identifying and evaluating functions.
- Engage students in a real-life application of functions to show their relevance beyond the classroom.