Lesson Objectives:- Students will use input-output pairs in a table to explore different “rules” for a relationship, some of which are a function and some of which are not.
- Students will develop the definition of a function.
- Students will explain if a relation is a function or not.
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| Grade: 9th grade (Algebra 1)Time frame: Linear/Exponential Functions Unit | Lesson Title: Definition of a Function |
Brain-based Strategies Used in the Lesson: - Practice: Students are given the opportunity to practice problems following the lesson.
- Images: This lesson uses an animated “rule machine” that receives an input and produces an output.
- Collaboration: Students will work in strategically selected groups or pairs.
- Active Learning: This lesson is student-centered with facilitation from the instructor.
| Formative or Summative Assessments: |
| Prior to this lesson: What understanding and/or knowledge was taught prior? Where does this lesson fit in your unit?In 8th grade, students start working with the idea of a function. They might even develop a definition in 8th grade. However, they do not use function notation. Though function notation is not developed in this lesson, it is in a lesson following this one. The context for most of students’ work with functions in 8th grade is in the linear context. Students understand that given an input, they can find an output. While this is mostly linear, they may work with some other examples and explain why they are not linear. In a previous lesson to this, students worked with different inputs and outputs by rewriting literal equations. For example, for the equation of the area of a square, often the input is the side length. However, there may be context where students are given the area and need to find the side length. Thus, changing to equation from to also changes the input to the area of the square. Understanding input-output pairs will be important to start this activity. |
Materials: Include a copy of everything required to teach. Use hyperlinks when possible. You may add additional pages to the bottom of this lesson plan also. Include the assignment that students will be completing.- Student laptops with Internet access
Technology materials: (hardware, websites, video links,etc.) |
| Content Core Standard: (List the standard(s) and then hyperlink it to the standards website. HSF.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).HSF.BF.A.1 Write a function that describes a relationship between two quantities |
| Technology used: Students will use laptops and a Desmos Activity. |
| Time | Materials | Lesson Procedures(Include the materials & technology.) |
| 5Mins | Laptops,Desmos Activity | Intro activity to activate schema (background information)/Warm-up/or Bell-ringer- Explain that today we will be looking at different input-output pairs in order to determine a “rule” for the relationship.
- In the Desmos, restrict students to screen 1. Pause the Desmos and direct students’ attention to the front. Project the first screen. Explain to students that their task is to figure out what Rule #1 could be based on one input-output pair. Click “Try It” and watch the animation together. Explain how the input, 15, went through the machine, was changed by the rule and got the output 5.
- Unpause the activity and have students click “Try It” and challenge them to determine would Rule #1 could be. Ask them if more than one of the rules could be Rule #1 (Divide by 3, Subject 10, and Take the ones digit are all possible rules).
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| 5 Mins. | Laptops,Desmos Activity | Introduce New Information: (Teaching)- Follow up with asking, “how could we narrow down our options?” Have students consider this with a partner for 30 seconds. Ask a pair of students to share. Discuss that we can pick more inputs and get their corresponding outputs to narrow it down.
- Open screen 2. Have students enter one more input into the table to determine Rule #1. Consider sharing on the projector several students’ choices for another input. See if any students had interesting inputs like decimals, negative numbers, or large numbers.
- Students should be able to see now that Rule #1 is subtract 10. Use the teacher dashboard to see which students did not get this and check in with them to clear up any misunderstanding.
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| 20 Mins | Laptops,Desmos Activity | Hands-on Activity Steps: (Prepare ways for students to practice the new information.)- Restrict students to screens 3-8. Their challenge remains to enter inputs (as many as they like) and get outputs in order to determine a rule.
- Have students work in pairs on these screens. When they think they have a rule figured out, have the pair find another pair and see if they found the same rule or if they disagree. Ensure pairs have a discussion on their different approaches.
- If students are stuck on Rule #3, encourage them to continue adding inputs or perhaps suggesting using smaller words or even a single letter like “a” or “I.”
- When most students have completed Rule #3 (screens 5-6), pause the activity and use the teacher dashboard to display different inputs from students. Begin a discussion where students justify their output predictions from screen 6 and critique each other’s reasoning.
- Note that on screen 6, “friend” appears twice as an input. Have a discussion about when we use the same input, we expect the same output.
- For screen 7, encourage students to try the same input more than once to see what happens.
- Debrief screens 7-8 highlighting interesting student responses from the teacher dashboard. After discussion, ask students “How is Rule #4 different from the other rules we have seen today?”
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| 10 Mins. | Laptops,Desmos Activity | Feedback: (How will the students provide feedback?) Group activity? Instructor feedback?- Restrict students to screen 9. Explain that Rules #1,2,3 are called functions and that Rule #4 is not a function. Have them answer screen 9 to make a prediction about what makes a rule a function.
- Share interesting student responses and have a conversation about different ideas.
- Explain to students that a function is a rule that assigns exactly one output to each possible input. Go through each rule explaining why it is or is not a function. Consider drawing mappings to demonstrate an input “going to” only one output for functions and “going to” multiple outputs for nonfunctions.
- Highlight that Rule #2 is a function even though the output is 7 every time because each input gives only one output.
- Highlight that Rule #4 is not a function because an input can have multiple outputs. For example, an input of “H” will give more than one output (Hailey and Hamza)
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| Homework or in-class assignment | Assessment(s): (assignments and/or activities)In-class:- Screens 10 and 11 will be used as formative assessment.
- Have students complete individually for 4-5 minutes and then allow them to share with a partner
- Use the teacher dashboard to monitor students. Consider highlighting different strategies for screen 10 as there are several correct pathways.
- Use the teacher dashboard to see which students are struggling. Use this to guide instruction in the next lesson (for example, if students need more practice considering what is and what is not a function).
Homework: |