Algebra 1: Constructing Quadratic Functions
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Lesson Topic: Constructing Quadratic Functions (IM Algebra 1 Unit 6 Lesson 3)
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Objective:
Students will be able to:
- Use information from a pattern to write a quadratic function
- Recognize how the lead coefficient of a quadratic function relates to the shape of its graph
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Time Required: 75 minutes
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Materials Needed:
- Teacher computer with internet access
- 1 computer/laptop per student with internet access
- Student Handouts from IM Lesson
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Teacher Preparation:
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Engage (10 minutes):
- Launch the Warm-Up: Quadratic Expressions and Area activity. Arrange students in groups of 2.
- Students complete the activity independently and then with a partner.
- Invite students to share their expressions and record and display them for all to see. Include all equivalent expressions. Students may notice that all the expressions have a variable or a term that is squared.
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Explore (15 minutes):
- Launch the activity Expanding Squares. Give students a moment to observe the pattern from the activity and ask them what they notice and what they wonder. Then, ask students to sketch the next step in the pattern and share their sketch with a partner.
- Make sure students see the connection between the equation and composition of the squares in the pattern
- Pause student activity where students get stuck or confused to discuss as a whole class.
- Review student responses and focus class discussion on the relationships between the patterns and how to express these patterns in function notation.
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Explain (10 minutes):
- Introduce quadratic function as a function that is defined by a quadratic expression. Like other functions, it can be represented with an equation, a table of values, a graph, and a description.
- Go through the different representations using the Expanding Squares pattern.
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Elaborate (35 minutes):
- Students log in and open the Tuva What is the Relationship Between Height and Font Size of a Paragraph?
- Students work through the activity independently stopping at the Group Discussion prompts as needed to discuss connections between the lesson activities and the Tuva activity.
- Assist students as needed with constructing the function.
- Wrap-up discussion may focus on how the graph representation relates to the pattern shown in the table and those discussed earlier in class.
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Evaluate (5 minutes):
- Students complete the Cool Down: A Quadratic Function?
- Circulate and address misconceptions as needed.
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Additional Lesson Strategies:
- Pause students as needed during the Tuva activity to model how to use the tools if students are struggling with that, particularly the sliders.
- Leave the work from the Explore/Explain on the board so that students can refer to it as they work on the practice problems.
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