Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 1
Math
Unit 4
8th Grade
Lesson 1 of 12
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Lesson Notes
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Define and identify functions.
The core standards covered in this lesson
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Put the letters A, B, C, and D around your classroom. Tell students that they should respond to each question you ask by standing under the letter that represents their answer.
Question 1: How many siblings do you have?
Question 2: How long did it take you to get to school today?
Question 3: What grade are you in?
Question 4: What color clothing are you wearing?
Question 5: In what month were you born?
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If Functions Are Aspirin, Then How Do You Create The Headache? by Dan Meyer is made available at dy/dan under the CC BY 4.0 license. Accessed Oct. 26, 2017, 7:55 p.m..
For each situation below, fill in the missing information in the tables. Then determine if each chart represents a function.
a. A parking meter takes only dimes, and each dime is worth 6 minutes on the meter.
b. Each point on the graph below shows how many shots a player on a basketball team took and made in the first half of a game.
Introducing Functions, accessed on Oct. 26, 2017, 7:57 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Create an input/output table for each rule below.
a. Input any number. Add 2, then square the number.
b. Input any number. If it is greater than or equal to 6, then record a 0; if it less than or equal to 6, then record a 1.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
In each example below, an arrow is used to show an input mapping to an output. Determine which relationships are functions. For each relationship that is not a function, explain why.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Use function language to describe functions. Identify function rules.
Topic A: Defining Functions
Standards
8.F.A.1
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Topic B: Representing and Interpreting Functions
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
8.F.A.18.F.A.28.F.B.4
Represent functions with equations.
8.F.A.18.F.B.4
Read inputs and outputs in graphs of functions. Determine if graphs are functions.
Identify properties of functions represented in graphs.
Topic C: Comparing Functions
Define and graph linear and nonlinear functions.
8.F.A.3
Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.
8.F.A.18.F.A.3
Compare functions represented in different ways (Part 1).
8.F.A.2
Compare functions represented in different ways (Part 2).
Topic D: Describing and Drawing Graphs of Functions
Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.
8.F.B.5
Sketch graphs of functions given qualitative descriptions of the relationship.
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