Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 2
Math
Unit 4
8th Grade
Lesson 2 of 12
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Lesson Notes
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Use function language to describe functions. Identify function rules.
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
In this lesson, focus on students using appropriate and correct language when describing functions and non-functions. They should use terminology including “input”, “output”, “function of”, etc. and use the context of the situation to help them make sense of the situation (as in Anchor Problem #2). Use small group or partner work where appropriate to ensure all students have the opportunity to describe functions and use function language.
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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
A function machine takes an input and, based on some rule, produces an output.
The tables below show some input-output pairs for different functions. For each table, describe a function rule in words that would produce the given outputs from the corresponding inputs. Then fill in the rest of the table values as inputs and outputs that are consistent with that rule.
a. Input values can be any English word. Output values are letters from the English alphabet.
b. Input values can be any rational number. Output values can be any rational number.
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Function Rules, accessed on Oct. 26, 2017, 8:07 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.
The table below shows the total distance a runner has covered over a given period of time.
a. Is distance, $$d$$, a function of time, $$t$$? Explain.
b. Is time, $$t$$, a function of distance, $$d$$? Explain.
Two input/output tables are shown below.
Table A:
Table B:
a. Table A is not a function. Change the table so that it is a function.
b. Table B is not a function. Complete the table with values to show it is not a function.
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
At a local bank, when you open an account, you provide certain information that is stored in the bank's records. The table below shows the names and mailing zip codes of some of the bank's customers.
a. Suppose F is the rule that takes a customer's name and provides their mailing zip code. According to the information in this table, is F a function? Explain your reasoning.
b. Suppose G is the rule that takes a customer's mailing zip code and provides their name. According to the information in this table, is G a function? Explain your reasoning.
c. If the bank is looking for a way to identify specific customers, why would using their zip code not be a good way to do this? What other input might the bank use instead?
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
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
Topic A: Defining Functions
Define and identify functions.
Standards
8.F.A.1
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Topic B: Representing and Interpreting 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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