Curriculum  /  Math  /  9th Grade  /  Unit 1: Functions, Graphs and Features  /  Lesson 11

Functions, Graphs and Features

Lesson 11

Math

Unit 1

9th Grade

Lesson 11 of 11

Objective

Analyze functions and identify parent functions of graphs. Identify variables of a situation and the scale of the associated graph. Represent a situation in a graph, table, and description.

Common Core Standards

Core Standards

  • F.IF.B.4 — For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.F.B.5

Criteria for Success

  1. Define variables presented in a problem in context. 
  2. Identify an appropriate domain and range based on the context presented.
  3. Model a contextual situation graphically, representing the intervals where a function is increasing/decreasing/constant, whether a function is linear, intercepts, and other key points. 
  4. Interpret a situation represented graphically for intervals of interest, points of interest, and comparison in rates of change. 

Tips for Teachers

  • In this unit, students have worked to define variables in context, name the assumptions/levels of precision that are necessary for a model, and interpret parts and features of a model presented graphically and in a table. We will continue to work within parts of the modeling cycle (although not linearly) throughout the year, but this is the first lesson where students will be given a context and asked to apply their knowledge from the unit. 
  • The target task for this lesson is Anchor Problem #2. 
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Anchor Problems

25-30 minutes

Problem 1

Consider the story: 
Darryl lives on the third floor of his apartment building. His bike is locked up outside on the ground floor. At 3:00 p.m., he leaves to go run errands, but as he is walking down the stairs, he realizes he forgot his wallet. He goes back up the stairs to get it and then leaves again. As he tries to unlock his bike, he realizes that he forgot his keys. One last time, he goes back up the stairs to get his keys. He then unlocks his bike, and he is on his way out at 3:10 p.m. 

Sketch a graph that depicts Darryl’s change in elevation over time. 

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 1 > Topic A > Lesson 3 — Example 1

Algebra I > Module 1 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Sam, John, and Bill all went to the basketball game at the gym and left from the high school. Sam’s mom picked him up, John took public transportation because he had to stop at the Copley library to pick up a reserved book, and Bill biked from the high school to the elementary school. 

Below are the modes of transportation necessary to make their full trip, and some information about the times and distances associated with each travel method. 

Guiding Questions

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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.

Additional Practice

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.

  • Choose a few of the matching cards from here to use—not all of them are appropriate given what the students have learned. Since we have not focused on writing an equation for any situation, do not include this in the matching graph.
  • Include problems that review major concepts from the unit.
  • Illustrative Mathematics Tides
  • Inside Mathematics Performance Assessment Tasks Grades 3-High School Vincent's Graphs

Lesson Map

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Topic A: Features of Functions

Topic B: Nonlinear Functions

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