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

Functions, Graphs and Features

Lesson 1

Math

Unit 1

9th Grade

Lesson 1 of 11

Objective

Model a contextual situation graphically using appropriate scales and features.

Common Core Standards

Core Standards

  • N.Q.A.1 — Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.
  • N.Q.A.3 — Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
  • 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.
  • F.IF.B.6 — Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 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. Identify variables to represent a contextual situation.
  2. Determine whether the variables represented are independent or dependent variables.
  3. Identify key features of the situation to represent graphically based on the context of the situation (start of the situation, when changes occur, at the end of the situation). 
  4. Describe the shape of the graph as relates to the context of the situation (the what) over particular intervals (the where). 

Tips for Teachers

  • This lesson gives the teacher an opportunity to assess students’ understanding of the components necessary to justify their reasoning. 
  • Even though this lesson does not ask students to recall mathematical language of x-intercept, y-intercept, rate of change, domain, and range, be sure to encourage students to use descriptive language related to the variables. For example, instead of “I know because the graph goes up…,” encourage students to use “The time is increasing as the mileage increases.”
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Anchor Problems

25-30 minutes

Problem 1

Below are two graphs that represent two different student commutes. Determine the main method of transportation for each student. Choose from the following options: 

Subway, Bus, Car, Walk

Guiding Questions

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Problem 2

Sketch the relationship you see in each of the three videos shown. 

Up and down the slide
(Screen 2)

 Water in a bowl
(Screen 4)		 Eggs in a carton
(Screen 5)

 

Guiding Questions

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References

Desmos Graphing Stories

Graphing Stories by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed June 26, 2017, 2:06 p.m..

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.

Target Task

5-10 minutes

Sylvia bikes home along a straight road from her friend’s house, a distance of 8 miles. The graph shows her journey: 

  1. Describe what may have happened. Be sure to include details about her pace, points that indicate a change in action, and where she starts and stops. 
  2. Are all sections of the graph realistic? Explain your reasoning.

References

MARS Formative Assessment Lesson for Grade 8 Interpreting Distance - Time Graphs — The Journey Home

Interpreting Distance - Time Graphs from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed June 22, 2017, 3:23 p.m..

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.

  • Illustrative Mathematics Distance — How does the change in variables change the meaning of the graphs?
  • Illustrative Mathematics Tides
  • Illustrative Mathematics Playing Catch
  • MARS Formative Assessment Lesson for Grade 8 Interpreting Distance - Time Graphs — This activity is also present in 8th grade curriculum. Use this as a reminder of what they know, and ask questions similar to the guiding questions from the lesson above.
  • Desmos Waterline — This activity is also present in the 8th grade curriculum. Teacher could also do this as a demonstration.
  • Illustrative Mathematics Riding by the Library — How would you sketch a graph given a description of the situation?

Next

Define functions and evaluate points in tables, graphs, and contextual situations using function notation.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Functions

Topic B: Nonlinear Functions

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