About This Chapter
Standard: 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. (CCSS.Math.Content.HSF-IF.B.4)
Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (CCSS.Math.Content.HSF-IF.B.5)
Standard: 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. (CCSS.Math.Content.HSF-IF.B.6)
Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima. (CCSS.Math.Content.HSF-IF.C.7a)
About This Chapter
A full comprehension of graphing allows students to adequately explain the relationships that exist in graphs and look at a graph to see how often a function changes. Students who understand the elements of graphing can recognize the most important features on a graph and will be able to connect a domain function to a graph. The lessons found in this standard include the following topics:
- The different parts of a graph
- Graphs as relationships between quantities
- Sketching graphs from tables or verbal descriptions of relationships
- Connecting domains to graphs of functions
- Find the average rate of change from a graph or table
- Calculate the average rate of change from an equation
- Graphs of equations as sets of solution points
Your students show they've mastered this standard by identifying the elements of a graph, using graphs to show the connections shared by quantities, and making graphs from listening to a description of a relationship. The combination of the standard and the lessons can help students get ready for higher education and jobs related to investment banking, aerospace or mechanical engineering, drafting, optometry and more.
How to Use These Lessons in Your Classroom
To get your students involved and more interested in graphing, you can employ the engaging video lessons related to these tips:
Utilize Different Learning Approaches
When you get to the Graphs as Relationships Between Quantities lesson, have your students draw out those relationships and write a short one- or two-sentence description about the pictured relationship. This is a good way to further engage students and can help them better understand the relationships they're learning about.
Have Students Sketch Graphs
Give your class verbal descriptions of graphs and have them draw them out. You could also group students and appoint one person in each group to describe a graph while the others draw them. If you like, you can include these with the lesson quizzes or have students complete them for extra points.
Make Real-World Connections
Have your students think of ways that they can use graphing in their day-to-day lives. Students might feel as though they'll never use what they're learning in real life, so show them that math can be just as useful outside of the classroom as it can inside of it. Give them a few examples of relevant industries and see if they can come up with specific occupations and how graphing would be used.
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Other chapters within the Common Core Math - Functions: High School Standards course
- Common Core HS Functions - Basics
- Common Core HS Functions - Sequences
- Common Core HS Functions - Linear Functions
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions
- Common Core HS Functions - Trigonometric Functions