Interpreting Functions

Length: 2-3 days (1.5-hour blocks)

The Metropolitan Nashville Arts Commission engaged two internationally-known artists, Thornton Dial and Lonnie Holley, to create site-specific public art works for the newly revitalized Edmondson Park (overseen by the Metropolitan Development and Housing Agency). This project honors William Edmondson, a native of Davidson County and a self-taught sculptor. Edmondson was the first African American artist to have a solo exhibition at the New York Museum of Modern Art (1937). Like Edmondson, Thornton Dial and Lonnie Holley are self-taught artists.

In this Mathmatics Lesson, students will:

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Attend to precision.

 

Standards & Objectives

Academic standards
CCSS.Math.Content.HSF-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...
CCSS.Math.Content.HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function...
CCSS.Math.Content.HSF-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...
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Learning objectives: 

Clear Learning Targets:

  • Students will be able to list the domain (independent variable) and the range (dependent variable and explain why the information is either independent or dependent.
  • Students will be able to show a constant rate of change between the data in the table.

Task Objectives (steps to reach mastery of clear learning targets):

  • Find numerical patterns. (How does x become y? Is this same for all?)
  • Understand the difference between independent and dependent variables.
  • Recognize that constant rate of change is the same thing as slope.
  • Create a function table (with a linear equation rule) of time spent and completion time.
Essential and guiding questions: 

Questioning: Planning to Illuminate Student Thinking
Assessing questions:

  • What patterns do you notice in the given table?
  • What patterns do you notice in the table that you created?
  • What relationship do you notice between the quantities?

Advancing questions:

  • How might you use previous learning to help solve the task?
  • What is another way/model you could illustrate your thinking?
  • What is another tool you could you to solve the problem?
  • If you change the hours/cost to ___, how would that change your answer?
  • How can you determine if there is a directly proportional relationship?

Lesson Variations

Blooms taxonomy level: 
Applying
Differentiation suggestions: 

Scaffolding opportunities (to address learning challenges)

  • The teacher will review the concept of ratios, rates, and unit rates.
  • The teacher will review how to set-up and solve a proportion.
  • The teacher will monitor students in small groups and use questioning to guide student learning.
  • The teacher will demonstrate how to recognize proportional relationships.

Opportunities to Differentiate Learning (explain how you address particular student needs by differentiating process, content, or product)

  • The teacher will group students strategically.
  • The teacher will use private think time, student to student think time, small group think time, and whole group think time to help students clarify mathematical thinking.

Helpful Hints

Materials and Resources

See attached materials and websites listed below in Teacher Actions and Appendices