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

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?

• 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.