Slippery Slope - Lesson Plan

Teaching Plan (1 week)

 Prerequisites(5minutes)

The objective of this lesson is to help identify students with deficiencies in adding, subtractin, and dividing integers (a skill required to calculate slope).

Using a computer projector, demonstrate how to go to the eNLVM website, go to your school and class, and login. (5 minutes)
(1 activity) Students add, subtract, multiply and divide integers. Instruct students to check their answers and seek help if they do not understand the concepts.

Rate of Change (15 minutes)

The objective of the lesson is to introduce the concept of slope as a rate of change using examples.

(3 activities) Students compare steepness of mountains, roofs, stairs, and a graph.
(3 activities) Students are introduced to slope as the rate of change, identify rise and run, and calculate slope.

Positive, Negative, Zero, Undefined Slope (15 minutes)

The objective of this lesson is to help students relate the concepts of positive, negative, zero, and undefined slopes with applications.

(4 activitiy) Students are presented with examples of positive, negative, zero, and undefined slopes.
(2 activities) Students are shown different types of slopes and identify examples of each.

 Slope Formulas(20 minutes)

The objective of this lesson is to help students learn to calculate slope given two points.

(1 activity) Students are presented with the formula for calculating slope. The variables are color coded and given explanations.
(2 activities) Students are guided through the process of finding the slope of a line using coordinate points.
(1 activity) Students practice finding the slope of a line given two coordinate points.

Exploring Slope (20 minutes)

The objective of this lesson is to help students explore graphed lines and their slopes.

(1 activity) Students observe the slope of a line calculated using different points on the line.
(2 activities) Students explore the relationship between the steepness and direction of a line and its slope.

 Comparing Slope (10 minutes)

(1 activity) Students are guided to discover the difference between steepness and slope.
(3 activities) Students are guided to discover the connection between slope values and the symbolic representation of the relationship.

Credits

Correlation to Standards

Correlation to NCTM Standards

Algebra - Represent and analyze mathematical situations and structures using algebraic symbols; Analyze change in various contexts.

• Grades 3-5
  • investigate how a change in one variable relates to a change in a second variable
  • identify and describe situations with constant or varying rates of change and compare them
• Grades 6-8
  • explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
  • use graphs to analyze the nature of changes in quantities in linear relationships
• Grades 9-12
  • analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior
  • approximate and interpret rates of change from graphical and numerical data

Correlation to Utah Standards

• PreAlgebra - 2.2 Represent, solve, and analyze mathematical situations and properties using algebraic symbols.
  • Determine the slope of a linear relation from a graph or ordered pairs
  • .
• Elementary Algebra - 2.1 Use patterns, relations, and functions to represent mathematical situations.
  • Identify the slope of a linear function as an average rate of change in real-world situations.
• Elementary Algebra - 2.3. Represent quantitative relationships using mathematical models and symbols.
  • Identify the slope of a line when given: a. A set of two ordered pairs; b. The graph of a linear function.
  •  
• Elementary Algebra 5.1 Formulate and answer questions by collecting, organizing, and analyzing data.
  • Analyze the meaning of the slope and y-intercept of a line of best fit as it relates to the data.

Correlation to Arizona Standards

Strand 3: Pattern, Algebra, and Functions. Concept 4: Analysis of Change. Analyze change in a variable over time and in various contexts

• Grade 7
  
  • Analyze change in various linear contextual situations.
• Grade 8
  • Identify the slope of a line as the rate of change (the ratio of rise over run).