Rise Run Triangles

This lesson helps students understand that through a graph and a right triangle that they are able to determine slope.  Students will determine rise over run to find slope.  Students also determine if slopes are positive or negative by the direction of the line.  Students also use fractions to show slope and show slope in the simplest fractions.

Standards & Objectives

Academic standards
CCSS.Math.Content.6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to...
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one...
CCSS.Math.Content.7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are...
CCSS.Math.Content.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
GLE 0606.3.1
Write and solve two-step equations and inequalities.
GLE 0606.3.2
Interpret and represent algebraic relationships with variables in expressions, simple equations and inequalities.
GLE 0706.3.1
Recognize and generate equivalent forms for simple algebraic expressions.
GLE 0706.3.2
Understand and compare various representations of relations and functions.
GLE 0706.3.7
Use mathematical models involving linear equations to analyze real-world phenomena.
GLE 0706.3.8
Use a variety of strategies to efficiently solve linear equations and inequalities.
GLE 0806.3.1
Recognize and generate equivalent forms for algebraic expressions.
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
GLE 0806.3.5
Use slope to analyze situations and solve problems.
SPI 0606.3.2
Use order of operations and parentheses to simplify expressions and solve problems.
SPI 0606.3.3
Write equations that correspond to given situations or represent a given mathematical relationship.
SPI 0606.3.4
Rewrite expressions to represent quantities in different ways.
SPI 0606.3.8
Select the qualitative graph that models a contextual situation (e.g., water filling then draining from a bathtub).
SPI 0706.3.3
Given a table of inputs x and outputs f(x), identify the function rule and continue the pattern.
SPI 0706.3.6
Solve linear equations with rational coefficients symbolically or graphically.
SPI 0706.3.7
Translate between verbal and symbolic representations of real-world phenomena involving linear equations.
SPI 0706.3.8
Solve contextual problems involving two-step linear equations.
SPI 0706.3.9
Solve linear inequalities in one variable with rational coefficients symbolically or graphically.
SPI 0806.1.2
Interpret a qualitative graph representing a contextual situation.
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.3.5
Determine the slope of a line from an equation, two given points, a table or a graph.
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
TSS.Math.6.EE.A.3
Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent...
TSS.Math.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another.
TSS.Math.7.EE.A.2
Understand that rewriting an expression in different forms in a contextual problem can provide multiple ways of interpreting the problem and how the...
TSS.Math.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
TSS.Math.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
TSS.Math.8.F.A.3
Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
TSS.Math.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description...
TSS.Math.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear...
 
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: 

Students will be able to:

  • Determine if the slope of a line is positive or negative
  • Express the slope of a line as a fraction
Essential and guiding questions: 
  • Which, if any, of the fractions did you have to simplify when you found the slope of a line? How can you avoid the need to simplify a fraction?
  • Suppose you have identified 3 slope triangles for a line to help you find the correct slope. What can you say about the relationship between these triangles?
  • Explain the difference between a line with positive slope and a line with negative slope.
  • Explain the difference between a line with slope 1/2 and a line with slope 2/1.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • Show students a given point on a coordinate grid and give them a value for the slope of a line. Ask them to draw a line that has that slope through the given point.
  • How does the slope triangle method apply to horizontal and vertical lines? What does the slope-triangle look like for a vertical line? What does the slope-triangle look like for a horizontal line? What problems arise, and how do they affect the slope?
  • How is slope formula consistent with the slope triangle method for finding the slope of a line? How does calculating y1 – y2 relate to the height of the slope triangle? How does calculating x1 – x2 relate to the length of the slope triangle?

 

Helpful Hints

Materials:

  • Counting for Slope Activity Sheet 
  • Colored pencils (optional)

References

Contributors: