ALEX | Alabama Learning Exchange

Take the Stairs to Slope!

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This lesson provided by:

Author:	Kenneth Webb
System:	Tuscaloosa City
School:	Tuscaloosa City Board Of Education
The event this resource created for:	CCRS

General Lesson Information

Lesson Plan ID:	33048
Title:	Take the Stairs to Slope!
Overview/Annotation:	This lesson allows students to investigate the slope criteria and characteristics of parallel lines using graphing calculators and school staircases. Students will also use equations and graphs. Students will work cooperatively to develop and justify ideas/conjectures. This is a College- and Career-Ready Standards showcase lesson plan.

Associated Standards and Objectives

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis

33. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Example: Find the equation of a line parallel or perpendicular to a given line that passes through a given point.

Unpacked Content

Evidence Of Student Attainment:

Students:
Given a line,

Create lines parallel to the given line and compare the slopes of parallel lines by examining the rise/run ratio of each line.
Create lines perpendicular to the given line by rotating the line 90 degrees and compare the slopes by examining the rise/run ratio of each line.
Use understandings of similar triangles and logical reasoning to prove that parallel lines have equal slopes and the slopes of perpendicular lines are negative reciprocals.Given a geometric problem involving parallel or perpendicular lines.
Apply the appropriate slope criteria to solve the problem and justify the solution including finding equations of lines parallel or perpendicular to a given line.

Teacher Vocabulary:

Parallel lines
Perpendicular lines
Slope
Slope triangle

Knowledge:

Students know:

Techniques to find the slope of a line.
Key features needed to solve geometric problems.
Techniques for presenting a proof of geometric theorems.

Skills:

Students are able to:

Explain and justify conclusions reached regarding the slopes of parallel and perpendicular lines.
Apply slope criteria for parallel and perpendicular lines to accurately find the solutions of geometric problems and justify the solutions.
Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.

Understanding:

Students understand that:

Relationships exist between the slope of a line and any line parallel or perpendicular to that line.
Slope criteria for parallel and perpendicular lines may be useful in solving geometric problems.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
GEO.33.1: Define slope, point slope formula, slope-intercept formula, standard form of a line, parallel lines, and perpendicular lines.
GEO.33.2: Demonstrate and explain algebraically how perpendicular lines have only one common point.
GEO.33.3: Demonstrate and explain algebraically how parallel lines have no common points.
GEO.33.4: Write and solve equations of parallel and perpendicular lines.
GEO.33.5: Illustrate graphically how perpendicular lines have only one common point.
GEO.33.6: Illustrate graphically how parallel lines have no common points.
GEO.33.7: Write an equation of a line in slope intercept form.
GEO.33.8: Find the slope of a given line.

Prior Knowledge Skills:

Define slope, intercept, linear, equation, and bivariate.
Recall how to determine the rate of change (slope) from a graph.
Identify the parts of the slope-intercept form of an equation.
Recognize how to read a graph.
Recall how to write an equation in slope-intercept form.
Apply the identification of the slope and the y-intercept to a real-world situation.
Create a graph to model a real-word situation.
Define proportional relationships, unit rate, and slope.
Demonstrate how to graph on a Cartesian plane.
Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept.
Define linear functions, nonlinear functions, slope, and y-intercept.
Recognize linear equations.
Identify ordered pairs.
Recognize ordered pairs.
Generate the slope of a line using given ordered pairs.
Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept.
Graph a function given the slope-intercept form of an equation.
Recognize that two sets of points with the same slope may have different y-intercepts.
Graph a linear equation given the slope-intercept form of an equation.

Alabama Alternate Achievement Standards

AAS Standard:
M.G.AAS.10.31a When given an isosceles triangle and a measure of a leg or base angle, identify the measure of the other leg or base angle.
M.G.AAS.10.31b When given a parallelogram and the measure of one side or one angle, identify the measure of the opposite side or angle.

Local/National Standards:

Primary Learning Objective(s):

Students will discover and use the properties of parallel lines.

Students will find equations of parallel lines given other equations of lines passing through other points.

Students will use slope definitions with rise over run and formulas to solve problems and justify reasoning for developed discoveries.

Additional Learning Objective(s):

Students will work cooperatively to discover patterns in the graph table of values while problem solving.

Students will verify conclusions by finding slope and understanding properties of paralell lines.

Students will measure and document lengths of stairs and compare values to determine parallel slopes.

Preparation Information

Total Duration:	31 to 60 Minutes
Materials and Resources:	Poster Paper or Poster with grid lines Sticky notes of different types Straight edge Markers Student may use their own devices or teacher-issued graphing calculators.
Technology Resources Needed:	Computer with Internet access LCD Projector and Document camera to share student work (helpful but not necessary) Smartview with calculator is needed
Background/Preparation:	Teacher: Locate staircases to be used for lesson. Have graphing calculator ready to be assigned. Students: Geometry students should be able to graph coordinates on Cartesian plane and measure the lengths of models with ruler. Students should be able to find slope algebraically and graphically, use slope intercept form to solve problems, and have some knowledge of using the graphing calculators.

Procedures/Activities:

ENGAGE

1. As students enter the classroom, they should be given a group indicator that tells them where to sit until dismissed to staircase work location. Inform the students that their mission will be to determine whether a pair of equations of lines are parallel.

EXPLORE

2. Student groups should measure the rise and the run of the steps to find the slope of the stairs. They should record these findings on their own paper (this information is to be used to key into their graphing calculators).

3. The students should come back to the classroom and key their information into their graphing calculators (using the list key on the graphing calculator) to determine if the staircases make parallel lines and have parallel slopes. They should look for patterns, develop equations based on data, and list slope conclusions based on data. The groups must agree on findings and be able to justify.

3. If students are unable to identify rise and run values, provide necessary feedback to move them forward with their thinking. Refer to Rise over Run: https://www.youtube.com/watch?v=zTa0xTu9Yv4 (if your school system does not allow YouTube access, you may download the video using http://www.keepvid.com/)

Refer to: https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/v/slope-of-a-line

EXPLAIN

4. The teacher should be sure that students are using slope correctly to verify parallel lines.

5. Groups will discuss properties discovered and begin justifying their ideas; along with creating equations and graphs to match their tables in the calculator.

6. Allow students time to prepare attractive posters to share with the class to begin discussions about parallel, along with having the groups share their findings using the Smartview function of the calculator.

Assessment

Assessment Strategies

EVALUATE

Use the rubric provided to assess student work individually and as a group. Students should justify all reasoning stated on poster. The Assessment Process is on-going. The teacher should visit each group and ask questions to make sure students apply the properties of parallel line definitions. Post the posters in the classroom and have students present conclusions. As students present posters and graphing calculator finds, they should compare posters for other information not listed on their group's poster.

Acceleration:	Extensions can be used to include formal proofs in geometry or have students justify the properties of parallel lines using coordinate proofs. Groups can be random or you can select groups to allow struggling students to find slopes using formulas or inputting infomation into calculator for graphs.
Intervention:	For extra practice or for students who were absent, have them visit What is the slope of a staircase? (if your school system does not allow YouTube access, you may download the video using http://www.keepvid.com/).

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.

ALEX Lesson Plan

Take the Stairs to Slope!