Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 37212
Exploring Slope Intercept Form with Graphs and Physical
Activity
Students will work in pairs and compose three different linear equations in slope intercept form. They will discover and describe how different values
for m and b correspond to specific characteristics of the graph. After graphing lines on graph paper, they will do a physical activity involving graphing.
Subject(s): Mathematics
Grade Level(s): 8, 9, 10
Intended Audience: Educators
Suggested Technology: Computer for Presenter
Instructional Time: 2 Hour(s) 30 Minute(s)
Freely Available: Yes
Keywords: Slope, y-intercept, linear equations, graphing, y=mx+b, linear function
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
slope int quiz.docx
alg 1 Graphing project rubric.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to create linear equations.
Students will be able to graph linear equations on a coordinate plane.
Students will be able to explain the meaning of slope (vertical change compared to horizontal change).
Students will be able to associate a positive slope with a line that rises to the right, and a negative slope with a line that falls to the right.
Students will be able to describe a line as "steep" if the magnitude of m is greater than 1 (because the rise is greater than the run), and "gradual" if the magnitude
of m is less than 1 (the rise is less than the run).
Students will be able to predict where a line crosses the y-axis by looking at the equation.
Prior Knowledge: What prior knowledge should students have for this lesson?
The students have learned the definition of a term, variable, slope, intercept, x-axis, and y-axis. The students have already been taught how to plot coordinates on a
graph as well as how to graph linear functions using the slope intercept form of an equation y = mx + b.
Students should also be familiar with the fundamental ways to express the meaning of slope: rise over run, vertical change over horizontal change, change in y over
change in x, or delta y over delta x.
Guiding Questions: What are the guiding questions for this lesson?
What does slope mean? What are some of the things we have learned about slope? What does slope tell us about a line?
If the slope of a line is negative, what does that tell us about the graph of the line?
page 1 of 3 If the slope of a line is positive, what does that tell us about the graph of the line?
What kinds of values for slope correspond to a line that is steep? Gradual? Why?
If you know the y-intercept of a line, what can you tell about the graph of that line?
Teaching Phase: How will the teacher present the concept or skill to students?
Start Day 1
1. As the students enter the room, the instructor should pass out the rubric for the lesson.
2. When the bell rings, instruct them to recall what they learned previously about slope-intercept form by writing down the equation and explaining what each variable
represents. The instructor should see y=mx+b, m is slope, and b is the y-intercept from all groups before moving on to the next step.
3. Once there is proof of understanding the equation and the variables, have the students briefly describe what slope means as well as what y-intercept means. The
instructor should observe, through questioning, the students expressing understanding of these terms.
4. After the discussion, the instructor will pair students into homogeneous groups. Homogeneous pairs result in students being more engaged and less dependent on
others. The teacher will be aware of the needs of each pair and provide appropriate guidance, as needed. If there is an odd number of students, let there be one
group of three.
5. Once the students have expressed a clear understanding of the prior knowledge the groups can then begin reading the rubric (see attached). Allow for the groups
to read the rubric and then explain specifications for their grades.
Go to Guided Practice
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Day 1 (continued)
6. Get the students to first create three functions, three different ways. The students must understand that the values of m and b can be negative, positive, or zero.
Make parameters for the functions to stay between so the graphs do not get too large. An example is, "The magnitude of your slope must be less than or equal to 5
and the magnitude of your y-intercept must be less than or equal to 5." Students should use a fractional value for at least one of their slopes. Be sure to check each
group's equations before moving on.
7. After the students have created their functions, have them describe the slope (direction) and y-intercept (where it crosses the y-axis) in words for each function
they have created. Have the groups explain the differences between slope and y-intercept in all three functions.
8. For the last ten minutes of class have the groups pair up with another group. Teachers instruct the students to label each line with its equation. The new groups of
four students should now have a total of six functions. The new groups should graph all six functions on paper and discuss how each is different. Their discussion
should be based on what variables were manipulated, and how the functions differ based on the different variables.
Throughout the lesson, the teacher should circulate the room checking for correctness and providing feedback.
End Day 1
Start Day 2
9. The field should be set up before the students arrive to class. The original groups of students will graph their three functions on the coordinate plane outside.
10. As each group of students comes to graph their function, they will give the instructor their rubric to grade.
11. One student will represent the y-intercept and the other will walk off the slope. They will have a piece of rope in their hands to represent the function.
12. After graphing each function, the students will have to explain what variable changed and how it affected the graph.
13. The instructor should ask questions to the students graphing as well as the rest of the class. An example of a question would be, "Does the line stop where they are
standing?"
End Day 2
Day 3 - Give Summative Assessment (Slope Intercept Quiz - attached)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The students will physically graph the three lines that they have created. Students will explain explain to the class the changes they made and how the changes affected
the graph of the function.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teacher leads the class in discussing the findings of the lesson, leaving some time at the end for question and answer.
Summative Assessment
On the third day the students will be given a four question quiz that asks them to graph a set of linear equations. See attached quiz.
Formative Assessment
On day 1, the students will be answering questions about y=mx+b. What is m, what does it represent? What is b, what does it mean? Discussion questions will review
what m and b represent, and how different numbers in place of m or b will change the way the graph looks.
After the discussion, the instructor will pair students into homogeneous groups. Homogeneous pairs result in students being more engaged and less dependent on
others. The teacher will be aware of the needs of each pair and provide appropriate guidance, as needed.
Feedback to Students
Groups will submit equations that they have created, receive feedback as soon as they have the equations created (that day), and have an opportunity to correct
mistakes. After equations are correct, the students will have three lines to graph outside on the field. After each line is graphed, there will be a group discussion about
the lines and if they are correct. Corrections will be made and the group will graph another line until they get it correct.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: If a student has a physical disability, pair them with someone who can do the physical movement for them as they describe where to go.
Extensions: How could the equation be changed to get a parallel line?
How could the equation be changed to get a vertical line?
Suggested Technology: Computer for Presenter
page 2 of 3 Special Materials Needed:
Printed rubric, painted field or masking tape on floor, and a piece of rope or string, Quiz
The activity will need either a painted football field to use a coordinate plane or field paint to paint a coordinate plane in the grass outside. If there is no paint or field
available, use masking tape to create a coordinate plane on the classroom floor. The students will also need string to represent the function and a rubric to know what
they are being graded on.
Further Recommendations: If using a football field, it is best to use the practice field in case you want to paint your own numbers or markings on the field.
SOURCE AND ACCESS INFORMATION
Contributed by: Kevin Helms
Name of Author/Source: Kevin Helms
District/Organization of Contributor(s): FSU Lab School
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.A-CED.1.2:
Description
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate
axes with labels and scales. ★
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