Slope and Rate of Change

Here’s a Microsoft Word document for the lesson plan on slope and rate of change, which includes photocopiable materials.

In this lesson plan, students learn to find the slope of a line given two points of the line, find the slope of a line given its equation, find the slopes of horizontal and vertical lines, and compare the slope of parallel and perpendicular lines.

Lesson Plan Template Draft: Section 3.4: Slope and Rate of Change

Teaching point / Objectives:

· Find the slope of a line given two points of the line

·  Find the slope of a line given its equation

· Find the slopes of horizontal and vertical lines

·  Compare the slope of parallel and perpendicular lines

·  Interpret slope as a rate of change

Length of lesson:











Text: Beginning and Intermediate Algebra 6th Edition-Elayne Martin Gay

Note-taking Guide (See below)

Memory Cards (See below)







Active learning strategies that this lesson employs:

1. Turn and Talk

In a turn and talk, a question is posed to the class and students simply turn to the person next to them to discuss. This can serve as a comfortable way for students to share their ideas with others and set the stage for them sharing with the larger group. The instructor doesn’t need to hear all (or any) of the ideas shared– the important aspect of this strategy is for the peers to share and for individuals to access their prior knowledge about a topic. Example prompt: Ask students to turn to someone next to them and discuss their responses to the following question. Tell them to take two minutes to discuss this with their partner with each person getting some time to talk.

2. Sorting strips
Small bits of information are separated into strips so that students can sort the strips into various categories, or organize them into a sequence depending on the topic. This strategy encourages discussion of competing ideas or organizations or order in which a process would take place. In this case, it is often the discussion and sharing of ideas that is the most important outcome of the activity.

Real-world connection / focus / word problem connecting lesson to real-world: (What is the connection between this content and a student’s future study or or the “real world”? What is the context of this lesson? What problem will you use to hook students into the lesson to make a real-world connection to content that they are going to learn today?)

How are you using this context to introduce or reinforce the teaching point?

Students come across more often than not in their daily lives. If they ever plan to own a home slope is an important concept that they should be aware of and will come across often. Depending on their respective career after college this is something they will encounter. For example:

v  The pitch of a roof, used by builders and architects is its slope.

v  The grade of a road is its slope.

v  According to federal regulations, a wheelchair ramp should rise no more than 1 foot for a horizontal distance of 12 feet. We can calculate the slope of this ramp.

v  The Guinness Book of Records has Baldwin Street, in Dunedin, New Zealand, as the world’s steepest street. For every 2.86 meters of horizontal distance, the vertical change is 1 meter.

v  See images of slopes below:

Source for image

Anticipated time Stage and aim

(Present, Practice, Produce)

10mins Lead in- To introduce the context of the lesson, to personalize the topic, to activate prior student knowledge ü  Show students the images above

ü  Particularly paying attention to the notion that there is a vertical component and a horizontal component

ü  Explore the images, ask students: What they notice? Why knowing the slope of each scenario may or may not be important?

ü  Activate prior knowledge or begin the lesson by asking if anyone can give a definition of slope based on what we’ve discussed. You can have students write down the appropriate definition at this point in the lesson or after you’ve gone over a few examples. Slope: is a measure of the steepness of a line)

10-15mins Task Setting- To give students an active way of engaging with the lecture content so that the teacher can later evaluate understanding



v  Give each student the Note-Taking Guide (see below)

v  This note taking guide will be for students to complete as you are going through the presentation stage so students are actively taking notes during presentation

v  You can incorporate turn and talks when you have a pause in the presentation to give students time to complete an example on their own


15mins Presentation of new concept- To clarify/ present the new material (as students work on something active)



































Ø  Spend 10-15mins presenting the following to students. With each objective choose 1 or 2 concrete examples from the textbook to take students from abstract to concrete

1.          Finding the slope of a line given two points.*

*Before beginning this abstract form of slope work with students to find the slope of one of the images in the lead-in by creating semi-realistic values for the vertical and horizontal change. You can create something along the lines of the following: If this car travels up a hill with a 60 feet incline & that’s 100 feet long how can we calculate the steepness of this hill? 60/100 (vertical change/ horizontal change). This tells us the slope of this hill.

2.     As we’ve explored in our previous lesson, straight lines (with or without a slant) can be written as an equation. The format of this equation is the same for all linear lines. Finding the slope of a line given its equation you will notice the following… (give one or two examples from textbook, pg. 210 if you will like to reinforce this idea even further).

3.     Find the slope of horizontal and vertical lines.**

**Before beginning this go back to the images in the lead-in section of this lesson and ask about the direction each slope is going in. You will hear students say it is “going up” (i.e, the car, plane, ladder), or “going down.” When students say this, you can then ask, if a line is going up how will we describe that slope using mathematical vocabulary? If it is going down how will we describe the line using mathematical vocabulary? What about when the line is horizontal? Why do you think a horizontal line has a slope of 0? What about a vertical line, how will you describe the slope? (Students may have to take a minute to think about this. Give them time. With a vertical slope there is no horizontal change, the line is going up and down, therefore, there is no slope, so in mathematics we say the slope is undefined).

4.  Compare the slopes of parallel and perpendicular lines

5.   Interpret slope as a rate of change: Choose any word problem from textbook pg. 213

Source 1

Source 2

5-10mins Controlled practice of new concept/ feedback- To provide students with practice and to generate an opportunity for questions/ Feedback: to clarify questions that emerged during the controlled practice v  Students will complete the memory cards activity with a partner (see memory cards below)

v  Some spaces are left blank in order for you to included more examples, if necessary






Anticipated problems and potential solutions in this lesson (These can be either problems with logistics / timing, or problems to anticipate with students’ knowledge / grasp of the content. Where will students have difficulties? What would you want a newer teacher to anticipate?)

Ø  Students may encounter difficulty when they have to find the slope and y-intercept of a line that is not written in slope-intercept form. It may be helpful to go through an example with students of how you can convert an equation from standard form to slope-intercept form so it is easier for them to distinguish the slope and y-intercept of the line.

Differentiation: In what places in the lesson are you differentiating for students in different ability groups?

v  The sorting strips activity engages all types of learners- auditory, visual, and kinesthetic.


v  This lesson begins with an activity that shows students images of what they’ve seen in reality, in a movie, pictures, etc. This visual aspect of what is slope and where we see slope is important for my visual learners.


v  During presentation students have a hands on task they are required to complete as we go through each objective


v  During the “presentation” component of lesson, I will be asking varied questions for learners at different levels. Giving everyone an opportunity to access this lesson no matter their background knowledge

Where are these on your lesson plan?  

·   The sorting strips will take place towards the end of the lesson. The images will be shown as the beginning of the lesson

·   Note-taking guide provided to students before the start of the presentation stage

·   During controlled practice part of the lesson        










Ideas for extensions, notes, considerations, or alternative plans:

Ø  During presentation try to use as much of the lead-in images as you can to connect students to the objective.

Ø  Giving students the formula too soon will contribute to a lack of conceptual understanding of slope and it will become procedural for them to find the slope if given the formula at the onset of the lesson

Ø  Circulate throughout the classroom to make sure students are filling in the examples in the Note-taking guide

Ø  During turn & talk circulate to hear students ideas, questions, and/or to quickly address a misconception

















Note-taking Guide Section 3.4


Instructor:                                                                                                   Date:

Guided Notes on Section 3.4 Slope and Rate of Change


As you listen to the lecture, we will complete the 5 objectives below. Please fill in an example for each objective as we cover the concept.


Part 1: Finding the slope of a line given two points.


Part 2: Finding the slope of a line given its equation.
Part 3: Finding the slopes of a horizontal and vertical line. Part 4: Compare the slope of parallel and perpendicular lines
Part 5: Interpret slope as a rate of change Notes-to-self












positive slope



negative slope






slope is undefined



formula for a parallel line



formula for a perpendicular line







Find the card with the slope of this line: Find the card with the y-intercept of this line:  






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