Lesson Plan
Steepness of a Story: Understanding Slope
Students will be able to calculate the slope of a line from a graph or two points and interpret it as a rate of change in a real-world context.
Understanding slope helps us describe how things change around us, like how fast a car is going or how much a plant grows each day. It's a fundamental concept in mathematics that applies to many real-world situations and is key to analyzing linear relationships.
Audience
9th Grade Students
Time
65 minutes
Approach
Through direct instruction, guided practice, and an engaging activity.
Materials
Whiteboard or Projector, Markers/Pens, Slope Superstars Activity, Rate of Change Worksheet, and Exit Ticket
Prep
Teacher Preparation
15 minutes
- Review the Steepness of a Story: Understanding Slope Slide Deck and practice delivery.
* Print copies of the Slope Superstars Activity (1 per small group).
* Print copies of the Rate of Change Worksheet (1 per student).
* Print copies of the Exit Ticket (1 per student).
* Ensure whiteboard or projector is ready for use.
* Review the generated materials as needed.
Step 1
Introduction & Hook: What's Your Story's Steepness?
10 minutes
- Begin with an engaging question: "Imagine you're climbing a hill. What makes one hill 'steeper' than another? How would you describe that difference to a friend?"
* Introduce the concept of slope as the 'steepness' of a line and its real-world relevance. Use the first few slides of the Steepness of a Story: Understanding Slope Slide Deck to guide this discussion.
Step 2
Direct Instruction: The Rise and Run of Real Life
20 minutes
- Use the Steepness of a Story: Understanding Slope Slide Deck to explain slope (rise over run) and how to calculate it from a graph and from two points.
* Define positive, negative, zero, and undefined slopes with visual examples.
* Connect slope to the idea of a 'rate of change' using simple real-world examples (e.g., speed, plant growth, money saved over time).
* Model how to calculate slope from a graph and from two points.
Step 3
Guided Practice: Slope Superstars!
15 minutes
- Divide students into small groups.
* Distribute the Slope Superstars Activity.
* Guide students through the activity, providing support and answering questions. Circulate among groups to check for understanding and facilitate discussions.
Step 4
Independent Practice: Charting Your Course with Rate of Change
15 minutes
- Distribute the Rate of Change Worksheet.
* Students work independently to complete the worksheet, applying their knowledge of calculating and interpreting slope.
* Circulate to offer individual support and clarification.
Step 5
Wrap-up & Assessment: Exit Ticket to Slope Success
5 minutes
- Bring the class back together.
* Facilitate a brief discussion to review key takeaways from the lesson.
* Distribute the Exit Ticket for students to complete and submit. This will serve as a quick assessment of their understanding of calculating slope and its meaning.
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Slide Deck
The Steepness of a Story
What makes one hill 'steeper' than another? How would you describe that difference?
Today, we'll learn how to measure the 'steepness' of a line and what it tells us about a story!
Greet students and start with an engaging question to hook their interest and connect to prior knowledge. Explain that today they will learn to describe 'steepness' mathematically.
What is Slope?
Slope is the measure of a line's steepness.
It tells us how much a line rises (changes vertically) for every unit it runs (changes horizontally).
Slope = Rise / Run
Introduce the formal definition of slope as 'rise over run'. Use the visual to reinforce the concept.
Finding Slope from a Graph
- Pick two points on the line.
- Count the vertical change (rise) between the points.
- Up is positive, Down is negative.
- Count the horizontal change (run) between the points.
- Right is positive, Left is negative.
- Write the ratio: Rise / Run
Explain how to calculate slope from a graph. Emphasize picking two clear points and counting the rise and run, paying attention to direction.
Finding Slope from Two Points
When you have two points (x1, y1) and (x2, y2), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Where 'm' represents the slope.
Introduce the slope formula. Explain that it's a more algebraic way to do the same thing as 'rise over run'. Emphasize consistency in choosing (x1, y1) and (x2, y2).
Types of Slope
- Positive Slope: Rises from left to right.
- Example: Money in a savings account over time.
- Negative Slope: Falls from left to right.
- Example: Fuel in a gas tank as you drive.
- Zero Slope: A horizontal line.
- Example: The horizon.
- Undefined Slope: A vertical line.
- Example: A wall.
Discuss the different types of slopes with examples. Encourage students to think of real-world scenarios for each type.
Slope as Rate of Change
Slope isn't just about lines on a graph; it tells us how one quantity changes in relation to another!
Rate of Change = Change in Y / Change in X
Examples:
- Speed (miles per hour)
- Earnings (dollars per hour)
- Growth (inches per week)
Crucially, connect slope to the idea of a rate of change. Provide clear, relatable examples.
Time to Be Slope Superstars!
Now, let's put your new slope skills to the test!
Work with your group on the Slope Superstars Activity. Remember to discuss and help each other!
Prepare students for the group activity. Briefly explain what they'll be doing and encourage collaboration.
Charting Your Own Course
It's time for some independent practice!
Complete the Rate of Change Worksheet on your own. Take your time and show your work.
Transition to independent practice. Remind them to apply what they've learned.
Slope Success: Wrap-Up!
You've tackled the steepness of stories today!
Complete this Exit Ticket to show what you've learned about calculating and interpreting slope.
Conclude the lesson and distribute the exit ticket for assessment. Reinforce the main idea.
Activity
Slope Superstars Activity
Objective: Work with your group to calculate the slope for various real-world scenarios and interpret its meaning.
Instructions:
- Each scenario below presents a real-world situation. Read each one carefully.
- For each scenario, you will be given either a graph or two points.
- As a group, calculate the slope of the line representing the scenario.
- Once you have the numerical slope, discuss and write down what that slope means in the context of the story.
Scenario 1: The Growing Plant
A plant's height was measured over several days.
Points: (Day 2, 4 cm) and (Day 5, 10 cm)
Calculate the Slope (m):
Interpret the Slope: What does this slope tell you about the plant's growth?
Scenario 2: Water Tank Drainage
A water tank is draining at a steady rate. The graph shows the amount of water (in liters) remaining in the tank over time (in minutes).
(Imagine a graph where the y-axis is 'Liters of Water' and the x-axis is 'Time in Minutes'. A line starts at (0, 100) and goes down to (10, 0).)
Calculate the Slope (m):
Interpret the Slope: What does this slope tell you about the water tank?
Scenario 3: Road Trip Miles
You are on a road trip, and your car's odometer reading is recorded at different times.
Points: (2 hours, 120 miles) and (5 hours, 300 miles)
Calculate the Slope (m):
Interpret the Slope: What does this slope tell you about the road trip?
Scenario 4: Balloon Ascent
A hot air balloon is ascending at a constant rate.
Points: (1 minute, 50 meters) and (3 minutes, 150 meters)
Calculate the Slope (m):
Interpret the Slope: What does this slope tell you about the balloon?
Worksheet
Rate of Change Worksheet: Mastering Slope
Instructions: For each problem, calculate the slope (rate of change) and then explain what the slope means in the context of the problem. Show all your work.
Part 1: Calculating Slope from Graphs
-
Figure 1: Savings Account
(Imagine a graph where the y-axis is 'Money Saved ($)' and the x-axis is 'Weeks'. A line starts at (0, 50) and goes up to (5, 150).)a. Calculate the Slope (m):
b. Interpret the Slope: What does the slope tell you about the savings account?
-
Figure 2: Distance Traveled
(Imagine a graph where the y-axis is 'Distance (km)' and the x-axis is 'Hours'. A line starts at (0, 0) and goes up to (3, 180).)a. Calculate the Slope (m):
b. Interpret the Slope: What does the slope tell you about the speed?
Part 2: Calculating Slope from Two Points
-
Temperature Change
At 8:00 AM, the temperature was 10°C. By 11:00 AM, the temperature was 16°C.a. Identify two points (time, temperature):
Point 1:
Point 2:b. Calculate the Slope (m):
c. Interpret the Slope: What does the slope tell you about the temperature?
-
Coffee Shop Sales
A coffee shop sold 50 cups of coffee on Monday and 80 cups of coffee on Friday.a. Identify two points (day, cups sold): (Assume Monday is Day 1, Tuesday is Day 2, etc.)
Point 1:
Point 2:b. Calculate the Slope (m):
c. Interpret the Slope: What does the slope tell you about coffee sales?
Part 3: Real-World Scenarios
-
Draining Pool
A swimming pool is being drained. After 1 hour, there are 9,000 gallons left. After 3 hours, there are 5,000 gallons left.a. Calculate the rate of change (slope) in gallons per hour:
b. Interpret the rate of change: What does this tell you about the pool drainage?
-
Subscription Cost
A streaming service costs $15 for 1 month and $45 for 3 months.a. Calculate the rate of change (slope) in dollars per month:
b. Interpret the rate of change: What does this tell you about the subscription cost?
Quiz
Exit Ticket