Lesson Plan
The Dual Highway
Students will be able to use double number line diagrams to solve rate problems, enhancing their proportional reasoning skills.
Understanding double number lines provides a visual and intuitive way to solve real-world rate problems, from calculating fuel efficiency to scaling recipes. This skill builds a strong foundation for future mathematical concepts involving ratios and proportions.
Audience
9th Grade
Time
60 minutes
Approach
Through guided examples and hands-on activities, students will construct and utilize double number lines.
Materials
The Dual Highway Slide Deck, Road Trip Challenge Activity, Double Number Line Practice Worksheet, Exit Ticket Worksheet, Whiteboard or Projector, Markers or Pens, and Rulers (optional)
Prep
Teacher Preparation
15 minutes
- Review the Lesson Plan and all generated materials (The Dual Highway Slide Deck, Road Trip Challenge Activity, Double Number Line Practice Worksheet, Exit Ticket Worksheet).
- Ensure projector or whiteboard is ready.
- Print copies of the Road Trip Challenge Activity, Double Number Line Practice Worksheet, and Exit Ticket Worksheet for each student.
Step 1
Connect to Number Lines (5 minutes)
5 minutes
- Teacher: Begin by asking students what they already know about number lines. "What are number lines used for? Where have you seen them before?" (e.g., measuring, showing ordered values, temperature scales).
- Teacher: Introduce the idea of using number lines to compare quantities.
- Activity: Briefly review basic number line concepts as a class, perhaps with a quick warm-up question on the The Dual Highway Slide Deck (Slide 1-2).
Step 2
Introduce the Double Number Line (15 minutes)
15 minutes
- Teacher: Introduce the concept of a double number line using The Dual Highway Slide Deck (Slides 3-5). Explain that it's like having two number lines running parallel, showing how two different quantities are related proportionally.
- Key Concepts: Define and discuss 'Double Number Line', 'Corresponding Values', 'Rate Pairs'.
- Example: Present a simple rate problem (e.g.,
Step 3
Guided Construction (15 minutes)
15 minutes
- Teacher: Guide students through constructing their first double number line together using an example from The Dual Highway Slide Deck (Slide 6). For instance: "If a car travels 60 miles in 1 hour, how far does it travel in 3 hours?"
- Steps: Emphasize identifying the two quantities, setting up the initial rate pair, and scaling up or down using multiplication/division.
- Activity: Students work along with the teacher on their own paper or mini-whiteboards.
Step 4
Problem Solving Together (20 minutes)
20 minutes
- Activity: Distribute the Road Trip Challenge Activity to students. Work through the first problem or two as a class, modeling how to set up and solve it using a double number line.
- Collaborative Work: Have students work in pairs or small groups on the remaining problems in the Road Trip Challenge Activity and the Double Number Line Practice Worksheet. Circulate to provide support and address misconceptions.
- Teacher: "Remember to show your work clearly on your double number lines!"
Step 5
Review and Share (5 minutes)
5 minutes
- Teacher: Bring the class back together. Ask a few groups to share their solutions and strategies for one of the problems from the Road Trip Challenge Activity or Double Number Line Practice Worksheet.
- Discussion: Highlight different approaches and reinforce the key concepts of 'Scale' and 'Proportional Reasoning'.
Step 6
Exit Ticket (Optional, 5 minutes)
5 minutes
- Assessment: Distribute the Exit Ticket Worksheet for students to complete individually. This will serve as a quick check for understanding of the lesson's objective.
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Slide Deck
Welcome to The Dual Highway!
What are number lines?
- Where have you seen them before?
- How do we use them?
Welcome students and get them thinking about number lines. Ask probing questions to activate prior knowledge.
Beyond the Single Line...
Today, we're going to explore how two number lines can work together to help us solve problems!
Transition to the main topic. Explain that today we're taking number lines to the next level to solve interesting problems.
Meet the Double Number Line!
A double number line is a pair of parallel number lines used to represent equivalent ratios.
- Each line represents a different quantity.
- Numbers that line up vertically are corresponding values and form a rate pair.
Introduce the core concept. Define 'Double Number Line' and 'Corresponding Values'. Emphasize the visual aspect.
Rate Pairs in Action
Example:
If you can read 2 books in 1 week:
- The top line shows Number of Weeks.
- The bottom line shows Number of Books.
Weeks: 0 --- 1 --- 2 --- 3 ---
Books: 0 --- 2 --- 4 --- 6 ---
Here, (1 week, 2 books) and (2 weeks, 4 books) are rate pairs.
Provide a simple, clear example to illustrate what a rate pair looks like on the double number line.
Scaling Up and Down
We can find new corresponding values by scaling (multiplying or dividing) both quantities in a rate pair by the same factor.
Weeks: 0 ----- 1 ----- 2 ----- 3 ---
x2 x2 x2
Books: 0 ----- 2 ----- 4 ----- 6 ---
This is the power of proportional reasoning!
Explain how scaling works – the core mechanism for solving problems with double number lines.
Let's Build One Together!
Problem:
If a car travels 60 miles in 1 hour, how far does it travel in 3 hours?
- Identify quantities: Miles and Hours.
- Draw two parallel lines.
- Mark the starting point (0,0).
- Plot the given rate pair: (1 hour, 60 miles).
- Scale up to find 3 hours!
Guide students through a classic rate problem step-by-step. Encourage them to draw along.
Your Turn! Road Trip Challenge
Now, let's hit the road and solve some problems!
Use your double number lines to navigate through the Road Trip Challenge Activity and the Double Number Line Practice Worksheet.
- Work with your groups.
- Show your scaling!
Set the stage for independent practice. Remind them of the strategy.
Recap: The Dual Highway
Double number lines are powerful tools for visualizing and solving rate problems. They show how two quantities change proportionally!
Concluding slide for the lesson. Briefly recap the main idea.
Time for Your Exit Ticket!
Please complete the Exit Ticket Worksheet individually to show what you've learned today about double number lines.
This slide can prompt students to start their exit ticket.
Activity
Road Trip Challenge: Double Number Line Adventures!
Get ready to hit the road and solve some real-world rate problems using your awesome double number line skills! For each problem, draw a clear double number line and show your work.
Problem 1: Fuel Efficiency
Your car uses 2 gallons of gas to travel 50 miles.
a. How many miles can you travel on 6 gallons of gas?
b. How many gallons of gas would you need to travel 125 miles?
Problem 2: Snack Stop
You buy 3 bags of chips for $4.50.
a. How much would 7 bags of chips cost?
b. How many bags of chips could you buy with $18.00?
Problem 3: Music Playlist
Your road trip playlist has 4 songs that play in 12 minutes.
a. How many songs would play in 30 minutes?
b. How long would it take to play 10 songs?
Problem 4: Driving Time
You drive at a steady speed and cover 180 miles in 3 hours.
a. How far would you travel in 5 hours?
b. How long would it take you to travel 300 miles?
Worksheet
Double Number Line Practice
Show your understanding of double number lines by solving the problems below. For each problem, draw a clear double number line diagram and show all your steps.
Part 1: Complete the Double Number Lines
Complete the missing values on each double number line.
Problem 1:
Oranges: 0 ----- 2 ----- ? ----- 6 -----
Cost ($): 0 ----- 1 ----- 2 ----- ? -----
Problem 2:
Minutes: 0 ----- 10 ----- 20 ----- ? ----- 40
Pages: 0 ----- 5 ------ ? ------ 15 ---- ?
Part 2: Solve the Problems
For each problem, draw your own double number line to find the solution.
Problem 3: Baking Cookies
A recipe calls for 3 cups of flour for every 2 cups of sugar.
a. If you use 9 cups of flour, how much sugar do you need?
b. If you use 5 cups of sugar, how much flour do you need?
Problem 4: Running Laps
It takes you 4 minutes to run 2 laps around the track.
a. How many laps can you run in 10 minutes?
b. How long would it take you to run 7 laps?
Problem 5: Juice Concentrate
A bottle of juice concentrate requires 1 part concentrate to 3 parts water.
a. If you use 2 cups of concentrate, how much water do you need?
b. If you use 12 cups of water, how much concentrate did you use?
Worksheet
Exit Ticket: Double Number Line Check-in
Name: ______________________
Date: ______________________
Answer the following questions to show what you learned about double number lines today. Draw a clear double number line for each problem and show your work.
Question 1:
If a baker uses 2 cups of sugar for every 5 cups of flour in a cake recipe, how many cups of flour are needed if the baker uses 6 cups of sugar?
Question 2:
It takes a factory worker 15 minutes to assemble 3 toys. How many toys can the worker assemble in 45 minutes?
Question 3:
In your own words, explain why double number lines are helpful for solving rate problems. What makes them a good tool?