The Polar Express Journey

Grade Levels: 6th and 8th Grade

Class Size: 81 Students
Duration: 71 minutes

Learning Objectives

For 6th Grade (CCSS - Mathematics):

CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, including unit rates.
CCSS.MATH.CONTENT.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

For 8th Grade (CCSS - Mathematics):

CCSS.MATH.CONTENT.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph.
CCSS.MATH.CONTENT.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output and graph functions on coordinate axes.

Essential Question

How can mathematical concepts such as ratios, rates, and functions help us understand the events and characters in The Polar Express?

Materials Needed

Projector/Smartboard
Copies of the Polar Express worksheet (one per student)
Pencils
Calculators (optional)
Timer

Lesson Breakdown

1. Introduction and Warm-up (8 minutes)

Briefly discuss the story and theme of The Polar Express to activate background knowledge.
Pose the question: “How do you think math is part of the journey in The Polar Express?”
Review the mathematical concepts to be explored: ratios, rates, variables for 6th grade; proportional relationships and functions for 8th grade.

2. Movie Viewing with Embedded Math Prompts (40 minutes)

Show selected clips (approximately 15-20 minutes total running time) from The Polar Express that lend themselves to calculation and analysis. Suggested scenes:
- The train’s speed and distance traveled.
- Number of bells vs. number of passengers.
- Ticket costs and calculations related to items on the train.
At strategic pause points, prompt students with quick mental math or short discussions related to the math concepts.
Example questions:
- “If the Polar Express travels 120 miles in 2 hours, what is its speed in miles per hour? How does this rate compare if the train speeds up to 90 miles in 1 hour?”
- “If each passenger receives one bell, and we see 50 bells, how many passengers are on the train?”
Use this time to reinforce connections between the story elements and math concepts.

3. Worksheet Activity (18 minutes)

Hand out the Polar Express Math Worksheet designed specifically for this lesson (see below).
Students work individually or in small pairs to answer questions related to the movie clips and concepts discussed.
Teachers circulate to provide support and check understanding.

4. Group Discussion and Wrap-Up (5 minutes)

Select 3-4 students to share their answers and thought processes.
Tie back to Common Core Standards: Discuss how ratios and rates describe real-world situations, and how functions can model relationships like speed over time.
Preview the next math lesson(s) related to rates, proportions, and functions for both grades.

Polar Express Math Worksheet

Instructions: Watch the clips and answer the questions below using your favorite problem-solving strategies.

For 6th Grade

The train travels 120 miles in 2 hours. Calculate the speed in miles per hour. If the train speeds up and travels 90 miles in 1 hour, how does the speed change?
There are 75 passengers on the train. If the conductor has a box of 150 bells, does every passenger get one bell? Explain your reasoning using ratios.
The conductor sells tickets for $12 each. Write an algebraic expression to represent the total amount collected for n tickets. If he sells 50 tickets, what is the total amount?

For 8th Grade

Plot the relationship between distance (miles) and time (hours) of the Polar Express as shown: (0,0), (2,120), (3,180). What is the slope of the line? What does it represent in this situation?
If the number of bells (b) given to passengers is a function of the number of passengers (p), where b = p. Graph this function for p = 0 to 100. What does the graph show?
The ticket price increases by $2 every year starting at $12 this year. Write a function T(y) that represents the ticket price y years from now. What will the ticket cost in 5 years?

Assessment

Completed worksheets demonstrating accuracy and proof of reasoning for all math problems.
Participation during pause-point discussions showing application of math concepts.
Informal checks for understanding during group sharing.

Differentiation Strategies

Flexible grouping during the worksheet activity to pair stronger and developing math students.
Provide sentence starters for problem explanations to support ELL and struggling writers.
Use calculators or visual aids as needed to scaffold calculations.

Extensions / Cross-curricular Ideas

Language Arts: Write a short story describing your own math-related adventure inspired by The Polar Express.
Art: Create posters showing the mathematical ratios and functions from the train journey.
Technology: Use graphing software or apps to digitally plot functions inspired by the movie scenes.

Reflection Notes for Teachers

This lesson capitalizes on a beloved movie to engage students in math through storytelling and real-world connections.
The combination of multisensory input (video + worksheet) supports diverse learning styles.
Monitor pacing closely during the movie viewing and embedded questions to keep students focused.
Use pre-lesson questions to activate prior knowledge and post-lesson reflections to deepen understanding.

End of plan.