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Math Matters: Off-Road Algebra

MathMatters: Offroad Algebra

Welcome to Math Matters, where we employ 21st century learning tools and methodologies to help make math relevant and fun again for both you and your students.

This 30-segment video resource focuses on ninth grade Pre-Algebra and Algebra. What makes this unit different from most? It revolves around the world of off-road motorcycle racing. Team HotChalk worked with a group of young HotChalk-sponsored cyclists, videotaping them jumping off ramps along dirt bike tracks and racing up the golden summer hills of a ranch overlooking the ocean in Central California. Courtesy of math teachers Jason Dyer (Pueblo High School, Tuscon, AZ), who scripted out the ‘real world’ algebra problems, and John Villavicencio (Berkeley High School, Berkeley, CA), who explains the step-by-step solutions in each segment, we are bringing you our first homemade model of YouTube-style learning, “Off-Road Algebra.”

Our hope is that you’ll try out this unit with your class, and let us know what you think. We’d like you to be active participants in helping to shape the digital resources we feel are at the heart of learning in the new century.

You may also be interested in our Financial Literacy for Students series.

Offroad Algebra Lesson Plan PDFClick here for a printable PDF of explanations and answers for all 30 problems Offroad Algebra Lesson Plan PDFClick here for a printable PDF of correllating all 30 problems to NCTM Standards
PROBLEMS 1 through 10:
Problem 1: Conversion Between Gallons and Liters
Japanese motorcycles use the metric system, so they give fuel capacity in liters, rather than gallons. Given that for every 1 gallon there are 3.785 liters, figure out how many gallons an 8-liter tank can hold.

Problem 2: Miles per Gallon
Suppose you were on a 1,296 mile race with a tank that holds 2.1 gallons and can take you 100 miles. How many more refills of gas will you need to finish the race?
Problem 3: Gallons per Mile
Another way to think of gallons per mile is in reverse, as miles per gallon. Given a motorcycle that gets 45 miles per one gallon, what percentage of a gallon does it get per mile?
Problem 4: Velocity X Time = Distance, Part I
Given a motorcycle traveling at 20 meters per second for a minute, using the equation velocity * time = distance, figure out how far the motorcycle travels.
Problem 5: Velocity X Time = Distance, Part II
Given a motorcycle traveling a distance of 300 meters for 20 seconds, at what velocity does the motorcycle travel?
Problem 6:
Problem 7:Comparing Decibels
A decibel is a measure of sound intensity. 0 decibels (dB) is silence. 10 decibels is 10 times the intensity of 0 decibels, 20 decibels 10 times the intensity of 10 decibels, 30 decibels 10 times the intensity of 20 decibels, and so on. If Bike A registers at 72 dB and Bike B registers at 92 dB, how many more times powerful is the dB level of Bike B than Bike A?
Problem 8:
Problem 9:Slope of Ramps, Part I
The slope of a hill (or gradient) is expressed as a percent. For example, an 8% slope up means that, for every 100 feet, the hill goes up by 8 feet. Given that a certain part of the course has a 30% gradient and considering the bottom of the hill to be the origin, express the slope as a fraction in lowest terms and write it as the equation of the line.
Problem 10: Slope of Ramps, Part II
How high is a 30% slope that measures 2 feet horizontally?
PROBLEMS 11 through 20:
Problem 11:Playing Catch-Up, Part I

Rider A is trailing in 2nd place, 20 meters behind Rider B. Rider B is traveling at a velocity of 30 meters per second. Rider A increases to a velocity of 35 meters per second. How long will it take for Rider A to catch up to Rider B?

Problem 12: Playing Catch-Up, Part II
You are racing in the Baja 1000. You are nearing the end, but you have fallen behind the lead racer. The trophy truck is 4 miles away from you, and 5 miles away from the finish line. The lead racer is travelling at a speed of 30 miles per hour and you are traveling at a speed of 40 miles per hour. Will you be able to catch up to the truck before the other rider?
Problem 13: GPS Axis
GPS coordinates need two numbers. The first one gives North or South, and the second one East or West. It’s very similar to the algebra coordinate system: You need an x value (East or West) and a y value (North or South). So what’s the GPS equivalent of the x axis and the y axis?
Problem 14:GPS Conversion

GPS coordinates are given in a combination of degrees and minutes. A minute is 1/60 of a degree. The starting point for a race is 32°40′ N, 115°28′ W. How would you express these coordinates in decimal form?

Problem 15: GPS Distance
Suppose you are in a race that travels between 32º 40′ N, 115º 28′ W and 31° 47′ N, 116° 36′ W. Suppose that the race goes straight and assume that this particular place on Earth is at the one degree point = 66 miles. How far does the race go?
Problem 16: Mixing Gas and Oil
For our particular engine, oil is mixed with gasoline at a ratio of 1 part oil to 40 parts gas, or 1:40. Let’s say you have 5 liters pre-mixed you got from someone who uses a 1:30 mixture. How much gasoline should you add so the mixture is the optimal 1:40?
Problem 17:Margin of Victory

Rider A, Rider B, and Rider C finish the race in 124.2 seconds, 128.3 seconds, and 132.1 seconds respectively. Who beat the rider just behind them by the largest margin?

Problem 18: Lap Time Math
Rider A does a five-lap race and gets lap times of 98.7 seconds, 93.5 seconds, 91.5 seconds, 91.6 seconds, and 92.4 seconds. What’s the best lap time? What’s the average lap time? What’s the median lap time?
Problem 19: Track Turn Angles
Rider A does three 60º left turns and two 40º left turns on a track. If the last turn is also to the left and it brings Rider A back to the start, what angle does that turn have to be?
Problem 20:Number of Revolutions

Say your cycle has a tire with a two-foot diameter that’s in a race that goes for 5 laps at 300 feet a lap. How many revolutions does the tire make to get through the race?

PROBLEMS 21 through 30:
Problem 21: Inside and Outside a Wheel
Take your motorcycle with a tire with a two-foot diameter and mark a point on the outside, then mark a point one-half foot in towards the center. How much faster does the point on the outside move than the point on the inside?

Problem 22: Choosing Between Mean and Median
Because of weather conditions, a rider’s times on a track may not be as fast on one day as the next. Let’s suppose you took 5 different days of races, and wanted to compare the five days to find out when track conditions were best. Using statistics from the races, what’s the best method should of comparison? What other elements might factor in your comparison?
Problem 23:Cylinder Volume

Motocross divisions are often categorized by ‘cc’, meaning ‘cubic centimeters’ — referring to the size of the engines in volume. For example, there is a 250 cc division and a 500 cc division. Suppose the engines are shaped like boxes. What are the possible dimensions of a 250 cc engine? What about a 500 cc engine?

Problem 24: Comparing the Volume
Engine A is 125 cc, and Engine B is 250 cc. You would think that Engine B would be twice the size of Engine A, but if you look at the two engines, the size difference doesn’t seem that great. Why might that be?
Problem 25: Graphing the Ride
When we take something in real life and graph it, there are all sorts of elements that might represent the x and the y axes. For example, in motorcycle riding, we could talk about the horizontal distance the cycle has traveled versus the vertical distance. What other elements related to cycle riding might you graph?
Problem 26:Acceleration, Part I

Acceleration refers to how fast something is changing velocity. If a rider is accelerating at 2 feet per second per second, how far has the rider traveled after 10 seconds?

Problem 27: Acceleration, Part II
Let’s take that rider again who was accelerating at 2 feet per second per second. Considering the solution to problem number 26, show how to express the relationship of time, acceleration, and velocity in a single formula.

Problem 28:Acceleration, Part III

You’ve seen in the last problem that in addition to the equation time * velocity = distance, we know that time * time * acceleration = distance. Let’s go back to our motorcycle with a constant acceleration of 2 feet per second per second. If we graphed time against distance, what would that graph look like? Graph it.

Problem 29: Calculating With the Contact Patch
If you look at a real motorcycle, the tire isn’t perfectly circular; there’s a flat part on the bottom because of the weight. This part of the tire that touches the ground is called the “contact patch.” The contact patch helps determine the tire’s traction on the dirt course. If a contact patch is 6”x3”, the bike weight is 280 lbs. and the rider weight is 180 lbs., what tire pressure is optimum for getting the best contact patch?
Problem 30: Tire Aspect Ratio
Tires are labeled with numbers that refer to width, aspect ratio and rim diameter. The term “aspect ratio” represents the percentage difference between the height of the sidewall and the width of the tire. If a tire displays the numbers 120 (width)/90 (aspect ratio)-18 (rim diameter), what is the height of the sidewall?
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