SCORE Mathematics

Standards Connections

Coaster Connections

By: Matt Gehrett and Leon Ryder

Introduction:

What science and math exists in a roller coaster?
Below, you will enter the world of roller coasters via hands-on activities, Internet information, online experts, and computer simulations.

Prior Knowledge:

You need to have an interest in roller coasters.
You need math skills such as solving proportions and trigonometric functions.
Physics topics such as velocity, momentum, and potential energy will be used.

Grade Level: 9-12

Tasks:

You will collect data from the Internet and make mathematical and scientific calculations.
You will learn about the history of roller coasters.
You will talk to online experts who design roller coasters.
You will build your own roller coaster and make calculations and compare it to the real coasters.

Resources: Click here to make a Coaster Connection!

Processes:

Gather information from the Internet about roller coasters.
Make calculations.
Correspond with online designers of roller coasters.
Create a roller coaster using simulation software.

Learning Advice: See above web pages.

Evaluation: See above web pages.

Extensions:

Take a trip to your local amusement park.
Collect data and repeat calculations with "real" roller coasters.
Interview online experts to create traditional reports or online reports.

Conclusion:

What factors contribute to successful design of a roller coaster? What is your criteria for deciding on the "best" roller coaster?

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California Mathematics Academic Standards:

Grade 3:
Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions
2.3 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning

Grade 4:
Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions.

2.3 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning

Grade 5:
Mathematical Reasoning
2.0 Students use strategies, skills and concepts in finding solutions.

2.3 use a variety of methods such, as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning

Grade 6:
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.

1.2 interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b)

Algebra and Functions
2.0 Students analyze and use tables, graphs and rules to solve problems involving rates and proportions.

2.3 solve problems involving rates, average speed, distance, and time

Mathematical Reasoning
2.0 Students use strategies, skills and concepts in finding solutions.

2.4 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning

Grade 7:
Algebra and Functions
4.0 Students solve simple linear equations and inequalities over the rational numbers.

4.2 solve multi-step problems involving rate, average speed, distance, and time or a direct variation

Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.

1.3 use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer

Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions.

2.5 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning
2.6 express the solution clearly and logically by using appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work

Grade 8-12:
Algebra I
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions

NCTM 9-12:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 4: MATHEMATICAL POWER
STANDARD 5: PROBLEM SOLVING
STANDARD 6: FUNCTIONS
STANDARD 8: MATHEMATICAL CONCEPTS
STANDARD 9: TRIGONOMETRY