Roller Coaster Math

Roller Coaster Math

Product Code: EK000103
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Description

Use math to design roller coasters

What does math have to do with thrilling roller coaster rides? How high does a coaster need to be to successfully navigate through a loop and on to the end of the track? How is the speed of the coaster related to the height of the coaster’s starting position? Explore all these questions with roller coaster math!

Curriculum topics: Velocity and speed, slope, rates, ratios, algebraic formulas, roller coasters

Kit includes: Idea Sheet, 1 6 ft pipe insulation, 1 stopwatch, 1 metric measuring tape, 1 marble, and 1 steel marble

Number served: 2 - 4 students

Grades: 6-12

Recommended for ages 11 and up.

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Standards: 

 

  • 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ""The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."" ""For every vote candidate A received, candidate C received nearly three votes.""

    (Common Core Mathematics /// Grade 6 /// Ratios And Proportional Relationships /// Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems)

  • 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b =? 0, and use rate language in the context of a ratio relationship. For example, ""This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar."" ""We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.""1

    (Common Core Mathematics /// Grade 6 /// Ratios And Proportional Relationships /// Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems)

  • 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

    (Common Core Mathematics /// Grade 6 /// Ratios And Proportional Relationships /// Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems)

  • 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers.

    (Common Core Mathematics /// Grade 6 /// Expressions And Equations /// Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions)

  • 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

    (Common Core Mathematics /// Grade 7 /// Ratios And Proportional Relationships /// Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems)

  • 7.RP.2. Recognize and represent proportional relationships between quantities.

    (Common Core Mathematics /// Grade 7 /// Ratios And Proportional Relationships /// Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems)

  • Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

    (Common Core Mathematics /// Grade 6 /// Mathematical Practices)

  • Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

    (Common Core Mathematics /// Grade 7 /// Mathematical Practices)

  • Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

    (Common Core Mathematics /// Grade 8 /// Mathematical Practices)

  • Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

    (Common Core Mathematics /// High School /// Mathematical Practices)

  • Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

    (Common Core Language Arts /// Grade 6 /// Language /// Vocabulary Acquisition and Use)

  • Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others' ideas and expressing their own clearly.

    (Common Core Language Arts /// Grade 6 /// Speaking & Listening /// Comprehension and Collaboration)

  • Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

    (Common Core Language Arts /// Grade 7 /// Language /// Vocabulary Acquisition and Use)

  • Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others' ideas and expressing their own clearly.

    (Common Core Language Arts /// Grade 7 /// Speaking & Listening /// Comprehension and Collaboration)

  • Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

    (Common Core Language Arts /// Grade 8 /// Language /// Vocabulary Acquisition and Use)

  • Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others' ideas and expressing their own clearly.

    (Common Core Language Arts /// Grade 8 /// Speaking & Listening /// Comprehension and Collaboration)

  • Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6-8 texts and topics.

    (Common Core Language Arts /// Grades 6-8 /// Reading Science/Technical /// Craft and Structure)

  • Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

    (Common Core Language Arts /// Grades 6-8 /// Reading Science/Technical /// Key Ideas and Details)

  • Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

    (Common Core Language Arts /// Grade 9-10 /// Language /// Vocabulary Acquisition and Use)

  • Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.

    (Common Core Language Arts /// Grade 9-10 /// Reading Science/Technical /// Craft and Structure)

  • Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

    (Common Core Language Arts /// Grade 9-10 /// Reading Science/Technical /// Key Ideas and Details)

  • Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9-10 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively.

    (Common Core Language Arts /// Grade 9-10 /// Speaking & Listening /// Comprehension and Collaboration)

  • Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

    (Common Core Language Arts /// Grade 11-12 /// Language /// Vocabulary Acquisition and Use)

  • Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics.

    (Common Core Language Arts /// Grade 11-12 /// Reading Science/Technical /// Craft and Structure)

  • Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.

    (Common Core Language Arts /// Grade 11-12 /// Reading Science/Technical /// Key Ideas and Details)

  • Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11-12 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively.

    (Common Core Language Arts /// Grade 11-12 /// Speaking & Listening /// Comprehension and Collaboration)

  • Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

    (Next Generation Science Standards /// High School /// Engineering Design)

  • Evaluate a solution to a complex real-world problem based on prioritized criteria & trade-offs that account for a range of constraints, including cost, safety, reliability, & aesthetics, as well as possible social, cultural, & environmental impacts.

    (Next Generation Science Standards /// High School /// Engineering Design)

  • Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people & the natural environment that may limit possible solutions.

    (Next Generation Science Standards /// Middle School /// Engineering Design)

  • Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

    (Next Generation Science Standards /// Middle School /// Engineering Design)

  • Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.

    (Next Generation Science Standards /// Middle School /// Engineering Design)

  • Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

    (Next Generation Science Standards /// Middle School /// Engineering Design)

  • Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, & its acceleration. [Objects subject to a net unbalanced force, e.g., an object falling , rolling down a ramp, or a moving- pulled by a constant force.]

    (Next Generation Science Standards /// High School /// Physical Science /// Motion and Stability: Forces and Interactions)

  • Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object & the mass of the object.

    (Next Generation Science Standards /// Middle School /// Physical Science /// Motion and Stability: Forces and Interactions )

  • Construct & present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects.

    (Next Generation Science Standards /// Middle School /// Physical Science /// Motion and Stability: Forces and Interactions )

  • Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. [Emphasis is on relative amounts of potential energy. Examples: the Earth & a roller coaster cart at varying positions on a hill, changing the direction/orientation of a magnet, & static electrical on a balloon.] [Assessment on two objects & electric, magnetic, & gravitational interactions.]

    (Next Generation Science Standards /// Middle School /// Physical Science /// Energy )

  • Construct, use, & present arguments to support the claim that when the motion energy of an object changes, energy is transferred to or from the object.

    (Next Generation Science Standards /// Middle School /// Physical Science /// Energy )

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