Speed of Light

Unit 3: Introduction to Functions

I Can…

● Identify linear functions using graphs and tables.

● Graph linear functions using data.

● Solve real-life problems using linear functions.

● Use slopes to solve real-life problems.

Mathematically proficient students map relationships between quantities using graphs and

analyze those relationships to mathematically draw conclusions.

Your Task

Have you ever wondered about the speed of light? What happens

when you turn on a light? Does it accelerate like a person riding a

bike or traveling in a car? When can motion be described by a

linear function and how can you graph that motion?

How will you be graded?

Your grading rubric is here.

K&T: 30 points

Written Communication: 10 points

Agency: 10 points

Collaboration: 20 points

https://www.google.com/url?q=https://docs.google.com/document/d/1_Cl2AGsyD3KHs9NthJ4NpSuxaMuqBknqzBtZvqiPLU4/edit?usp%3Dsharing&sa=D&source=editors&ust=1616469772333000&usg=AOvVaw1pso8Z0TkZ-DMH-w1qBoIQ

The table shows the speed s in feet per second of a bicyclist t seconds after

the beginning of a race

Using this website, plot the

ordered pairs. Then, take a

snipping of your graph and

paste it in the red box to the

right.

Use this video to help you.

Paste your graph here.

https://www.google.com/url?q=https://www.desmos.com/calculator/mhq4hsncnh&sa=D&source=editors&ust=1616469772440000&usg=AOvVaw01ZwEHruU5P4yu7FS36lGP

https://www.google.com/url?q=https://drive.google.com/file/d/1ALnFFjiC3NT8UwUEp8Y4-8xIlseD1bFQ/view&sa=D&source=editors&ust=1616469772441000&usg=AOvVaw3-x3aAGE2MsahUiYp27uno

Using the information from the graph on slide 6, answer the questions below.

Is the data linear?

What is the slope?

What does the shape of the graph tell you about the acceleration of the bicyclist?

Explain.

Unlike a moving bicycle, light photons travel at a constant speed. The speed of

light is about 299,792,458 meters per second. Use the speed of light to

complete the table. Round your answers to the nearest kilometer.

Time, t (in seconds) Distance, d (km)

1

2

3

4

5

Plot the points from the previous slide using the same website as before.

Then, answer the questions.

Paste your graph here. Is the data linear?

How does the graph show the constant speed? (look at the

slope)

What does the graph representing speed in terms of time

look like? Explain.

https://www.google.com/url?q=https://www.desmos.com/calculator/mhq4hsncnh&sa=D&source=editors&ust=1616469772474000&usg=AOvVaw08bvaEtAqr4dyeGTPLpukk

Write a function that represents the distance d (in kilometers) light travels after t seconds.

Given that the average distance from Earth to the sun is about 150 million kilometers, how long would it take

a photon of light to travel from the sun to Earth? Round your answer to the nearest tenth of a minute.

Future Wind Power

Unit 3: Introduction to Functions

I Can…

● Convert between different units of electrical power.

● Write an equation of a line given two points on the line.

● Write equations in slope-intercept form.

● Use linear equations to solve real-life problems.

Mathematically proficient students are careful about specifying units of measure. They

calculate accurately and efficiently when converting between different units of electrical

power.

Your Task

Have you ever wondered how much of the energy you use comes

from wind power? Can the growth of the number of wind farms in

the United States be modeled by a linear function? Can you

determine how much wind power will be needed in the future?

How will you be graded?

Your grading rubric is here.

K&T: 30 points

Written Communication: 10 points

Agency: 10 points

Collaboration: 20 points

https://www.google.com/url?q=https://docs.google.com/document/d/1_Cl2AGsyD3KHs9NthJ4NpSuxaMuqBknqzBtZvqiPLU4/edit?usp%3Dsharing&sa=D&source=editors&ust=1616469545636000&usg=AOvVaw2UvHp_KWH89LawoWwRT9dA

In 2012, the United States generated approximately 3.5% of its electricity from

wind power. Approximately 4 trillion kilowatt hours (kWh) of electricity was used.

a. A terawatt hour (TWh) is equal to 1,000,000,000 kilowatt hours. How many terawatt hours is equal to

4 trillion kilowatt hours?

b. How much of the electricity in 2012 came from wind power? Write your answer in terawatt hours.

c. You will be writing an equation which represents wind farm growth since 2012. What ordered pair can

you use as your initial value?

One goal for the United States is to be able to generate 20% of its electricity by the year 2030 using

wind power. If the country used the same amount of electricity in 2030 as it did in 2012, how much

of the electricity (in terawatt hours) would be generated by wind power?

What ordered pair can you use to represent this value?

Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind

power would need to grow to make this goal. Use years for the independent variable and terawatt

hours for the dependent variable. Let year 0 represent year 2012.

a. Write your equation in slope-intercept form.

b. Explain what the slope and y-intercept represent in this situation.

Plot the points from the previous slide using the same website from the last

task.

Paste your graph here. If an average wind farm produces a quarter of a

terawatt hour of energy per year, approximately

how many wind farms would be needed each

year to meet the growth from your equation?

Explain your reasoning

https://www.google.com/url?q=https://www.desmos.com/calculator/mhq4hsncnh&sa=D&source=editors&ust=1616469545653000&usg=AOvVaw2i935_wPnQyRyvIqsUj7gj

Problem/Content Specific Indicators

Scoring Domain

Emerging

E/D

Developing

D/P

Proficient

P/A

Advanced

Math: Knowledge and Thinking

Scoring Domain

Emerging

E/D

Developing

D/P

Proficient

P/A

Advanced

Problem Solving

· Does not provide a model

· Ignores given constraints

· Uses few, if any, problem solving strategies and tools

· Creates a limited model to simplify a complicated situation

· Attends to some of the given constraints

· Uses inappropriate or inefficient problem solving strategies and tools

· Creates a model to simplify a complicated situation

· Analyzes all given constraints, goals and definitions

· Uses appropriate problem solving strategies and tools

· Creates a model to simplify a complicated situation and identifies limitations of model

· Analyzes all given constraints, goals and definitions and implied assumptions

· Uses novel problem solving strategies and tools and/or extends previous knowledge correctly to a given problem

Reasoning and Proof

· Provides partially correct or incorrect solutions without justifications

· Results are not interpreted in terms of context

· Provides partially correct solutions with justification or correct solutions without logic or justification

· Results are interpreted partially or incorrectly in terms of context

· Constructs logical, correct, complete solution with justifications

· Results are interpreted correctly in terms of context, including addressing reasonableness of final answer

· Constructs logical, correct, complete solution with justifications and identifies any sources of error.

· Results are interpreted correctly in terms of context, including addressing reasonableness of final answer, and makes connections to similar math content in different contexts

Written Communication

Scoring Domain

Emerging

E/D

Developing

D/P

Proficient

P/A

Advanced

Development

· Ideas and evidence are underdeveloped

· Ideas and evidence are somewhat developed

· Ideas and evidence are mostly developed

· Ideas and evidence are developed

Organization

· Ideas and evidence are disorganized, making relationships unclear

· No transitions are used, or are used ineffectively

· Ideas and evidence are loosely sequenced or organization may be formulaic

· Transitions connect ideas with some lapses; may be repetitive or formulaic

· Ideas and evidence are sequenced to show relationships

· Transitions connect ideas

· Ideas and evidence are logically sequenced to show clear relationships

· Transitions are varied and connect ideas, showing clear relationships

Agency

Scoring Domain

Emerging

E/D

Developing

D/P

Proficient

P/A

Advanced

Tackle and Monitor Learning

· For a task or project, superficially identifies what is known, what needs to be learned, and how hard it will be

·

· For a task or project, identifies what is known, what needs to be learned, and how hard it will be; but may not use a strategy to tackle the task or does not monitor how well the strategy is working

·

· For a task or project identifies what is known, what needs to be learned, and how hard it will be; uses a strategy and steps to tackle the task; and monitors how well the approach and effort are working

·

· For a task or project, identifies what is known, what needs to be learned, and how hard it will be; selects an appropriate strategy and takes steps to tackle the task; and monitors and adjusts based on how well the approach and effort are working

Collaboration

Scoring Domain

Emerging

E/D

Developing

D/P

Proficient

P/A

Advanced

Contribution and Development of Ideas

Ideas lack supporting reasoning

Limited acknowledgement of others’ thinking

Shares ideas, and explains the reasons behind them

Acknowledges others’ thinking

Provides ideas or arguments with convincing reasons

Builds on the thinking of others

Acknowledges the strengths and limitations of their ideas

Builds on the thinking of others and checks back for agreement

Roles

Knows role, and fulfills it only some of the time

Accepts role and shows understanding by fulfilling it

Knows the roles of self and others, and uses the roles to maximize group effectiveness

In addition to proficient, uses group roles as opportunities to use strengths or address areas of weakness

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