What Would You Need to Know to Answer the Questions

Linear Functions.3Step Up

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LAUNCH

What would you need to know to answer the questions?

• How many steps would it take you to walk the length of a football field?

• How many minutes would it take you to walk the length of a football field?

How could you determine…

• your average walking rate in feet per second.

• your length in feet of your stride (distance between steps).

My Functions

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

A.CED I can create equations that describe numbers or relationships.

F-IFc I can analyze functions using different representations

F-LE I can construct and compare linear, quadratic and exponential models and solve problems.

F-BF I can build a function.

Find your quantities. Include units.

1. ______distance walked (I will determine the distance)
2. ______time it took you to walk that distance
3. ______number of steps taken when you walked that distance
4. Is your walking rate a linear function? How do you know?
5. Is your stride (the distance you walk) a linear function? How do you know?

Use your quantities and function notation to write functions

1. w(x) to determine how many steps would it take you to walk the length of a football field, and
2. s(x) to determine how many minutes would it take you to walk the length of a football field.

Define any variables you use and the corresponding measurement units.

Represent your both functions with a graph and a table.

1. walking rate

1. stride

1. You need to draw each of these graphs differently. Describe the difference.

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My Times & Distances

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

A.CED I can create equations that describe numbers or relationships.

A-REIc I can represent and solve equations graphically.

F-IFc I can analyze functions using different representations

F-LE I can construct and compare linear, quadratic and exponential models and solve problems.

F-BF I can build a function.

Write all of your answers in function notation.

Support your answer with at least 1 representation (equation, table, graph or diagram). You must use at least 2 representations in this set of questions.

1. Find the distance you can walk in 12 minutes.
2. Find the distance you can walk in 12 strides.
3. Find the time it would take you to walk 100 feet.
4. Find the number of strides it would take you to walk 100 feet.
5. Find the distance you can walk in 7.5 minutes.
6. Find the distance you can walk in 7.5 strides.
7. Pick a time and find your distance.
8. Pick a distance and find your time.

Exchange graphs your elbow partner.

1. How long will it take your partner to walk the length of a football field?
2. If your partner walked 1500 sets, what distance did they travel?
3. Identify the domain and range of each function you and one other group member.

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Pedometers

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

A-REIc I can represent and solve equations graphically.

F-IFb I can interpret functions that arise in applications in terms of the context.

We gave you a pedometer and asked you to record the time and total number of steps shown on the pedometer during the day.

1. Match the sections of Mrs. Schneider’s graph with her activities.

1. Find Mrs. Schneider’s fastest walking rate.
2. Find Mrs. Schneider’s slowest walking rate.
3. Find Mrs. Schneider’s average walking rate of the time recorded.
4. Could Mrs. Schneider have been sitting still during segment 4? Support your answer.

Here is Jared’s pedometer data.

1. Find Jared’s fastest walking rate.
2. Find Jared’s slowest walking rate.
3. Find Jared’s average walking rate of the time recorded.
4. Could Jared have been sitting still? Justify your claim.

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Compare Functions

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

A.CED I can create equations that describe numbers or relationships.

F-IFa I can understand the concept of a function and use function notation.

F-IFc I can analyze functions using different representations

F-LE I can construct and compare linear, quadratic and exponential models and solve problems.

F-BF I can build a function.

Support all of your answers using information from the equation and graph.

1. Who walks faster?
2. Who will be farther in 20 seconds?

1. How far apart are they in 2 minutes?

Support all of your answers using information from the equation and graph.

1. Who walks faster?
2. Who will be farther in 21 seconds?

1. How many minutes will it take Aryonna to walk the same distance Keith walked in 3 minutes?

Cecilia’s stride is 2.1 feet per step.

1. Write a function c(x) to find the number of steps Cecilia takes as a function of feet, x.

c(x) = ______

1. Use your equation to find:

1. Find c(8) =

1. Find c(150) =

1. Use your answer to “b” above to explain what c(150) = means.

1. Use your equation to solve for x.

1. c(x) = 21

1. c(x) = 105

1. c(x) = 262.5

1. Use your answer to “b” above to explain what c(x) = 105 means.

1. Write a function d(x) to find the distance (in feet) Cecilia has traveled as a function of the number of steps she had taken, x.

d(x) = ______

The function d(x) is the inverse function of c(x), because they undo each other. In other words, when d(a) = b, then c(b) = a.

1. Use d(x) to verify your answers to #10.
2. Is the function, d(x), linear?

Support your answer with words, numbers and/or diagrams.

1. Find the value of x where c(x) = d(x).

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Walking to School 1

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

F-IFa I can understand the concept of a function and use function notation.

F-IFb I can interpret functions that arise in applications in terms of the context.

F-IFc I can analyze functions using different representations

F-LE I can construct and compare linear, quadratic and exponential models and solve problems.

F-BF I can build a function.

Josh walks 0.5 miles to school each morning. His walking rate is 3.5 feet per second.

The function d(x) = 2640 – 210x can be used to determine the distance Josh has left to get to school as a function of minutes. We will assume that Josh walks at a constant rate.

1. Why is the constant 2640 in this equation?

1. Why is the rate 210 in the equation?

1. Monday morning, Josh walked to school.

Find the following of the function d(x):

1. Tuesday morning, Josh walked to school but his Dad drove him part of the way to school. His Dad dropped him off 1500 feet from home.

Find the following of the function f(x):

e)Write the equation of Josh’s walk to school on Tuesday f(x).

1. Wednesday morning, Josh walked to school but his Mom drove him the distance it would have taken him to walk in 5 minutes.

Find the following of the function g(x):

e) Write the equation of Josh’s walk to school on Wednesday g(x).

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Walking to School 2

Linear Functions Learning Targets

Practice 4. Model with mathematics.

Practice 8. Look for and express regularity in repeated reasoning.

A.CED I can create equations that describe numbers or relationships.

A-REIc I can represent and solve equations graphically.

F-IFa I can understand the concept of a function and use function notation.

F-IFb I can interpret functions that arise in applications in terms of the context.

Josh walks 0.5 miles to school each morning. His walking rate is 3.5 feet per second.

The function d(x) = 2640 – 210x can be used to determine the distance Josh has left to get to school as a function of minutes. We will assume that Josh walks at a constant rate.

1. Thursday morning, Josh woke up late. In order to make it to school on time, he walked to school at 1.5 times his normal walking rate.

Find the following of the function h(x):

e)Write the equation of Josh’s walk to school on Thursday h(x).

1. Friday morning, Josh walked with his friend Gabbi. She lives farther way than Josh, so she walked to his house. His mom dropped them off half way to school. They talked as they walked which slowed Josh down to half his normal walking rate.

Find the following of the function k(x):

e) Write the equation of Josh’s walk to school on Friday k(x).

Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 Page 1 of 12