Copy of Participant Workbook.pdf

Analyzing High School Functions with Real-World

Mathematics

ParticipantWorkbook

Session 1: The Concept of a Function 2 | P a g e

Session 1 - The Concept of a Function

Goals for Session 1:

• Define a function• Understand that functions can show relationships

between varying quantities• Identify situations that represent a function• Understanding Domain and Range• Examine common misconceptions of students’ thinking

about functions


In what mathematical fields, careers, or real-life events is the concept of a function useful?


Function Wall

Where do you stand?

1. Time of travel to the workshop?a) If it took you, 0 ≤ x <30 minutes, stand under A.b) If it took you, 30 ≤ x <60 minutes, stand under B.c) If it took you, 60 ≤ x <90 minutes, stand under C.d) If it took you, x ≥ 90 minutes, stand under D.

2. Clothinga) If you’re wearing blue, stand under A.b) If you’re wearing red, stand under B.c) If you’re wearing black, stand under C.d) If you’re wearing white, stand under D.

3. Birthdaya) If you were born in January, stand under A.b) If you were born in February, stand under B.c) If you were born in March, stand under C.d) If you were born in April, stand under D.


Is the caterpillar’s location a function of time?


Function Finder

Goal Understand the definition of a function.

Question Which of these relationships are functions? Decide whether each of the relationships below is a function. If it isn’t a function, demonstrate how it fails to satisfy the definition of a function by showing elements of each set that do not “work.” If it is a function, explain why, and also show several elements of each set.

Session 2: Covariance 7 | P a g e

Session 2 - Covariance

Goals for Session 2: ● Identify the covariance of two variables.● Understand a rate of change describes the

covariance between two variables.● Use the rate of change to identify what type of

function can model a real-world phenomenon.


What is covariation and rate of change?

Try to identify Derek’s and Marta’s current understanding of covariation.

During an afternoon break in the car wash, Derek and Marta are looking at their supplies, trying to figure out whether they will last all day. Through-out the day, Marta has filled in a chart of the number of bottles of soap that their volunteers have used (see fig. 2.1)

“Well, we were certainly consistent.” Derek observes. “If we keep going like this, we are going to have more than enough bottles to finish the car wash,” said Marta. “How do you figure?” “We are using five bottles every time you check. We have way more than five bottles left.” As Derek and Marta start to pack up and return to the car wash, Mr. Ramirez comes up beside them and looks at Marta’s chart. “You guys may be in more trouble than you think,” he says. Seeing their blank looks, he continues, “I think you are misunderstanding something called covariation here.”


Reflect ● What do you think Derek and Marta are missing in the covariance relationship

represented in Marta’s chart?

● What questions would you ask them if you were their teachers?

● How would you assess their understanding of the relationship between time andthe number of bottles of soap used?


Supporting Local and Global Perspectives on Covariation

• How would you describe the covariance of the two variables “day” and “depthof lake” in the Lake Depth example, shown in figure 2.4?

• Does this graph give any additional insight? Compare the two graphs.


Local or Global Perspective?

1. In the table of data on the water depth (fig. 2.4), what does the gap in days meanabout the measurement process?

2. In the graph (fig. 2.6), what is the rate of change for each of the lines?

3. What could explain the consistent depth measures in the lake depth dataconsidering the gap in those measures? (What happened to the lake?)

4. How does the gap in days in the table of data affect the covariance between theday and the lake depth?

5. Describe the meaning of the dashed line in the graph (fig. 2.6).

6. How does the overall average rate of change in lake depth compare to theaverage rate of change of the dashed line?

7. How would you describe the change in lake depth over time?

8. If the rate of change in lake depth remained constant (increase indepth per day), what depth would the park ranger have measured at time 3? At times 4 and 5?


Expert

Horsing Around Before the Derby

Blazing Bill, the horse is at the end of a line of 50 horses waiting to be shod before the derby. But being an impatient sort of a horse, Blazing Bill moves up the line two places every time the farrier takes a horse from the front to be shod. So, for example, while the first horse is being shod, Blazing Bill moves ahead so that there are two horses behind him in line. If at some point it is possible for Blazing Bill to move only one place, he does that instead of moving ahead two places.

How many horses get shod before Blazing Bill?


Apprentice

Horsing Around before the DerbyBlazing Bill, the horse is at the end of a line of 50 horses waiting to be shod before the derby. But being an impatient sort of a horse, Blazing Bill moves up the line two places every time the farrier takes a horse from the front to be shod. So, for example, while the first horse is being shod, Blazing Bill moves ahead so that there are two horses behind him in line. If at some point it is possible for Blazing Bill to move only one place, he does that instead of moving ahead two places.

How many horses get shod before Blazing Bill?

1. Predict a solution “in your head.”2. Use manipulatives or anything else to solve these two problems:

Number in front of Blazing Bill 6 11

Number shorn before Blazing Bill

3. What pattern did you notice that could help you solve the original problemin which Blazing Bill is at the end of a line of 50 horses?

4. Explore other numbers and put the results into the table.


Number in front of Blazing Bill

Number shod before Blazing Bill

5. Describe how you could work out the answer for any number of horses.

6. Work out the solutions for the boxes left blank.

Number in front of Blazing Bill

Number shod before Blazing Bill

7. Bill gets more and more impatient! Explore how your rule changes ifBlazing Bill sneaks past 3 at a time, 4 at a time, or even 10 at a time. Assoon as someone tells you how many horses are in front of Blazing Bill andhow many he sneaks past at a time, describe how you could work out theanswer.


Falling Object Consider how students might explore the case of an object that starts falling at a height of 400 feet—a scenario that is modeled by the function graphed in figure 2.12.

1. What are reasonable values for the domain and range of this function, and why?

2. What does the value 32 represent in the equation of the function?

3. What is the direction of the object? How is this shown in the graph?

4. What is the distance that the object has fallen in 1 second? In 2 seconds?


5. How long does the object take to hit the ground?

6. What does the shape of the graph indicate about the rate of fail?

7. What does the slope mean at when time equals 2 seconds? What will it be when

time equals 3 seconds? What will it be at when time equals 5 seconds?

8. In the graph of distance fallen as a function of time, can you find a pattern in the

instantaneous slope and the time?

9. What does a slope of zero mean in this situation?

10. What is the maximum rate of change?

11. What does the slope mean in terms of the story?

12. If the object started at 500 feet, how would the graph change?

Session 3: Transformations of Functions 18 | P a g e

Session 3 - Transformations of Functions

Goals for Session 3:

● Operations of functions.● Explore the relationships between families of functions● Extend the understanding of composing functions● Build new functions from existing functions by identifying

the shifts and scale changes in the formula or the graph


Extending the car-wash scenario can provide an opportunity for students to add functions while giving specials attention to domain and range. The expanded scenario includes a new development: Derek and Marta are now working to advertise the event:

Derek and Marta are creating posters to advertise their service club’s car wash. Derek is able to make 2 posters per hour, but in the first hour he gathers his supplies and sets up a workspace and then completes just 1 poster and ½ another. Marta can make posters at a rate of 3 posters per hour, but in the first hour she is also gets everything set and then completes just 2 posters and ⅔ of another.

● Write a function that models the number of posters that each student makes per hour,where x represents the number of hours.

● Combine the functions to get an overall rate of poster making.

● Graph f(x), g(x), and f(x) + g(x), and describe how the three functions are thesame and different.


Guiding Questions 1. What is the meaning of the slope of f(x), g(x), and f(x) + g(x) in terms of the graph and

the story?

2. What does the intercept tell you about the making of posters?

3. How would f(x) change if Derek had to discard one poster each hour?


More questions:

1. What is the domain of f(x), g(x), and f(x) + g(x)? How do you know?

2. What would be the meaning of an x-value greater than 60 for f(x), g(x), and f(x) + g(x)?

3. Compare the ranges of f(x), g(x), and f(x) + g(x) and explain your thinking.

4. How is the range of f(x) + g(x) related to those of f(x) and g(x)?

Reflect

● How would you expect your students to respond to the guiding questions in the twopreceding groups, and how would you explain the answers to your students?


Family of functions

For each of the following functions, decide which major family of functions to which the relationship belongs? How do you decide?

a) The function that associates to the input x the output y given byy = 5x2 + 3.

b) The 2010 Census shows that Smallville has a population of 40,000 people. Socialscientists predict that Smallville will experience a growth rate of 5% per year over thenext 20 years. Let P be the function such that P(t) is the predicted population ofSmallville t years from now (for t between 0 and 20)

c) A movie theater has operating cost of $1025 per day. Tickets cost $7.50 each. Thetheater’s profit each day depends on the number of tickets sold. Let P be the functionsuch that P(t) is the profit that the movie theater will make on a day when it sells ttickets.

d) The function whose input-output table is shown below:


e) The function whose graph is shown below:

f) Fred is deciding which size of pizza is the best buy. He wonders how the area of thepizza is related to its diameter. Let A be the function such that A(r) is the area of acircular pizza of radius r.


Parent Function Name:

Equation:

Domain:

Range:

Continuity:

Symmetry:

Decreasing interval:

Increasing Interval:

Boundedness:

Extrema:

Horizontal asymptote:

End Behavior:


Functions Photo Album –Technology Required During high school, you have learned about several parent functions. For this project, you will create a photo album that displays 12 function families. Below is a list of requirements for the photo album.

I. Title page 1. Your name2. Title of the photo album

II. Parent Function Photo and Details1. There should be one page for each parent function: identity, absolute value, squaring,

cubing, reciprocal, square root, exponential, natural logarithm, sine, cosine, greatestinteger, and logistic.

2. Complete an analysis of each parent function. The analysis should include the followingdetails: parent function equation, parent function graph, domain, range, continuity,symmetry, decreasing interval, increasing interval, boundedness, extrema, horizontalasymptote, vertical asymptote, and end behavior.

3. Include a digital photograph that resembles the graph of each parent function.A. Each photo should be your photo. In other words, you are the photographer.

Exception: You will be allowed to upload one photo from the internet. If you choose to do so, be sure to cite the source correctly and include necessary information on the reference page.

B. Do not use people in your photo. C. Do not take an object and form the graph. For example, do not utilize your cell phone

charger to make a cubic function. 4. Each page should include an example of how the function is utilized in the real world and

a real world math problem. Note: DO NOT SOLVE THE PROBLEM! CITE YOUR SOURCES. 5. Utilize GeoGebra to insert each picture onto a coordinate plane. Utilize the instructions

below. A. Download the program form https://www.geogebra.org/. B. After downloading GeoGebra, Open the program. C. Click “View” and select “Algebra”. This will turn the Algebra View off.

https://www.geogebra.org/


D. Show the grid.

E. To insert the image, click “Edit”, select “Insert Image From”, and select “File”.

F. After inserting the photograph, manipulate the photograph to the desired position on the grid.

G. Next, insert broader axes onto the photograph. Click on the “Line” tool and select two points on the vertical axis. Then follow the cues below to make each axis broader.


H. Insert the image into your Power Point presentation by pressing Ctrl + Shift + C or by selecting “Edit” and “Graphics View to Clipboard”.

Paste the graphic to your presentation. III. Glossary

Include the definition of each of the following terms. Be sure to cite your sources.1. Asymptotes2. Continuity3. Dilation4. Domain5. End Behavior

6. Extrema7. Horizontal Translation8. Nonridged Transformation9. Range10. Reflections

11. Rigid Transformation12. Symmetry13. Transformation14. Translation15. Vertical Translation

IV. Reference PageUtilize APA format to cite your sources.


Functions Photo Album During high school, you have learned about several parent functions. For this project, you will create a photo album that displays 12 function families. Below is a list of requirements for the photo album.

I. Title page 1. Your name2. Title of the photo album

II. Parent Function Photo and Details1. There should be one page for each parent function: identity, absolute value, squaring,

cubing, reciprocal, square root, exponential, natural logarithm, sine, cosine, greatestinteger, and logistic.

2. Complete an analysis of each parent function. The analysis should include the followingdetails: parent function equation, parent function graph, domain, range, continuity,symmetry, decreasing interval, increasing interval, boundedness, extrema, horizontalasymptote, vertical asymptote, and end behavior. You may not use a parent functiongraph from the Internet. You must graph the function on graph paper.

3. Include a picture that resembles the graph of each parent function. You may usemagazines, newspapers, brochures, flyers, or any other printed text. You may not printpictures from the Internet.

4. Each page should include an example of how the function is utilized in the real world anda real world math problem. Note: DO NOT SOLVE THE PROBLEM! CITE YOUR SOURCES.

III. GlossaryInclude the definition of each of the following terms. Be sure to cite your sources.1. Asymptotes2. Continuity3. Dilation4. Domain5. End Behavior

6. Extrema7. Horizontal Translation8. Nonridged Transformation9. Range10. Reflections

11. Rigid Transformation12. Symmetry13. Transformation14. Translation15. Vertical Translation

IV. Reference PageUtilize APA format to cite your sources.


Car-wash Coupons and Discounts

Read the vignette, “Extending Understanding: Car-wash coupons and discounts”. Page 69-70 in Putting Essential Understanding of Functions into Practice.

Let x = the original price of the car-wash. a. Let f(x) = the price after the discount. Write a function to represent each of the

time periods.

b. Write the function where g(x) is the price with the $2.00 coupon.


Car –Wash Coupons and discounts

Find the equations that represents f◦g and the g◦f for each time period.

x = original price of the car-wash f(x) = price after discount g(x) = price with $2.00 coupon

1. What property is used to simplify 0.85(x – 2)?

2. In the function, f(g(x)) = 0.85x – 1.70, what does 1.70 mean in the context? Whatdoes the 0.85 mean? How does this apply to other functions in the list?

3. How would the composite function represent a customer without a coupon?

4. How would the function change if coupons were worth $2.50?

Time Discount f(x) g(x) f(g(x)) g(f(x))

8:00 a.m. – 10:00 a.m.

15% f(x) =0.85x g(x) = x - 2 f(g(x)) = 0.85x –1.70

g(f(x)) = 0.85x - 2

10:00 a.m.– Noon

5% f(x) =0.95x g(x) = x - 2

Noon – 2:00 p.m.

0% f(x) = x g(x) = x - 2

2:00 p.m. – 4:00 p.m.

0% f(x) = x g(x) = x - 2

4:00 p.m. – 6:00 p.m.

10% f(x) =0.90x g(x) = x - 2

6:00 p.m. – 8:00 p.m.

20% f(x) =0.80x g(x) = x - 2


The price of the car-wash is $12.00 per car. Find the f◦g and the g◦f for each time period.

Time of day Discount f(g(x)) g(f(x))

8:00 a.m. - 10:00 a.m. 0.85

10:00 a.m. - noon 0.95

Noon - 2:00 p.m. 1

2:00 p.m. - 4:00 p.m. 1

4:00 p.m. - 6:00 p.m. 0.9

6:00 p.m. - 8:00 p.m. 0.8

Which composition should be used and why?


Painting the Mascot Students at Grover Cleveland High School are proud of the painting of their mascot over the entry door. This small image is 56 centimeters high and located just below the school’s name. The club has proposed that a large mural 2.8 meters high be painted in the main hallway just outside the school cafeteria. The art club has offered to create the mural.

How much paint will be needed in all? How much of each color?

Paint used in the original image. Color Amount (ml)

White (as shown in figure 3.11) 4.7

Orange (richest shade in the figure) 2.3

Yellow ( for tiger’s eyes; light shade in the figure)

2.5

Black ( as shown in the figure) 2.5 Red (for tiger’s tongue, gums, nose; medium

shade in the figure) 0.7

Ivory ( for tiger’s teeth; palest shade in the figure

0.3

Total 13.0 A table showing the milliliters of paint used for the small image of the school mascot.


Student Results Last week, students in another school worked on the same problem and got the following mixed

results.

Responses from students at another school

Total Paint Percentage of students

65 ml 43%

325 ml 43%

Other 14%

Reponses of fictitious students at another school to the problem about the total amount of paint needed for the enlargement image.

a) How did one group of student at that school have arrived at 325 milliliters as the totalamount of paint needed?

b) One student said that if the height is multiplied by 5, the width must be multiplied by 5,so the amount of paint must be multiplied by 25. Do you agree? Why or why not?

c) Draw a rectangle around each of the two tiger figures.• How would you determine the area of the two rectangle?• How much larger is the large rectangle than the small one?• How much larger is the area of the large tiger than the small one?• How much more paint will you need to paint the large tiger than the small one?

d) Create a function that will yield the amount of paint needed for the large image.

e) How would the functions change if the size of the larger mural were 3.08 meters? 2.24meters?

f) How are the graphs of these three functions (for the amounts of paint for images of 2.8,3.08, and 2.24 meters) the same? How are they different?


Transformation Activity

https://goo.gl/PgdgY0

This activity is an exploration of transformations of functions. By manipulating parameters a, h, and k, the effect of the variables on a parent graph can be analyzed.

1. Which family does the graph you are analyzing belong too?

2. What is the parent function?

3. Describe the effect that k has on the graph.

4. Describe the effect that h has on the graph.

5. Describe the effect that a has on the graph.

6. If a is greater than 1, describe the effect that a has on graph.

https://goo.gl/PgdgY0


7. If a is between 0 and 1, describe the effect that a has on the graph.

8. If a = -1, describe the effect that a has on the graph.

9. Describe the transformation if a = 1, h = -3, and k = -4?

10. Describe the transformation if a = -1, h = 0, and k = 5?

11. Describe the transformation if a = 0.5, h = 4, and k = 2.5?

12. What would make the function a horizontal line?


Water’s Surface Area on the End of a Trough

A water trough has a base of 10 inches and a height of 10 inches. Both the front and the back side of the trough form a 135-degree angle at the base of the trough. Water is filling the trough at a constant rate and has reached a height of 4 inches and a width of 18 inches across the end of the trough.

A water trough with an isosceles trapezoidal cross section.

Problem a) What is the function that shows the surface area of the water on the end of the

trough in terms of the height of the water, given a height of 10 inches and a base width of 10 inches?

b) What is the function that shows the surface area of the water on the end of thetrough, given a height of 10 inches, if the base width is 6 inches? If the basewidth is 0 inches?


Refer to the graphs showing surface area of the water on the end of a trough as a function of the water’s height, h, for changing sizes of trough bases.

Questions

1. What do the three functions that you found in (a) and (b) describe together?

2. How does changing the width of the base of the trough change the function?

3. What happens at h = 0?


4. What is the value for each of the functions at h = 1? What does this mean interms of water in the trough?

5. What is changing in the functions? What stays the same? Describe whatchanges and what stays the same in terms of the water in the trough and interms of the graph.

6. How would the function change if both sides of the trough were changed?

7. What are the limits of the domain and range for these functions?


Transformation Card Sort

A1

𝑓𝑓(𝑥𝑥) = −𝑥𝑥2 + 2

A2

𝑓𝑓(𝑥𝑥) = (𝑥𝑥 − 1)2 + 1

A3

𝑓𝑓(𝑥𝑥) = −2(𝑥𝑥 + 1)2

A4

𝑓𝑓(𝑥𝑥) =12 (𝑥𝑥 − 3)2 − 4

A5

𝑓𝑓(𝑥𝑥) = − √𝑥𝑥 + 1

A6

𝑓𝑓(𝑥𝑥) = √−𝑥𝑥 − 2 + 3

A7

𝑓𝑓(𝑥𝑥) = 2√𝑥𝑥 + 3

A8

𝑓𝑓(𝑥𝑥) = − √2𝑥𝑥 − 1 + 2

A9

𝑓𝑓(𝑥𝑥) = −3𝑥𝑥3 + 2

A10

𝑓𝑓(𝑥𝑥) = (𝑥𝑥 − 2)3 + 3

A11

𝑓𝑓(𝑥𝑥) = 0.5(𝑥𝑥 − 4)3 − 2

A12

𝑓𝑓(𝑥𝑥) = (−𝑥𝑥 − 1)3

A13

𝑓𝑓(𝑥𝑥) = √𝑥𝑥

A14

𝑓𝑓(𝑥𝑥) = 𝑥𝑥3A15

𝑓𝑓(𝑥𝑥) = 𝑥𝑥2


B 1 B2 B3

B4 B5 B6


B7 B8 B9

B10 B11 B12


B13 B14 B15


C1

• Horizontal Shift: Right 3 unit• Vertical Shift: Down 4 units• Vertical Compression: 1

2

C2

• Horizontal Shift: Left 1 unit• Reflection across the x-axis

C3

• Vertical Shift: Up 2 units• Reflection across the x-axis• Vertical Stretch: 3

C4

• Horizontal Shift: Left 3 units• Vertical Stretch: 2

C5

• Vertical Shift: Up 2 units• Reflection across the x-axis

C6

• Horizontal Shift: Right 4 units• Vertical Shift: Down 2 units• Vertical Compression: 0.5

C7

• Horizontal Shift: Right 2 units• Vertical Shift: Up 3 units

C8

• Horizontal Shift: Left 1 unit• Reflection across the y-axis

C9

• Vertical Stretch: 2• Horizontal Shift: Left 1 unit• Reflection across the x-axis

C10

• Horizontal Shift: Right 1 unit• Vertical Shift: Up 1 unit

C11

• Horizontal Shift: Left 2 units• Vertical Shift: Up 3 units• Reflection across the y-axis

C12

• Horizontal Shift: Right 12 unit

• Vertical Shift: Up 2 units• Reflection across the x-axis

Session 4: Graphs as Representations of Functions 44 | P a g e

Session 4- Graphs as Representations of Functions

Goals for Session 4: • Explore graphs that represent functions that

model various relationships• Address common misconceptions that students

have about graphs• Stress the importance that interpretations of

graphs fall into two concise types- qualitative(global) and quantitative (local)


Handout 4.1

What would you say to Marta if you were Mr. Ramirez?

How would you help her understand the situation?


Velocity of One Car

What do the two line segments in the graph indicate? Compare the velocity represented by the oblique (slanted) segments with the velocity represented by the horizontal segment.

People may misinterpret the meaning of the straight line segments in the graph. Do these straight segments indicate no change? How does the oblique segment differ from the horizontal segment in meaning? What would the car have to do for these lines to be more “wavy”?

How would you compare the car’s action at t = 0 and its action at t = 3? What does it mean that the graph starts at a velocity of 10 miles per hour? Can a car be going 10 miles per hour at time t = 0? What can you say about the velocity of the car at t = 6?

What happens at t = 2? Does the car stop? Write a short story (just a few lines) describing what it would be like if you were in the car represented by this graph.


Comparing Two Cars, Given Distance

Describe what is happening at t = 2. Which car is going faster? How can you tell? Which car has gone farther? How far apart are the two cars?

Are the cars ever moving at the same speed? At what time? Explain how the graph represents this event.

Describe the location of the cars at t = 0. What can be said about the speeds of the cars at this time?

Does one car ever pass the other? At what time?

Do the two cars ever travel the same distance? At what time?


Comparing Two Cars, Given Speed

Which car is traveling faster at t = 0.75 hours?

Describe what happens at t = 1.

Describe the relationship between the cars at t = 0.25 (¼ hr).

Which car travels farther?

What is the closest that the cars come to each other?


Two Walkers ActivityAmanda and Joe are standing next to each other and start walking at the same time, along parallel lines. Amanda starts by taking big steps, and each step grows smaller as she walks. Joe starts with small steps, and each step gets larger as he walks. The table in figure 1 shows Amanda’s and Joe’s steps and step sizes. Describe Amanda’s and Joe’s trips. Step size (ft.) S

Questions 1. What do Amanda’s and Joe’s trips look like?

2. What happens at the fifth step, s = 5?

3. What happens to Joe at s = 1?

4. Who travels farther?

5. Who is ahead at s = 7?

6. At what time have Amanda and Joe traveled the same distance? Does Joe ever catchAmanda?


Graphing Stories

Task

In this activity we will investigate the relationship between different quantities that are shown in

a series of 10 video clips. Each clip includes a real time part, half speed playback, and a

possible solution. (This allows students to make an initial sketch, adjust their sketch, and

validate their results.)

For each video clip, watch the first part showing the situation in real time and then stop. At that

point, sketch a graph of the relationship demonstrated on the set of graphs provided. In each

graph pay special attention to key features such as increasing and decreasing intervals,

maximums and minimums, intercepts, and constant and variable rates of change.

After drawing the initial sketch, watch the second part of the video showing the situation in half

speed to double check your graph and revise it as appropriate.

Compare and discuss your graph with a neighbor or a different group. When you have reached

an agreement of what the graph should look like, watch the last part of the video to see a

possible solution. Did it agree with your graph? What was different, what was similar?


Discussion Questions

Video # 1

1. Why does the graph start and end so far above the time axis?

2. At what time and for how long does the man stop to look over the rail? How does your

graph reflect that?

3. Where is the slope of the graph positive/negative? Why?

4. When does he reach the highest point on the bridge? How do you know?

Video # 2 1. Where is the slope of the graph positive/negative/neither?

2. What does a negative slope represent in the video?


3. What does a positive slope represent in the video?

Video # 3 1. Because of the similarity between this video and video #2, this video could be used as

an opportunity for students to check for understanding. In pairs, have students describe their graphs to each other in the context of the video.

Video # 4

1. How is this graph similar to the previous 3? How is it different?

2. When does the man jump the highest?

3. How does the “shape” of his jumps change when he jumps higher or lower?

4. When does he jump the highest? How do you know?

Video # 5

1. How long does it take the man to do one “lap” (down one side and back up the other)?

2. How does the graph of his first lap compare to that of his second lap?


3. How high is he when the video starts? How high when it ends? How do you know?

Video # 6

1. What units could we use to measure pain? Are there set units for pain? What do doctors

use?

2. What does the end of the graph look like?

3. What might the graph look like if he hit his thumb earlier, then put it in ice?

Video # 7

1. When does the driver begin breaking? Use your graph.

Videos # 8, 9, and 10 are the same clip of a man running up a curved road.

1. How are the three graphs the same? How are they different?

2. When is the runner running the fastest? When is he running slowest?


3. When has he run halfway up the hill?

4. What other graphs could we make using this same video?

Copy of Participant Workbook.pdf

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Transcript of Copy of Participant Workbook.pdf