Fastfood workout 2
Teacher Edition
List of Activities for this Unit:
ACTIVITY / STRAND / DESCRIPTION1 – Kayla’s workout / AS / Writing rules, slope, y-intercept, independent and dependent variables
2 – Eleanor’s workout / AS / Writing rules, slope, y-intercept, independent and dependent variables; graphing equation
3 – Leg Bone Problem / AS/PS / Line of best fit and predictions
4 – Robert Wadlow Story / AS/PS / Line of best fit and predictions; graphing data, slope, y-intercept
5 – Fast Food workout Multiple Choice Practice / PS / 4 multiple choice practice questions
COE Connections / Old Faithful Eruptions
Salmon Populations
The Robert Wadlow Story
MATERIALS / Rulers
Yardsticks
Measuring Tapes
Calculators
Warm-Ups
(in Segmented Extras Folder) / Tall Paul
Ernie the Elephant
Vocabulary: Mathematics and ELL
calories / ordered paircontext / predict
define / quotient
dependent / responding
femur / rule
function / situation
independent / slope
maintain / variable
manipulate / Workout
median / y-intercept
model
Essential Questions:
- What is an informative title for a graph?
- What are appropriate intervals for the x- and y-axes?
- What is meant by dependent (responding) and independent (manipulated) variable?
- How are the dependent and independent variable determined?
- When reading a graph, where are the x- and y-intercepts?
- What is the meaning of the y-intercept in the context of a problem?
- What is the relationship between the intercepts and the context of any problem?
- How is the slope of the line determined after putting points on a graph?
- What is the meaning of the slope in the context of a problem?
- When is a line graph more appropriate than another type of graph?
- How is a fitted line determined?
- How are the intervals on a graph determined?
- What is a calorie?
- What activities burn calories?
- How is a fitted line represented as an equation?
- How is a fitted line used to make a prediction?
- In what contexts are predictions made using a fitted line not as valid as in other contexts?
- How can you support a conclusion that you make?
- What evidence from graphs can be used to support/justify your conclusion?
Lesson Overview:
- Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to exercise programs they are involved in or any activities in a job or sport that requires physical activity.
- Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to growth of people, tall people who they know. Pike Place Market in Seattle has a model downstairs of Robert Wadlow.
- Discuss a “fitted line”—What is it? How would a person use a fitted line? How would you show an understanding of a fitted line? Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?
- Use resources from your building.
Performance Expectations:
5.4.DGraph ordered pairs in the coordinate plane for two sets of data related by a linear rule and draw the line they determine.
6.2.BDraw a first-quadrant graph in the coordinate plane to represent information in a table or given situation.
6.3.BWrite ratios to represent a variety of rates.
7.5.AGraph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane.
8.1.CRepresent a linear function with a verbal description, table, graph, or symbolic expression, and make connections among these representations.
8.1.DDetermine the slope and y-intercept of a linear function described by a symbolic expression, table, or graph.
8.1.EInterpret the slope and y-intercept of the graph of a linear function representing a contextual situation.
8.1.FSolve single- and multi-step word problems involving linear functions and verify the solutions.
8.3.CCreate a scatterplot for a two-variable data set, and, when appropriate, sketch and use a trend line to make predictions.
A1.4.BWrite and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.
A1.4.CIdentify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.
A1.6.DFind the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
G.6.FSolve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.
Performance Expectations and Aligned Problems
Chapter 25“Fast Food Workout 2”Subsections: / 1-
Kayla’s workout / 2-
Eleanor’s workout / 3-
Leg Bone Problem / 4-
Robert Wadlow Story / 5-
Fast Food workout Multiple Choice Practice
Problems Supporting:
PE 5.4.D ≈ 6.2.B ≈ 7.5.A / 1 / 6 / 15
Problems Supporting:
PE 6.3.B / 2, 4, 5 / 6 / 14 / 18, 21, 22
Problems Supporting:
PE 8.1.C / 2 / 6 / 7, 10 – 13 / 18
Problems Supporting:
PE 8.1.D ≈ 8.1.E ≈ 8.1.F ≈ A1.4.B ≈ A1.4.C ≈A1.6.D ≈ G.6.F / 2
Linear equations in context are conversion problems. / 6 / 7, 10 - 14 / 15, 18, 21 – 23
Problems Supporting:
PE 8.3.C / 2 / 7, 10, 11, 14 / 18 - 23
Assessment: Use the multiple choice and short answer items from Probability and Statistics that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.
Kayla’s Workout
Fast food has become a part of the busy American lifestyle. Experts point out that fast food is often high in calories.
Kayla eats fast food often. To maintain her weight, Kayla exercises on her bicycle. She knows one hour of bicycling burns many calories. Kayla also knows a female should eat about 2,000 calories per day to maintain her weight.
1. What does the point (10, 3500) on the graph mean? ______
10 hours of bicycling burns 3500 calories______
2. Write a functionor specific ruleto show the relationship between the number of hours on a bicycle and the number of calories burned. Be sure to define your variables. ______
Let c = the number of calories burnt and h = the number of hours cycling. c = 350•h
Show your work using words, numbers and/or diagrams.
A functionor specific rule is a formula expressing a relation between two things. E.g. y = 2x the rule is y-values are twice the amount of the x-value
a. What is the slope of the line? ___350 calories per 1 hour cycling_OR______
{The slope is the quotient of the change in vertical units to the change in horizontal units.}
b. What is the y-interceptof the line? ____(0,0) Intercepts are an ordered pair. There is no point on the Cartesian coordinate system identified by the single number 0.
{The y-interceptis the point (ordered pair) where a graph crosses the y-axis.}
c. What does the slope mean in the context of this problem? ______
Calories burnt by cycling only happen if you cycle!
______
d. What does the y-intercept mean in the context of the problem? ______
There were zero calories burnt when zero hours of cycling were done.
______
e. Which variable is dependent (responding)? _____The number ofCalories burnt.______
The dependent variable is “ruled” by the independent variable. The height of a person depends, is ruled by: age, growth hormones, genetics, and other factors such as nutrition. In y = 2x the y-value will depend, is ruled by what x-value is used; y is the dependent variable.
f. Which variable is independent (manipulated)? ___The hours spent cycling.______
The independent variable is the variable we can often choose (manipulate); we can allow the independent variable to be a number and then calculate the dependent variable.
In y = 5x if we let x = 1,2,and 3, then the y-values are: 5•1 =5, 5•2 =10, and 5•3 =15; the x-values were chosen and we calculated the y-values. The x-values were independent and the y-values dependentor restricted to 5, 10, and 15 because of our rule y = 5x and on the x’s we choose.
3. Kayla will go bicycling three days a week for one hour a day. Predict how many calories she will
burn in a week. ______1050 calories______
Show your work using words, numbers, and/or diagrams.
c = • 3 hours = 1050 calories
4. How long does Kayla have to ride her bicycle to burn up calories from a hamburger, fries, and a
soda if the meal has a total of 1,155 calories? 3 hours and 20 minutes______
Show your work using words, numbers, and/or diagrams.
1,155 calories = • h hours
= h
3. hours = h OR h= 3 hours and 20 minutes (hour) •() = 20 minutes
5. Kayla tends to eat an average of 2,100 calories per day. How many hours per week does she need
to bicycle to maintain her weight? ______2 hours ______
Show your work using words, numbers, and/or diagrams.
2100 – 2000 = 100 extra calories per day implies 700 calories per week.
700 calories = • h hours implies = h
2 hours = h
ELEANOR’S WORKOUT
6. Eleanor uses 10 calories of energy in warming up for her morning run. In addition, for every minute of running time, she uses 15 calories. She wants to know how many minutes she will need to run to burn up 1,000 calories.
a. Write an equation that would allow her to determine how many minutes she will need to
run to burn up 1,000 calories. ______c = 15 (• m (minutes)+ 10 calories______
Show your work using words, numbers and/or diagrams.
1000 calories =15 ( • m (minutes)+ 10 calories
1000 calories - 10 calories = 15 ( • m
990 calories = 15 ( • m Implies = m
m = 66 minutes OR 1 hour and 6 minutes
b. What do the variables represent? Small c is the total number of calories burnt from running. Small m is the number of minutes Eleanor runs.
c. What is the slope of the line? _ The slope is .
d. What is the y-intercept of the line? __The y-intercept is (0, 10).
The ordered pairs are in the form (Time in minutes, Calories burnt running)
e. What does the slope mean in the context of this problem? _ The slope is the number of calories burnt per minute._
f. What does the y-intercept mean in the context of the problem? __The warn-up calories burnt; no running has yet occurred______
g. Graph the equation for Eleanor’s workout so that another person would be able to access the same information from the graph as the equation. Remember to title the graph, label each axis, and use appropriate scales.
Eleanor’s Calories Burnt by Minutes Spent Running
0 20 40 60 80 100
Minutes Running
LEG BONE PROBLEM
Anthropologists and archaeologists often try to determine the height of a person from the size of the bones they find. Anthropologists know the height of a person and the length of their upper leg bone, the femur, are related.
This table was created last year call it data set A:
length of femur in inches / 14 / 16 / 21 / 15 / 11height of person in inches / 54 / 62 / 71 / 59 / 46
Each student measures his/her own femur and enters that value in the chart. Ask six (6) more students in the class for their femur measurement and height.
Put the data collected by you and six other studentsin the table; this table is data setB:
length of femur in inchesheight of person in inches
- Graph both sets of data with the height as a function of femur length.
__Height vs Femur Length____
Femur length in Inches
- Define the dependent (responding) variable? _____h =height______
______
______
- Define the independent (manipulated) variable? ___f = femur______
______
______
- Draw a line that best fits last year’s data (data set A).
a. Choose two points on that line. ______
b. Determine the slope between these two points. ____ m ≈ 2.5
Show your work using words, number and/or diagrams.
c. Determine y-intercept of the line. __(0, 19.8)______
d. Write an equation of the line for last year’s data. ______
Show your work using words, number and/or diagrams.
- Using a different color, draw a line that best fits the data for your class (data set B).
a. Choose two points on this line. ______
b. Determine the slope between these two points. ______
Show your work using words, number and/or diagrams.
c. Determine the y-intercept of the line. ______
d. Write an equation of the line for your class data. ______
Show your work using words, number and/or diagrams.
12. Give the values and meanings of the slopes of your lines within the context of this situation.
Change in height in relationship to femur length which was ___???____ for this year and about 2.5 for last year.
______
______
13. Give the values and meanings of the y-intercepts of your lines within the context of this situation.
Initial height when the femur begins which is approximately 20 in for last year and ______in for this year.
______
______
14. Use your equations of the fitted lines to predict: h = () •f + 19.8 inches
a.The height of a person whose femur was 18.25 inches long.
Height (data set A) 65.4 inches_Height (data set B) _____???______
Show your work using words, numbers, and/or diagrams.
h = () (18.25 inches) + 19.8 inches
h = 65.4 inches OR 5 feet 4.8 inches tall NOTE: •12 inches = 4.8 inches
b. The femur length of a person who was 71 inches tall.
Length (data set A) _20.5 inches__Length (data set B) ______
Show your work using words, numbers, and/or diagrams.
71 inches of height = () f + 19.8 inches of height
71 inches of height – 19.8 inches of height = () f
= f= 20.5 inches of femur
The Robert Wadlow Story
Born: February 22, 1918 Died: July 15, 1940
Robert Pershing Wadlow was born, educated and buried in Alton, Illinois. His height of 8’ 11.1” qualifies him as the tallest person in history, as recorded in the Guinness Book of Records. At the time of his death he weighed 490 pounds. At birth he weighed a very normal eight pounds, six ounces. He drew attention to himself when at six months old he weighed 30 pounds. A year later, at 18 months, he weighed 67 pounds. He continued to grow at an astounding rate, reaching six feet, two inches and 180 pounds by the time he was nine years old.
GROWTH CHART FOR ROBERT WADLOW
Age (yrs)
/ 5 / 8 / 10 / 14 / 16 / 20 / 21 / 22.4Height
(in) / 64 / 72 / 77 / 89 / 94 / 103 / 104 / 107.1Weight
(lbs) / 105 / 169 / 210 / 301 / 374 / 488 / 492 / 490- Graph the data on two separate graphs; height on one graph and weight on the other graph.
(Do this on the next page) Graphs on page 13
- Determine the dependent (responding) and independent (manipulated) variable. Explain your thinking for the choices you made?
-Independent (manipulated) variable is age. Dependent (responding) variable is weight and height.
- No real control over his age – the weight and height were dependent on the time he was alive.
______
______
- Draw a line that best fits the data for each graph and write the equation for each line.
Height equation: __h = 2.5a + 52.3_____,where h = height in inches and a = age in years
Weight equation: __w = 24.1a - 22___,where h = height in inches and a = age in years
- Use your model, best fit line, to estimate how tall Robert was at age 14? __87.4 inches______
20. Use your model, best fit line, to determine how tall Robert would have been if he had lived to be 35 years old. __140.2 inches OR about 11 feet 8 inches…not realistic the model fails to predict with reasonable accuracy when used to far from the actual dataset__
21. For the graph of Roberts’s height, what is the y-intercept of the graph? _52.3 inches (at birth!…not realistic; the model fails to predict with reasonable accuracy when used to far from the actual data set.)_
a. What does this y-intercept represent in this situation? Does the y-intercept have meaning? Explain.
The y-intercept is the height of Robert at birth.
______
______
______
- What is the slope of the height line? _m = 2.5 inches of growth per year_
- What meaning does the slope have in this situation?
The slope is the is the number of inches Robert gains each year.
______
______
22. Using your model, how much does Robert weigh at: 17 years old? 388 lbs, 35 years old? 822 lbs
a. What is the y-intercept of the line? _-22 lbs at birth!_____
b. What is the slope of the weight line? _24.1 lbs per year_____
c. Does the y-intercept match what was stated in the first paragraph about Robert? Why or why not?
No, 8 lbs 6oz is not -22 lbs; this occured because we did not have the data point (0, 8.375) in our table and the model fails to predict with reasonable accuracy when used to far from the actual data set.
d. What meaning does the slope have in this situation?
Robert gains 24.1 lbs per year.
______
23. Is a linear function appropriate to use when graphing a person’s growth? Explain/support your answer.
No. People don’t grow at a consistent rate each year of their life. Many factors influence a person’s growth rate such as: diet, exercise, illnesses, hormone production by the pituitary gland etc.
______
FASTFOOD WORKOUT MULTIPLE CHOICE PRATICE
24. The bar graph describes the speed of four runners in a recent race.
Which conclusion is true?
A. Everyone ran faster than 6 meters per second.
B. The best possible rate for the 100-meter dash is 5 meters per second.
C. The first-place runner was four times as fast as the fourth-place runner.
D. The second-place and third-place runners were closest in time to one another.
25. The left side of a solid block is held at a constant temperature of 200°C. The temperature within the block is given by where x is the distance, in centimeters, from the left side of the block and T is the temperature in degrees Celsius at location x.
What is the distance, x, when the temperature, T, is50°C?
A. x = 5 cm
B. x = 10 cm
C. x = 15 cm
D. x = 20 cm
26. The number of games won over four years for three teams is shown on the graph below.
Which statement is true based on this information?
A. Team 3 always came in second.
B. Team 1 had the best average overall.
C. Team 1 always won more games than Team 3.
D. Team 2 won more games each year than in the previous year.
27. The bar graph represents the numbers of blocks each of 10 students walks to school each day.
Which is the median number of blocks that these students walk to school each day?
A. 3.5
B. 4.0
C. 4.5
D. 5.0
Teacher: Ch. 25 “Fast Food Workout 2” 5/02/08 Page 1 of 20