€¦ · Web view2018. 10. 22. · Thinking with Mathematical Models Homework #1. A group of...

Name: _____________________________________________ Period: __________ Date: ________________

Thinking with Mathematical Models Homework #1

A group of students conducted the bridge-thickness experiment with construction paper. The table below contains their results.

1. Make a graph of the (number of layers, breaking weight) data.

2. Describe the relationship between breaking weight and number of layers.

3. Suppose it is possible to use half-layers of construction paper. What breaking weight would you predict for a bridge 3.5 layers thick? ______Explain.

4. Predict the breaking weight for a construction paper bridge of 8 layers. ______Explain how you made your prediction.

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjCt9-bk4LWAhUq7oMKHUpBDCcQjRwIBw&url=http://etc.usf.edu/clipart/42600/42675/grid_42675.htm&psig=AFQjCNF_aHtVapYOhnp44b9LANUaceNHnw&ust=1504292172894736

Name: _____________________________________________ Period: __________ Date: ________________


The table shows the maximum weight a crane arm can lift at various distances from its cab.

1. Describe the relationship between distance and weight for the crane.

2. Make a graph of the (distance, weight) data.

3. Explain how the graphs shape shows the relationship you described in Question 1.

4. Estimate the weight the crane can lift at each distance from the cab.

a. 18 feet = ______ b. 30 feet = ______ c. 72 feet = ______

5. Is this relationship linear or nonlinear? __________

a. How can you know using the table?

b. How can you know using the graph?


Name: _____________________________________________ Period: __________ Date: ________________


Directions: Using the drawings below to make a table and graph and answer questions. 0 minutes 1 minute 2 minutes 3 minutes

1. Make a table based on the picture.

2. Make a graph from your table.



b. How can you know using the graph?

4. How many dots will there be after 50minutes? Explain or show work for answer.


Name: _____________________________________________ Period: __________ Date: ________________


Directions: Using the drawings below to make a table and graph and answer questions. 0 Hours 1 Hour 2 Hours 3 Hours

2. Make a table based on the picture.

2. Make a graph from your table.



c. How can you know using the graph?

5. How many x’s will there be after 15 hours? Explain or show work for answer.


Name: _____________________________________________ Period: __________ Date: ________________


Directions: The table below gives the distance Jose, Mario, and Melanie travel for the first 3 hours. Assume that each person cycles at a constant rate.

Cycling Time(hours)

Distance (miles)Jose Mario Melanie

0 0 0 01 5 7 92 10 14 183 15 21 27456

1. Complete the table above to find the distance each person travels in the first 7 hours.

2. Find the average rate at which each person travels. Explain each answer.

Person Rate Explain answer.

Jose

Mario

Melanie

Name: _____________________________________________ Period: __________ Date: ________________


Directions: The table below gives the distance Jose, Mario, and Melanie travel for the first 3 hours. Assume that each person cycles at a constant rate.

Cycling Time(hours)

Distance (miles)Jose Mario Melanie

0 0 0 01 5 7 92 10 14 183 15 21 27456

1. Complete the table above to find the distance each person travels in the first 7 hours.

2. Graph the time and distance data for all three riders on the same coordinate axes.

3. Write an equation for each person.

Jose’s equation: _______________

Mario’s equation: _______________

Melanie’s equation: _______________

4. How does rate show up in each equation?


Name: _____________________________________________ Period: __________ Date: ________________


Directions: Jamal’s parents give him money to spend at camp. Jamal spends the same amount of money on snacks each day. The table below shows the amount of money, in dollars, he has left at the end of each day.

Snack MoneyDays 0 1 2 3 4 5 6Money Left $20 $18 $16 $14 $12 $10 $8

1. How much money does Jamal have at the start of camp? Explain.

2. How much money is spent each day? Explain.

3. Assume that Jamal’s spending pattern continues. Is the relationship between the number of days and the amount of money left in Jamal’s wallet a linear relationship? Explain.

4. Graph the table above.

5. Write an equation that represents the relationship. Explain what information the numbers and variables represent.


Name: _____________________________________________ Period: __________ Date: ________________


Directions: Make equations from the table or graph provided.1. Start Number (y-intercept): ________________ 2. Start Number (y-intercept): ________________ Rate of change (slope): ________________ Rate of change (slope): ________________ Equation: ________________ Equation: ________________

3. Start Number (y-intercept): ________________ 4. Start Number (y-intercept): ________________ Rate of change (slope): ________________ Rate of change (slope): ________________ Equation: ________________ Equation: ________________

5. Start Number (y-intercept): ________________ 6. Start Number (y-intercept): ________________ Rate of change (slope): ________________ Rate of change (slope): ________________ Equation: ________________ Equation: ________________

x y0 161 132 103 74 4

x y0 -41 -12 23 54 8

Name: _____________________________________________ Period: __________ Date: ________________


A school committee is assigned the task of selecting a DJ for the end-of-school-year party. Jamille obtain several quotes for the cost of three DJs.

Tom’s Tunes charges $60 an hour Solidus’ Sounds charges $100 plus $40 an hour Light Plastic charges $175 plus $30 an hour

1. For each DJ, write an equation that shows how to calculate the total cost from the total number of hours?

Tom’s Tunes: _____________________

Solidus’ Sounds: _____________________

Light Plastic: _____________________

2. What information does the coefficient of x represent for each DJ?

3. What information does the y-intercept represent for each DJ?

4. Suppose the DJ will need to work 6 hours. What is the cost of each DJ?Tom’s Tunes:

Solidus’ Sounds:

Light Plastic:

5. Suppose the committee has only $300 dollars to spend on a DJ. For how many hours could each DJ play?

Name: _____________________________________________ Period: __________ Date: ________________


Ms. Chang's class decides to give T-shirts to each person who participates in the walkathon. They receive bids for the cost of the T-shirt from two different companies. Mighty Tee charges $49 plus $1 per T-shirt. No-Shrink Tee charges $4.50 per T-shirt. Ms. Chang writes the following equations to represent he relationship between cost and the number of T-shirts:

Mighty Tee = 49 + xNo-Shrink = 4.5x

The table below represents the costs from another company, the Big TN C0 343 41.55 46.58 54

10 59

1. Compare the costs for The Big T with Mighty Tee and No-Shrink.Compare with Might Tee

Similar:

Different:

Compare with No-Shrink

Similar:

Different:

2. Is The Big T representing a linear relationship? Yes/NoExplain:

3. Could the point (20, 84) lie on the graph of The Big T? Yes/NoExplain:

4. What information about the number of T-Shirts and cost do the coordinates of the point (20, 84) represent?

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Circle the correct answer.

1. –8 + x = 4; x = –12, 4, or 12 2. 9 – x = 3; x = 3, 6, or 12

3. c + 2.1 = 3.5; c = 1.4, 5.6, or 6.6 4. g – 27 = 148; g = 121, 165, or 175

5. 5 + m = 10; m = -5, 5, or 15 6. k – 2.1 = –6.3; k = –8.4, –4.2, or 4.2

7. –3 – p = 2; p = –5, –1, or 5 8. x – 10 = –4; x = –14, –6, or 6

9. 6 – y = –3; y = –3, 6, or 9 10. m + 2.3 = 7; m = 4.7, 5.7, or 9.3

11. x – 10 = 15 12. x + 6.26 = 7.26 13. m + 54 = 36

14. x + 14 = –25 15. x – 3.6 = 7 16. y – 7.5 = –2.7

Name: _____________________________________________ Period: __________ Date: ________________


Solving Equations by Using Division1. 4x = –36 2. 9x = 108 3. –5x = 125 4. –2y = –17

5. –6t = 72 6. 3a = 42 7. 7x = –42 8. 11x = 660

Solving Equations by Using Multiplication9. m = 9 10. –4 = x 11. w = –4 12. p = 7 8 5 3.1 –6

13. –12 = x 14. t = –2 15. y = 5 16. –8 = k 6 7 3 13

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Solve for the missing variable.

1. 6x = 48 2. 20b = 40

3. –4y = –28 4. 5a = –45

5. 3x = 1 6. –9m = –81

7. 5b = 2 8. –8x = 56

9. 10y = 5 10. 13 x = 10

11. 25 x = –8 12.

14 x = 9

13. – 34 x = 12 14.

– 16 x = –3

15. 17 x = 3 16.

18 x = 11

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Solve for the missing variable.1. 2x + 1 = 5 2. 2y – 4 = 10 3. 6 + 3z = 18

4. 7 – 5w = 22 5. –15 – 6c = 3 6. 9b + 4 = –14

7. x + 1 = 5 8. 10 = y – 4 9. 3 + z = 6 2 2 3

10. w + 8 = 28 11. –30 – c = 10 12. b + 3 = –4 7 5 9

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Solve for the missing variable.

1. 2x + 1 = 7 2. 3y – 7 = 20 3. 3x + 2 = 23

4. 4x + 3 = 27 5. x/2 + 9 = 15 6. x/5 – 1 = 7

7. 7k + 6 = 27 8. 2w + 9 = 25 9. m/6 + 4 = 10

10. t/5 – 3 = 2 11. 9p – 4 = 77 12. 3y – 8 = 1

13. 6r + 18 = 30 14. b/10 + 4 = 13 15. x/5 – 11 = 3

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Write an equation for each word problem. Solve each problem. Show Work!!

1. 331 students went on a field trip. Six buses were filled and 7 students traveled in cards. How many students were in each bus?

Equation: _________________________________________ Answer: ______________

2. Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

Equation: _________________________________________ Answer: ______________

3. You bought a magazine for $5 and 4 erasers. You spent a total of $25. How much did each eraser cost?

Equation: _________________________________________ Answer: ______________

4. The Girl Scouts were having a sale. Maria bought 7 boxes of cookies and one t-shirt. The t-shirt cost $15. If Maria paid $57, how much did each box of cookies cost?

Equation: _________________________________________ Answer: ______________

5. We need 11 new calculators for math class. We have to pay $12 for shipping charges. If our bill is $111, how much does each calculator cost?

Equation: _________________________________________ Answer: ______________

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Show your work for each problem. Show that you have checked at least two problems.

1. 14p – 8 = 22 + 20p Check:

2. 63 – 1x = 2x + 3 Check:

3. 12r – 18 = 13r + 18 Check:

4. 1z + 81 = 9z – 7 Check:

5. 3n + 46 = 1 + 8n Check:

Name: _____________________________________________ Period: __________ Date: ________________

Thinking with Mathematical Models Homework #18Directions: Solve for the missing variable.

1. 6x – 19 = 4x + 11 2. 7x + 19 = 4x + 64

3. 7x + 16 = 2x – 44 4. 5x – 44 = 3x – 8

5. 9x + 23 = 8x + 9 6. 4y – 16 = 20 – 2y

7. 19 – 2z = 3z – 46 8. 7m – 27 = –3m – 117

9. 2x + 9 = 4x + 17 10. 3y – 13 = 23 – y

Name: _____________________________________________ Period: __________ Date: ________________


Plans for a set of stairs for the front of a new community center use the ratio of rise to run of 2 units to 5 units.

1. Are these stairs within carpenters’ guidelines, which state that the ratio of rise to run should be between 0.45 and 0.60? Explain.

2. Sketch a set of stairs that meet the rise to run ratio of 2 units to 5 units.

3. Sketch the graph of a line where the y-values change by 2 units for each 5-unit change in the x-values.

4. Write an equation for your line from question 3.

Name: _____________________________________________ Period: __________ Date: ________________


Write an equation for each table, graph, and pair of two points.

1.

Equation: _________________

4.

5.

X 0 1 2 3 4Y 0 2 4 6 8

Name: _____________________________________________ Period: __________ Date: ________________

Thinking with Mathematical Models Homework #21Equation A: y = 2x - 3

1. Complete the Table:x -4 -3 -2 -1 0 1 2 3 4

y

2. Sketch a Graph: 3. What is the slope?

4. Make a situation that could represented by the equation:

7. (0, 5) and (3, -1)

Equation: _________________

X 2 3 4 5 6Y -11 -14 -17 -20 -23

X 0 1 2 3 4Y 3.5 4.5 5.5 6.5 7.5

Name: _____________________________________________ Period: __________ Date: ________________

Equation B: y = -x + 55. Complete the Table:

x -4 -3 -2 -1 0 1 2 3 4

y

6. Sketch a Graph: 7. What is the slope?



Name: _____________________________________________ Period: __________ Date: ________________


Directions: Find the equation from the two points. 1. (2, 4) (4, 7) 2. (3, 3) (5, 9)

Equation: _____________________ Equation: _____________________

3. (4, 0) (8, 3) 4. (6, 5) (8, 4)

Equation: _____________________ Equation: _____________________

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Write the equation of each graph.

1. Equation: _____________________ 2. Equation: _____________________

3. Equation: _____________________ 4. Equation: _____________________

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Graph each equation.

1. y = 34 x – 3 2. y = 3x – 2 3. y =

−43 x + 4

4. y = 2x – 5 5. y = -2x + 4 6. y = 12x

7. y = −12 x + 1 8. y =

−32 x – 1 9. y =

23x – 3

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Write each equation in slope-intercept form.

1. Write an equation parallel to y = 3x – 10. ___________________________

2. Write an equation perpendicular to y = 3x – 10. ___________________________

3. Write an equation parallel to y = 12x + 7 with a y-intercept of 4. ___________________________

4. Write an equation perpendicular to y = 12x + 7 with a y-intercept of 8.

___________________________

5. Write an equation parallel to y = −23 x – 5 with a y-intercept of 9.

_______________________________

6. Write an equation perpendicular to y = −23 x – 5 that goes through the origin.

_____________________

7. Write an equation parallel to y = 2x + 5 with a y-intercept of 11. _________________________

8. Write an equation perpendicular to y = 2x + 5 with a y-intercept of 15. _________________________

9. Write an equation that is parallel to y = 3x – 9 and goes through the point (3, 2)

Name: _____________________________________________ Period: __________ Date: ________________

Thinking with Mathematical Models Homework #26Find the slope and y-intercept of each line. Then, write the equation of each line.

1. 2.

3. 4.

y-intercept: Slope:

Equation:

y-intercept: Slope:

Equation:

y-intercept: Slope:

Equation:

y-intercept: Slope:

Equation:

5. The points (4, 2) and (-1, 7) lie on a line.

a. What is the slope of the line?

b. Find two more points that lie on the line.

c. What is the y-intercept of the line?

d. Write an equation for the line that passes through these two points.

Name: _____________________________________________ Period: __________ Date: ________________


1. Plot the data relating number of layers and breaking weight on the graph.

2. Draw a line of best fit on your graph.

3. Find the equation of your line of best fit.

4. Use your equation to predict the breaking weights of paper bridges 10 layers thick.

5. Use your equation to predict the number of layers for a breaking weight of 85 pennies.

Name: _____________________________________________ Period: __________ Date: ________________


1. On each graph, draw a line of best fit.

2. Write the equation for your line of best fit on each graph.

Graph A Equation:

Graph B Equation:

Graph C Equation:


0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

543210

9876

543210

9876

543210

9876

Name: _____________________________________________ Period: __________ Date: ________________The U-Wash-It car wash did market research to determine how much to charge for a car wash. The company made this table based on its findings.

1. Graph the data. Draw a line on your graph that models the data pattern.

2. Explain what the slope and y-intercept tell you about the relationship between price per wash and customers expected per day.

Slope:_____ Meaning:

y-intercept:_____ Meaning:

3. Write an equation for your line of best fit using p for price per wash and n for number of customers expected per day.

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Answer the equation based on the scatter plot.

1. Draw an approximate Line of Best Fit on the graph above.

2. What is the y-intercept of your line? What does it represent in this context?

3. What is the slope of your line? What do the slope represent in this context?

4. What is the equation of your Line of Best Fit? __________________________________

5. Based on your Line of Best Fit, what would your weight be if your height was 80?

Name: _____________________________________________ Period: __________ Date: ________________


Directions: Answer the equation based on the scatter plot.

1. Using the points (10, 70) and (15, 55) to find the equation in the form y = mx + b for the modeling line. Show your work.

2. Explain what the slope and y-intercept tell you about the relationship between the number of classes missed and the score on the exam.Slope:

y-intercept:

3. How much would you score on the exam if you missed 17 classes?

4. How many classes did you miss if you scored a 90 on the exam?

Name: _____________________________________________ Period: __________ Date: ________________


1. Complete the tableLike Skateboards Do not like

skateboardsTotal

Like Snowmobiles 80 25

Do not like snowmobiles

45 10

Total

2. Find the fraction, decimal, percent for each scenario.

a. Like skateboards: _________ = _________ = _________

b. Like snowmobiles: _________ = _________ = _________

c. Do not like skateboards: _________ = _________ = _________

d. Do not like snowmobiles: _________ = _________ = _________

e. Like skateboards and snowmobiles: _________ = _________ = _________

f. Like skateboards, but not snowmobiles: _________ = _________ = _________

g. Do not like skateboards or snowmobiles: _________ = _________ = _________

h. Like snowmobiles, but not skateboards: _________ = _________ = _________

Name: _____________________________________________ Period: __________ Date: ________________


1. Complete the table based on the filled in information.


a. Females surveyed: _________ = _________ = _________

b. Males surveyed: _________ = _________ = _________

c. People with high school diploma’s: _________ = _________ = _________

d. People with Bachelor’s degree: _________ = _________ = _________

e. People with Master’s or Doctoral Degree: _________ = _________ = _________

f. Female with a Bachelor’s degree: _________ = _________ = _________

g. Male with a High School Diploma: _________ = _________ = _________

3. Are you more likely to survey a male or a female with a bachelor’s degree? Explain your answer.

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjT0YX2oaLXAhVHfiYKHYrqAdIQjRwIBw&url=https://goalbookapp.com/pathways/#!/items/d8556ad6-97ee-41cc-58dd-486cc1918696&psig=AOvVaw2HH_IzZNWlSkcIQzwNNJ1W&ust=1509793119240945

Name: _____________________________________________ Period: __________ Date: ________________


1. Complete the table Football Rugby Other Total

Male 10 10 32

Female 8 28

Total 23


a. Females surveyed: _________ = _________ = _________

b. Males surveyed: _________ = _________ = _________

c. People that play Rugby: _________ = _________ = _________

d. People that play football: _________ = _________ = _________

e. People that play other sports: _________ = _________ = _________

f. Female that plays football: _________ = _________ = _________

g. Male that plays other sports: _________ = _________ = _________

3. Are you more likely to survey a male or a female that plays Rugby? Explain your answer.

€¦ · Web view2018. 10. 22. · Thinking with Mathematical Models Homework #1. A group of...

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