Probability, Percent, and Rational Number Equivalence Math A Honors

Module #1 Homework 2017-2018

Created in collaboration with Utah Middle School Math Project A University of Utah Partnership Project

San Dieguito Union High School District

1.0A Homework: American Football Name:

Period:

Complete by showing all of your work. Do NOT use a calculator. 1.

4.

7.

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+    

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2. 5 + 2  

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−    

5. 17 − 6  

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8. 2  ×5  

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11. 2   ÷ 5  

10.   ÷    

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+   +  

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6. 18 − 10  

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 ×    ×    

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3.

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9. 6  ×15  ×    

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12. 16   ÷ 2   ÷    

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Spiral Review: Simplify: 13. 5 − 4 ∙ 3

14.

7 − 3 + 2(2)

15. −5

16.

5 + 3(2) – 4

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.0B Homework: Fraction Review Name:

Period:

1. Fill in the boxes below to show how you can convert between fractions, decimals, and percentages. a. How can you write a percent as a fraction?

b. How can you write a fraction as a decimal?

c. How can you write a decimal as a percent?

Show how to use the steps you described to complete the following problems. 2.

Write 45% as a fraction in simplest form.

4.

Write

6.

Write 1 as a percent.

1 as a decimal. 9

3 as a decimal. 5

3.

Write

5.

Write 0.45 as a percent.

7.

Write 0.002 as a fraction.

Answer the following questions. Show your work. Answer in a complete sentence. 8. Your food costs are $2,500. Your total food 9. James hired a new employee to work in his sales are $17,500. What fraction of your food bakeshop. In one hour, the employee burned sales do the food costs represent? 625 chocolate chip cookies. If this represented 25% of the day’s production, how many cookies did James plan on producing that day? 10.

In order to select new board members, the French Club held an election. 56 out of the 80 members of the French club voted in the election. What percentage of the members voted?

11.

There are 18 empty seats and 54 occupied seats on a train. What percentage of the seats on the train are empty?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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12.

A serving of ice cream contains 1200 calories. One hundred forty-four calories come from fat. What percent of the total calories come from fat?

Fill in each blank with the equivalent fraction, decimal or percent. Use bar notation for repeating decimals. Show and number your work over here! Fraction Decimal Percent 13. 14.

6 10 4 25

15.

0.42

16.

0.8

17. 18.

32%

9 20

19.

21%

20.

0.06

21. 22.

7%

1 8

23.

0.99

24. 25.

75%

1 4

26. 27.

20% 6 15

28.

1.5

29.

250 %

30. 31. 32.

3.0 8 11 2 3

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.1A Homework: Solve Probability Predictions* Name:

Period:

Find the theoretical probability of each outcome if you use a standard die with 8 sides. Express your answer as a simplified fraction, decimal, and percent. 1.

P(5)

2.

P(odd number)

3.

P(a number less than 7)

4.

P(a number greater than 4)

5.

P(a multiple of 2)

6.

P(a number less than 9)

Each of the 12 cards shown below has a letter, a number, and a color (gray or white). Each card is equally likely to be drawn. Find each theoretical probability. Express your answer as a simplified fraction, decimal, and percent.

A 1

A 2

A 3

A 4

B 1

B 2

B 3

B 4

C 1

C 2

C 3

C 4

7.

P(C)

8.

P(gray)

9.

P(not C)

10.

P(not 1, or 2, or 3)

11.

P(prime number)

12.

P(not 1)

13. Adrienne flipped a coin 50 times and got 23 heads. What is the experimental and theoretical probability of getting a head? Write your answer as a simplified fraction, decimal and percent.

Experimental Probability: ______________

Theoretical Probability: ______________

14. Based on Adrienne’s experiment from #13: If she flipped a coin 100 times, how many heads could she expect to get? Explain your answer.

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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15. You want to design an experiment using 800 marbles and you want six different colors—blue, red, green, yellow, purple, and pink. You also do not want more than two colors to have the same probability. State the number of each color you are going to put in the bag and what the theoretical probability of drawing the color will be (answers will vary.) a. Blue: Actual number of blue ___________ and P(B)___________ b. Red: Actual number of red ___________and P(R)___________ c. Green: Actual number of green ___________and P(G)___________ d. Yellow: Actual number of yellow ___________and P(Y)___________ e. Purple: Actual number of purple ___________and P(P)___________ f.

Pink: Actual number of pink ___________and P(P)___________

g. To check your answer, the sum of the fractions should be ___________. Explain.

h. To check your answer, the sum of the marbles should be )___________. Explain.

Spiral Review: 16. Order the following fractions from least to greatest. Place and label the fractions on the number line below. Explain how you decided where the fractions would be placed on the number line. What was your method? 1 2     ,                 , 2 5

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!

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!

3 , 5

3 , 8

1 , 3

1 5

17. 1 ∙ (3 )

18. 18 2 + 4   ÷ 2

19. 5 +   −5

20. 3   ÷ 6

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1.1B Homework: Probability* Name:

Period

Write all probabilities as a simplified fraction. 1. A coin is flipped four times. a. How many possible outcomes are there? Justify by showing your Fundamental Counting Principle work. b. List the sample space.

c. Draw a tree diagram representing this situation. You will need a separate page.

2. Based on #1, what is the theoretical probability, written as a simplified fraction, for the following: a. HEADS for all four flips? b. HEADS at least once in four flips? c. HEADS exactly three times in four flips?

3. Seek and Win The fast food chain, Macduff’s, is running a contest. With every order, you get a card which has 12 covered circles. You can scratch off up to four circles. You win if 3 or more palm trees are revealed, but lose if 2 or more crabs are revealed. If you win, you can then scratch off one of the three squares (on the shell) to reveal what you have won. One of the cards is shown below with all the circles and all the squares revealed. Macduff’s wants the game to be both fun to play and relatively easy to win. a. What is the ratio of palm trees in the circles to crabs in the circles?

If all the circles are then covered up, find each probability (as a simplified fraction): b. P(revealing a palm tree)

c. P(revealing a crab)

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Assume that you revealed a palm tree on your first go. Then on the second go, find the next probability (as a simplified fraction): d. P(revealing a palm tree) e. P(revealing a crab) 4. Draw a tree diagram illustrating the outcomes of throwing two 6-sided dice.

5. Two dice are rolled. How would the sample space for the product of two dice be the same/different from the sample space of the sum of two dice?

Use the tree diagram above to find the probability of each sum. Write your answer as a simplified fraction. 6. P(5 or 11)

7. P(less than 8)

8. P(1)

9. P(at most 7)

Answer the following questions using your knowledge of probability. Hint: A tree diagram will help. 10. Three coins are tossed. Find the probability (as a simplified fraction) of obtaining the following: a. P(at least two tails) b. P(exactly 1 tail) c. P(at most 2 heads) 11. You have one penny, one nickel, one dime, and one quarter in your pocket. You select two coins at random. What is the probability (as a simplified fraction) that you have taken at least 25 cents from your pocket? Spiral Review: 12. Find the area of a rectangle with a length of 10 inches and a height of 4 inches. Start with a formula and give units.

14. Simplify and show all work.

! !!! !

13. Simplify and show all work. 18 ÷  6   ∙ 4 + 12

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15. Use a bar model to represent .

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.1C Homework: More Probability Practice* Name:

Period:

Express all probabilities as a simplified fraction. 1. Jenn told her friend Alice to choose what she wants to do to celebrate her birthday. Alice gets to pick the restaurant and an activity for the day. Jenn will choose a gift for her. The local restaurants include Mexican, Chinese, or Italian. The activities Alice can choose from are Putt Putt, bowling, or movies. Jenn will buy her either candy or flowers. Costs are given in the table below. Use the Fundamental Counting Principle. Cost of Dinner for Two Mexican - $20 Chinese - $25 Italian - $15

Activity Cost for Two Putt Putt - $14 Bowling - $10 Movie - $20

Gift Cost Flowers - $25 Candy - $7

a. How many outcomes are there for these three decisions? b. Draw a tree diagram to illustrate the choices and their associated costs.

2. If all the possible outcomes are equally likely, what is the probability that the celebration will cost Jenn at least $50? 3. What is Jenn’s maximum cost for the day? 4. What is Jenn’s minimum cost for the day? 5. To the nearest dollar, what is Jenn’s average cost for this day? 6. What is the probability that the day costs exactly $60? 7. What is the probability that the day costs under $40? SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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8. A bag of marbles contains 3 red marbles, 5 blue marbles, and 2 yellow marbles. a. What is P(red)? b. What is P(blue)? c. What is P(yellow)? d. What is the most likely outcome when drawing a marble out of the bag? Explain. e. What is the least likely outcome when drawing a marble out of the bag? Explain. f.

Have you been computing theoretical or experimental probabilities? Explain.

g. Give an example of an outcome that has a probability of zero for the experiment. h. Give an example of an outcome that has a probability of one for the experiment.

9. A spinner contains three letters of the alphabet. a. How many outcomes are possible if the spinner is spun 3 times? b. What is the sample space when the spinner is spun 3 times?

c. What is the probability of getting exactly one H? d. What is the probability of getting exactly two V’s? e. What is the probability of getting three T’s? f.

What outcome(s) is/are most likely for 3 spins?

g. Give an example of an outcome that has a probability of zero for the experiment. h. Give an example of an outcome that has a probability of one for the experiment. Spiral Review: Simplify the following. Show all work. 10.

4   ∙ 5 + 6!   ÷ 9

11.

−5 + 12

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Section 1.1 Review Name: Period: Be sure to write all fraction answers in simplest form. Remember to write your probability statements as simplified fractions unless otherwise instructed. 1. A company manufactures phones. The quality control department checks 700 phones and discovers that 72 of them are defective. What is the probability that a phone is not defective? Is this an example of experimental or theoretical probability? Explain. 2. After 40 spins, Chris landed on blue 16 times. a. What is the experimental probability of landing on a blue? b. What is the theoretical probability of landing on a blue? c. What is the sample space for 1 spin?

3. Create a table showing the sums of two six-sided dice. You will have to use separate paper. a. How many outcomes are possible? b. Find P(sum of 10) c. Find P(sum less than 4) d. What type of probability is this? e. Find P(sum at least 10) 4. Chloe and Angelo rolled a pair of dice ten times. Their sums are recorded below. Roll # Sum

1 5

2 3

3 7

4 9

5 7

6 8

7 6

8 7

9 5

10 9

a. What is the experimental probability of rolling a sum of 9? b. Explain why the theoretical and experimental probabilities for rolling a sum of 9 are the same/different.

5. There is a bag of pink, purple, and black marbles. There is an 18% possibility of randomly picking a pink marble and a 60% chance of randomly picking a black marble. What is the probability of picking a purple marble? Write your answer as a fraction, decimal, and percent.

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6. Talia has a bag containing 5 black tiles, 6 pink tiles, and 4 yellow tiles. If one tile is drawn and then replaced (put back in the bag before the next one is drawn): a. What is the sample space for one draw? b. What is the probability that Talia will pick a pink tile? c. What is the probability that Talia will pick a black or yellow tile? d. If Talia picks a tile from the bag and returns it 30 times, predict how many times you would expect her to pick a black tile. Explain your reasoning.

7. Plot the fractions on the number line below. Be sure to label your points.  

8. Order the fractions from least to greatest.

9. Lulu has a box full of magnets. The box has 2 yellow magnets, 7 black magnets, 4 red magnets, 6 pink magnets, 3 green magnets, and 8 brown magnets. If Lulu is randomly choosing magnets out of the box one at a time and then returning them, circle all of the statements that are true. Show your calculations for each part. A. Lulu has a

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chance of picking a pink magnet.

B. Lulu is more likely to pick a brown magnet than a red magnet. C. Lulu has a

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chance of picking a magnet that is NOT brown.

D. Lulu has an equal chance of choosing any color magnet. E. Lulu has a

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chance of choosing a green magnet.

10. Ryan flips three coins. a. Create a tree diagram to show all of the possible outcomes.

b. How many outcomes are possible? c. What is the probability of getting at most 2 tails? SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.2A Homework: Equivalent Fractions* Name: 1.

Period: Write an equivalent fraction. Draw a bar model for questions “a” and “b” to show the equivalent fractions. If you need more space to draw the bar models, use the back of this page.

a.

1 = 2 6

b.

2 = 5 15

c.

2 = 3 15

d.

4 = 7 14

e.

5 = 8 24

f.

3 = 4 24

2. a.

d.

Simplify each fraction. Draw a bar model for questions “a” and “b” to show equivalent fractions. !

b.

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3.

a.

d.

e.

!

c.

!

! !"

f.

!" !"

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Change each improper fraction to a mixed number. Draw a bar model for questions “a” and “b”. If you need more space to draw the bar models, use the back of this page. !" !

!" !"

b.

e.

!" !

!" !

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

c.

f.

!" !

!" !

13

4.

Complete the table: Decimal A.

Fraction in Simplest Form

Percent

0.45 1 4

B. C.

55% 2 5

D. E.

0.65

F. G.

125% 0.96 1 3

H. I. J. K.

13% 0.02 1 25

Spiral Review: Simplify each problem without the use of a calculator, showing each step. 5. 77.2 − 43.778 6. 2.072 ÷ 5.6 7. 4.4×2.727

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.2B Homework: Rational Number Ordering and Estimation* Name:

Period:

1. Peter has one half dollar, one quarter, and two dimes. Express the total value as a fraction of a dollar.

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2. Rick pays five cents of every dollar he earns to the government for taxes. Jason pays of his !" earnings for taxes. Do they pay equivalent fractions of their earnings for taxes? Explain.

3. In an 8th grade class of 30 students, there are 15 students who can speak both Spanish and English. There are 12 others who can speak both French and English. The rest speak only English. a. What fraction of the class can speak Spanish? b. What fraction of the class can speak French? c. What fraction of the class can speak English? d. What fraction of the class can speak a second language? 4. Ned jogged for one-third of a mile, Trey jogged for one-half of a mile, and Steven jogged for one-fifth of a mile. Order these distances from least to greatest. What is the sum of their distances?

5. A magazine sells one advertisement that is seven-eighths of a page and another advertisement that is five-sixths of a page. If both advertisements cost the same amount, which one is the better deal?

6. Derek’s dad travels one and a half hours each way to work. What part of his day is spent commuting to and from work? !

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7. Order the following set of numbers from least to greatest:

1 , 1.73, 1 , 1.78

8. Order the following set of numbers from least to greatest:

−0.26, −

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, −0.35, −

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9. Plot each rational number on the number line. Write them in order from least to greatest: 3 3 , −0.38, , −0.43 8 7

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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Fill in the blank with <, >, or =. Justify each with a model or number-line or explanation. 10. 1

4 ___ 1.2 25

11. −1

4 ___ -1.2 25

12. -2.34 ___ −2

13.

Justification:

4 11

5 ___ 0.45 11

14. −3

19 ___ -3.94 20

Justification:

Justification:

Justification:

Justification:

Spiral Review: 15. Write

! !

as a decimal and percent.

17. Use =, <, or > to make a true statement. Show your work. 4.2   ÷ 2 _____ 0.7(3)

16. Simplify: 114.5 – (6.3 + 2.7)2

18. Simplify: 4!  

Spiral Review Determine the first expression to evaluate in each problem. Example: 5 + 8×5 + 72 ÷ 8 19. 5 + 9 + 10 + 16 ÷ 4 8×5

20. 10 − 7 + 12 ÷ 6 + 60 ÷ 6

21. 10 + 5 + 7! + 6! + 8

23. 2 + 3! + 2! + (7×4)

22. 6 − 4 + 54 ÷ 6×3

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.2C Homework: Probability, Fractions, Percentage, & Ratio* Name:

Period:

Express each fraction as a percent. 1. 2.

! ! ! !"

3. 4.

! !" ! !

Express each percent as a fraction in simplest form. 5. 60%

8. 10%

6. 80%

9. 5%

7. 75%

10. 25%

Solve each using a model. Show your work. Answer in a complete sentence. 11. Find 80% of 150.

14. What percent of 80 is 60?

12. Find 40% of 40.

15. 40 is 8% of what number?

13. What percent of 30 is 15?

16. 60 is 30% of what number?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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For #17-18, use a model to SOLVE each of the following. Answer in a complete sentence. 17. Milo can run 10 miles in 60 minutes. If he wants to reduce his time by 20%, how many minutes does he have to take off his time?

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18. The computer store has a laptop regularly priced at $2160. Frank negotiated a 33 % discount. How ! much money will Frank save buying the laptop on sale? How much will he have to pay for the laptop?

Spiral Review: ! 19. Write as a decimal and percent. !

20. How does a number line help you order fractions?

21. Compare these two fractions using < or >. Explain your answer. ! !      ____       !"

!"

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.2D Homework: Rational Numbers in Applications with Models* Name:

Period:

Use a model to fill in the table below: Fraction 1.

2.

Decimal

Percent

SHOW YOUR WORK HERE:

3 5

4 25

3. 0.15 4.

2 3

5. 0.45

For #6-14, use a model to solve each problem. Answer in a complete sentence. 6. Fletcher paid $287.50 in taxes this year to his school district. This was a 15% increase from last year. What did Fletcher pay in school taxes last year?

7. Marisa earned money for helping a local business organize their inventory. She spent half of her earnings on accessories for her phone, and half of the remaining money on a gift for her mother. If she has $15 left, how much did she make organizing the inventory?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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8. Pedro has $80 left from the money he earned during the summer helping at his father’s business. He ! ! ! spent of his earnings on climbing equipment;   on camping gear; and of the remainder on ! ! ! entertainment during the summer. How much did he earn in total?

9. A snowmobile manufacturer claims that its newest model is 15% lighter than last year’s model. If this year’s model weighs 799 pounds, how much did last year’s model weigh?

10. Nick estimates that 50% of his income goes toward living expenses (rent, utilities and food). Of the rest, 50% goes to paying for his car and 25% of what is left goes to his other expenses. If Nick has $300 left at the end of the month, how much does he earn?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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11. Urivan earned $360 helping his grandfather at his business. He spent his mother and put

1 of his earnings on a gift for 4

2 of the rest into a savings account. How much does Urivan have left over for fun? 3

12. A color of paint used to paint a race car includes a mixture of yellow and green paint. Scotty wants to lighten the color by increasing the amount of yellow paint by 30%. If a new mixture contains 3.9 liters of yellow paint, how many liters of yellow paint did he use in the previous mixture?

13. Julia found a great pair of boots for $240, but that was more than she wanted to spend. A few months later they were on sale for 40% off. She searched online and found a coupon for an additional 25% off the sale price. How much will she pay for the boots?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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14. Bjorn is a supervisor and spends 20% of his typical work day in meetings and 20% of that meeting time in his daily team meeting. If he starts each day at 7:30 a.m., and his daily team meeting is from 8:00 a.m. to 8:20 a.m., when does Bjorn’s typical work day end?

Spiral Review: Simplify the following expressions: 15. 6! + 34 ÷ 7   16. 8 + 6(5! )

17. 3(2)2

18. Round to the hundredths place: 132.934 19. Round to the tenths place: 429.372 20. Round to the tens place: 285.286

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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Section 1.2 Review Name:

Period:

Show all work. Be sure to write all fraction answers in simplest form. Read the directions carefully! For #1-6, write each in fraction, decimal, and percent form. 1.

4.

! !

! !

2. 2.45

3. 38%

5. 0.006

6. 82%

For #7-12, solve using a model. Show all work. Answer in a complete sentence. 7. What is 40% of 85?

8. What percent of 60 is 15?

9. 45 is what percent of 270?

10. What is 150% of 40?

11. You get 75% correct on a science quiz with 80 questions. How many questions did you get correct?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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12. A) A blue sweater normally sells for $120. George has a coupon he can use to get 40% off the original price. How much will George have to pay for the sweater?

B) The store that sells the sweater wants customers to come in early so they decide to offer an Early Bird Special. Anyone shopping before 10:00 a.m. can take an additional 15% off their total bill. If George gets to the store early, how much will he have to pay for the sweater?

13. Which of the following is NOT equivalent to the other three? Explain your reasoning. !" !" A) B) 6.5% C) D) .065 !""

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!

!

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14. Plot the following on a number line: 1.65, -0.4, , −1 , .25

15. Using the bar model below, name the two equivalent fractions being shown.

16. Find the equivalent fraction. Draw a bar model to show the equivalence between the original fraction ! ! and the new one. = !

?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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17. At Nellie’s BBQ restaurant, 15 out of 60 customers ordered their BBQ extra spicy. What percent did not order the extra spicy BBQ? Draw a model to find the solution.

18. At KFC, customers ordered either extra crispy, crispy, original, or grilled chicken. !

! !  

of the customers

ordered extra crispy chicken, 20% ordered crispy chicken, and ordered original chicken. If 75 ! customers ordered grilled chicken, how many total customers were there? Draw a model.

Spiral Review: 19. Evaluate if a = 4 and b = 2. Show your substitution step. A) ab

B) 4a – b

C) a2 – b2

20. What is the probability of drawing a red marble out of a bag with 6 green marbles, 4 purple marbles, 3 black marbles, and 2 red marbles?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.3A Homework: Model Percent and Fraction Problems* Name:

Period:

Use a model to answer #1-3 below. Then write a number sentence that reflects your model and answer. For #4-11, use a method of your choice to solve. Show your work. Answer in a complete sentence. 1. A) Last year Stella harvested 42 tomatoes from her backyard garden. This year, her harvest increased by 1/3. How many tomatoes did she harvest this year?

B) If next year, she harvests 1/3 less than this year, will the number of tomatoes harvested return to 42? Why or why not? Justify your answer.

2. Adam is taking care of a vacant lot in his neighborhood. There are approximately 64 dandelions in the lot. He decided to try a homemade weed killer his grandmother suggested. Five weeks later, the dandelions have decreased by 75%. Approximately how many dandelions are in the vacant lot now?

3. Maria is learning to play golf. She has been working particularly hard on driving. Before lessons, her drives average 240 yards. After her first lesson, her drives increased 25%. After her second lesson, her new average increased another 25%. How far are her average drives after her two lessons?

4. Two stores have the same necklace on sale. The original price of the necklace is $200. At store AAA, it’s on sale for 30% off with a rewards coupon that allows an additional 20% off the sale price at the time of purchase. At store BBB, the necklace is on sale for 50% off. Will the price for the necklace be the same at both stores? If not, which store has the better deal?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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5. Two schools start with 1000 students. The first school’s enrollment increases 20% in 2012 and then decreases 20% in 2013; the second school’s enrollment stays constant in both 2012 and 2013. Which school has the most students in 2013?

6. Twelve percent of the total worth of a retirement fund is invested in oil stocks. If $45 million is invested in oil stocks, what is the total worth of the retirement fund?

7. A shirt costs $8.00 to manufacture. If the designer, distributor, and wholesaler each add a 50% markup on top of the cost, what is the final selling price of the shirt?

8. The Sound Off Siren Company tests every fifth siren for sound quality and every eighth siren for mechanical quality. The daily output is 350 sirens. a. What percent is tested for sound quality?

b. What percent is tested for mechanical quality?

c. What percent is tested for both types of quality at the same time?

9. A bag of candy contains 300 pieces of which 28% are red. a. How many pieces are NOT red? b. What is the probability that you pull a red piece of candy out of the bag?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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10. Sydney inflated 24 balloons for decorations at the middle school dance. a. If Sydney inflated 15% of the balloons for the dance, how many balloons are there in total?

b. What is the probability that a balloon chosen at random is a balloon that Sydney did not inflate?

11. Haley is making admission tickets to the middle school dance. So far she has made 112 tickets on purple paper, and her plan is to make 320 tickets total. Haley ran out of purple paper and needs to make the rest on gold paper. a. What percent of the admission tickets has Haley produced so far?

b. What is the probability that a ticket pulled at random is purple?

Spiral Review: Write all probabilities as fractions, decimals and percentages. 12. Suppose you were to roll a fair number cube once, then flip a coin. List the sample space.

13. What is the P(2, H)?

14. What is the probability that you would roll an even number and flip heads?

15. What is the probability that you would roll an even number or flip heads?

16. Find the area of the triangle below. Start with a formula, and answer with units.

5m 16 m

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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1.3B Homework: Transition to Numeric Expressions* Name:

Period:

1. For each problem below, use a model to answer the question. Context

Model

Fraction Change

Fraction of Original

Percent Change

Percent of Original

a. At the beginning of the year there were 32 students in Ms. Herrera’s class. There are now 36 students in her class. b. During the school year, Jose works 15 hours a week. In the summer he works 30 hours a week. Write a number sentence and solve the following problems. You may also use a model if helpful. State your answer in a complete sentence. 2. The weight of a granola bar was decreased by 20%. What is the new weight if the original weight was 4.5 oz?

3. The number of seats on the new Jet Blue airliner is a 36% increase over the old model. The old plane seated 374 passengers. How many passengers will the new model seat?

4. Last year, the population of Springfield grew from 1250 to 1300. If the population of the town grows by the same percent this year, what will the new population be?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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5. Contributions to The Cougar Pep Band were 10% greater in 2014 than 2013. In 2013, contributions were 15% greater than they were in 2012. If contributions in 2012 totaled $4355, what was the total in 2014?

6. A small business’s profits in 2011 were $120,000. In 2012 they decreased by 25%. How much did the business make in profits in 2012?        

7. The selling price of a skateboard that had sold for $220 last year was increased by 15%. What is the new price?

8. A BluRay player that originally cost $200 was discounted 25% for a Memorial Day sale. After the sale was over, the BluRay was marked up 25%. Harper and Jameson missed the sale. Harper says that the BluRay player is less expensive than its original price even after the markup. Jameson says that the BluRay costs $200 after the markup. Who is correct? Explain.

9. A skateboard is marked $200 at Hansen’s. The store is offering 20% off for their Fourth of July sale. They are offering an additional 20% off if you come early to shop between the hours of 8AM-9AM. How does this deal compare to 40% off the skateboard that they will offer for their Labor Day sale? When should I buy the skateboard?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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Module 1 Review Name:

Period:

Read each set of directions carefully. You must show ALL of your work to earn credit. Be sure to write all fraction answers in simplest form. Good luck! 1. Six different decimals are shown: 1. 6, 0.16, 0. 7, 1. 42, 1. 1, 0. 73 Which of the following fractions are equivalent to one of the six decimals? Select all that apply. ! !" ! !" ! !! a. b. c. d. e. f. !

!

!

!

!

!"

2. Miki goes jogging every morning. In which of the following situations does Miki jog a total distance of 5 miles for Monday and Tuesday combined? Select all that apply. a. On Monday, Miki jogs 4 miles. On Tuesday, Miki jogs 25% of the distance she jogged on Monday. b. On Monday, Miki jogs 2 miles. On Tuesday, Miki jogs 150% of the distance that she jogged on Monday. !

c. On Monday, Miki jogs 3 miles. On Tuesday, Miki jogs 1.5 miles more than on Monday. ! !

d. On Monday, Miki jogs 1 miles. On Tuesday, Miki jogs 2.25 miles more than on Monday. !

3. Marco’s Quality Sandals can make 840 sandals in an 8-hour period. Due to strict quality control standards, the company must then discard an average of 2.5% of their sandals that contain manufacturing defects. a. How many sandals does Marco’s discard in an average 24-hour day? Show your work.

b. Marco’s received an order of 39,312 sandals from a large retail store. How many full 24-hour days will it take Marco’s to make the sandals with this discard rate?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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4. A small furniture manufacturer sells their tables to a distributor. The distributor then sells the tables to a variety of furniture stores. The cost for the manufacturer to make their tables is $400. Each needs to add an amount to their cost so that they make a profit. This is called a mark up. a. The manufacturer wishes to make a profit of at least $160 on each table. What minimum percentage should the manufacturer use to mark up its price?

b. The price markup for the distributor and furniture store is shown in the table below: Markup Distributor 15% Furniture Store 35% If the manufacturer makes $160 profit on every piece of furniture it sells, what is the final price of the furniture at the store?

5. James counts the hair colors of the 22 people in class, including himself. He finds that there are 4 people with blonde hair, 8 people with brown hair, and 10 people with black hair. What is the probability that a randomly chosen student in the class does not have red hair? Explain.

6. A spinner has four equally sized sections lettered A, B, C, and D. The table shows the results of several spins. Find the experimental probability of spinning each letter as a fraction in simplest form, a decimal, and a percent. Letter A B C D Frequency 14 7 11 8 A: ________________

B: ________________

C: ________________

D: ________________

What is the theoretical probability for each of the spinner’s sections in number 6? How does the theoretical probability for each letter compare to the experimental probabilities?

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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7. A soccer coach claimed that, on average, only 80% of the team comes to practice each day. The table shows the number of students that came to practice for 8 days. Days Number of Students

1 18

2 15

3 18

4 17

5 17

6 19

7 20

8 20

If the team has 20 members, how many team members would come to practice daily to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning.

8. What is the probability of not rolling a 5 on a standard six-sided die?

9. How many possible outcomes are there for rolling four standard six-sided dice?

10. When rolling four six-sided standard dice, what is the probability of rolling a sum of two? Explain your answer.

11. A jar contains 10 blue marbles, 2 yellow marbles, and 8 red marbles. a.

If you were to draw one marble from the jar, what is the theoretical probability, as a fraction, that you’d choose a yellow marble? What about blue? And red? P(Yellow): ________________ P(Blue): ________________ P(Red): ________________

b.

If Max picks a marble from the bag and returns it 80 times, predict how many times you would expect him to pick a red marble. Explain your reasoning.

c.

What is the sum of the probabilities that you found in part a? Explain why this answer makes sense and what it represents.

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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12. In a different jar of colored marbles, there are blue, red, yellow, and green marbles. There is a 40% possibility of randomly picking a blue marble, a 5% chance of choosing a red marble, and a 30% chance of randomly picking a yellow one. What is the probability of picking a green marble?

13. Complete the table below. Fractions must be in simplest form. Decimal

Fraction in Simplest Form

Percent

0.65 2 99 105% 1.04 Solve. Use a model to show your work. Answer in a sentence. 14. What percent of 400 is 20? 15. Find 45% of 12.

17. Answer the questions below. a. In a small town in Utah, 40,000 homes used to have land-line phones. If there was a 12.5% decrease, how many homes now have land-line phones.

16. 20% of what number is 24?

b. A small business’s profits in 2011 were $120,000. If there was a 25% increase in 2012, what were the profits in 2012?

18. A customer paid $12 in tax. His tax rate was 5%. Find the dollar amount of his purchase.

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

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19. A bicycle that usually sells for $240 is on sale for 15% off. Find the sale price.

!

!

!"

!

!

!"

20. Mark the location of −1 , − ,

!

!

!

!"

, −1.6, 2 , −

on the number line shown below.

For #21-22, read the word problem carefully and analyze the model. Determine the following: a. b. c.

Does the model accurately represent the problem? If no, explain why it is incorrect, fix it, and solve the problem. If yes, use it to solve the problem. Answer in a sentence.

21. 15% of the number of people who attended a concert arrived late. If 30 people arrived late, find the number of people who attended the concert.

22. At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many total visitors are at the museum?

100%

100% 15%

30 people

40% 36 children

? people

SDUHSD Math A Honors – Module #1 - HOMEWORK 2017-2018

? visitors

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