Probability, Percent, Rational Number Equivalence Math A College Prep

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

1.1A Homework: Solve Probability Predictions* Name:

Period:

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

2. Based on your flips from #1: What if you flipped the coin 100 times, how many heads would you expect to get? Explain your answer.

3. A coin is tossed 20 times. It lands on heads 9 times. What is P(H) according to your experiment? Write your answer as a fraction, decimal and percent.

4. You’re a teacher in a 7th grade math class and you want to create an experiment for your class with red, yellow, and purple marbles in a bag. You want the theoretical probability of drawing a red marble to be ½, the theoretical probability of drawing a yellow to be ¼ and the theoretical probability of drawing a purple to also be ¼. If you want a total of 80 marbles in the bag: a. How many red marbles are you going to put in the bag? Why? b. How many yellow marbles are you going to put in the bag? Why? c. How many purple marbles are you going to put in the bag? Why?’ 5. You’ve decided you want to make the marble experiment a little more difficult. You want to use 400 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. Can you predict what the sum of the fractions below should be? If so, what is the sum? b. Blue: P(B) ________ and actual number of blue ________ c. Red: P(R) ________ and actual number of red ________ d. Green: P(G) ________ and actual number of green ________ e. Yellow: P(Y) ________ and actual number of yellow ________ f.

Purple: P(P) ________ and actual number of purple ________

g. Pink: P(P) ________ and actual number of pink ________ h. Add up your marbles above. What is your total? i.

Add up your fractions above. What is your sum? How does it compare to your prediction in part a?

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1.1B Homework: Probability* Name:

Period

Write all probabilities as a simplified fraction, decimal and percent. 1. Find all the possible outcomes of flipping a coin (heads or tails) FOUR times (how many heads and tails in four flips). How many outcomes are there? Justify your answers using a model or table.

2. Based on #1, what is the theoretical probability that you: a. Get HEADS for all four flips? b. Get HEADS at least once in four flips? c. Get HEADS exactly three times in four flips? d. Get TAILS exactly two times in four flips? e. Get TAILS at least twice in four flips? 3. When rolling two dice, is 1,3 the same as 3,1? Explain.

Write all probabilities as simplified fractions, decimals and percents. 4. 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.

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1.1C Homework: Sample Spaces, Outcomes, and Probabilities* Name:

Period

For #1-2, use a tree diagram to answer the following questions. Write all fractional answers in simplest form. 1. A movie theater sells 3 sizes of popcorn (small, medium, large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?

a. How many outcomes are in this sample space? __________ b. What is the P(medium)? __________ c. What is the P(any amount of butter)? __________ 2. A frozen yogurt shop has the following choices for yogurt: vanilla, chocolate, strawberry, cookies and cream, peanut butter, and cake batter. They are running short on toppings though. Your topping choices are: gummie bears, cookie dough, and sprinkles. If you choose one flavor of yogurt and one topping and can choose to have it in a cup or a waffle cone, how many options do you have?

a. How many outcomes are in this sample space? __________ b. List the outcomes: c. What is the P(peanut butter)? __________ d. What is the P(vanilla and sprinkles)? __________ e. What is the P(vanilla or sprinkles)? __________ 3. If there are x number of choices for event #1 and y number of choices for event #2, which of the following best represents how many choices there are: a. 𝑥 + 𝑦 b. 𝑥 − 𝑦 c. 𝑥 ∙ 𝑦 d. 𝑥 ÷ 𝑦  

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For #4-6, use the Fundamental Counting Principle to answer the following questions. Write all fractional answers in simplest form. 4. I am out to dinner with my parents and I am feeling indecisive. Do I want rice or potatoes? Do I want to drink lemonade, soda, or iced tea. For dessert do I want cake, ice cream, fruit, or a brownie. How many different combinations must I consider before ordering? Show work that justifies your answer.

a. How many outcomes are in this sample space? __________ b. What is the P(potatoes)? __________ 5. You and your friend go ice skating all the time. You have decided it’s probably most cost effective to buy a pair of skates rather than rent. When looking online you find the following best deal possible for $39.99. You get to choose from the following: Colors – white, beige, pink, yellow, blue Sizes – 6,7,8,9,10 Extras – tassels, stripped laces, bells. If all skates are sold with ONE extra, how many possible arrangements exist? Show work that justifies your answer.

6. A spinner contains three letters of the alphabet.

a. How many outcomes are in this sample space if the spinner is spun 3 times? __________ b. List the outcomes:

c. What is the P(exactly one H)? __________ d. What is the P(exactly two V’s)? __________ e. What is the P(three T’s)? __________

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Section 1.1 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. 1. A company manufactures football helmets. The quality control department checks 400 football helmets and discovers that 4 of them are defective. What is the probability that a helmet is not defective? Write your answer as a fraction in simplest form.

2. After 40 spins, Chris landed on blue 16 times. What is the experimental probability of landing on blue? What is the theoretical probability of landing on blue? Write your answer as a fraction in simplest form. Experimental Probability = Theoretical Probability =

3. The table below shows the sums when two six-sided dice are rolled. What is the experimental probability of rolling a sum of 9 based on the table? Write your answer as a fraction in simplest form. Trial Sum

1 5

2 3

3 7

4 9

5 7

6 8

7 6

8 7

9 5

10 9

4. When you roll a die (or game cube) with 6 sides, what is the probability it will land on a number less than 3? Write your answer as a fraction in simplest form.

5. There is a bag of pink, purple, and black marbles. There is a 16% possibility of randomly picking a pink marble and a 62% chance of randomly picking a black marble. What is the probability of picking a purple marble? Write your answer as a percent.

6. Melia has a bag containing 5 black tiles, 6 pink tiles, and 4 purple tiles. a. What is the probability that Melia will pick a black tile? Write your answer as a fraction in simplest form. b. If Melia 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.

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7. In your own words, explain what it means when an event has a probability of one. Give an example.

8. In your own words, explain what it means when an event has a probability of zero. Give an example.

9. Lori has a craft box full of feathers. The craft box has 2 yellow feathers, 7 black feathers, 4 red feathers, 6 pink feathers, 3 green feathers, and 8 brown feathers. If Lori is randomly choosing feathers out of the box one at a time and then returning them, CIRCLE all the statements that are true. a. b. c. d. e.

!

Lori has a chance of picking a pink feather. !" Lori will more likely pick a brown feather than a red feather. !! Lori has an chance of picking a feather that is NOT brown. !" Lori has an equal chance of choosing any color feather. ! Lori has a chance of choosing a green feather. !"

For #10, use a tree diagram to answer the following questions. Write all fractional answers in simplest form. 10. At a restaurant for breakfast, with your eggs, you can pick a side from pancakes, waffles or home fries. For a drink, you can pick from: coffee, juice, hot chocolate, and tea. How many different choices of sides and drink combinations do you have to go with your eggs?

a. How many outcomes are in this sample space? __________ b. What is the P(waffles)? __________ c. What is the P(pancakes or hot chocolate)? __________ For #11, use the Fundamental Counting Principle to answer the following questions. Write all fractional answers in simplest form. 11. A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there? Show work that justifies your answer.

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1.2A Homework: Equivalent Fractions* Name:

Period:

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

d.

! !

!" !"

b.

e.

! !

! !"

c.

f.

!" !"

! !"

2. Write an equivalent fraction. Draw a bar model for questions “a” and “b” to show the equivalent fractions. a.

1 = 2 6

b.

2 = 5 15

c.

2 = 3 15

d.

4 = 7 14

e.

5 = 8 24

f.

3 = 4 24

3. Change each fraction to a mixed number. Draw a bar model for questions “a” and “b”. a.

d.

!" !

!" !"

b.

e.

!" !

!" !

SDUHSD Math A College Prep Module #1 – HOMEWORK 2017-2018

c.

f.

!" !

!" !

8

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

Period:

Fill in the table below. Is the fraction closer to 0, ½, or 1? Justify your answer with either words or a model. The first one is done for you. Fraction

Decimal

Percent

11 20

0.55

55%

Justification

1. This is close to

!" !"

!

 𝑜𝑟   . !

2.

16 25 3. 92 100 4. 6 11 5. 1 9

Fill in the blank with <, >, or =. Justify each with a picture or number line or explanation.

4 _____1.2 25

Justification:

5 _____ 0.45 11

Justification:

5 10 _____ 4 6 13

Justification:

6. 1

7.

8. 4

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!

!"

!

!"

9. Order the following set of numbers from least to greatest: 1 , 1.73,

, 1.78  

10. Plot each rational number from the problem above on the number line.

11. For each problem below, circle the number that is bigger. Explain how you know. a. 0.007 and 0.05

b. 0.123 and 0.8

c. 0.22 and 0.2

12. Order the following fractions from least to greatest. Explain your process. 6 3 ,                   , 5 10

13. Place the fractions on the number line below. 6 3 ,                   , 5 10

1 , 5

1 , 5

3 2

3   2

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14. Without using a calculator, determine which fraction is bigger in each pair. Justify your answer. a.

1 9

or

1 10

b.

8 9

or

9 10

c.

5 9

or

5 11

d.

5 5 or 12 14

15. Classify these fractions as close to 0, close to 1 , 2

Close to 0

4 , 28

3 , 5

! !

, close to 1. 2 , 7

5 , 14

Close to

2 , 11

! !

4 , 5

7 9

Close to 1

16. Order the above numbers from least to greatest. Fractions: ______, ______, ______, ______, ______, ______, ______, ______

Spiral Review Simplify without the use of a calculator. 17. 77.2 − 43.778 18. 2.072 ÷ 5.6

SDUHSD Math A College Prep Module #1 – HOMEWORK 2017-2018

19. 4.23×9

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

Period:

Express each fraction as a percent. 1.

3.

! !

! !"

2.

4.

! !"

! !

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

6. 10%

7. 75%

8. 25%

Solve each using a model. Show your work. 9. Find 80% of 150.

10. What percent of 80 is 60?

11. What percent of 30 is 15?

12. 12 is 30% of what number?

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Use a model to solve each problem. 13. Makayla got a score of 75% on her English final. If there were 48 questions on the test, approximately how many questions did she get right?

14. Milo can run 10 miles in 60 minutes. If he needs to reduce his time by 20%, approximately how many minutes does he have to take off his time?

Spiral Review Rewrite the number as a multiplication problem. Example: 9! 15. 4! 9×9×9×9

16. 6!

Rewrite the multiplication problem in exponential notation. Example: 3×3×3×3 17. 5×5 3!

18. 7×7×7

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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.

Decimal

Percent

3 5

2.

4 25

3. 0.15 4.

2 3

5. 0.45

Use a model to solve each problem. 6. Marisa earned money for helping a local business with organizing 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?

7. Pedro has $80 left from the money he earned during the summer helping at his father’s business. He had spent

1 1 1 of his earnings on climbing equipment, on camping gear and of the remainder on 3 3 2

entertainment during the summer. How much did he earn during the summer?

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8. 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?

9. Marco earned $360 helping his grandfather at his business. He spent mother and put

1 of his earnings on a gift for his 4

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

10. 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 25% off the sale price. How much will she pay for the boots?

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Section 1.2 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. 1. Complete the table below. Fractions must be in simplest form. Show work to the side of the table. Fraction in Simplest Form

Decimal

Percent

0.65 3 25 1% 1.05

2. Which of the following is NOT equivalent to the other three? !" !" A. B. C. 6.5% D. 0.065 !""

3. How is

!"

! !

written as a decimal? B. 2. 6

A. 0.375

C. 0.125

D. 0.3 !

4. Which letter represents the placement of the fraction 5 in decimal form? !" A B C

D

Write each fraction in simplest form. Your answer may be a proper fraction, improper fraction, or mixed number. Show all work. 5.

6.

!"# !"#

!" !"

7. Plot each number on the number line below. ! ! ! 2.10, 0.25, , , 1 ! !

!

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8. Four students compared their final grades from their Literature class. Their results, given in decimal, percent, or fraction form, are shown below: Student Charlie Bridgette Jamal Ana

Final Grade 0.66 66.7% 33 50 0. 6

Which of the following are correct? Select all that apply. a. Charlie had a higher score than Bridgette. b. Charlie had a lower score than Ana. c. Bridgette had a higher score than Jamal. d. Charlie had the same score than Jamal. e. Bridgette had a higher score than Ana. f. Jamal had a higher score than Ana. For #9-11, use a model to solve. 9. 60 is 80% of what number?

10. Jerry is taking care of a vacant lot in his neighborhood. There are approximately 64 thistle weeds in the lot. He decided to try a homemade weed killer his grandmother suggested. Five weeks later, the thistles have decrease by 75%. Approximately how many thistles are in the vacant lot now?

11. Maria is learning to play golf. She learned when the ball is hit hard it is called “driving the ball”. Before her lessons, her drive average was 240 yards. After her first lesson, her drive average increased 25%. After her second lesson, her drive average increased another 25%. How far are her average drives after the two lessons?

12. Order the fractions from least to greatest.

1 5 3 4 1 ,       ,       ,        , 2 6 8 5 8

Fractions: ______, ______, ______, ______, ______ SDUHSD Math A College Prep Module #1 – HOMEWORK 2017-2018

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

Period:

Use a model to solve each of the following multi-step problems. Then write a number sentence that reflects your model and answer. 1. Larry has a piece of rope that’s 12 feet long. He cuts 25% of the rope off. How long is the rope now? a. Solve by using a model.

b. Solve by writing and using a number sentence.

2. Lydia invested $150. If Lydia earned 10% on her investment, how much money does she have now? a. Solve by using a model.

b. Solve by writing and using a number sentence.

3. Li planted a 12 foot tall tree in her yard. 10 years later it is 18 feet tall. What is the tree’s percent of growth? a. Solve by using a model.

b. Solve by writing and using a number sentence.

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4. At Lincoln Middle School 300 students participated in the Science Fair in 2011. In 2012, 400 students participated. What was the percent of growth? a. Solve by using a model.

b. Solve by writing and using a number sentence.

5. Last year Cory harvested 42 tomatoes from his backyard garden. This year, his harvest increased by 1/3. How many tomatoes did he harvest this year? a. Solve by using a model.

b. Solve by writing and using a number sentence.

Spiral Review Determine the first expression to evaluate in each problem. Example: 5 + 8×5 + 72 ÷ 8 6. 5 + 9 + 10 + 16 ÷ 4 8×5

7. 10 − 7 + 12 ÷ 6 + 60 ÷ 6

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

10. 2 + 3! + 2! + (7×4)

9. 6 − 4 + 54 ÷ 6×3

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1.3B Homework: Percent and Fraction Problems* Name:

Period:

Write a number sentence to solve the following problems. You may also use a model if helpful. 1. What percent of 20 is 11?

2. What is 56% of 75?

3. 120 is 15% of what number?

4. At the beginning of the school year Marilee had $480 in her bank account. That was only 15% of the amount in her bank account at the end of the school year. How much money was in her account at the end of the school year?

5. A computer store pays $6 for a computer mouse. The percent of markup is 75%. How much will the store sell the mouse to the public?

6. Store CC is selling a shirt for 20% off the store’s regular price of $25.95. Store BB is selling the same shirt for 30% of the store’s regular price of $29.50. Which store’s sale price is lower? How much lower is it?

7. 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 now?

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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?

10. How can you explain why the deals in #12 above are not the same?

Spiral Review Write all probabilities as fractions, decimals and percentages. 11. Suppose you were to roll a fair number cube once, then flip a coin. Draw a tree diagram and list the sample space.

12. What is the total number of outcomes in your sample space in the above problem? Use the Fundamental Counting Principle to show this.

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

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

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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. 1. James counts the hair colors of the 22 people in class, including him. 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.

2. Michelle landed on blue 27 times after 75 spins total. What is her experimental probability of landing on blue? What is the theoretical probability of landing on blue?

3. A spinner has four equal 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: _______________

4. What is the theoretical probability for each of the spinner’s sections in number 3? How does the theoretical probability for each letter compare to the experimental probabilities?

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5. 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 should come to practice to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning.

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

7. 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 that you’d choose a yellow marble? What about blue? And red? Yellow: _______________

Blue: _______________

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.

8.

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? Express your answer as a percent.

9.

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

Write as a simplified fraction. Show all work. 10. 0.01 11. 0.48

12.

3.63

SDUHSD Math A College Prep Module #1 – HOMEWORK 2017-2018

13.

2.04

23

Write as a decimal. Show all work. ! ! 14. 15.       !

!!

16. 3

! !"

17.

! !

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

Fraction in Simplest Form

Percent

0.65

5 8 105% 1.04 Solve. Use a model sentence to show your work. 19. Cameron bought a new mattress for $400. He had a $20 off coupon. What percent was the discount? 20. A bicycle that usually sells for $240 is on sale for 15% off. Find the sale price.

21. Margo’s receipt was smudged and she couldn’t read the original price of the scooter she bought. Margo could see that 20% of the original price was $24. How much was the original price of the scooter?

Solve. Use a number sentence to show your work. 22. A salesperson paid $12 in tax. His tax rate was 5%. Find the dollar amount of his purchase.

23. A Tech Deck costs $12 wholesale. If you want to mark up the Tech Deck 45%, how much will you have to raise your price?

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!

24. Which letter best shows ? !

For #25–26, read the word problem carefully and analyze the model. Determine the following: a. b. c.

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

25. 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.

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

100% = ? people 100% 15% 40% 30 people 36 children

? visitors

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