Name: ____________________________________________________

Pre-Algebra Workbook

Unit I: Probability and Data Analysis

Pre-Algebra Units and Essential Learning Outcomes

Pre-Algebra Unit I: Probability and Data Analysis

I can show and explain my reasoning so others can understand it. (ELO1; Standard MP3)

3 I consistently show and explain my reasoning so others can understand it.

2 I sometimes show and explain my reasoning so others can understand it.

1 I rarely show and explain my reasoning so others can understand it.

I can be precise with my work, notation, and vocabulary. (ELO2; Standard MP6)

3 I consistently am precise with my work, notation, and vocabulary.

2 I sometimes am precise with my work, notation, and vocabulary.

1 I rarely am precise with my work, notation, and vocabulary.

I can find probabilities of events. (ELO23; Standard 7SP5,7SP6,7SP7,7SP8)

4 I am proficient at level 3 and I can do work beyond the level that was taught. For example, I can:

design a probability game.

find the probability of conditional events.

3 I can:

find the probability of a compound event.

represent the sample space of a compound event using an organized list, table, or tree diagram.

2

I can recognize and recall specific vocabulary such as:

tree diagram, outcome, event, favorable, sample space, simple event, equally likely, simulation, compound event, probability, and notations such as 𝑃(𝐴).

understand that probability is between 0 and 1. I can perform basic processes such as:

use organized lists, tables, tree diagrams, and simulations to find the probability of compound events.

find the probability of a simple event.

make inferences about the likelihood (impossible, unlikely, equally likely, likely, certain) of an event given its probability.

1 I can do the level 2 and 3 targets with help.

I can compare data from two different populations. (ELO24; Standards 7SP2 and 7SP4)

4 I am proficient at level 3 and I can do work beyond the level that was taught. For example, I can:

explain or calculate other measures of variability.

3 I can:

calculate the mean, median, mode, range, and mean absolute deviation (MAD) of a set of data.

make inferences about the data using the measures of center and measures of spread.

2

I can recognize and recall specific vocabulary such as:

mean, median, mode, range, and mean absolute deviation. I can perform basic processes such as:

order numbers, compare numbers, and basic arithmetic.

1 I can do the level 2 and 3 targets with help.

(continued on next page)

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Pre-Algebra Units and Essential Learning Outcomes

Pre-Algebra Unit I: Probability and Data Analysis (continued)

I can use random sampling to draw inferences about data. (ELO25; Standards 7SP5, 7SP6, & 7SP7)

4 I am proficient at level 3 and I can do work beyond the level that was taught. For example, I can:

conduct my own experiment and draw inferences from the results of the experiment.

3 I can:

use random samples to draw inferences about data.

use experimental or theoretical probability to make predictions.

2

I can recognize and recall specific vocabulary such as:

probability, event, outcome, favorable outcome, random sampling, population, sample, biased sample, margin of error, inference, and hypothesis.

I can perform basic processes such as:

Identify and explain various sampling methods.

1 I can do the level 2 and 3 targets with help.

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What’s on the test?

Date of the test: Number of questions: Number of points:

Describe the topic or standard: Number of questions?

How well do I know this?

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Pre-Algebra Unit I

Homework assignments

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Pre-Algebra I1 Intro to probability

1) Place the letter for each of the following events on an appropriate location on the probability scale.

The numbers 1 to 10 are written on small pieces of paper and placed in a bag. A piece of paper will be drawn from the bag.

A. A piece of paper with a 5 is drawn from the bag.

B. A piece of paper with an even number is drawn.

C. A piece of paper with a 12 is drawn.

D. A piece of paper with a number other than 1 is drawn.

E. A piece of paper with a number divisible by 5 is drawn.

2) Write the word; impossible, unlikely, equally likely, likely or certain below the spinner to describe the

chance of the spinner landing on black.

SPINNER A SPINNER B SPINNER C SPINNER D SPINNER E

3) Label the cubes below red or blue so that it would be equally likely to choose a blue or red cube.

4) Label the cubes below red or blue so that it would be likely, but not certain, to choose a red cube from the bag.

5) Label the cubes below red or blue so that it would be unlikely, but not impossible, to choose a red cube from the bag.

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Pre-Algebra I1 Intro to probability

6) Label the cubes below red or blue so that it would be impossible to choose a red cube from the bag.

Jill is playing golf. She has 5 white golf balls, 4 yellow golf balls, and 1 red golf ball in her golf bag. At the first hole, she randomly draws a golf ball from her bag.

7) What is the probability that she draws a white golf ball? Write it as a fraction, decimal, and percent.

8) What is the probability that she draws a yellow golf ball? Write it as a fraction, decimal, and percent.

9) What is the probability that she draws a green golf ball? Write it as a fraction, decimal, and percent.

10) If there are 200 balls in her bag with the same distribution, predict how many will be white?

The next section is about designing a spinner.

11) What do you think it means for an event to have the probability of 1

4 ?

12) Draw a spinner that has 2 sections (yellow & green) where the probability of landing on green is 1

4.

13) What is the probability of landing on the yellow section in the spinner you designed above?

14) How many times do you think the spinner will land on each section after 100 spins in the spinner you designed above?

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Pre-Algebra I2 Probability and making predictions

1) Micha flips a penny four times, and it land on heads up all four times. On her fifth flip, what is the probability that the penny will land tails up? Explain.

2) Label the spinner below so that the given probabilities hold true for one spin on the spinner. Explain your reasoning.

A standard deck of playing cards has 52 cards. The deck is divided into 4 suits: spades, hearts, diamonds, and clubs. There are 13 cards of each suit.

3) If you randomly draw a card from a standard deck of playing cards, what is the probability that you will draw a heart?

4) If you randomly draw a card from a standard deck of playing cards, what is the probability that you will draw a diamond or a club?

5) If you draw 12 cards, how many diamonds could you expect to draw? Explain.

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Pre-Algebra I2 Probability and making predictions

A bag contains red, yellow, and white beads. The probability of randomly choosing a red bead is 30%, the probability of randomly choosing a yellow bead is 20%, and the probability of randomly choosing a white bead is 50%.

6) Determine the number of red beads, yellow beads, and white beads in the bag if there is a total of 80 beads in the bag.

7) Determine the total number of beads in the bag if there are 20 white beads in the bag.

8) A student played a game using one of the spinners below. The table shows the results of 15 spins. Which spinner did the student use? Explain your answer.

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Pre-Algebra I4 Sample spaces and equally likely outcomes

Consider an experiment of randomly selecting a letter from the word algebra.

1) What is the sample space?

2) List the probability of each outcome in the sample space.

3) Is each outcome equally likely? Explain.

4) What is the probability of selecting a vowel?

5) What is the probability of selecting the letter j?

Students are playing a game that requires spinning the two spinners shown here. A student wins the game if both spins land on red.

6) List the sample space (all the possible outcomes) of the game.

7) What is the probability of landing on two colors that are the same?

8) What is the probability of winning the game?

9) If the game would be played 100 times, predict how many times someone would spin “red” and “red”.

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Pre-Algebra I4 Sample spaces and equally likely outcomes

A chance experiment consists of flipping a coin and rolling a six-sided number cube.

10) List the sample space or all of the possible outcomes of this experiment.

11) Is each outcome equally likely? Explain.

12) What is the probability of getting a heads on the coin and the number 3 on the number cube?

13) What is the probability of getting a tails on the coin and an odd number on the number cube?

14) What is the probability of getting tails on the coin and any number on the number cube?

15) Give an example of an outcome that has a probability of 1

3 for this experiment.

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Pre-Algebra I5 Tree diagrams

Draw a tree diagram to show all the possibilities.

1) Today, the school’s cafeteria is offering a choice of pizza or spaghetti. You can get milk or juice to drink. For dessert, you can get pudding or an apple. You must take one of each choice.

2) A clothing store sells shirts in 3 sizes: small, medium, and large. The shirts come with buttons or snaps. The colors available are blue or beige.

A computer store sells 4 models of a computer (m1, m2, m3, and m4). Each model can be fitted with 3 sizes of hard drive (A, B, and C).

3) Draw a tree diagram.

4) What is the probability of choosing a computer with a size C hard drive at random?

5) What is the probability of choosing a model 2 computer with a size A hard drive at random?

Suppose that you roll two number cubes. Use a tree diagram to find the probability of each event.

6) P(both numbers are even) =

7) P(roll a 2 and a 4) =

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Pre-Algebra I6 Measures of center and spread

1) The table shows the amount of money raised by the advisory classes for two grade levels at a middle school. Find the mean, median, mode, range, and mean absolute deviation for each set of data. Round to the nearest hundredth if needed. Then write a 2 sentences comparing their center and spread.

2) The table shows the lengths of the longest bridges in the United States and in Europe. Find the mean, median, mode, range, and mean absolute deviation for each set of data. Round to the nearest hundredth if needed. Then write a 2 sentences comparing their center and spread.

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Pre-Algebra I6 Measures of center and spread

3) The table shows the number of points scored each game for two different basketball teams. Find the mean, median, mode, range, and mean absolute deviation for each set of data. Round to the nearest hundredth if needed. Then write a 2 sentences comparing their center and spread.

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Pre-Algebra I7 Collecting data

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Pre-Algebra I7 Collecting data

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Pre-Algebra I8 Interpreting data

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Pre-Algebra I8 Interpreting data

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Pre-Algebra I9 Unit review

1) Explain the difference between experimental probability and theoretical probability.

2) What does it mean for something to have the probability of 0?

3) Give an example of something with the probability of 0.

4) What does it mean for something to have the probability of 1?

5) Give an example of something with the probability of 1.

A six-sided number cube is rolled 450 times. Two comes up 76 times.

6) What is the theoretical probability of rolling a two?

7) What is the experimental probability of rolling a two?

8) A six-sided number cube is rolled. Will the probability be closer to 0 or 1 for a number greater than 4 to be rolled? Justify your answer.

9) There are three colors of marbles is a container: red, white, and blue. If the probability of red is 1

2 and

the probability of white is 1

10, what is the probability of blue?

10) Dana tossed a coin 25 times and got tails 13 times. Based on those results, how many tails would you predict that Dana would get if she tossed a coin 100 times?

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Pre-Algebra I9 Unit review

11) Erica went to the ice cream store to buy an ice cream cone. Her choices for the cone were sugar and waffle. The ice cream flavors were strawberry, vanilla, and chocolate. How many ice cream cone choices did she have? Use a tree diagram to find the answer.

12) If an ice cream cone was randomly made for Erica (from the previous problem), what is the probability it would be chocolate ice cream in a sugar cone?

13) Find the mean, median, mode, range, and mean absolute deviation for EACH of the two companies listed below. Write 2 sentences comparing the number of calories at each sandwich shop.

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Pre-Algebra Unit I

Homework answer keys

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Pre-Algebra Homework answer keys

I1 answer key:

1) A – between impossible and unlikely. B – equal chance. C – Certain. D – between likely-certain. E – around unlikely.

2) A – unlikely, B – Likely, C – impossible, D – equally likely, E – certain.

3) Half should be marked blue and half should be red

4) Most, but not all, should be labeled red, and maybe 1-2 should be labeled blue.

5) Most, but not all, should be labeled blue, and maybe 1-2 should be labeled red.

6) All should be labeled blue.

7) 1

2, 0.5, 50%

8) 2

5, 0.4, 40%

9) 0

10, 0, 0%

10) Half of them should be white, so 100.

11) It means that it is unlikely, but not impossible to happen.

12) One-fourth should be green and the rest should be yellow.

13) 3

4, 0.75, 75%

14) 25 times on green, 75 times on yellow.

I2 answer key:

1) 1

2 because there are 2

outcomes and one of them is the favorable outcome.

2) 1 section should be red, 2 sections should be yellow, 3 sections should be blue, and nothing is green.

3) 1

4

4) 1

2

5) 3 because the probability

of getting a diamond is 1

4

and 1

4 of 12 is 3.

6) 24 red, 16 yellow, and 40 white beads

7) 40 total beads

8) They must have used spinner B since the result “3” only happened 3 out of 15 tries, so that is “unlikely”. The only spinner where “3” is “unlikely” is spinner B.

I4 answer key:

1) Sample space: a, l, g, e, b, and r.

2) A has a probability of 2

7 and

L, G, E, B, and R have a

probability of 1

7.

3) No, since there are 2 A’s in the word, that letter has a better chance of being selected.

4) 3

7

5) 0

6) RR, RB, RG, RY, BR, BB, BG, BY

7) 1

4

8) 1

8

9) About 12 or 13 times.

10) H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

11) Yes, each outcome has the same probability.

12) 1

12

13) 1

4

14) 1

2

15) Answers may vary. Sample: P(tails on coin and number less than 5 on dice)

I5 answer key:

1) Diagrams may vary a little.

2) Diagrams may vary a little.

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Pre-Algebra Homework answer keys

3) Diagrams may vary a little.

4) 1

3

5) 1

12

6) 9

36=

1

4

7) 2

36=

1

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I6 answer key:

1) 6th grade - Mean: 107, Median: 110, Mode: none, Range: 36, MAD: 10. 6̅. 7th grade - Mean: 114, Median: 118, Mode: none, Range: 41, MAD: 13. 3̅. Sentences may vary: The 7th grade seems to have raised more money per class since their mean and median are both higher. They have a higher range and MAD, so that means the amounts of money were more spread out than the 6th grade.

2) US - Mean: 19.91, Median: 15.3, Mode: 8.9, Range: 29.5, MAD: 9.772. Europe - Mean: 7.45, Median: 6.35, Mode: none, Range: 13.3, MAD: 2.87. Sentences may vary: It seems like the bridges in

the US are longer than those in Europe because the mean and median are both much higher in the US. The range and MAD for the US bridges is also higher, so this means that the lengths of the bridges here vary more compared to the mean.

3) Lakeside - Mean: 41, Median: 41, Mode: none, Range: 28, MAD: 7. 6̅. Jefferson - Mean: 56, Median: 60, Mode: none, Range: 30, MAD: 10. Sentences may vary: It looks like the Jefferson team scores more points per game than the Lakeside team because Jefferson has a higher mean and median. The range and MAD for Lakeside is lower so they are more consistent in the number of points they score per game.

I7 answer key:

1) Self-selected

2) Systematic

3) Convenience

4) Stratified

5) Population: residents of the state; sampling method: systematic sample; no; Sample answer: The customers entering a computer store in a mall are likely purchasing equipment for their home, and therefore are more likely to approve of home computers.

6) Population: residents of the town; sampling

method: systematic sample; no; Sample answer: The patrons at a library are more likely to be more enthusiastic about books, and therefore do not represent the population.

7) A) Population: members of the audience; sampling method: self-selected B) Sample answer: No; the people who decide to fill out the form are likely those with strong opinions, and as such may not represent the views of most members of the audience.

8) Yes; Sample answer: The question is biased because it suggests that building a new stadium is a waste of money. An alternative question is “Do you support building a new stadium?”

9) No; Sample answer: The question is straightforward and can be answered with a simple numerical fact.

10) Yes; Sample answer: The question is biased because it suggests that a new park would be good for the town. An alternative question is “Would you like to see a new park in town?”

11) A) Sample answer: No; a random sample should be representative. B) Sample answer: Yes; people in one portion might be more similar in age. C) Sample answer: Yes; if some people were unusually old, they would make the

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Pre-Algebra Homework answer keys

average age higher than might be “typical” for the city.

I8 answer key:

1) About 825 new parents

2) About 1260 people

3) president: too close to call; vice president: leading candidate; secretary: too close to call; treasurer: leading candidate

4) Yes; Sample answer: The sample percent is 38%. If the population percent is the same, then 38% of 3200, or about 1216 people, should provide their signatures.

5) Sample answer: I do not trust the survey or the conclusions. First, the population is just the shoppers at the local market. Also, there is no information as to how the survey was carried out or what sampling method was used to ensure that the survey truly represents even those people at the local market. The survey is even more troublesome because the survey conductor has an interest in the popularity of unusual fruit.

6) 300 to 500 residents

I10 answer key:

1) Experimental probability is based on the results of an experiment that someone has done. Theoretical probability is based on what should happen in the situation.

2) It is impossible.

3) Sample answer: There is going to be a snowstorm inside the classroom.

4) It is certain.

5) You are going to gain weight if you eat four pizzas in the next two hours.

6) 1

6

7) 76

450=

38

225

8) Closer to zero because the probability is less than half.

9) 4

10=

2

5

10) 52

11) 6; diagrams may vary.

12) 1

6

13) Susan’s - Mean: 415, Median: 420, Mode: none, Range: 240, MAD: 61. 6̅. Picnic Basket - Mean: 443. 3̅, Median: 445, Mode: none, Range: 320, MAD: 100. Sentences may vary: Susan’s shop has sandwiches with lower mean and median calorie amounts. They have a lower range and MAD, so that means the amounts of

calories vary less (less spread out) compared to the other shop.

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Pre-Algebra Unit I Student & Parent Resources

Use your phone to scan the QR Codes to access the resources. Your teacher may also share this

document with you electronically so you can click on the links.

Find probability of events:

What is probability?

Theoretical vs. experimental probability

Sample spaces and tree diagrams

Basic probability practice

Practice with tree diagrams

Videos on probability

Compare data using statistics:

Mean, median, and mode

Mean absolute deviation

Measures of spread

Videos on measures of center and spread

Video on how to find the MAD

Compare 2 sets of data

Sampling methods:

What is random sampling?

Videos on sampling and unbiased samples

Video on types of sampling methods

How to gather data