middle school content academy probability & statistics sol 6.14, 6.15, 6.16, 7.9, 7.10, 7.11,...

Middle School Content AcademyPROBABILITY & STATISTICS

SOL 6.14, 6.15, 6.16, 7.9, 7.10, 7.11, 8.12, 8.13

MARCH 18, 2015

Reporting Category: Probability & Statistics

Grade 6

Grade 7

Grade 8

2011-12 Reporting Category: Probability, Statistics, Patterns, Functions, and AlgebraMean Scaled Score: 33.9









Look for trends!

Grade 6 Focus: Practical Applications of StatisticsGrade 7 Focus: Applications of Statistics and ProbabilityGrade 8 Focus: Statistical Analysis of Graphs and Problem Situations

Vertical Articulation of ContentSOL 6.14, 7.11, 8.13

2014 SPBQ Data – 6.14, 7.11, 8.13 SOL Description of Question % Correct in

Division

6.14 Interpret information presented in a circle graph to draw conclusions.

70

6.14 Identify a circle graph that represents given data. 76

6.14 Recognize multiple graphical representations of the same data set.

81

7.11 Make inferences and comparisons for data sets displayed using different graphical representations.

82

7.11 Construct and analyze histograms for a given data set. 73

7.11 Construct and analyze histograms for a given data set. 77

8.13 Make comparisons, predictions, and inferences about information displayed in various graphical representations.

64

8.13 Collect, organize, and interpret data using scatterplots. 64

8.13 Make comparisons, predictions, and inferences about information displayed in various graphical representations.

39

Students need additional practice solving problems involving circle graphs.A car salesman sold 40 cars last month. The circle graph shows the results of his sales by car color.

1. Identify the car color that most likely represents exactly

10 cars.

2. Identify two car colors that most likely represent a

combined total of 25 cars.

2013 - Suggested Practice for SOL 6.14b

Car Sales

BlueRedGreenPurple

BlueGreen

Red

Purple

Common Errors? Misconceptions?

Students need additional practice comparing data in circle graphs with data in other graphs.Bob asked a group of people to identify their favorite vegetable. The circle graph shows the results. Which graph on the next slide could represent the same data?

2013 - Suggested Practice for SOL 6.14c

Favorite Vegetable

CornBeansCarrotsBroccoliAsparagus

Corn

Carrots

Beans

Broccoli

Asparagus


2013 - Suggested Practice for SOL 6.14cFavorite Vegetable

CornBeansCarrotsBroccoliAsparagus

Corn

Carrots

Beans

Broccoli

Asparagus

Which bar graph could represent the same data?


2014 - Suggested Practice for SOL 6.14bStudents need additional practice interpreting information presented in a circle graph.

Mr. Walker surveyed 24 students. He asked each student to rate a television show. The results are shown in this circle graph.

Which fraction of the students best represents those who rated the show as “Above Average?”

A B C D

Rating of Television Show


2014 - Suggested Practice for SOL 6.14cStudents need additional practice comparing and contrasting graphs that represent the same data set.

Twelve students answered a question that had answer choices labeled as A, B, C, and D. This circle graph represents the answer choices selected by the 12 students.

Answer Choices Selected

C

B

D

A

Which of these represents the data shown in the circle graph?

A C

B D


Answer Choices SelectedAnswer Choices Selected



Students need additional practice analyzing histograms.

2013 - Suggested Practice for SOL 7.11a

The graph describes the number of students in each classroom during first block at a high school.

What percent of the classrooms have at least 21 students during first block?

11-15 16-20 21-25 26-30 31-350

1

2

3

4

5

6

7

8

9Number of Students By Classroom in First Block

Number of StudentsN

umbe

r of

Clas

sroo

ms


Students need additional practice determining which graphical representation is the best to use for a given analysis.

Jamie recorded the time it took 25 students to complete a mathematics test. She created a histogram and a stem-and-leaf plot to represent the data. To determine the median of the data set, Jamie analyzed the –

a) histogram because it showed each value in the set of datab) stem-and-leaf-plot because it showed each value in the set of datac) histogram because the median is always the bar with the greatest heightd) stem-and-leaf-plot because the median is always the “leaf” that appears most often



2012 - Suggested Practice for SOL 8.13Students need additional practice interpreting the information displayed in graphs.This graph displays the high temperatures for Hampton, VA over five days in September.

65

67

69

71

73

75

77

79

81

83

85

Degre

es

Fahre

nheit

Date

High Temperatures in Hampton, VA

The mean high temperature in Bristol, VA for these same dates was 89°F.

What is the difference in the mean high temperatures of Bristol and Hampton for these five days, rounded to the nearest degree?


2013 - Suggested Practice for SOL 8.13aStudents need additional practice using data represented in a graph to make inferences or answer questions.

The numbers and prices of meals sold at a restaurant are represented in the graph.

6 7 8 90123456789

10

Meals Sold at a Restaurant

Num

ber o

f Mea

ls S

old

Price of a Meal (in dollars)

Based on the information in the graph:a) What is the mean price of all of the

meals sold?

b) What is the median price of all the meals sold?

c) What is the total number of meals costing more than 7 dollars?



a) the graph shows a positive relationship for the average price of a gallon of gas

b) the graph shows a negative relationship for the average price of a gallon of gas

c) the graph shows the average price of a gallon of gas remains constant

d) the graph shows no relationship between the average price of a gallon of gas and the months

This scatterplot shows the average price of a gallon of gas during each month in 2013. Which statement best describes the gas prices as the months progress from January to December?

July

Octo

ber

Augu

stSe

ptem

ber

Nove

mbe

r2.903.003.103.203.303.403.503.603.703.80

2013 National Average Gas Prices

Pric

e of

a G

allo

n of

G

as (

in d

olla

rs)

Months

Janu

ary

Febr

uary

Mar

ch May

June

April

Dece

mbe

r


2014 - Suggested Practice for SOL 8.13aStudents would benefit from experiences with data represented in a variety of graphical forms.

The circle graph displays the items sold at the football concession stand.

The concession stand sold a total of 450 items. How many more nachos were purchased than popcorn?

Items Sold at Football Concession Stand

Gatorade

Nachos

Cotton Candy

Hot Chocolate

Popcorn



Mr. Robert took a survey of his sixth period class to determine what breeds of dogs the students have as pets. The results are shown in this graph.

What percentage of the dogs owned by Mr. Robert’s class are a beagle or a terrier?

Beagle Labrador Poodle Terrier Bulldog0

2

4

6

8

10

Dogs Owned by Mr. Robert’s 6th Period Class

Dog Breeds

Num

ber o

f Dog

s



Vertical Articulation of ContentSOL 6.16, 7.9, 7.10, 8.12

2014 SPBQ Data – 6.16, 7.9, 7.10, 8.12

SOL Description of Question % Correct in Division

6.16 Find the probability of two independent events. 42

6.16 Determine if two events are dependent or independent 57

6.16 Find the probability of two dependent events. 43

7.9 Apply or describe the experimental and theoretical probability formulas to determine or calculate the probability of a compound event.

63

7.10 Apply the Fundamental Basic Counting Principle to determine the number of possible outcomes of compound events.

75

7.10 Determine the probability of a compound event. 42

8.12 Determine the probability of dependent and independent events. 37



2012 - Suggested Practice for SOL 6.16Students need additional practice finding the probability of dependent and independent events.This chart shows the three pairs of pants and four shirts that Bobby packed for a trip. Bobby will randomly select an outfit to wear. He can choose one pair of pants and one shirt. Using the chart, determine the probability that he will select a pair of blue jeans and the yellow shirt.

Pants Shirt Color

Blue Jeans Orange

Blue Jeans Yellow

Khakis Green

Red


2012 - Suggested Practice for SOL 6.16Alexis has a deck of cards labeled as follows:

• 3 cards with a heart • 2 cards with a circle • 1 card with a flower • 1 card with a ball

a) What is the probability that she will randomly select a card with a heart, replace it, and then select a card with a ball?

b) What is the probability that she will randomly select a card with a circle, NOT replace it, and then select a card with a circle?


Students need additional practice determining probabilities for dependent and independent events.

There are 6 classic rock CD’s, 2 jazz CD’s, and 5 country CD’s in a bin. Teagan will randomly select a CD, give it to her brother, and then randomly select another CD. Which of these can be used to find the probability that Teagan will select a jazz CD as her first selection and a country CD as her second selection?

A. C.

B. D.



This table shows the drink and dessert selections at a party.

Kayla will randomly select one drink and one dessert from these lists. What is the probability that Kayla will select water and apple pie?

A. C.

B. D.


Drink Dessert

Apple Juice Chocolate Cake

Orange Juice Apple Pie

Cola

Water

Students need additional practice determining the theoretical and/or experimental probability of an event.

These cards are the same size and shape. They are placed inside a bag.

A card is randomly selected and then placed back inside the bag. This is done 30 times. The card with an A is selected 3 times. 1)What is the theoretical probability of selecting a card with an A?2)What was the experimental probability of selecting a card with an A?3) Compare and contrast the theoretical and experimental probabilities of selecting a card

with an A after a card is randomly selected 1,000 times.

2013 - Suggested Practice for SOL 7.9

BA C D E F


Students need additional practice using the Fundamental Counting Principle to determine the number of possible outcomes.

The letters A, B, C, D, and E can be used to create a four letter code for a lock. Each letter can be repeated. What is the total number of four letter codes can be made using these letters?



Students need additional practice determining the probability of compound events.

A fair coin has faces labeled heads and tails. A fair cube has faces labeled A, B, C, D, E, and F. Adam will flip this coin and roll the cube one time each. What is the probability that the coin will land with tails face-up and the cube will land on the letter A?



Students need additional practice using the Fundamental Counting Principle to determine the number of possible outcomes.

The letters A, B, C, and D can be used to create a code for a lock. 1) Each letter can be repeated. What is the total number of four-letter codes that

can be made using these letters?

2) Each letter can be repeated. What is the total number of three-letter codes that can be made using these letters?

Extension: No letter can be repeated. What is the total number of three-letter codes that can be made using these letters?



Students need additional practice determining the probability of compound events.

A fair coin has faces labeled heads and tails. A fair cube has faces labeled 1, 2, 3, 4, 5, and 6. Adam will flip this coin and roll the cube one time each.

1) What is the probability that the coin will land with heads facing up and the top side of the cube will be a number that is composite?

2) What is the probability that the coin will land with tails facing up and the top side of the cube will be a number that is a multiple of 2?



Students need additional practice determining probability of compound events.

This table shows the types of pizza and drink selections at a party.

Maya will randomly select one type of pizza and one drink from these choices. What is the probability that Maya will select pepperoni pizza and cola?

A B C D


Type of Pizza Drink

Pepperoni Apple Juice

Vegetable Orange Juice

Plain Cheese Cola

Water

Students need additional practice calculating probability of independent and dependent events with and without replacement.a) Sue flips a fair coin three times. What is the probability that the coin will land on tails all three

times?

b) If the spinner for a game is spun once, there is a 20% chance it will land on red. What is the chance that it will NOT land on red on both the first and second spin in a game? Plot the value of this probability on the number line and label it.


01


• Juan has a bag of candy with 20 pieces that are the same shape and size. • 40% of the pieces are only chocolate.• 20% of the pieces are only caramel.• The remainder of the pieces are only toffee.

Juan eats 1 piece of caramel candy from the bag and then gives the bag to her friend Susanna. If Susanna takes one piece of candy from the bag without looking, what is the probability the piece she takes will be chocolate?


Olivia has hard pieces of candy in a bowl. They are all the same size and shape. There are 1 green, 4 blue, and 5 red pieces of candy in the bowl.

a) Olivia picks two pieces of candy without looking. What is the probability that Olivia will pick a red piece of candy and then a blue piece of candy?

b) Olivia picks two pieces of candy without looking. What is the probability that Olivia will pick a red piece of candy, put it back into the bowl, and then pick a blue piece of candy?



A spinner is divided into eight equal sections as shown.

What is the probability that the spinner will NOT land on a section labeled 2 on the first spin and will land on a section labeled 2 on the second spin?

1 2

2

2

3

3

4

3



Students need additional practice determining the probability of dependent and independent events.

Cynthia has 14 roses in a vase.

• 2 yellow roses• 5 pink roses• 3 white roses• 4 red roses

Cynthia will randomly select 2 roses from the vase with no replacement. What is the probability that Cynthia will select a red rose and then a pink rose?



Eric and Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls.

• Eric will select a treat, replace it, and then select a second treat.• Sue will select a treat, not replace it, and then select a second treat.

Who has the greater probability of selecting 1 lollipop and then 1 gum ball?



Mario rolls a fair number cube with faces labeled 1 through 6 three times. Place a point on the number line to represent the probability that the number landing face up will be an even number all three times.




Vertical Articulation of ContentSOL 6.15

2014 SPBQ Data – 6.15SOL Description of Question % Correct in

Division

6.15 Use a number line to define the mean as a balance point for a given set of data.

55

6.15 Describe the best measure of central tendency for a given set of data.

45

6.15 Use a number line to define the mean as a balance point for a given set of data.

62

Students need additional practice using a line plot to determine the mean as balance point.

This line plot shows the number of books that a group of students have read. Use this data to determine where on the line plot the mean will appear.



Students need additional practice determining the appropriate measure of center.

This data shows the ages of members of a youth book club and the age of the facilitator.

11 12 13 14 15 16 17 57

What is the most appropriate measure of center for this data?



Students need additional practice finding the balance point of a set of data represented on a line plot.

Jill recorded the number of pull-ups each of ten students did on this line plot. What is the balance point for this data?

1 2 3 4 5 6 7 8 9

Pull-Ups

Each X represents 1 student.

Number of Pull-Ups

XX

XX

X

X

X XX

X



Students need additional practice determining the best measure of center for a given situation.Andy surveyed his friends to determine the number of books each of them read in February. These are the results of the survey.

3, 2, 3, 19, 2, 1, 2, 2, 2, 2

1.What is the mean for this data set? 2.What is the median for this data set?

3.Is the mean or median a more appropriate measure of center to use for this data? Why?



Students need additional practice determining which measure of center is most appropriate for a given situation.

The number of cookies that were made at a bakery for each of seven days is shown:108, 96, 96, 84, 108, 240, and 84

The best measure of center for this data set is the-

a)mean because all of the values are close to one another in valueb)median because all of the values are close to one another in valuec)mean because 240 is much higher than the other numbers in the data setd)median because 240 is much higher than the other numbers in the data set



middle school content academy probability & statistics sol 6.14, 6.15, 6.16, 7.9, 7.10, 7.11,...

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