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PROBABILITY & STATISTICS
SOL 6.14, 6.15, 6.16, 7.9, 7.10, 7.11, 8.12, 8.13
MARCH 18, 2015
Curriculum framework

Probability & Statistics strand information!
Reporting Category: Probability &
Statistics

Let’s examine the SOL in this reporting category strand.

Which are in the Probability & Statistics reporting category?
Curriculum framework –
Unpack the standard
Henrico Curriculum Guide

http://blogs.henrico.k12.va.us/math/courses/
Pacing
SOL 6.14, 6.15, 6.16
SOL 7.9, 7.10, 7.11
SOL 8.12, 8.13
Reporting Category:
Probability & Statistics

Grade 6
2011-12
2012-13
2013-14

Mean Scaled Score: 33.9
Mean Scaled Score: 35.1
Mean Scaled Score: 33.7
Grade 7
2011-12
2012-13
2013-14

Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Mean Scaled Score: 31.0
Mean Scaled Score: 33.0
Mean Scaled Score: 31.6
Grade 8
2011-12
2012-13
2013-14
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra
Mean Scaled Score: 29.7
Mean Scaled Score: 29.5
Mean Scaled Score: 30.0
Formulas

What formulas do
students need to know
related to the P & S
strand?

What formulas are
provided on the
formula sheet related
to the P & S strand?
Vertical Articulation of Content
SOL 6.14, 7.11, 8.13
Grade 6 Focus: Practical Applications of Statistics
Grade 7 Focus: Applications of Statistics and Probability
Grade 8 Focus: Statistical Analysis of Graphs and Problem Situations
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
Performance Analysis Comparison
SOL 6.14, 7.11, 8.13
2012
SOL 6.14 – None
SOL 7.11 – None
SOL 8.13 - The student will
a)
b)
make comparisons, predictions, and inferences, using information displayed in graphs; and
construct and analyze scatterplots.
2013
SOL 6.14 - The student, given a problem situation, will
a)
b)
c)
construct circle graphs;
draw conclusions and make predictions, using circle graphs; and
compare and contrast graphs that present information from the same data set.
SOL 7.11 – The student, given data in a practical situation, will
a)
b)
construct and analyze histograms; and
compare and contrast histograms with other types of graphs presenting information from the same data set.
SOL 8.13 - The student will
a)
b)
make comparisons, predictions, and inferences, using information displayed in graphs; and
construct and analyze scatterplots.
Performance Analysis Comparison
SOL 6.14, 7.11, 8.13
2014
SOL 6.14 - The student, given a problem situation, will
a)
b)
c)
construct circle graphs;
draw conclusions and make predictions, using circle graphs; and
compare and contrast graphs that present information from the same data set.
SOL 7.11 – None
SOL 8.13 - The student will
a)
b)
make comparisons, predictions, and inferences, using information displayed in graphs; and
construct and analyze scatterplots.
2013 - Suggested Practice for SOL 6.14b
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.
Car Sales
Purple
Green
1. Identify the car color that most likely represents exactly
Blue
Blue
Red
Green
Red
Purple
10 cars.
Green
2. Identify two car colors that most likely represent a
combined total of 25 cars.
Blue and Purple OR Blue and Red
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 6.14c
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?
Favorite Vegetable
Asparagus
Corn
Broccoli
Corn
Carrots
Beans
Carrots
Beans
Broccoli
Asparagus
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 6.14c
Favorite Vegetable
Asparagus
Broccoli
Corn
Carrots
Corn
Beans
Carrots
Beans
Broccoli
Asparagus
Which bar graph could represent the same data?
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 6.14b
Students 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.
Rating of Television Show
Most common error
Which fraction of the students best represents those who rated the show as “Above Average?”
A
B
C
D
Common Errors? Misconceptions?
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 6.14c
Students 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.
Which of these represents the data shown in the circle graph?
Answer Choices Selected
A
C
Answer Choices Selected
Answer Choices Selected
C
A
B
D
Answer Choices Selected
Answer Choices Selected
B
D
2013 - Suggested Practice for SOL 7.11a
Students need additional practice analyzing histograms.
Number of Students By Classroom in First Block
The graph describes the number of
students in each classroom during first
block at a high school.
9
8
8
What percent of the classrooms have at
least 21 students during first block?
Number of
Classrooms
7
6
5
4
4
4
3
2
2
2
1
0
11-15
16-20
21-25
26-30
31-35
Number of Students
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 7.11b
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)
b)
c)
d)
histogram because it showed each value in the set of data
stem-and-leaf-plot because it showed each value in the set of data
histogram because the median is always the bar with the greatest height
stem-and-leaf-plot because the median is always the “leaf” that appears most often
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 8.13
Students need additional practice interpreting the information displayed in graphs.
This graph displays the high temperatures for Hampton, VA over five days in September.
High Temperatures in Hampton, VA
85
The mean high temperature in Bristol, VA
for these same dates was 89°F.
Degrees Fahrenheit
83
81
79
77
What is the difference in the mean high
temperatures of Bristol and Hampton for
these five days, rounded to the nearest
degree?
75
73
71
69
67
65
Date
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 8.13a
Students 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.
Number of Meals Sold
Meals Sold at a Restaurant
10
9
8
7
6
5
4
3
2
1
0
Based on the information in the graph:
a) What is the mean price of all of the
meals sold?
$7.24
b) What is the median price of all the
meals sold? $7.00
6
7
8
9
c) What is the total number of meals
costing more than 7 dollars?
Price of a Meal (in dollars)
9
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 8.13b
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?
2013 National Average Gas Prices
Price of a Gallon of
Gas ( in dollars)
3.80
a) the graph shows a positive relationship for
the average price of a gallon of gas
3.70
b) the graph shows a negative relationship
for the average price of a gallon of gas
3.60
3.50
3.40
3.30
c) the graph shows the average price of a
gallon of gas remains constant
3.20
3.10
Months
d) the graph shows no relationship between
the average price of a gallon of gas and the
months
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 8.13a
Students 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
Popcorn
Hot Chocolate
Gatorade
Cotton Candy
Nachos
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 8.13a
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.
Dogs Owned by Mr. Robert’s 6th Period Class
Number of Dogs
10
8
6
4
2
0
Beagle
Labrador
Poodle
Terrier
Bulldog
Dog Breeds
What percentage of the dogs owned by Mr. Robert’s class are a beagle or a terrier?
Common Errors? Misconceptions?
Vertical Articulation of Content
SOL 6.16, 7.9, 7.10, 8.12
Grade 6 Focus: Practical Applications of Statistics
Grade 7 Focus: Applications of Statistics and Probability
Grade 8 Focus: Statistical Analysis of Graphs and Problem Situations
2014 SPBQ Data – 6.16, 7.9, 7.10, 8.12
% Correct in
Division
SOL
Description of Question
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
8.12
Determine the probability of dependent and independent events.
38
8.12
Determine the probability of dependent and independent events.
10
Performance Analysis Comparison
SOL 6.16, 7.9, 7.10, 8.12
2012
SOL 6.16 – The student will
a)
b)
compare and contrast dependent and independent events; and
determine probabilities for dependent and independent events.
SOL 7.9 – None
SOL 7.10 – The student will determine the probability of compound events, using the Fundamental (Basic)
Counting Principle.
SOL 8.12 – The student will determine the probability of independent and dependent events with and without
replacement.
2013
SOL 6.16 – None
SOL 7.9 – The student will investigate and describe the difference between the experimental probability and
theoretical probability of an event.
SOL 7.10 – The student will determine the probability of compound events, using the Fundamental (Basic)
Counting Principle.
SOL 8.12 – None
Performance Analysis Comparison
SOL 6.16, 7.9, 7.10, 8.12
2014
SOL 6.16 – The student will
a)
b)
compare and contrast dependent and independent events; and
determine probabilities for dependent and independent events.
SOL 7.9 – None
SOL 7.10 – The student will determine the probability of compound events, using the Fundamental (Basic)
Counting Principle.
SOL 8.12 – The student will determine the probability of independent and dependent events with and without
replacement.
2012 - Suggested Practice for SOL 6.16
Students 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
𝟏
𝐨𝐫 𝐚𝐩𝐩𝐫𝐨𝐱𝐢𝐦𝐚𝐭𝐞𝐥𝐲 𝟏𝟔. 𝟕%
𝟔
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 6.16
Alexis 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?
or approximately 6.1%
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?
or approximately 4.8%
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 6.16b
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.
Most common C.
error
B.
D.
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 6.16b
This table shows the drink and dessert selections at a party.
Drink
Dessert
Apple Juice
Chocolate Cake
Orange Juice
Apple Pie
Cola
Water
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.
Most common error
B.
D.
2013 - Suggested Practice for SOL 7.9
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
B
C
D
E
F
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.
Sample Answer: The theoretical probability of selecting a card with an A stays the same. The experimental
probability should get closer to the theoretical probability.
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 7.10
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?
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 7.10
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?
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 7.10
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?
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 7.10
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?
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 7.10
Students need additional practice determining probability of compound
events.
This table shows the types of pizza and drink selections at a party.
Type of Pizza
Drink
Pepperoni
Apple Juice
Vegetable
Orange Juice
Plain Cheese
Cola
Water
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
Most common error
D
2012 - Suggested Practice for SOL 8.12
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.
0
1
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 8.12
•
•
•
•
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?
𝟖
𝐨𝐫
𝟏𝟗
2012 - Suggested Practice for SOL 8.12
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?
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 8.12
A spinner is divided into eight equal sections as shown.
1
2
4
2
2
3
3
3
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?
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 8.12
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?
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 8.12
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?
Sue because
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 8.12
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.
Common Errors? Misconceptions?
Vertical Articulation of Content
SOL 6.15
Grade 6 Focus: Practical Applications of Statistics
Grade 7 Focus: Applications of Statistics and Probability
Grade 8 Focus: Statistical Analysis of Graphs and Problem Situations
2014 SPBQ Data – 6.15
SOL
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
Performance Analysis Comparison
SOL 6.15
2012
SOL 6.15 – The student will
a)
b)
describe mean as balance point; and
decide which measure of center is appropriate for a given purpose
2013
SOL 6.15 – The student will
a)
b)
describe mean as balance point; and
decide which measure of center is appropriate for a given purpose
2014
SOL 6.15 – The student will
a)
b)
describe mean as balance point; and
decide which measure of center is appropriate for a given purpose
2012 - Suggested Practice for SOL 6.15
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.
x
Common Errors? Misconceptions?
2012 - Suggested Practice for SOL 6.15
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?
Sample answer: Median because the age of the facilitator is much higher than the ages of the other members,
and there is no mode.
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 6.15a
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?
Pull-Ups
X
X
1
X
X
X
2
X
X
X
X
X
3
4
5
6
7
8
The balance point
for this data is 5.
9
Number of Pull-Ups
Each X represents 1 student.
Common Errors? Misconceptions?
2013 - Suggested Practice for SOL 6.15a
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? 3.8 books
2.
What is the median for this data set? 2 books
3.
Is the mean or median a more appropriate measure of center to use for this data? Why?
Sample answer:
Since one friend read significantly more books (19), the median provides a more accurate
measure. The friend who read 19 books caused the mean to be higher than the number of
books read by nine of the ten friends.
Common Errors? Misconceptions?
2014 - Suggested Practice for SOL 6.15b
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 thea)
b)
c)
d)
mean because all of the values are close to one another in value
median because all of the values are close to one another in value
mean because 240 is much higher than the other numbers in the data set
median because 240 is much higher than the other numbers in the data set
Common Errors? Misconceptions?
Resources
1.
ExamView Banks
2.
NextLesson.org
3.
HCPS Math Website http://teachers.henrico.k12.va.us/math/courses/
4.

VDOE Enhanced Scope and Sequence

Skills - JMU Pivotal Items
ExploreLearning

Teaching Strategies

Student Engagement

Activities