1. Middle School Content Academy PROBABILITY & STATISTICS SOL 6.14, 6.15, 6.16, 7.9, 7.10, 7.11, 8.12, 8.13 MARCH 18, 2015

2. Reporting Category: Probability & Statistics  Grade 6  Grade 7  Grade 8 2011-12Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 33.9 2012-13Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 35.1 2013-14Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 33.7 2011-12Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 31.0 2012-13Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 33.0 2013-14Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 31.6 2011-12Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 29.7 2012-13Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 29.5 2013-14Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 30.0

3. 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 Vertical Articulation of Content SOL 6.14, 7.11, 8.13

4. 2014 SPBQ Data – 6.14, 7.11, 8.13 SOLDescription of Question% Correct in Division 6.14Interpret information presented in a circle graph to draw conclusions. 70 6.14Identify a circle graph that represents given data.76 6.14Recognize multiple graphical representations of the same data set. 81 7.11Make inferences and comparisons for data sets displayed using different graphical representations. 82 7.11Construct and analyze histograms for a given data set.73 7.11Construct and analyze histograms for a given data set.77 8.13Make comparisons, predictions, and inferences about information displayed in various graphical representations. 64 8.13Collect, organize, and interpret data using scatterplots.64 8.13Make comparisons, predictions, and inferences about information displayed in various graphical representations. 39

5. 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 BlueGreen Red Purple Common Errors ? Misconceptions?

6. 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 Corn Carrots Beans Broccoli Asparagus Common Errors ? Misconceptions?

7. 2013 - Suggested Practice for SOL 6.14c Corn Carrots Beans Broccoli Asparagus Which bar graph could represent the same data? Common Errors ? Misconceptions?

8. 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. Which fraction of the students best represents those who rated the show as “Above Average?” A B C D Rating of Television Show Common Errors ? Misconceptions?

9. 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. Answer Choices Selected Which of these represents the data shown in the circle graph? A C B D Answer Choices Selected Common Errors ? Misconceptions?

10. 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? Number of Students By Classroom in First Block Number of Students Number of Classrooms Common Errors ? Misconceptions?

11. 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 data b)stem-and-leaf-plot because it showed each value in the set of data c)histogram because the median is always the bar with the greatest height d)stem-and-leaf-plot because the median is always the “leaf” that appears most often 2013 - Suggested Practice for SOL 7.11b Common Errors ? Misconceptions?

12. 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. 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? Common Errors ? Misconceptions?

13. 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 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? Common Errors ? Misconceptions?

14. 2013 - Suggested Practice for SOL 8.13b 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 October August September November 2013 National Average Gas Prices Price of a Gallon of Gas ( in dollars) Months January February March May June April December Common Errors ? Misconceptions?

15. 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 Gatorade Nachos Cotton Candy Hot Chocolate Popcorn Common Errors ? Misconceptions?

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

17. 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 Vertical Articulation of Content SOL 6.16, 7.9, 7.10, 8.12

18. 2014 SPBQ Data – 6.16, 7.9, 7.10, 8.12 SOLDescription of Question % Correct in Division 6.16Find the probability of two independent events.42 6.16Determine if two events are dependent or independent57 6.16Find the probability of two dependent events.43 7.9Apply or describe the experimental and theoretical probability formulas to determine or calculate the probability of a compound event. 63 7.10Apply the Fundamental Basic Counting Principle to determine the number of possible outcomes of compound events. 75 7.10Determine the probability of a compound event.42 8.12Determine the probability of dependent and independent events.37 8.12Determine the probability of dependent and independent events.38 8.12Determine the probability of dependent and independent events.10

19. 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. PantsShirt Color Blue JeansOrange Blue JeansYellow KhakisGreen Red Common Errors ? Misconceptions?

20. 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? 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? Common Errors ? Misconceptions?

21. 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. 2014 - Suggested Practice for SOL 6.16b Common Errors ? Misconceptions?

22. 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. 2014 - Suggested Practice for SOL 6.16b DrinkDessert Apple JuiceChocolate Cake Orange JuiceApple Pie Cola Water

23. 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 BACDEF Common Errors ? Misconceptions?

24. 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? 2012 - Suggested Practice for SOL 7.10 Common Errors ? Misconceptions?

25. 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? 2012 - Suggested Practice for SOL 7.10 Common Errors ? Misconceptions?

26. 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? 2013 - Suggested Practice for SOL 7.10 Common Errors ? Misconceptions?

27. 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? 2013 - Suggested Practice for SOL 7.10 Common Errors ? Misconceptions?

28. 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 2014 - Suggested Practice for SOL 7.10 Type of PizzaDrink PepperoniApple Juice VegetableOrange Juice Plain CheeseCola Water

29. 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. 2012 - Suggested Practice for SOL 8.12 0 1 Common Errors ? Misconceptions?

30. 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? 2012 - Suggested Practice for SOL 8.12

31. 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? 2012 - Suggested Practice for SOL 8.12 Common Errors ? Misconceptions?

32. 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? 12 2 2 3 3 4 3 2012 - Suggested Practice for SOL 8.12 Common Errors ? Misconceptions?

33. 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? 2012 - Suggested Practice for SOL 8.12 Common Errors ? Misconceptions?

34. 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? 2014 - Suggested Practice for SOL 8.12 Common Errors ? Misconceptions?

35. 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. 2014 - Suggested Practice for SOL 8.12 Common Errors ? Misconceptions?

36. 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 Vertical Articulation of Content SOL 6.15

37. 2014 SPBQ Data – 6.15 SOLDescription of Question% Correct in Division 6.15Use a number line to define the mean as a balance point for a given set of data. 55 6.15Describe the best measure of central tendency for a given set of data. 45 6.15Use a number line to define the mean as a balance point for a given set of data. 62

38. 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. 2012 - Suggested Practice for SOL 6.15 Common Errors ? Misconceptions?

39. 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 1757 What is the most appropriate measure of center for this data? 2012 - Suggested Practice for SOL 6.15 Common Errors ? Misconceptions?

40. 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 X X X X X X XX X X 2013 - Suggested Practice for SOL 6.15a Common Errors ? Misconceptions?

41. 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? 2013 - Suggested Practice for SOL 6.15a Common Errors ? Misconceptions?

42. 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 value b)median because all of the values are close to one another in value c)mean because 240 is much higher than the other numbers in the data set d)median because 240 is much higher than the other numbers in the data set 2014 - Suggested Practice for SOL 6.15b Common Errors ? Misconceptions?