Middle School Content Academy

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

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
What are the verbs?

Henrico Curriculum Guide

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 Grade 7 Grade 8 Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 33.9 Mean Scaled Score: 35.1 Mean Scaled Score: 33.7 Look for trends! Reporting Category: Probability, Statistics, Patterns, Functions, and Algebra Mean Scaled Score: 31.0 Mean Scaled Score: 33.0 Mean Scaled Score: 31.6 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 Identify a circle graph that represents given data. 76 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 Construct and analyze histograms for a given data set. 73 77 8.13 Make comparisons, predictions, and inferences about information displayed in various graphical representations. 64 Collect, organize, and interpret data using scatterplots. 39

Performance Analysis Comparison SOL 6.14, 7.11, 8.13
2012 SOL 6.14 – None SOL 7.11 – None SOL The student will make comparisons, predictions, and inferences, using information displayed in graphs; and construct and analyze scatterplots. 2013 SOL The student, given a problem situation, will 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 construct and analyze histograms; and compare and contrast histograms with other types of graphs presenting information from the same data set.

Performance Analysis Comparison SOL 6.14, 7.11, 8.13
2014 SOL The student, given a problem situation, will 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 The student will 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. 1. Identify the car color that most likely represents exactly 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 Blue Green Red Purple For SOL 6.14b, students need additional practice solving problems involving circle graphs. Take a moment to read the example shown on the screen. Students are having difficulty making the connection between the percent or fraction represented by a section of the graph and the number of data elements represented by the same section. In the first example provided, 10 out of 40 cars represents 25%, or ¼ of the data. Students must, in turn, recognize that the green section of the graph most closely represents 25% or ¼ of the data. Student performance data indicate that a common student misconception is to attribute 25 data elements to the green section because it represents 25% of the data. Therefore, students would NOT correctly name the green section as representative of 10 cars. Similarly, in example 2, a common student error might be to choose the purple and red sections of the graph as representing 25 cars since those combined pieces represent about 25% of the data. The answers are shown on the screen. 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? Corn Carrots Beans Broccoli Asparagus For this standard, students need additional practice comparing data in circle graphs with data in other graphs. In particular, students need additional practice using the data in a circle graph when specific numbers are not provided. Teachers are encouraged to have students discuss the data in the circle graph and what conclusions can be drawn, even though the number of people surveyed is not given. For example, in this graph, asparagus was selected by the fewest people. It also appears that half of the people surveyed selected beans as their favorite vegetable and ¼ of the people surveyed selected corn . This means there were twice as many people who selected beans as their favorite vegetable as there were people who selected corn as their favorite vegetable. Another conclusion is that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn. Once students have drawn conclusions based on the circle graph, they can proceed to analyze other graphs to determine which one represents the same data. See the next slide for the remainder of this question. Common Errors? Misconceptions?

Corn Carrots Beans Broccoli Asparagus Which bar graph could represent the same data? When comparing these bar graphs to the circle graph, students need to identify the bar graph that represents the data in the same relationships as shown in the circle graph. Students should reference the conclusions they drew from the circle graph, when selecting the correct answer. For example, one of the conclusions drawn from the circle graph was that asparagus was selected by the fewest people. In each of the bar graphs, asparagus was selected by the fewest people, so that statement will not help eliminate a choice. Another conclusion drawn from the circle graph was that there were twice as many people who selected beans as there favorite vegetable as there were people who selected corn as their favorite vegetable. This statement will eliminate the first and second graph, because these graphs do not show this relationship. The other conclusion previously drawn, that the sum of the number of people who selected carrots, broccoli, and asparagus should equal the number of people who selected corn, can be checked against the third graph to confirm its selection. It is important for students to be asked to explain their reasoning for eliminating a graph, and eventually selecting the correct graph. Common Errors? Misconceptions?

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 For SOL 6.14b, students need additional practice interpreting information presented in a circle graph. In the example provided, students should recognize that the different-sized sections of the circle represent different fractions of the whole. The most common error in a question similar to the one shown on the screen was to interpret each piece of the circle graph to be one fifth of the whole. Students should be able to accurately estimate the fractional size of the section of a circle graph. The answer to the question is shown on the screen. Most common error Common Errors? Misconceptions?

Common Errors? Misconceptions? 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? A C B D Answer Choices Selected Answer Choices Selected Answer Choices Selected For SOL 6.14c, students need additional practice comparing and contrasting graphs that represent the same data set. The information shown on this screen should be used to answer the question shown on the next screen. Answer Choices Selected Answer Choices Selected

2013 - Suggested Practice for SOL 7.11a
Students need additional practice analyzing histograms. 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 8 4 4 For SOL 7.11a, students need additional practice analyzing histograms. This example demonstrates one skill with which students are having difficulty: identifying a percent of the data that meets certain criteria. In this example, the question asks for the percent of classrooms that have at least 21 students during first block. In order to solve this problem, students need to add the heights of each of the bars to find the total number of classrooms, which is 20, and then add the heights of bars three, four, and five to find the number of classrooms that have at least 21 students. There are 14 classrooms that have at least 21 students. The answer to the question is shown on the screen. 2 2 Common Errors? Misconceptions?

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 – 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 For SOL 7.11b, students need additional practice determining which graphical representation is best used for a given analysis and what makes that type of graph the most appropriate choice. An example and its answer are shown on the screen. 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. 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?

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: What is the mean price of all of the meals sold? What is the median price of all the meals sold? What is the total number of meals costing more than 7 dollars? $7.24 Students have difficulty making inferences when data is represented in a graph and is not represented as a set of numbers. Teachers are encouraged to provide experiences where data is represented in a variety of graphical forms such as bar graphs, circle graphs, and line graphs. The answers are shown on the screen. $7.00 9 Common Errors? Misconceptions?

This scatterplot shows the average price of a gallon of gas during each month in Which statement best describes the gas prices as the months progress from January to December? the graph shows a positive relationship for the average price of a gallon of gas the graph shows a negative relationship for the average price of a gallon of gas the graph shows the average price of a gallon of gas remains constant the graph shows no relationship between the average price of a gallon of gas and the months 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 For SOL 8.13b, students also have difficulty determining the type of relationship that exists within a data set represented in a scatterplot. The answer to the example shown is option B. Common Errors? Misconceptions?

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 Students have difficulty making inferences when data is represented in a graph and is not represented as a set of numbers. Teachers are encouraged to provide experiences where data is represented in a variety of graphical forms such as bar graphs, circle graphs, and line graphs. In the example shown, students need to note that a total of 450 items were sold as well as the percentage of each item sold. Data analysis indicated a common student error would be to subtract the percent of popcorn sold from the percent of nachos sold and get an answer of 6. The correct answer is shown on the screen. Common Errors? Misconceptions?

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? In this example for SOL 8.13, students are referring to a bar graph to determine what percentage of the dogs owned by Mr. Robert’s sixth period class are Beagles or Terriers. A common student error in a problem similar to this would be for students to add the number of Beagles and Terriers (7), convert it to a percentage by dividing (1/7) and mistakenly think 14% is the answer. The correct answer is shown on the screen. Common Errors? Misconceptions?

Vertical Articulation of Content SOL 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 Determine if two events are dependent or independent 57 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 Determine the probability of a compound event. 8.12 Determine the probability of dependent and independent events. 37 38 10

Performance Analysis Comparison SOL 6.16, 7.9, 7.10, 8.12
2012 SOL 6.16 – The student will 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 8.12 – None

Performance Analysis Comparison SOL 6.16, 7.9, 7.10, 8.12
2014 SOL 6.16 – The student will 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.

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 Yellow Khakis Green Red 𝟏 𝟔 𝐨𝐫 𝐚𝐩𝐩𝐫𝐨𝐱𝐢𝐦𝐚𝐭𝐞𝐥𝐲 𝟏𝟔.𝟕% Common Errors? Misconceptions?

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 What is the probability that she will randomly select a card with a heart, replace it, and then select a card with a ball? 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 6.1% or approximately 4.8% Common Errors? Misconceptions?

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. Most common error For SOL 6.16b, students need additional practice determining probabilities for dependent and independent events. The example on the screen asks for the probability of two dependent events. Since Teagan is randomly selecting a CD, and not replacing it before she selects another, the events are considered dependent events without replacement. The most common error students make is not realizing the denominator of the probability for the second event is one less than the denominator of the probability for the first event. In other test questions, student performance indicated that students can generally identify events as dependent or independent, but performance of items like the one shown on the screen indicate that perhaps students are not making the connection between this identification and its impact on the denominator of the second fraction. The correct answer is shown on the screen. Common Errors? Misconceptions?

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 Here is another example for SOL 6.16b. The most common student error in a question like the one on the screen is to surmise that the sample space is six rather than eight, and erroneously determine that the probability of the event is two-sixths, which is equivalent to one-third. Students should understand that there are eight possible outcomes in the sample space from which Kayla can select a drink and dessert, and the “water and apple pie” selection is one out of the eight possible drink/dessert selections. Alternately, students can also multiply the probabilities of these two independent events, one-fourth and one-half, to get one-eighth. Most common error

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. What is the theoretical probability of selecting a card with an A? What was the experimental probability of selecting a card with an A? Compare and contrast the theoretical and experimental probabilities of selecting a card with an A after a card is randomly selected 1,000 times. A B C D E F For this standard students need additional practice determining the theoretical and/or experimental probability of an event. It is important for students to understand that the experimental probability of an event approaches the theoretical probability of an event as the number of trials increases. The answers to the three questions are shown on the screen. 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?

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?

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?

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. Each letter can be repeated. What is the total number of four-letter codes that can be made using these letters? 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? For SOL 7.10, students need additional practice using the Fundamental Counting Principle to determine the number of possible outcomes. Students performed well on many of the items that assessed the use of the Fundamental Counting Principle but did not perform as well on the application of the Fundamental Counting Principle as illustrated by the first two examples on the screen. The answers are provided. As an extension for this type of item, have students determine the number of three letter codes that can be made if no letter can repeat. First students must determine the number of possible choices for each letter of the code, and find the product of those numbers to determine the total number of three-letter codes. The answer to the extension example is shown on the screen. Common Errors? Misconceptions?

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. 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? 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? For SOL 7.10, students also need additional practice determining the probability of compound events. These two examples demonstrate how prior knowledge may be used in an item. For example, students would need to know what the word composite means in order to correctly answer question one. Similarly, students need to understand the concept of a multiple to answer question two. When prime numbers are mentioned in probability items, a common error is to include the number one as a prime number, and another error is NOT including the number two as a prime number. The answers to these two questions are shown on the screen. Common Errors? Misconceptions?

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 Here is an example for SOL The most common student error in a question like the one on the screen is to surmise that the sample space is seven rather than twelve and erroneously determine that the probability of the event is two-sevenths. Students should understand that there are twelve possible ways in which Maya can select one type of pizza and one drink, and the “pepperoni pizza and cola” selection is one out of the twelve possible pizza/drink selections. Alternately, students can also multiply the probabilities of these two independent events, one-third and one-fourth, to get one-twelfth. Most common error

Students need additional practice calculating probability of independent and dependent events with and without replacement. Sue flips a fair coin three times. What is the probability that the coin will land on tails all three times? 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. 1 Common Errors? Misconceptions?

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 𝟏𝟗 𝐨𝐫

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. 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? 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?

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 3 4 Common Errors? Misconceptions?

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? For standard 8.12, students would benefit from additional practice that requires them to determine the probability of dependent and independent events. In the example shown, the roses are NOT replaced, which indicates that the two events (selecting a red rose and then a pink rose) are dependent. Data indicate that a common student error is to add 4/15 and 5/14 for a probability of 9/14. The correct answer is shown on the screen. Common Errors? Misconceptions?

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 In this example for standard 8.12, students are required to compare the probabilities of Eric’s selections and Sue’s selections. Eric replaces the treat, which indicates that his two events (selecting a lollipop and then a gum ball) are independent. Sue does not replace the treat, which indicates that her two events (selecting a lollipop and then a gum ball) are dependent. Eric’s probability of selecting one lollipop and then one gumball is calculated by multiplying 6/10 by 4/10 to get 6/25. *animation Sue’s probability of selecting one lollipop and then one gumball is calculated by multiplying 6/10 by 4/9 to get 4/15. *animation The correct answer is shown on the screen. Common Errors? Misconceptions?

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. In the last example for 8.12, data indicate students are challenged by items requiring them to determine the probability of multiple independent events, such as flipping two coins at the same time, flipping one coin consecutively, or spinning two spinners at the same time. Teachers are also encouraged to include opportunities for students to consider the probability of events that will NOT occur. For an example of this type of item, please refer to the 2013 grade 8 mathematics PowerPoint. In the example shown, a common misconception is for students to select ½-the probability of one of the single events of rolling the fair number cube. Mario rolls the fair number cube three times, and the probability of each of the independent events is ½. To find the probability of all these events occurring, students should multiply ½ x ½ x ½, thereby resulting in the probability of 1/8. The answer to the example is shown on the screen. Common Errors? Misconceptions?

Vertical Articulation of Content SOL 6.15

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 Describe the best measure of central tendency for a given set of data. 45 62

Performance Analysis Comparison SOL 6.15
2012 SOL 6.15 – The student will describe mean as balance point; and decide which measure of center is appropriate for a given purpose 2013 2014

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?

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. 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?

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 The balance point for this data is 5. X X X X For SOL 6.15a, students need additional practice interpreting data represented on line plots to determine the balance point. The answer to this question is shown on the screen. Students should be able to connect the terms “balance point” and “arithmetic mean.” As an extension, teachers could ask students to compare the balance point with the median and mode and ask which is a better representation of the average number of pull-ups for these ten students. This will help students with the skills associated with SOL 6.15b, which was also an area where students struggled. X X X X Number of Pull-Ups Each X represents 1 student. Common Errors? Misconceptions?

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 What is the mean for this data set? What is the median for this data set? Is the mean or median a more appropriate measure of center to use for this data? Why? 3.8 books 2 books For SOL 6.15b, students showed inconsistent performance when determining which measure of center was most appropriate for a data set. The answers to these questions are shown on the screen. Teachers are encouraged to have students plot this data on a line plot as it will provide a visual representation that may help them understand why the median is a better measure of center for this data set. 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?

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- 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 For SOL 6.15, students need additional practice determining which measure of center is most appropriate for a given situation. Using the mean is best when the set of data has no especially high or especially low numbers. These especially high or especially low numbers are typically referred to as outliers, though test questions in grade six do not specifically use the word “outlier.” Using the median to describe a data set is a good choice when there are one or more outliers in the data set, as the median is not as susceptible to the influence of an outlier or outliers as the mean. Mode is best when the set of data is categorical or when a numerical data set has many elements of the same value. The answer to the question is shown on the screen. Common Errors? Misconceptions?

Resources ExamView Banks NextLesson.org
HCPS Math Website - VDOE Enhanced Scope and Sequence Skills - JMU Pivotal Items ExploreLearning Teaching Strategies Student Engagement Activities

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