Interquartile Range as a Measure of Variation 21st Century Lessons Interquartile Range as a Measure of Variation Primary Lesson Designer: Katelyn Fournier

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Lesson Overview (1 of 7) Lesson Objective Lesson Description SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Student- Friendly Objective: SWBAT explain what the IQR is, why we use it, and how to find it. Lesson Description The lesson begins with students engaging in a whole-class review of range. Following the review, students participate in an activity in which they have to evaluate how a class performed on a test based on limited information (they are only given the range of the scores). The activity is designed to show students that the range may not be a useful measure of variation when a data set contains one or more outliers. During the explore time, students move from using the range as a measure of variation to using the interquartile range as a measure of variation. Much of the launch and explore time is conducted using a think-pair-share where students discuss the questions with a partner before reporting out to the class. During the practice time, students will practice finding the interquartile range of different sets of data. They will also evaluate what the IQR actually represents. During the practice time, students are expected to work individually, while also regularly checking in with a nearby partner. Following the practice, students will share their answers and strategies with the class. This share-out will serve as an additional summary of the lesson. An exit ticket will be used to assess student understanding of the concepts of both range and interquartile range.

Lesson Overview (2 of 7) Lesson Vocabulary Quartiles: the points that divide a data set into roughly four equally-sized parts Interquartile Range (IQR): the difference between the third and first quartiles in a data set. Upper quartile (Q3) – lower quartile (Q1) Materials 1) Exit tickets from the previous lesson on range 2) IQR class work handout 3) Exit ticket 4) IQR homework 5) Notes for struggling students

Lesson Overview (3 of 7) Scaffolding Enrichment Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to find the IQR is provided for struggling students. Enrichment Advanced Objective: SWBAT identify real world situations where one would use the range or IQR to better inform himself/herself. Ask students to brainstorm real life applications of this concept. To support students in doing this, a copy of a newspaper or magazine may provide some ideas.

Lesson Overview (4 of 7) Online Resources for Absent Students http://www.ixl.com/math/grade-6/interpret-charts-to-find-mean-median-mode-and-range http://www.ixl.com/math/grade-6/mean-median-mode-and-range-find-the-missing-number   http://www.ixl.com/math/grade-6/calculate-mean-median-mode-and-range Common Core State Standard 6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Lesson Overview (5 of 7) Before and After While Grade 4 provides students with some opportunities to do the pre-work necessary to understand measures of variation, measures of variation are not formally introduced until grade 6. In Grade 4, 4.MD.4 says that students "find and interpret the difference in length between the longest and shortest specimens in an insect collection," using a line plot. This provides students with limited access to the concept of range. Aside from the basic groundwork laid out in grade 4, coming into this lesson, students will have had four lessons related to statistics. The unit began with an introduction to statistical questions. From there, the mean and median were introduced as measures of center that can be used to summarize a set of data gathered in response to a statistical question. This is the second lesson in the next cluster of lessons where spread is introduced as a measure to describe the variability of a set of data gathered in response to a statistical question. By the end of the unit, students should recognize the differences between measures of center and measures of variation and also what they are useful for despite the fact that both are used to describe data sets.

Lesson Overview (6 of 7) Before and After Continued The previous lesson in this cluster of lessons covered range as a measure of variation. This lesson will build on students’ understanding of range to explore the interquartile range as a measure of spread or variation. At the end of this lesson, students should be able to break a set of data into quartiles to find the interquartile range. They should understand why and how the interquartile range is useful, particularly when the range is not. An understanding of both range and interquartile range will lay the groundwork for future lessons on how to create and analyze box plots. This lesson is one of a group of lessons designed to show that sets of data generated by statistical questions can be analyzed by looking at the spread of the data. In Grade 6 students see that the data collected in response to a statistical question have certain attributes (center, spread, overall shape). In Grade 7, when students expand their study of statistics to work with samples, students will see that these attributes relate important information about the sample from which the data were collected.

Lesson Overview (7 of 7) Topic Background Turn and Talk/Think-Pair-Share: “Various researchers (e.g. Douglas Reeves, Richard Allington, Vygotsky) have linked academic success with the capacity to engage in conversation and to ask and answer questions in full sentences. One of the most powerful and easy to implement moves is called: Turn and talk, or think, pair, share, or partner talk. All of these are variations of a practice that has far reaching benefits for students. Simply defined, “turn and talk” is a teacher offered opportunity for students to turn to another student and talk something through for a very brief period of time before whole group discussion or lecture resumes.” -Lucy West & Antonia Cameron Metamorphosis Teaching Learning Communities

Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. Yesterday in class, you filled out an index card with real world examples of data sets with wide ranges and narrow ranges. Today as our warm up, the class will be tested on its understanding of range using the examples you created! (5 min) 0-5 In-Class Notes Begin by having a student read the instructions aloud. Preparation Notes This warm-up was designed to review range. The examples that will be used come from the exit tickets that were used as an assessment tool during the previous lesson. This slide just explains to the students where the examples that will be read aloud on the next slide came from. The students’ examples (only the examples, not the explanations) should be read aloud. Agenda

Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. After an example has been read aloud: IN YOUR HEAD, determine whether the example represents a data set with a wide range or a narrow range. When you hear a clap, move your arms to represent your answer. Arm Movements (5 min) 0 – 5 In-Class Notes Begin by having a student read the instructions aloud. Once students understand expectations, read the students’ examples (only the examples, not the explanations) aloud one at a time. After an example has been read aloud, students should take about 10 seconds to think about whether the data set has a narrow or wide range. Clap (or use some sort of signal) to indicate that it is time for students to show their answers. SHOW is the key word here. Students do not need to talk at all until the discussion portion of each example. After students have moved their arms for an example, have one student explain why he/she moved his/her arms the way he/she did. Allow for discussion if students disagree. Optional: Have students make their arm movements with their eyes closed. Preparation Notes Have students’ exit slips (the index cards) from the previous lesson prepared. Wide range = Arms are outstretched Narrow range = Hands are close together Agenda

Agenda: 1) Warm Up – Review of the Range (Whole Class) 5 Mins OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. 1) Warm Up – Review of the Range (Whole Class) 5 Mins 2) Launch – Test Scores: Is the Range Useful? (Partner) 10 Mins 3) Explore – Las Vegas Weather: What Can You Expect? 20 Mins (Whole Class) 4) Summary – IQR in Simple Terms (Whole Class) 5 Mins (1 min) 5 – 6 In-Class Notes Briefly review today’s objective and agenda, pointing out that students will do some exploring as a class, have an opportunity to do some partner practice and some individual work, and then be asked to show what they’ve learned on an exit ticket. Preparation Notes This lesson is a continuation of the previous lesson where students were introduced to range as a measure of center. 5) Practice – IQR Class Work (Individual) 15 Mins 6) Assessment – Exit Ticket (Individual) 5 Mins

Launch – Review Turn and Talk (30 sec) number of toppings students like When we analyze data, what are we looking for? Median Center Mean Range Today! Spread (Measure of Variation) Interquartile Range Mean Absolute Deviation (2 min) 6 – 8 In-Class Notes Ask students to discuss the question, “What are we looking for when we analyze data?” in pairs or small groups for 30 seconds. After students have shared their own answers, click to show desired answers. Explain to students that the focus of today’s lesson will be on the spread of a data distribution. Make it clear that the measures of variability that will be introduced today is interquartile range. Mean Absolute Deviation will be introduced later in the unit. Preparation Notes The focus of today’s lesson is using the spread, or measures of variation (specifically interquartile range), to describe data distributions. However, it is important for students to realize that the spread is just one way to describe a data distribution; there are multiple ways to describe a set of data. The previous lessons focused on using the median and mean to describe data distributions. In a future lesson, shape will be looked at as a way to describe sets of data. By the end of the unit, students should recognize three different ways to describe data (center, spread, shape). This exact slide was part of three previous lessons (lessons on median, mean, and range). Since this is the fourth time they are seeing it, students should remember the terminology (center, spread, shape, median, mean, and range) and they should have an understanding of what the words mean. Shape Agenda

Launch Think-Pair-Share Test Scores: Would you expect a wide or narrow range? Twenty students take a social studies test. The range of the scores is 98 points. The teacher is worried that there is such a wide range of scores. How do you think the students performed? (2 min) 8 – 10 In-Class Notes Begin by polling students to see if they think test scores traditionally have a wide or narrow range. Click to present the scenario to students. Students should think about the question independently for about 15 seconds. Then they should confer with a peer for about 15 seconds before sharing out to the class. Preparation Notes Agenda

Launch Whole Class The test scores are below. 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 How do you think the students performed? (2 min) 10 – 12 In-Class Notes Give students about 30 seconds to think about this question independently before calling on anyone. Students should see that although the range of the scores is 98, in reality, most of the data is clustered together and in terms of test scores, the data is decent. The goal is for students to see that in this case, the range is not necessarily representative of the class scores, as most of the scores were clustered together. Preparation Notes Agenda

Launch Whole Class In this example, was the range a useful measure of variation to use to determine how a class of students performed? NO!! (1 min) 12 – 13 In-Class Notes Ask students if they remember another example from the previous lesson where range was not a useful measure of variation (the example with Las Vegas weather). Give students about 15 seconds to think about this question before calling on someone. Push students to explain why the range is not a useful measure of variation in this example. Preparation Notes This slide is essentially a review of the summary of the previous lesson. Students have already seen an example in which the range was not a useful measure of variation. This slide serves as a bridge between where the last lesson left off and where this lesson is picking up. Agenda

Explore Turn and Talk inter quartile Since the range is greatly influenced by outliers, we also use the interquartile range (IQR) to describe the variability of a data set. Are there any parts of the word interquartile that look familiar to you? (2 min) 13 – 15 In-Class Notes Students should discuss this question with a peer and then share out to the class. Scaffolding: Show the hint that breaks apart the word interquartile. Inform students that before they learn about the interquartile range, they will first learn about quartiles. Ask students to hypothesize what a quartile is before moving onto the next slide where the formal definition will be given. Preparation Notes inter quartile Between Quarters Agenda

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: 1) Find the median 64° 60° 62° 67° 59° 62° 59° 70° 66° 70° 62° 62° 67° 65° 80° (<1 min) 15-17 In-Class Notes Students should write the definition of quartiles in their notes. Their notes should be labeled “Interquartile Range (IQR).” They should also write down the steps for finding the quartiles of a set of data. Before clicking to show step #1, ask students what the first step should be if one is dividing a data set into four parts. Students should find the median on their own in their notes. Finding the median should take them about 30 seconds. Once they have identified the median as 64 degrees, click to show how to find it. Seeing how to find the median will benefit those who are struggling. Ask students why the word roughly is included in the definition. Preparation Notes 59° 60° 62° 64° 65° 66° 67° 70° 80° median Agenda 19 19

Explore Whole Class Now that we have found the median (64°), how many equal parts do we have? Two roughly equal parts! What should we do next to break our data set into quartiles? Break the two parts we have in half to make four parts! Remember that quartiles are the points that divide a data set into roughly four equally-sized parts! (2 min) 17-19 In-Class Notes Accommodation: Once the second question is asked, click on hint to remind students what quartiles are. Preparation Notes 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° median Agenda 20 20

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median (<1 min) 19-21 In-Class Notes Before clicking to show step #2, ask students what they think step #2 is. Students should find Q1 on their own in their notes. This should take them about 30 seconds. Once they have identified Q1 as 62°, click to show how to find Q1. Seeing how to find Q1 will benefit those who are struggling. Preparation Notes 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° lower quartile (Q1) Agenda 21 21

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median Find the upper quartile (Q3): the median of all values above the median (<1 min) 21-23 In-Class Notes Before clicking to show step #3, ask students what they think step #3 is. Students should find Q3 on their own in their notes. This should take them about 30 seconds. Once they have identified Q3 as 67°, click to show how to find Q3. Seeing how to find Q3 will benefit those who are struggling. Preparation Notes 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° upper quartile (Q3) Agenda 22 22

Explore Check Your Work! median upper quartile (Q3) lower quartile (Q1) 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° (<1 min) 21-23 In-Class Notes Review the notes of those students who struggle with taking notes. Ask students why there is no Q2 or Q4 on the slide. Then ask what the values of Q2 and Q4 are for this set of data. Preparation Notes The purpose of this slide is to ensure that each student has copied down the information correctly. Students should take about 10 seconds to compare their notes to this slide. Agenda 23

Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° (2 min) 23-25 In-Class Notes Students should attempt the questions on their own. They can check in with a peer when they are done. Then the questions should be reviewed at the whole-class level. There are several possible answers for Question 1, as some students might make three groups of 4 and one group of 3. The illustration included on the slide is the ideal answer. Accommodation: Click hint to show one group of four being circled. Preparation Notes Hint Agenda Answer #1 Answer #2

Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° (<1 min) 23-25 In-Class Notes Students should attempt the questions on their own. They can check in with a peer when they are done. Then the questions should be reviewed at the whole-class level. There are several possible answers for Question 1, as some students might make three groups of 4 and one group of 3. The illustration included on the slide is the ideal answer. Accommodation: Click hint to show one group of four being circled. Preparation Notes Q1 Q2 Q3 Q4 Next

Explore Turn-and-talk Now that the data has been divided into four groups, form statements about the set of data below. Word Bank 25% data Between ¼ 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° (2 min) 25-27 In-Class Notes Anticipate that students will assume that the range is split up four ways by the quartiles. Emphasize that the quartiles divide the data into four roughly equally-sized groups. They do not divide the range into four equal distances. It is important that students see the “mini” ranges created by the quartiles. This understanding is integral to understanding what the IQR represents. Scaffolding: Provide the sentence starters for students who are struggling to create statements. Ensure that students are putting their statements in the context of the data. They should be labeling the numbers in degrees and reporting the quarters in days. For example, “25% of the days were less than 62°” as opposed to “25% of the data values are less than 62.” Preparation Notes This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them. Q1 Q2 Q3 Q4 “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°” Hint Agenda

Explore Whole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Between data Less than ½ 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° (2 min) 27-29 In-Class Notes Give students an opportunity to think about this question independently. Then ask volunteers to share out. Ensure that students are putting their statements in the context of the data. They should be labeling the numbers in degrees and reporting the halves as days. For example, “50% of the days were less than 64°” as opposed to “50% of the data values are less than 64.” Ask students which 50% would best represent the data and why (62-67). Students should be able to explain why the middle values are most representative of the data set. Follow-up question: Why might someone only focus on the middle 50% of the data rather than looking at all of the data? Before moving onto the next slide, inform students that there is a term for the range of the middle 50% of the data. Ask them if they remember the term from the beginning of the lesson (interquartile range). Scaffolding: Provide the sentence starters for students who are struggling to create statements. Preparation Notes This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them. “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Sentence Starters Agenda Hint

Explore Turn and Talk Now that we know what quartiles are, what is the interquartile range? (1 min) 29 – 30 In-Class Notes Students should discuss this question with a peer and then share out to the class. Scaffolding: Show the hint that breaks apart the word interquartile and gives meaning to the words. Preparation Notes Hint Agenda

Explore Vocabulary What is the interquartile range? The interquartile range is the difference between the upper and lower quartiles in a data set. Interquartile Range = upper quartile (Q3) – lower quartile (Q1) 67° – 62° = 5° Interquartile range (3 min) 30-33 In-Class Notes Teacher asks question and asks students to create a definition of interquartile range in their groups (30 seconds). Discuss ideas about the definition of interquartile range. Click to show formal definition. Students should write the definition down in their notes (preferably in a vocabulary section). Ask students to compare the interquartile range with the range of this set of data. Once they have compared the two measures of variation, ask them why the interquartile range might be considered a more valuable measure of variability in comparison to range for this set of data. Preparation Notes 59° 60° 62° 64° 65° 66° 67° 70° 80° lower quartile (Q1) upper quartile (Q3) Agenda

Summary Think-Pair-Share How could you explain the interquartile range in sixth grade language? Sentence starters could include: The interquartile range represents… The interquartile range is the spread of… (2 min) 33-35 In-Class Notes Students should think about this question individually for about 30 seconds, then talk about it with a partner for 30 seconds, and then share ideas and come to a consensus as a class. When explaining the interquartile range, most students will say it is the difference between Q1 and Q3. Push students to explain what this means. The IQR really tells us the spread across the middle of the data, or how spread out the middle values are. They should be able to explain that it Is used as a measure of variation because it doesn’t take into account any extreme values. Preparation Notes This slide is connected to Math PS 6 – Attend to Precision: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning. Scaffolding Agenda

Practice – Part 1 Small Group Let’s go back to the test scores with a range of 98. 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 What is the interquartile range of the data? (3 min) 35-38 In-Class Notes Students should complete this problem with the peers at their table (or with a single peer, depending on how the classroom is set up). Give students about 3 minutes to complete the problem and then quickly review it as a class. This is the first time students have been asked to find the IQR for a set of data with an even number of data points. Anticipate that students will have questions about finding Q1 and Q3 as it is not as straightforward in this example. Ensure that students do not use the median (83) when finding the lower and upper quartiles. Walk around as groups work through the problem to assess students’ understanding of IQR. Preparation Notes This slide is connected to Math PS 1 - Make sense of problems and persevere in solving them: Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. Agenda

Practice – Part 1 Whole Class 1) Find the median 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 Median = 83 points (<1 min) 35-38 In-Class Notes Students should share their answers before showing how to find the median. Click to show how to find the median. Preparation Notes Agenda

Practice – Part 1 Whole Class Find the median Find the lower quartile (Q1): the median of all values below the median Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 (<1 min) 35-38 In-Class Notes Students should share their answers before showing how to find Q1. Click to show how to find Q1. Preparation Notes Agenda

Practice – Part 1 Whole Class Find the median Find the lower quartile (Q1): the median of all values below the median Find the upper quartile (Q3): the median of all values above the median 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 (<1 min) 35-38 In-Class Notes Students should share their answers before showing how to find Q3. Click to show how to find Q3. Preparation Notes Upper quartile (Q3) = 89 points Agenda

Practice – Part 1 Whole Class Interquartile Range = 89 – 74 = 15 points Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 (<1 min) 35-38 In-Class Notes Students should share their answers before showing how to find the IQR. Click to show how to find the IQR. Preparation Notes Upper quartile (Q3) = 89 points Agenda

Practice – Part 1 Think-Pair-Share Interquartile Range = 89 – 74 = 15 points What does an interquartile range of 15 points actually mean? 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 (2 min) 38-40 In-Class Notes Students should spend about 15 seconds thinking about this question before discussing it with a peer. After students have talked with a peer, discuss the question as a class. Students should understand that an interquartile range of 15 points means that the middle 50% of the class’s scores vary by 15 points. That means the middle portion of the class obtained similar scores and are “on the same page.” Ask students to compare an IQR of 15 to the original range of 98. Ask students what it would mean if the interquartile range of a set of tests was much higher, for example, 47 points. Preparation Note This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them. Agenda

In 10 minutes you will be asked to stop and share your answers! Practice – Part 2 Part 2 - (10 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out Online timer link on slide - 10 min (40-50) In-Class Notes Pass out Class Work handout. Students should complete work independently and then share with a partner to check and see if they have similar answers and/or similar strategies. The purpose of working independently is to build independence. Click on the timer! In 10 minutes you will be asked to stop and share your answers! Agenda

Practice – Complete Class Work Part 2 – (10 Min) (10 min) 40 – 50 In-Class Notes Students should complete work independently and then share with a partner to check and see if they have similar answers and/or similar strategies. The purpose of working independently is to build independence. Teacher should circulate around the room to provide additional support for students who need it and also to assess student work. Scaffolding: Modify class work to include steps for finding the IQR. Preparation Notes Agenda

Practice – Student Share Out Part 3 – (5 Min) Students share out work. (5 min) 50 – 55 In-Class Notes The practice summary reviews some of the work that students completed independently on their class work (Questions 1, 4, and 5). The summary should begin with students sharing their methods for solving the problems. Display the key questions if possible while students share (using document camera, overhead projector, or another normal routine you have for sharing student work). If a document camera, overhead projector, etc. is not accessible, possible solutions are provided in the upcoming slides. Not every question is part of the review. However, if there is time available, reviewing each question is an option. Reviewing the work provides students with an opportunity to assess their own work. For each question, after students have shared their own answers, click to show desired answers. Preparation Notes It is possible to conduct the summary without a student share-out. However, the thinking behind having students share their methods is that it builds in incentive for students to work for interesting solutions and ideas during the Explore time (today and in the future), it provides students a chance to take pride in their work and to practice presentation skills, and it helps with student engagement to have students listen to other students instead of the teacher’s voice when possible. Classwork Questions Agenda

Practice – Sharing Question #1 Identify the range, median, Q1, Q3, and interquartile range (IQR).   Weights of pumpkins (in lbs) 5 16 23 20 15 7 8 11 12 24 16 Range = 24 – 5 = 19 pounds Interquartile range = 20 – 8 = 12 pounds 5 7 8 11 12 15 16 16 20 23 24 (1 min) 50-51 In-Class Notes Remind students to follow along on their handout, which they use to take notes if they do not already have similar answers recorded from their Explore time. This slide reviews #1 from the Class Work handout. After students have shared their own answers, click to show desired answers. These are the only possible answers. Follow-up questions to ask: Is the range a reliable measure of variation in this example? Does the weight of pumpkins in this data set have a narrow or wide range? Can you think of a date set that would result in a wide range of weights? Preparation Notes Q1 median Q3 Agenda

Practice – Sharing Question #4 Ms. Wheeler asked each student in her class to write their age in months on a sticky note. The 27 students in the class brought their sticky note to the front of the room and posted them in order on the white board. The data set is listed below in order from least to greatest. What are some observations that can be made from the data display? (Hint: Think about measures of variation) Q1 Median Q3 Range = 150 – 130 = 20 Interquartile range = 143 – 132 = 11 (2 min) 51-53 In-Class Notes Remind students to follow along on their handout, which they use to take notes if they do not already have similar answers recorded from their Explore time. This slide reviews #4 from the Class Work handout. After students have shared their own answers, click to show desired answers. Ensure that students understand that these are just SOME possible answers. Follow-up questions to ask: Is the range a reliable measure of variation in this example? Does the age of students in this data set have a narrow or wide range? Would the range change if the students were asked to write their age in years? Can you think of an example of a data set that would represent a wide range of ages? Preparation Notes The statements in yellow are simply a few possible solutions. Students should have additional statements to share. ¼ of the students in the class are between 130 and 132 months old. 25% of the students in the class are 143 months old or older. ½ of the class is between 132 and 143 months old. Agenda

Practice – Sharing Question #5 Write a data set of any 7 numbers that has all of the characteristics given below.   range equal to 18 interquartile range equal to 8 median equal to 7 2 6 6 7 10 14 20 7 7 7 7 15 15 25 (2 min) 53-55 In-Class Notes Remind students to follow along on their handout, which they use to take notes if they do not already have similar answers recorded from their Explore time. This slide reviews #5 from the Class Work handout. After students have shared their own answers, click to show desired answers. Ensure that students understand that these are just SOME possible answers. For each example provided, ask students to think of a context for the set of data. Ask students to write down at least one possible solution aside from their own for Question #5 on the handout. Preparation Notes These are just a few of many possible solutions for #5. This question should help students see that data sets can share the same measure of center and/or measure of variation, yet still have different data points. This slide is connected to Math PS 1 - Make sense of problems and persevere in solving them: Understand the approaches of others to solving complex problems and identify correspondences between different approaches. 1 2 6 7 9 10 19 Agenda

Assessment - Exit Ticket Individual I am a bit confused! Today we talked about measures of center, measures of variation, range, quartiles, and interquartile range. These words still look like jibberish to me! Can you give me an overview of: what measures of variation are how to find measures of variation why measures of variation are used Please include range, quartiles, and interquartile range in your explanation. (5 min) 55-60 In-Class Notes Distribute Exit Tickets. Remind students to clearly show all of their thinking and work. Encourage students to create a data set to help explain their ideas. All work should be independently and done without notes. Preparation Notes The rationale of using this Exit Ticket is to collect individual student data assessing their understanding of the concept of measures of variation, specifically range and interquartile range. This slide is connected to Math PS 6 – Attend to Precision: Communicate precisely to others. Use clear definitions in discussion with others and in their own reasoning. Agenda

21st Century Lessons The goal… The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons.  These lessons are intended to:   Support an increase in student achievement; Engage teachers and students; Align to the National Common Core Standards and the Massachusetts curriculum frameworks; Embed best teaching practices, such as differentiated instruction; Incorporate high-quality multi-media and design (e.g., PowerPoint); Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; Be available, along with videos and supporting materials, to teachers free of charge via the Internet. Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers.

21st Century Lessons The people… Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21st Century Lessons Brian Connor – Technology Coordinator