Displaying Numerical Data Using Box Plots

Displaying Numerical Data Using Box Plots

Lesson Overview (1 of 6) Lesson Objective Lesson Description
SWBAT display and analyze numerical data using box plots. Lesson Description The lesson begins with students engaging in a whole-class review of how to find the median, range, and IQR, with the IQR being the main focus. Following the review of the warm-up, students are introduced to the five-number summary of a data set. They then use that information to create a box plot. During the explore time, students continue to build on their understanding of how to create box plots by creating a poster-sized box plot in small groups using data generated from a class activity. After creating their box plots in small groups, students then assess the box plots of their peers. This provides an opportunity to clear up misconceptions related to the creation of box plots. The summary at the end of the small group activity focuses on the purpose of box plots. During the practice time, students move from creating box plots to analyzing box plots. The practice consists of a game of Four Corners where students are given a particular interval (less than the median, for example) and have to decide what percent of the data values fall within that interval. They move to the corner of the room that corresponds to their choice. Following the practice, students will be assessed on their understanding of box plots through an activity that utilizes paper plates. Throughout this portion of the lesson, students will be asked multiple choice questions (and T/F) and they will answer the questions by holding up a paper plate with the letter of their answer choice written on it. This allows the teacher to visually see which students have mastered the goals of the lesson and which need additional practice.

Lesson Overview (2 of 6) Lesson Vocabulary
Box Plot: A graph that uses a rectangle to represent the middle 50% of a set of data and “whiskers” at both ends to represent the remainder of the data. Five-Number Summary: Minimum Lower Quartile (Q1) Median Upper Quartile (Q3) Maximum Materials 1) Box plot class work handout 5) Colored Pencils/Markers 2) Notes handout ) Chart Paper 3) Box plot homework ) Post-Its 4) Steps to make a Box plot ) Index cards handout ) Paper plates

Lesson Overview (3 of 6) Scaffolding Enrichment
Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to read and create box plots is provided for struggling students. Enrichment Advanced Objective: SWBAT identify real world situations where one would use a box plot. 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 6) Online Resources for Absent Students
Common Core State Standard 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Lesson Overview (5 of 6) Before and After
Box plots, or box-and-whisker plots, are traditionally an eighth grade concept. As a result, this is most likely the first time that students at the sixth grade level will see box plots. While it is a new concept, students do come into the lesson with prior knowledge that will help them to create and analyze box plots. In the previous two lessons, students learned about the range and interquartile range. Through these lessons, students built an understanding of maximum, minimum, Q1 and Q3. Throughout the unit students have also been learning about the median. These are the five components of the five-number summary that is required to create a box plot. Knowing these five vocabulary words will serve very useful as students learn about box plots. Going forward, students will continue to work with box plots as they use them to compare multiple sets of data. It is important that students have a firm grasp on box plots by the end of this lesson, as the next lesson requires students to create double box plots.

Lesson Overview (6 of 6) 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 display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to describe all parts of a box plot to a partner. A group of taste testers reviewed a brand of natural peanut butter. They gave the peanut butter a rating of points depending on its quality. The ratings are below: Find the minimum, maximum, median, range, and interquartile range (IQR) for this set of data. Challenge: What would the 15th score have to be in order for the peanut butter to have a mean rating of 63 points? (5 min) 0 – 5 In-Class Notes Anticipate that students may not know which data points to use to find the lower and upper quartile since there are an even number of data points (they may forget whether they should use 61.5 as a value when finding these values). Review answers as a class before clicking to show answers. Ensure that students report their answers with a label (points). Scaffolding: Show how to find the IQR. Follow-up questions: What does a median of 61.5 points mean? What does a range of 55 points mean? What does an interquartile range of 12 points mean? Challenge question follow-up: After the 16th score, the mean falls to 60 points. What do you know has to be true about score #16? 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. Min = 34 points Max = 89 points Median = 61.5 points Range = 55 points Interquartile range (IQR) = 12 points 86 points Hint Agenda

Warm Up OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to describe all parts of a box plot to a partner. A group of taste testers reviewed a brand of natural peanut butter. They gave the peanut butter a rating of points depending on its quality. The ratings are below: IQR = Q3 – Q1 Find the minimum, maximum, median, range, and interquartile range (IQR) for this set of data. Challenge: What would the 15th score have to be in order for the peanut butter to have a mean rating of 63 points? (5 min) 0 – 5 In-Class Notes Anticipate that students may not know which data points to use to find the lower and upper quartile since there are an even number of data points (they may forget whether they should use 61.5 as a value when finding these values). Review answers as a class before clicking to show answers. Ensure that students report their answers with a label (points). Scaffolding: Show how to find the IQR. Follow-up questions: What does a median of 61.5 points mean? What does a range of 55 points mean? What does an interquartile range of 12 points mean? Challenge question follow-up: After the 16th score, the mean falls to 60 points. What do you know has to be true about score #16? 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. Min = 34 points Max = 89 points Median = 61.5 points Range = 55 points Interquartile range (IQR) = 12 points 86 points Hint Agenda

Agenda: OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to describe all parts of a box plot to a partner. Warm Up – Review of median, range, and IQR (Individual) Launch – Intro to Box Plots (Whole Class) Explore – Box Plots & Electronics Usage (Small Group) Summary – Why Use Box Plots? (Whole Class) Practice – Four Corners ( Whole Class) Assessment –Paper Plates Discussion (Partner) (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 small group work, and then be asked to show what they’ve learned on an exit ticket. Preparation Notes The structure of today’s lesson is designed to provide an in-depth study of box plots and their usefulness in representing data distributions. Sixth grade students will not have had experience working with box plots in earlier grades. However, their experience working with the range and IQR in previous lessons should help them grasp the concept. Once students understand how to create a box plot, the focus shifts from how to create box plots to how to analyze box plots. By the end of the lesson, students should be able to both create and analyze box plots.

Launch Think-Pair-Share
List some of the ways this information could be displayed visually. Bar Graph? Line Plot? Circle Graph? (2 min) 6 – 8 In-Class Notes Poll students to see if they prefer to analyze data sets by just looking at the data (like it is presented on this slide) or if they prefer to use tables/graphs. This will help highlight the purpose of box plots. Ask students, Would you prefer to analyze this data in table or graph form? Which visual display is more useful to you? Ask students to brainstorm ways to display this information visually (tables, graphs, etc). After students have shared out, click to show possible representations. Ask students to assess each visual representation. For example, “Would it make sense to use a line plot to represent this set of data? Why/why not?” Preparation Notes Table? Agenda

Launch Whole Class A box plot is one of the ways this data can be displayed. (<1 min) 6 – 8 In-Class Notes Inform students that today in class they will learn about constructing box plots, which allow readers to easily analyze a set of data. Preparation Notes Agenda

Launch Whole Class Example of a box plot: Agenda (1 min) 8 – 9
In-Class Notes Questions to ask: What is the box plot about? What is a quality rating? What do you notice about the box plot? Can you make any educated guesses about how to “translate” the box plot? Can you see why it is sometimes called a box-and-whisker plot? Point out that like other graphs they have seen before, a box plot needs a title and a label along the x-axis Preparation Notes This slide is included to just show students what a box plot looks like before dissecting it. Students do not need to understand how to read this box plot. It is included to provide exposure before going into context. Agenda

Launch Vocabulary Box Plot:
A graph that uses a rectangle (box) to represent the middle 50% of a set of data and “whiskers” at both ends to represent the remainder of the data. (3 min) 9 – 12 In-Class Notes Inform students that box plots are also called box-and-whisker plots. Before showing the definition, ask students to create a definition of a box plot in their groups (30 seconds). Keep in mind that this is the first time that they will have seen box plots. Discuss ideas about the definition of box plots. Click to show formal definition. Students should write the definition down in their notes (preferably in a vocabulary section). Ask a student to come up and point to the “rectangle” or the “box.” Ask another student to come up and point to the “whiskers.” Ask a student to point to where the middle 50% of the data lies. Follow-up questions: If the rectangle represents 50% of the data, how is that 50% broken down within the two areas of the box? If the box represents 50% of the data, where does the other 50% of the data lie? Preparation Notes Agenda

Launch Turn-and-talk A box plot is constructed from the five-number summary of a set of data. Using the graph and what you know about range and interquartile range, what do you think the five-number summary consists of? (2 min) 12 – 14 In-Class Notes Ask students to talk about this question with a partner before discussing it as a class. For students who are struggling, click on hint to show the yellow dots on the number line. Inform students that these yellow dots represent the values from the five-number summary. Remind them to use their understanding of quartiles (specifically Q1 and Q3) to help them. Question to ask: Why is the graph drawn above the number line instead of on the number line? 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. Hint Agenda

Launch Notes Five-Number Summary Minimum Lower Quartile (Q1) Median
Upper Quartile (Q3) Maximum Median = 61.5 (2 min) 14 – 16 In-Class Notes Begin by listing the five components of the five-number summary. Students should write what the five-number summary is made up of and the set of data provided in their notebooks. Notes should be titled “Box Plots.” Ask students to work with a partner to find each part of the five-number summary for this set of data. Refer them to their warm-up where they found the range and IQR if they need support. Once students have finished and have shared out, click to show answers. Anticipate the following misconception: Students will have trouble defining Q1 and Q3. The word quartile leads students to believe it will be a section on the graph. In reality, students should view Q1 and Q3 as medians. Instead of being the median of the whole set of data, they are the median of the lower and upper half of the data, respectively. Push students to explain in their own words what Q1 and Q3 represent before moving on. When a student has succinctly defined Q1 and Q3, ask a few other students to repeat or paraphrase that student’s ideas. Preparation Notes Minimum Upper Quartile (Q3) Lower Quartile (Q1) Maximum Agenda

Launch Think-Pair-Share
The box plot below shows how the five-number summary corresponds to the box and whiskers of the box plot. (2 min) 16 – 18 In-Class Notes Students should think about this question independently for 30 seconds before talking to a peer. Once pairs have discussed the question for about 1 minute, review ideas as a class. Questions to ask: Why is the graph drawn above the number line instead of on top of it? Does the number line for every box plot range from 0-100? Could the creator of this box plot have chosen a different range for the number line? How would this have affected the intervals, or scale, of the number line? Inform students that typically the five-number summary is not included on a box plot (the words minimum value, lower quartile, etc.). They are included today just to reinforce what the values represent. Preparation Notes Based on the figures above, how do you make a box plot using the five-number summary? Agenda

Launch Notes Once you have found the five-number summary, follow these steps to make a box plot: 1. Write the data in order from least to greatest 2. Draw a number line that can show the data in equal intervals 3. Mark the median 4. Mark the median of the upper half (the upper quartile, or Q3) 5. Mark the median of the lower half (the lower quartile, or Q1) 6. Mark the maximum (the greatest number) 7. Mark the minimum (the lowest number) 8. Draw a box between the lower quartile and the upper quartile 9. Draw a vertical line through the median inside the box 10. Draw two horizontal lines ("whiskers") from the rectangle to the extremes (minimum and maximum) (3 min) 18 – 21 In-Class Notes Distribute the hand out that includes these steps and the blank box plot. Read through the steps as a class. Ask students to use the steps to fill in the values on the box plot. Preparation Notes Before class, have these steps and a blank box plot drawn on paper for kids for the set of data from Slide 19. Hand out a copy of this to each student. It may be helpful to have these steps written on chart paper so that they can be posted in the classroom. Agenda

Launch Check Your Work! Agenda
(<1 min) 18 – 21 In-Class Notes Give students about 30 seconds to compare their box plot to what it should look like. Poll students to see what they chose to use as the range and scale for their number lines. Follow-Up Questions: Why are the whiskers longer than the box? What does that tell you about the range of the different quartiles? Why is one portion of the box bigger than the other? Ask students to make statements about the peanut butter using the box plot. For example, 50% of the ratings were between roughly 57 points and 70 points. 75% of the ratings were below 70 points. If 75% of the ratings were below 70 points, how would you judge the quality of this peanut butter? Anticipate that it may be difficult for some students to see that each “section” of the graph represents 25% of the data values, as students see 25% as one of four equal pieces, and in terms of actual size, the four “sections” are not equal. 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. Agenda

Explore – Class Challenge!
In your head, estimate the NUMBER OF HOURS you spend using electronics in ONE WEEK . -TV -Computer -Video Games, etc. On the paper in front of you, in large writing, write your estimate. Without talking, form a line from least to greatest in the front of the room. Hold your estimates in front of you for people to see. (3 min) 21 – 24 In-Class Notes Ask a student to read the directions aloud before beginning the activity. Cell phone usage should not be included in the students’ estimates, as students could spend an excessive amount of class time trying to calculate the amount of time they spend on the phone. Preparation Notes Hand out index cards or half sheets of paper to each student before beginning the activity. This slide is connected to Math PS 4 - Model With Mathematics: Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Agenda

Number of hours per week 6th graders spend using electronics.
Explore Number of hours per week 6th graders spend using electronics. To Do: 1) Quietly return to your seat 2) Record the information above in your notes (1 min) 24 – 25 In-Class Notes Once students have lined up from least to greatest, they should read aloud their estimates one at a time (from least to greatest). As students share their answers, record the data on this slide. After the data has been recorded, students should return to their seats so they can record the data in their notes. Click on To Do to show them their next steps. Preparation Notes Agenda

Explore Next Steps: Using the data, independently find the five-number summary in your notes Compare your five-number summary with those of your group members 3) As a group, construct one poster that has the following: a) Data ordered from least to greatest b) Five-number summary c) Box Plot (12 min) 25 – 37 In-Class Notes Distribute Notes Handout before students begin. They should use this as they create their box plots. It will provide additional support for students should they require it. As students create posters, circulate throughout the room and assess student work. Preparation Notes If students are not already seated in groups, groups will need to be created before the lesson begins. Make copies of the Notes Handout for every student. Chart paper or some sort of large poster paper will also be necessary. Each group will need one piece of chart paper along with colored pencils and/or markers. Create an example of what the final product should look like or a graphic organizer and show it to the students before they go off on their own. You have 12 minutes! Agenda

Explore Small Group How does your box plot compare?
Quietly walk around the room to view the box plots made by other groups. Questions to think about: -What is great about the mathematics you see? -What suggestions do you have for the other groups? You have 3 minutes! (3 min) 37 – 40 In-Class Notes Guiding questions include: Did the group use an appropriate range and scale for the number line? Is it clear where the minimum, lower quartile, median, upper quartile, and maximum values are on the box plot? Do these values match the values from the five-number summary? Does the box plot have a title and a label on the x-axis? Students should travel with their groups as they look at other groups’ work. They only need to talk to their own groups. Optional: Give students post-its and make them responsible for leaving a comment or question on the other posters. When the timer has gone off, students should be back in their seats. Preparation Notes 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. Agenda

Summary Whole Class Questions to discuss:
-What is great about the mathematics you saw? -What suggestions do you have for the other groups? -Based on the data that we collected, how much time does the typical student spend using electronics weekly? -When are box plots useful? For example, why would someone choose to create a box plot instead of a bar graph? (3 min) 40 – 43 In-Class Notes Using the questions on this slide (#1 and #2) and using the guiding questions from the previous slide, conduct a follow-up discussion to allow students to give each other feedback. Click to show the fourth question. Preparation Notes 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. Agenda

Explore Whole Class Let’s compare your box plot with a box plot that was created using an applet! (1 min) 43 – 44 In-Class Notes Begin by explaining what an applet is for those students who may not know. Click on “Online Tool” to get access to the applet. Once the applet is open, enter the data for the class. Then students can compare the box plot they made to the electronic version. Follow-up by asking students for similarities and differences between their box plots and the electronic version. Ask students to make statements about the data using the box plot. For example, 25% of students use electronics between _______ and _______ hours each week. 75% of students use electronics more than _________ hours each week. This part of the activity can be skipped if timing is an issue. Preparation Notes Alternative Applet: This is a similar applet that a teacher may also choose to use. This applet has examples that could be shown to the class. Questions could be posed to the students based on the examples provided. This slide is connected to Math PS 2 - Reason Abstractly and Quantitatively: Attend to the meaning of quantities, not just how to compute them. Online Tool Agenda

Practice Four Corners The five-number summary divides a data distribution into four parts. In this activity you will have to decide what percent of the data values fall in given intervals. 1 4 2 3 (5 min) 44 – 49 In-Class Notes Before the game begins, walk through the relationship between the lower quartile, median, upper quartile, the maximum and the spread of the data. Explain to students that 50% of the data is less than the median and 50% is greater than the median. Using that reasoning, since Q1 is the median of the lower half of the data, 25% of the data is less than Q1, which leaves 75% of the data greater than Q1. Ask follow-up questions around this idea to assess student understanding. For example, how could you figure out what % of the data is included in areas 2 and 3 combined in the box plot? Explain to students that when an interval appears in the upcoming slides, they have to decide in their heads what percentage (25%, 50%, 75%, or 100%) of the data values fall in that interval. They will have about 15 seconds to decide. On a cue from the teacher, students will then walk to the corner of the room that corresponds to that percentage. Once students are in their chosen corners, ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Anticipate that it may be difficult for some students to see that each “section” of the graph represents 25% of the data values, as students see 25% as one of four equal pieces, and in terms of actual size, the four “sections” are not equal. Before beginning activity, ask a few questions related to the different pieces of the graph. For example, why are the whiskers on one side longer than the other? Why is one portion of the rectangle much bigger than the other? Why is the box bigger than the whiskers? If time is an issue, this exercise can be done with students at their seats. Alternatively, one can limit the number of examples used in class. Preparation Notes Create four posters. There should be a poster marked 25%, 50%, 75%, and 100%. Post one poster in each corner of the room. The four-corners exercise is included to generate student movement. However, these questions can be posed and answered without having students participate in Four Corners. Agenda

Practice Four Corners 25%
About what percent of the data values fall in the following interval? after the upper quartile 25% (5 min) 44 – 49 In-Class Notes Use this question as an example before beginning the game. Students should talk through this question in small groups. Ask students to share out answers and ask for supporting explanations. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? before the median 50% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? after the median 50% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? in the box (between the upper and lower quartiles) 50% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? before the upper quartile 75% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? before the lower quartile 25% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? after the lower quartile 75% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? between the median and the upper quartile 25% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

About what percent of the data values fall in the following interval? between the median and the lower quartile 25% (5 min) 44 – 49 In-Class Notes Give students about 15 seconds to think about this question in their heads. On a cue from the teacher, students should move to their chosen corners. Ask students to support their answers. Give students the opportunity to move to a different corner based on a peer’s explanation of his/her choice. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

Assessment – Paper Plate Discussion!
At your seats, you and your partner have four paper plates. Each plate has a letter on it: a, b, c, or d. Each of the following slides has a multiple choice question on it. The possible answers are a, b, c, or d. For each question, think about the answer in your head. Then turn to your partner and explain your answer. After your discussion, you or your partner should put the plate in your hand that represents what you believe is the correct answer. When you hear two claps, raise your plate in the air. (1 min) 49 – 50 In-Class Notes Have a student read the instructions aloud before moving onto the next slide. Ask a student to repeat the directions in his/her own words (without reading the slide). Accommodation: Give a copy of the questions to struggling learners. Preparation Notes This activity can be done with or without the class work handout. If time is an issue, it is recommended to do the activity without the handout so that students are answering each question on the spot. Alternatively, the paper plates can be excluded from the activity and the handout can be the main focus. If paper plates are going to be used, prepare a set for each student (or each pair of students). Each student (or pair) should have four plates. Agenda

Ms. Simmons made the box-and-whisker plot below to show some statistics about the ages of the students in her class at a community college. Which of the following best represents the median age of the students in her class? A. 25 B. 27 C. 29 D. 31 (1 min) 50 – 51 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

The box-and-whisker plot below shows the distribution of the daily high temperatures, in degrees Fahrenheit, in the town of Clifton during the year 2004. Based on the box-and-whisker plot, in which of the following intervals of temperatures is it most likely that exactly 50% of the daily high temperatures are located? A. 38°F to 54°F B. 38°F to 81°F C. 54°F to 72°F D. 54°F to 81°F (1 min) 51 – 52 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

Ms. Dumont kept a record of the numbers of students enrolled in foreign language classes at Central High School during the past 20 years. She used her data to make the box-and-whisker plot shown below. Based on Ms. Dumont’s plot, what is the interquartile range of the numbers of students enrolled in foreign language classes? A. 5 C. 30 B D. 50 (1 min) 52 – 53 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

A community center offers classes for students. The range of the number of students in each class is 13. The median number of students in each class is 9. Which of the following box-and-whisker plots could represent the numbers of students in the classes? (1 min) 53 – 54 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Agenda

At your seats, you have two paper plates in front of you. Each plate has a word on it: True or False. Each of the following slides has a statement that is either true or false. For each statement, determine if it is true or false. Then turn to a neighbor and explain your answer. After your discussion, put the plate in your hand that represents what you believe is the correct answer. When you hear two claps, raise your plate in the air. (1 min) 54 – 55 In-Class Notes Have a student read the instructions aloud before moving onto the next slide. Collect the original sets of paper plates and distribute the new sets (true or false) while the directions are being read aloud. Ask a student to repeat the directions in his/her own words (without reading the slide). Accommodation: Give a copy of the questions to struggling learners. Preparation Notes This activity can be done with or without the class work handout. If time is an issue, it is recommended to do the activity without the handout so that students are answering each question on the spot. Alternatively, the paper plates can be excluded from the activity and the handout can be the main focus. If paper plates are going to be used, prepare a set for each student (or each pair of students). Each student (or pair) should have two plates. Agenda

True or False? (1 min) 55 – 56 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. The class median is less than 80. True Agenda

True or False? (1 min) 56 – 57 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Half the class scored between 60 and 80. True Agenda

True or False? (1 min) 57 – 58 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. At least one student earned a score of 100. True Agenda

True or False? (1 min) 58 – 59 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. The class mean is probably less than the median. True Agenda

True or False? (1 min) 59 – 60 In-Class Notes Have one student read the question aloud. Give students a total of about 30 seconds to think about the question and confer with a peer. Clap twice (or use some other cue) to inform students to put plates up in the air. Ask students to support their answers once the plates are up. If students are swayed one way or another by a peer’s argument, they can change the plate they are holding. Ask students who are swayed to explain why they changed their answers. Click for answer. Preparation Notes This slide is connected to Math PS 3 – Construct Viable Arguments and Critique the Reasoning of Others: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. If there are 30 students in the class, at least 10 scored above 80. False Agenda

Standards for This Unit
The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: *6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. *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. Next Slide Back to Overview

Standards for This Unit
*6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs. *6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Next Slide Back to Overview

Displaying Numerical Data Using Box Plots

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Displaying Numerical Data Using Box Plots

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