Displaying Numerical Data on Histograms

Displaying Numerical Data on Histograms

Lesson Overview (1 of 6) Lesson Objective
Lesson Objective: SWBAT display numerical data on a histogram. Student- Friendly Objective: SWBAT create and analyze a histogram. Lesson Description The lesson begins with students engaging in a whole-class review of measures of center, measures of spread, and representations of data. Reviewing line plots and box plots during the warm-up sets the stage for this lesson: using another graph to represent data. Following the review, students participate in a mini lesson on what a histogram is and how to display data on a histogram. Students then work in small groups to create a histogram based on a given set of data. 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. The practice time is broken into two parts. During the first half, students will practice interpreting histograms in a whole class activity.

Lesson Overview (2 of 6) Lesson Description
The second portion of the practice time gives students the opportunity to work independently to create and analyze histograms. During this 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 informal summary of the lesson. The formal assessment of the lesson requires students to take an online quiz. This quiz could be taken individually, with a partner, or as a whole group. Important Note: This is a long lesson, and if it is necessary to break it into 2 days, Slide 65 serves as a good stopping point. Alternatively, ONE portion of the lesson could be skipped. The small group activity, white board math, or the class work could be eliminated, as each targeted skill in these portions is captured through at least one other exercise.

Lesson Overview (3 of 6) Lesson Vocabulary
Histogram: A graphical display of data. The data is grouped into intervals (such as "40 to 49"), and then plotted as bars. Frequency Table: A table that is used to group data values into intervals Frequency: The number of values that lie in an interval Materials 1) Class work handouts 2) Notes for struggling students 3) Challenge work for advanced students 4) Histograms homework 6) Small white boards (optional) 7) Large white boards (optional) 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 (4 of 6) Scaffolding
Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to create a histogram is provided for struggling students. Two versions of the class work and homework exist – one regular and one that has been modified. Enrichment An extension is provided for advanced students. The extension consists of a collecting data to answer a statistical question and then using the data to create a histogram and circle graph (using a protractor and compass). Online Resources for Absent Students

Lesson Overview (5 of 6) Before and After
Coming into this lesson, students will have had many lessons related to statistics. The first group of lessons focused on measures of center including median and mean. The second group of lessons focused on measures of spread including range, interquartile range (IQR), and mean absolute deviation (MAD). Throughout these lessons students created and analyzed both line plots and box plots. This lesson on histograms comes directly after the lessons on box plots, giving students the opportunity to compare the two representations in a timely manner. However, this lesson could be taught after the concept of shape has been covered instead. In this case, histograms, while being a new idea, could also serve as a review of shape. Histograms will be a completely new concept for sixth graders. However, students can apply their knowledge of bar graphs that they acquired in previous years to quickly gain an understanding of how to create and interpret histograms. By the end of this lesson, students should be able to both create and analyze histograms. They should also be able to determine which type of graph is appropriate to use to represent a particular set of data. Ultimately students should be able to look at different representations and describe the data distributions’ center, spread, and shape.

Lesson Overview (6 of 6) Before and After
The overarching goal of the unit is for students to 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. Topic Background The term "histogram" is from the Greek language, and was coined by Karl Pearson, a famous statistician. Simply stated, it means a "common form of graphical representation." It is unclear when histograms were first created, but they have been useful tools for quite some time. "The Commercial and Political Atlas," written by William Playfair and published in 1786, contained the oldest known bar chart. In 1859, Florence Nightingale used histograms to show the difference in mortality between civilians and the military. Florence Nightingale tried to show that military men died more frequently than civilians, which gave her the evidence she needed to improve army hygiene. When facts are visualized and labeled, it can help to make positive changes in the world (

Warm Up OBJECTIVE: SWBAT display numerical data on a histogram.
Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. Name an appropriate graph that could be used to summarize these birth weights. Explain your choice. Describe the distribution of birth weights for the puppies using one measure of center (mean, median) or one measure of spread (range, IQR). (5 min) 0 – 5 In-Class Notes SWBAT = Student Will Be Able To Students should answer these questions independently on paper. Agenda

Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. Name an appropriate graph that could be used to summarize these birth weights. Explain your choice. (5 min) 0 – 5 In-Class Notes Review answer as a class before clicking to show line plot. Ask students if there might have been other appropriate ways to display this information (students should suggest a box plot and might suggest a bar graph). Point out important components of the line plot as review: title, labels, key, appropriate numbering (15 is included even though there is no data point on 15), etc. Optional review as necessary: Ask students questions that require them to interpret the line plot. Examples: How do you know 15 puppies were weighed just by looking at the line plot? How many puppies weighted more than 18 ounces? How many puppies weighed 14 ounces or less? Answer Agenda

Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. Name an appropriate graph that could be used to summarize these birth weights. Explain your choice. Puppy Weights Key: X – one puppy X (5 min) 0 – 5 In-Class Notes Review answer as a class before clicking to show line plot. Ask students if there might have been other appropriate ways to display this information (students should suggest a box plot and might suggest a bar graph). Point out important components of the line plot as review: title, labels, key, appropriate numbering (15 is included even though there is no data point on 15), etc. Optional review as necessary: Ask students questions that require them to interpret the line plot. Examples: How do you know 15 puppies were weighed just by looking at the line plot? How many puppies weighted more than 18 ounces? How many puppies weighed 14 ounces or less? Ounces Agenda

Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. b. Describe the distribution of birth weights for the puppies using one measure of center (mean, median) or one measure of spread (range, IQR). (5 min) 0 – 5 In-Class Notes Review answers as a class before clicking to show answers. Optional review as necessary: Review measures of center and spread. For example: How do you find the mean for a set of data? What does it represent? How do you find the median for a set of data? What does it represent? How do you find the range for a set of data? What does it represent? How do you find the IQR for a set of data? What does it represent? Why might the IQR be used instead of the range as a measure of spread? How are measures of center and spread different? How are measures of center and spread similar? Answer Agenda

Warm Up Measures of Center Mean: Median: Measures of Spread Range:
OBJECTIVE: SWBAT display numerical data on a histogram. Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. b. Describe the distribution of birth weights for the puppies using one measure of center (mean, median) or one measure of spread (range, IQR). Measures of Center Mean: Median: Measures of Spread Range: IQR: (5 min) 0 – 5 In-Class Notes Review answers as a class before clicking to show answers. Optional review as necessary: Review measures of center and spread. For example: How do you find the mean for a set of data? What does it represent? How do you find the median for a set of data? What does it represent? How do you find the range for a set of data? What does it represent? How do you find the IQR for a set of data? What does it represent? Why might the IQR be used instead of the range as a measure of spread? How are measures of center and spread different? How are measures of center and spread similar? 17 ounces 8 ounces 18 ounces 5 ounces Agenda

Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. c. Use a measure of center to explain what the typical birth weight is for puppies. (5 min) 0 – 5 In-Class Notes Review answers as a class before clicking to show answers. It is important that students understand that all three answers are acceptable. The most important part of their answers is the rationale. They need to be able to explain why the mean, median, or mode is “typical” for this set of data. Answer Agenda

Language Objective: SWBAT orally describe how to create a histogram. Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months. c. Use a measure of center to explain what the typical birth weight is for puppies. The mean is 17 ounces. The typical weight could be 17 ounces, because that would be like redistributing the puppy weight so that each puppy weighed the same. The median is 18 ounces. The typical weight could be 18 ounces, because that would mean that half of the puppies weighed less than or equal to 18 ounces and half of the puppies weight greater than or equal to 18 ounces. The mode, or most frequent weight, is 19 ounces. The typical weight could be 19 ounces, because most puppies weighed that amount at birth. (5 min) 0 – 5 In-Class Notes Review answers as a class before clicking to show answers. It is important that students understand that all three answers are acceptable. The most important part of their answers is the rationale. They need to be able to explain why the mean, median, or mode is “typical” for this set of data. Agenda

Language Objective: SWBAT orally describe how to create a histogram. Challenge: Find the Mean Absolute Deviation (MAD) of the 15 puppy weights. (5 min) 0 – 5 In-Class Notes MAD is an “exploratory” concept in the Common Core. Skip this slide if the topic was not previously covered in instruction. If MAD has not been covered, this could be used an extension problem for students who get through the content quickly at any point in the lesson. Notes about Mean Absolute Deviation would have to be provided for students completing the extension. Answer Agenda

Warm Up OBJECTIVE: SWBAT display numerical data on a histogram. Language Objective: SWBAT orally describe how to create a histogram. Challenge: Find the Mean Absolute Deviation (MAD) of the 15 puppy weights. Mean = 17 ounces = 32 (5 min) 0 – 5 In-Class Notes MAD is an “exploratory” concept in the Common Core. Skip this slide if the topic was not previously covered in instruction. If MAD has not been covered, this could be used an extension problem for students who get through the content quickly at any point in the lesson. Notes about Mean Absolute Deviation would have to be provided for students completing the extension. MAD = 2.13 ounces 32 ÷ 15 = 2.13 Agenda

Agenda 1) Warm Up – Review of Graphs (Individual) 5 mins
OBJECTIVE: SWBAT display numerical data on a histogram. Language Objective: SWBAT orally describe how to create a histogram. 1) Warm Up – Review of Graphs (Individual) 5 mins 2) Launch – What is a Histogram? (Whole Class) 5 mins 3) Explore – How Do You Create a Histogram? 30 mins (Whole Class/Small Group) 4) Summary – Why Use a Histogram? (Whole Class) 5 mins 5) Practice (I)– How Do You Read a Histogram? 10 mins (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 individual work, and then be asked to show what they’ve learned through an online quiz. 6) Practice (II)– Histogram Class Work 15 mins (Independent/Partner) 7) Assessment – Online Quiz (Whole Class) 5 mins

Center Spread Shape Launch – Review Turn and Talk (30 sec) Today!
When we analyze data, what are we looking for? Center Median Mean Today! Spread (measure of variation) Range Interquartile Range Mean Absolute Deviation (1 min) 6 – 7 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. Preparation Notes The focus of today’s lesson is using a histogram to represent data distributions. It is important for students to realize that one can learn about the center and spread of a set of data by interpreting a histogram. In the upcoming lessons, shape will be looked at as a way to describe a set of data and at that point, the connection between histograms and the shape of data can be made. By the end of the unit, students should be able to explain three different ways to describe data (center, spread, shape) and also three ways to represent data (line plots, box plots, histograms). This exact slide was part of the previous lessons (center and spread) in the unit. Shape Agenda

Launch Turn-and-talk Let’s go back to our line plot. Looking at the line plot, where do you see data clustered? Puppy Weights Key: X – one puppy X X X X X X X X (1 min) 7 – 8 In-Class Notes Scaffolding: Show the definition of clustered. Students should discuss with a partner for 30 seconds before sharing out to the class. Students should see that most of the data is clustered around ounces. They should also recognize a small cluster from ounces. Ounces Scaffolding Agenda

Launch Turn-and-talk Let’s go back to our line plot. Looking at the line plot, where do you see data clustered? Clustered: located very close to one another, like in a group Puppy Weights Key: X – one puppy X X X X X X X X (1 min) 7 – 8 In-Class Notes Scaffolding: Show the definition of clustered. Students should discuss with a partner for 30 seconds before sharing out to the class. Students should see that most of the data is clustered around ounces. They should also recognize a small cluster from ounces. Ounces Agenda

Launch Turn-and-talk Let’s go back to our box plot. Looking at the box plot, where do you see data clustered? Puppy Weights (1 min) 8 – 9 In-Class Notes Scaffolding: Show the definition of clustered. This question will be more difficult than the previous question, as students really need to understand how to interpret a box plot to answer this question. Students should discuss with a partner for 30 seconds before sharing out to the class. Desired answer: Since each section of the box plot represents about 25% of the data, the data is most closely clustered between ounces and ounces. Those are the most narrow parts of the box plot, indicating narrow ranges of data. Since each sections of the box plot contains the same amount of data, when there is a narrow range a section, it means that that data is also clustered together in that section. As students discuss their ideas with a peer, circulate and try to find someone who is articulating this idea. Ask that person to share his/her idea with the class. Ask other student(s) to explain the idea in their own words and/or defend why it makes sense. Many students will think that since the “box” is so big between ounces, most of the data Is clustered there. To address this misconception, ask students, “Why might someone think that the data is clustered between ounces?” Ounces Scaffolding Agenda

Launch Turn-and-talk Let’s go back to our box plot. Looking at the box plot, where do you see data clustered? Clustered: located very close to one another, like in a group Puppy Weights (1 min) 8 – 9 In-Class Notes Scaffolding: Show the definition of clustered. This question will be more difficult than the previous question, as students really need to understand how to interpret a box plot to answer this question. Students should discuss with a partner for 30 seconds before sharing out to the class. Desired answer: Since each section of the box plot represents about 25% of the data, the data is most closely clustered between ounces and ounces. Those are the most narrow parts of the box plot, indicating narrow ranges of data. Since each sections of the box plot contains the same amount of data, when there is a narrow range a section, it means that that data is also clustered together in that section. As students discuss their ideas with a peer, circulate and try to find someone who is articulating this idea. Ask that person to share his/her idea with the class. Ask other student(s) to explain the idea in their own words and/or defend why it makes sense. Many students will think that since the “box” is so big between ounces, most of the data Is clustered there. To address this misconception, ask students, “Why might someone think that the data is clustered between ounces?” Ounces Agenda

Launch Turn-and-talk Let’s go back to both plots. How are the clusters in the line plot represented in the box plot? Puppy Weights X X X X X X X X (1 min) 9 – 10 In-Class Notes Students should discuss with a partner for 30 seconds before sharing out to the class. Students should see that where there are a lot of X’s on the line plot (18, 19, 20), the corresponding sections on the box plot are narrow. Whereas where there are not a lot of X’s on the box plot (15, 16), the corresponding section of the box plot is wide. Therefore, highly concentrated data on a line plot is shown through a lot of X’s over only a few numbers, whereas on a box plot, it is shown in the more narrow sections. Ounces Agenda

Do you know the name of this graph?
Launch Today in class we will be looking at another type of graph that displays data. This graph makes it easy to see where data is clustered. Do you know the name of this graph? (1 min) 10 – 11 In-Class Notes Students may know the name of the graph, because it was included in the lesson objective on the warm-up and agenda slides. Histograms will be a new topic for the the vast majority, if not the entirety, of the class. Agenda

It looks like this… Launch Agenda (<1 min) 10 – 11 In-Class Notes
Students may know the name of the graph, because it was included in the lesson objective on the warm-up and agenda slides. Histograms will be a new topic for the the vast majority, if not the entirety, of the class. Many students will say that this is a bar graph. This would be a good opportunity to point out the differences between a bar graph and a histogram. Agenda

…and it is called… Launch Agenda (<1 min) 10 – 11 In-Class Notes
Students may know the name of the graph, because it was included in the lesson objective on the warm-up and agenda slides. Histograms will be a new topic for the the vast majority, if not the entirety, of the class. Many students will say that this is a bar graph. This would be a good opportunity to point out the differences between a bar graph and a histogram. Agenda

…a histogram! Launch Agenda (<1 min) 10 – 11 In-Class Notes
Have everyone say the word histogram aloud before moving on. Agenda

What is a histogram? Launch Turn-and-talk Agenda (1 min) 11 – 12
In-Class Notes Students should discuss with a partner for 30 seconds before sharing out to the class. Guiding questions: What are the important features of a histogram? How is a histogram different than a bar graph? How would you interpret (read) a histogram? What is a histogram used for? Before moving onto the next slide, point out the intervals on the x-axis and the frequencies on the y-axis (both of these words are on the following slide so students should have a basic understanding of what they mean). Agenda

Launch Whole Class Word Bank frequency intervals spaces graph bars
A histogram is a ___________________ that displays data. Like a bar graph, a histogram uses ___________________ to represent data. The bars in a histogram do not have any ___________________ between them. In order to construct a histogram, you must divide the data into ___________________. The number of data points that fall into an interval is the___________________. This tells you the ____________________ of each bar on a histogram. (2 min) 12 – 14 In-Class Notes Optional: Provide fill-in-the-blank worksheet for students (see worksheet included in the accompanying lesson resources) Give students about 30 seconds to read through the sentences and think about where the words from the word bank belong. As a class, review the fill in the blanks. After each fill in the blank, click for the correct answer to appear. Have a student read the entire paragraph aloud after the fill-in-the-blank portion of the activity is complete. Students may struggle with the words intervals and frequency. If this is the case, refer back to the previous slide and ask a student to come to the board to point out the intervals on the x-axis and the frequencies on the y-axis. Word Bank frequency intervals spaces graph bars height Agenda

How was this histogram created?
Explore How was this histogram created? (<1 min) 12 – 14 In-Class Notes Explain to students that creating a histogram is a multi-step process, and over the next few slides, they will learn the steps involved in creating a histogram. Agenda

We start with a set of data.
Explore We start with a set of data. 62 4 29 8 30 55 31 12 36 34 30 20 27 25 26 29 30 (1 min) 14 – 15 In-Class Notes Explain to students that every histogram starts with a set of data that was collected by asking a statistical question. 67 17 12 15 39 6 38 Agenda

Explore It is helpful to have the data ordered from... least to
62 4 least to greatest! 29 8 30 55 31 12 36 34 30 20 27 25 26 29 30 (<1 min) 14 – 15 In-Class Notes Ask students how the data should be ordered. Once answer is given, click to show the data being ordered from least to greatest. 67 17 12 15 39 6 38 Agenda

Age of People Attending a Movie
Explore Now we use our organized set of data to create a frequency table. Age of People Attending a Movie Age Ranges Tally Frequency 29 30 8 30 12 30 31 34 36 39 55 62 (1 min) 15 – 16 In-Class Notes Ask students what they think a frequency table might be. Make the connection to the word frequently since that is a word students will be familiar with. After students share out, click to show definition, and then click to show the example of a frequency table. Definition Agenda

Explore Now we use our organized set of data to create a frequency table. 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency Frequency Table: A table that is used to group data values into intervals (1 min) 15 – 16 In-Class Notes Ask students what they think a frequency table might be. Make the connection to the word frequently since that is a word students will be familiar with. After students share out, click to show definition, and then click to show the example of a frequency table. Agenda

Explore Turn-and-talk
What should we use for our intervals, or our age ranges? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency (1 min) 16 – 17 In-Class Notes Before students talk about their ideas with a peer, review what the word interval means. It may be helpful to go back to the histogram on Slide 30 to point out the intervals or simply provide some written exemplars on the board. For example: 0-19, 20-39, 40-59 1-5, 6-10, 11-15, 16-20, 21-25 Determining intervals is one of the most difficult aspects of creating a histogram for students as there are many errors students can make. Common mistakes: Repeating a number in intervals (1-10, 10-20, 20-30, etc) Not having equal intervals (0-10, 11-20, 21-30) or (1-10, 11-20, 21-24) Click on scaffolding to provide reminders for students as necessary. Scaffolding Agenda

What should we use for our intervals, or our age ranges? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency Important things to remember! Each interval needs to be equal (count by 3’s, 5’s, etc.) Your intervals cannot overlap or exclude any values. (1 min) 16 – 17 In-Class Notes Before students talk about their ideas with a peer, review what the word interval means. It may be helpful to go back to the histogram on Slide 30 to point out the intervals or simply provide some written exemplars on the board. For example: 0-19, 20-39, 40-59 1-5, 6-10, 11-15, 16-20, 21-25 Determining intervals is one of the most difficult aspects of creating a histogram for students as there are many errors students can make. Common mistakes: Repeating a number in intervals (1-10, 10-20, 20-30, etc) Not having equal intervals (0-10, 11-20, 21-30) or (1-10, 11-20, 21-24) Click on scaffolding to provide reminders for students as necessary. Agenda

What should we use for our intervals, or our age ranges? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency 0 - 9 (1 min) 17 – 18 In-Class Notes Once students have shared their ideas, click to show answers. Point out that none of the numbers are repeated in the column. For example, the first interval ends with 9 and the next begins with 10. A common mistake would be ending the first interval with 10 and beginning the second interval with 10. Ask students if the intervals provided in the table are the only possible choices for intervals. Students should understand that there are countless options for intervals, but typically we choose benchmarks like 0, 1, 5, 10, etc. as the starting and ending points of our intervals. Ask students how our interval choice might affect the appearance of our histogram (the wider the intervals, the fewer the bars). Agenda

Explore Turn-and-talk What strategy should we use to tally our data? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency 0 - 9 (1 min) 18 – 19 In-Class Notes Click on scaffolding to remind students what a tally is as necessary. Student should discuss for 20 seconds before sharing out. As students discuss their ideas with a peer, circulate and try to find someone who mentions crossing off each number and making a tally mark one at a time. Ask that person to share his/her idea with the class. Then move to the next slide to show the strategy. Agenda Scaffolding

Explore Turn-and-talk What strategy should we use to tally our data? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency 0 - 9 A tally mark, I, represents one data value. The mark IIII represents five data values. (1 min) 18 – 19 In-Class Notes Click on scaffolding to remind students what a tally is as necessary. Student should discuss for 20 seconds before sharing out. As students discuss their ideas with a peer, circulate and try to find someone who mentions crossing off each number and making a tally mark one at a time. Ask that person to share his/her idea with the class. Then move to the next slide to show the strategy. Agenda

Explore What strategy should we use to tally our data? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency Cross off each number and make a tally mark one at a time! 0 - 9 (<1 min) 18 – 19 In-Class Notes Ask students why it is important to cross off one number and make one tally at a time. Inform students that it is really important that they use this strategy, because it is really easy to make a mistake (forgetting to include a number, including a number twice, etc.) if it is not used. Agenda

Explore 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency I I I 0 - 9 I I I I I I I I I I I I I I I I (1 min) 19 – 20 In-Class Notes Point out that one number is being crossed off and tallied at a time. This is the strategy that students should use as well. I I I Agenda

Explore Are we ready to complete the frequency column? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency III IIII IIII I IIII III I II 0 - 9 (1 min) 20 – 21 In-Class Notes Review the word frequency before moving onto the next slide (click to show definition). Ask students to relate the word frequency to everyday life (for example, the word frequently tells you how often something occurs). Ask students how they would determine what numbers belong in the frequency column of the table. Agenda Definition

Explore Are we ready to complete the frequency column? 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency III IIII IIII I IIII III I II 0 - 9 Frequency: The number of values that lie in an interval (1 min) 20 – 21 In-Class Notes Review the word frequency before moving onto the next slide (click to show definition). Ask students to relate the word frequency to everyday life (for example, the word frequently tells you how often something occurs). Ask students how they would determine what numbers belong in the frequency column of the table. Agenda

Explore 29 30 8 30 12 30 31 34 36 39 55 62 Age of People Attending a Movie Age Ranges Tally Frequency III IIII IIII I IIII III I II 0 - 9 3 4 6 8 (<1 min) 20 – 21 In-Class Notes Click for frequencies to appear. 1 2 Agenda

Explore Think-Pair-Share
So we have to do all of that work for a frequency table and we haven’t even made a histogram yet? Ugh. This seems like a lot to remember. (1 min) 21 – 22 In-Class Notes Have a student read aloud what the cartoon is thinking. Indicate that a lot of students might be feeling the same way as the cartoon, so it is important to review has been covered so far. Agenda

Review the steps for creating a Frequency Table with the person next to you. So we have to do all of that work for a frequency table and we haven’t even made a histogram yet? Ugh. This seems like a lot to remember. (1 min) 22 – 23 In-Class Notes Students should think about this question independently (20 seconds) before discussing with a neighbor (20 seconds). As students discuss their ideas with a peer, circulate and try to find people who mention steps that are part of the strategy (outlined on the next slide). Ask those students to share one of the steps with the class. Then move to the next slide to show the strategy. Agenda

Steps for creating a Frequency Table: Choose intervals of equal size. Start by looking at the minimum and maximum value in the data set to make sure your intervals cover the entire range of the data set. Make a tally mark for each data point next to the appropriate interval. Write the frequency for each interval by totaling the number of tally marks for the interval. (1 min) 23 – 24 In-Class Notes Have student(s) read steps aloud to the class. After reading the second part of Step 1, ask students what it means and why it is included. Agenda

Explore Now we can create our histogram! Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 (1 min) 24 – 25 In-Class Notes Explain to students that once the frequency table is complete, we can begin making the histogram. Agenda

Explore Here we have the x- and y-axis for our histogram. Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 (<1 min) 24 – 25 In-Class Notes Ask students to show which axis is the x-axis by making its shape with their arms (they should like like they are airplanes with their arms stretched out horizontally). Then ask students to show what the y-axis looks like with their arms (one arm should be pointing up and one arm should be pointing down). Optional: Have students come up to the board to point out the x- and y-axis. Agenda

Explore What do we need to include to let the reader know what the graph is about? Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 A Title and Labels! (<1 min) 24 – 25 In-Class Notes Have a student read the question aloud. Once answers have been given, click to show them. Agenda

Explore We have our x-axis labeled… What else do we need on the x-axis? Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie Number of People (Frequency) (1 min) 25 – 26 In-Class Notes Optional: Have a student come up to the board to point out the x-axis. Desired answer: Equal spaces and numbers (intervals). Age Agenda

Explore We need to be sure that we make equal spaces for our intervals! Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie Number of People (Frequency) (<1 min) 25 – 26 In-Class Notes Point out that each hashmark on the x-axis divides the x-axis into equal spaces. Stress the importance of equal spacing. It may be helpful for students to share out their own successful strategies for making equal spaces. Age Agenda

Explore Notice that there are not any duplicate numbers on the x-axis! Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie Number of People (Frequency) (<1 min) 25 – 26 In-Class Notes Ask students how they determine which numbers belong on the x-axis. Click for intervals to appear. Although it was already addressed when the frequency table was made, remind students that none of the numbers are repeated on the x-axis. For example, the first interval ends with 9 and the next begins with 10. 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Age Agenda

Explore We have our y-axis labeled… what else do we need on the y-axis? Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie Notice the equal spaces! Number of People (Frequency) (1 min) 26 – 27 In-Class Notes Optional: Have a student come up to the board to point out the y-axis. Desired answer: Equal spaces and numbers (frequencies). Point out that each hashmark on the y-axis divides the y-axis into equal spaces. 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Age Agenda

Explore Notice that we have a scale on the y-axis – we are counting by 1’s Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie 9 8 7 6 Number of People (Frequency) 5 4 3 (<1 min) 26 – 27 In-Class Notes Point out the scale on the y-axis. Ask students if another scale (like counting by 2’s) could have been used. Students should understand that there are a few options for the scale, but typically we choose numbers that are easy to work with, like 1’s, 5’s, 10’s, etc. as our scale and we choose a scale based on our range. In this case, since our range is narrow, counting by 1’s makes sense. If our range were 1,000, then counting by 100’s would be more appropriate. Ask students how our scale choice might affect the appearance of our histogram (for example, in this case, if we had chosen a scale of 5, and had the y-axis go up to 20, the bars would not have been as tall). 2 1 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Age Agenda

Explore Now we can put the bars on our histogram! Age of People Attending a Movie Age Ranges Tally Frequency 0 – 9 III 3 10 – 19 IIII 4 20 – 29 IIII I 6 30 – 39 IIII III 8 40 – 49 50 – 59 I 1 60 – 69 II 2 Ages of People Attending a Movie 9 8 3 7 4 6 Number of People (Frequency) 6 5 4 8 3 (<1 min) 26 – 27 In-Class Notes Before showing bars, ask students what is important about how we place the bars. Desired answer: No spaces between the bars! Click to show bars appearing on the slide. 2 1 1 2 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Age Agenda

Explore How does our histogram compare to the original histogram?
(1 min) 27 – 28 In-Class Notes Students can signal an answer by showing a thumbs up or thumbs down. Students should see that although the histograms do not look exactly the same, they show exactly the same information. Agenda

Explore: Review Data Frequency Table Histogram Agenda (1 min) 28 – 29
In-Class Notes Before clicking for table to appear, ask students what is important about the order of the data (ordered from least to greatest). After table appears, ask students what is next (frequency table). After frequency table appears, ask students what is next (histogram). Optional: Ask students to share out important things to remember for each part of the process (don’t repeat numbers for the intervals, don’t include spaces between the bars on the histogram, cross off numbers in a list of data as you tally, etc.). Agenda

Explore Small Group Create a histogram with your group to represent
Minutes spent texting daily for 24 sixth grade students: ___Title Create a histogram with your group to represent the texting times. ___Labels ___Equal intervals on both axes ___No spaces between bars (8 min) 29 – 37 In-Class Notes Encourage students to use this slide as a final check when they are done with their histogram. Students should work in small groups (3 – 4 students) to create the histogram. Students should work collaboratively, but each student should be writing down his/her own work. Give students about 8 minutes to work on the problem before reviewing the solution. Teacher should be circulating to ensure that groups are working as teams – make sure that ALL students are participating. Preparation Notes Optional: Distribute handouts with the data on it. Large (3 ft by 6 ft) white boards are recommended for this activity. Alternatively, each group could write its problem on a small white board or simply a piece of paper. ___No duplicate #’s on either axis Agenda

Summary How does your histogram compare?
Quietly walk around the room to view the histograms 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 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 white boards. When the timer has gone off, students should be back in their seats. Conduct a follow-up discussion to allow students to give each other feedback. Guiding questions include: Did the group use an appropriate scale and intervals for the y- and x-axis? Are there equal spaces on the x- and y-axis? Is it clear what frequency each bar represents? Does the histogram have a title and a label on the x- and y-axis? Agenda

Summary We started class today by making line plots and box plots. Then we began making histograms. If we already have two different types of graphs to represent data, why do we need to know about histograms? (2 min) 40 – 42 In-Class Notes This is a long lesson, and if it is necessary to break it into 2 days, this slide serves as a good stopping point. Click on scaffolding and the hint for additional support as necessary. Students should recognize that graphs serve different purposes. It is important to choose an appropriate graph based on the set of data. For example, a line plot would not be appropriate for a data set that ranges from Likewise, a box plot and histogram would not be appropriate to represent a set of data with only 4 data points. If one needs to know the actual data values, then a line plot would be appropriate. Whereas histograms and box plots give a more general overview of a set of data. A histogram is a good choice when one doesn’t need to know every data point in the set of data and wants to make some general conclusions about the center, spread and shape of the data. Optional: Ask students to identify one pro and one con of each type of representation (line plot, box plot, histogram). Agenda Scaffolding Hint Hint

Summary We started class today by making line plots and box plots. Then we began making histograms. If we already have two different types of graphs to represent data, why do we need to know about histograms? Guiding Question: Can you think of some situations where a histogram might be more appropriate to use than a line plot or box plot? (2 min) 40 – 42 In-Class Notes This is a long lesson, and if it is necessary to break it into 2 days, this slide serves as a good stopping point. Click on scaffolding and the hint for additional support as necessary. Students should recognize that graphs serve different purposes. It is important to choose an appropriate graph based on the set of data. For example, a line plot would not be appropriate for a data set that ranges from Likewise, a box plot and histogram would not be appropriate to represent a set of data with only 4 data points. If one needs to know the actual data values, then a line plot would be appropriate. Whereas histograms and box plots give a more general overview of a set of data. A histogram is a good choice when one doesn’t need to know every data point in the set of data and wants to make some general conclusions about the center, spread and shape of the data. Optional: Ask students to identify one pro and one con of each type of representation (line plot, box plot, histogram). Agenda Hint

Summary We started class today by making line plots and box plots. Then we began making histograms. If we already have two different types of graphs to represent data, why do we need to know about histograms? (2 min) 40 – 42 In-Class Notes This is a long lesson, and if it is necessary to break it into 2 days, this slide serves as a good stopping point. Click on scaffolding and the hint for additional support as necessary. Students should recognize that graphs serve different purposes. It is important to choose an appropriate graph based on the set of data. For example, a line plot would not be appropriate for a data set that ranges from Likewise, a box plot and histogram would not be appropriate to represent a set of data with only 4 data points. If one needs to know the actual data values, then a line plot would be appropriate. Whereas histograms and box plots give a more general overview of a set of data. A histogram is a good choice when one doesn’t need to know every data point in the set of data and wants to make some general conclusions about the center, spread and shape of the data. Optional: Ask students to identify one pro and one con of each type of representation (line plot, box plot, histogram). Hint: What would a line plot look like if your data ranged from 1 to 683? Agenda Scaffolding

Create ☐Interpret Practice: Part I histograms
(1 min) 42 – 43 In-Class Notes This is a long lesson, and if it is necessary to break it into 2 days, this slide serves as a good starting point for the second portion of the lesson. Have a student read the slide aloud before moving onto the next slide. It may be helpful to clarify that in this case the word interpret means to understand or read. Now that we know how to create histograms, we need to make sure we know how to interpret them! Agenda

Practice: White Board Math
On each of the following slides you will see a question about the related histogram. Your job – after the question has been read aloud: Read the question a second time to yourself (silently) Write your answer down on your white board Confer with a peer Wait quietly as everyone finishes When you hear two claps, silently raise your white board in the air (1 min) 43 – 44 In-Class Notes Have a student read the instructions aloud. Preparation Notes If white boards are not available, an alternative would be to make each question a multiple-choice question. Then give students a set of letters (a, b, c, d), and when it is time to show answers, the students would hold up their chosen letter. Agenda

What interval represents the most number of cars? (1 min) 44 – 45 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Agenda Answer

What interval represents the most number of cars? (<1 min) 44 – 45 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Answer: 12:00 – 12:59 Agenda

How many cars passed through between 2:00 P.M. and 4:59 P.M.? (1 min) 45 – 46 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Agenda Answer

How many cars passed through between 2:00 P.M. and 4:59 P.M.? 20 35 40 (<1 min) 45 – 46 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Answer: 95 cars Agenda

How many months had six or more days of rain? (1 min) 46 – 47 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Agenda Answer

How many months had six or more days of rain? 3 1 (<1 min) 46 – 47 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 white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Answer: 4 months Agenda

What fraction of the months had less than 2 days of rain? (1 min) 47 – 48 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common errors: Students will report answer as a whole number rather than as a fraction. Students will include the column representing 2-3 days in their calculation. Click for answer. Agenda Answer

What fraction of the months had less than 2 days of rain? = 12 (<1 min) 47 – 48 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common errors: Students will report answer as a whole number rather than as a fraction. Students will include the column representing 2-3 days in their calculation. Click for answer. Answer: or of the months Agenda

How many bracelets have at least five beads? (1 min) 48 – 49 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common struggle: Understanding the phrase “at least.” Click for answer. Agenda Answer

How many bracelets have at least five beads? 4 5 8 (<1 min) 48 – 49 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common struggle: Understanding the phrase “at least.” Click for answer. Answer: 17 bracelets Agenda

What percent of the bracelets have 4 beads or less? (1 min) 49 – 50 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common error: Students will report answer as a whole number rather than as a percent. Click for answer. Agenda Answer

What percent of the bracelets have 4 beads or less? × = = 20 (<1 min) 49 – 50 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 white boards up in the air. Ask students to support their answers once the white boards are up. Common error: Students will report answer as a whole number rather than as a percent. Click for answer. Answer: 15% of the bracelets Agenda

Which intervals can be used to make a frequency table of the lengths, in inches, of alligators at an alligator farm? 140, 127, 103, 140, 118, 100, 117, 101, 116, 129, 130, 105, 99, 143 90–110, 111–130, 131–150 91–110, 111–130, 131–150 90–110, 110–130, 130–150 81–100, 101–120, 121–140 (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. Hint for students: First focus on the provided answers rather than the set of data to eliminate at least 2 choices. Clap twice (or use some other cue) to inform students to put white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Agenda Answer

Which intervals can be used to make a frequency table of the lengths, in inches, of alligators at an alligator farm? 140, 127, 103, 140, 118, 100, 117, 101, 116, 129, 130, 105, 99, 143 90–110, 111–130, 131–150 91–110, 111–130, 131–150 90–110, 110–130, 130–150 81–100, 101–120, 121–140 (<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. Hint for students: First focus on the provided answers rather than the set of data to eliminate at least 2 choices. Clap twice (or use some other cue) to inform students to put white boards up in the air. Ask students to support their answers once the white boards are up. Click for answer. Agenda

The histogram above shows the butterflies spotted in a butterfly garden between 8 A.M. and 8 P.M. Make an observation about the data. (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. Scaffolding: Provide word bank. Clap twice (or use some other cue) to inform students to put white boards up in the air. Ask students to support their answers once the white boards are up. Click for answers. Agenda Sentence Starters

Possible Sentence Starters:
Practice: White Board Math Possible Sentence Starters: The most butterflies… There were ____ butterflies... The fewest number of butterflies… The histogram above shows the butterflies spotted in a butterfly garden between 8 A.M. and 8 P.M. Make an observation about the data. (<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. Scaffolding: Provide word bank. Clap twice (or use some other cue) to inform students to put white boards up in the air. Ask students to support their answers once the white boards are up. Click for answers. Agenda

The histogram above shows the butterflies spotted in a butterfly garden between 8 A.M. and 8 P.M. Make an observation about the data. The most butterflies were in the garden between 12:01 – 2:00. There were 5 butterflies in the garden from 6:01 – 8:00. The fewest number of butterflies were in the garden between 6:01 – 8:00. The number of butterflies increased during the morning. After 2:00 P.M., the number of butterflies decreased. (1 min) 52 – 53 In-Class Notes Inform students that these are just some (of many) possible answers. Ask students whose answers are not included on this slide to share their observations. Ask additional questions based on context. For example: If you wanted to film butterflies visiting a garden when would be the best time to set up your camera? Why do you think the least amount of butterflies visited the garden from :00? Agenda

In 10 minutes you will be asked to stop and share your answers!
Practice – Part II 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 (53 – 63) In-Class Notes Pass out Class Work handout accordingly (there is one regular version and one modified version). Distribute Class Notes to struggling students. 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 (53 – 63) 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: Give students who need extra support the modified version of Class Work and the Class Notes. Preparation Notes Agenda

Practice – Student Share Out
Part 3 – (5 Min) Students share out work. (7 min) 63 – 70 In-Class Notes The practice summary reviews the work that students completed independently on their class work. 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 necessary to 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. For students who don’t need an in depth explanation, provide them with an answer key to quickly check their work and then move them onto the extension (provide them with the challenge worksheet). 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 Practice 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 #1a
Use intervals 1–20, 21–40, 41–60, 61–80, and 81–100 to make a frequency table. (1 min) 63 – 64 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1a from the Class Work handout. After students have shared their own answers, click to show desired answer. Answer

Practice – Sharing Question #1a
Use intervals 1–20, 21–40, 41–60, 61–80, and 81–100 to make a frequency table. (1 min) 63 – 64 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1a from the Class Work handout. After students have shared their own answers, click to show desired answer.

Practice – Sharing Question #1b
Use the frequency table you created to construct a histogram. (1 min) 64 – 65 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1b from the Class Work handout. After students have shared their own answers, click to show desired answer. Point out the important features of the histogram (title, labels, no spaces between bars, equal spaces on the x- and y-axis, etc.) Answer

Practice – Sharing Question #1b
Use the frequency table you created to construct a histogram. (1 min) 64 – 65 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1b from the Class Work handout. After students have shared their own answers, click to show desired answer. Point out the important features of the histogram (title, labels, no spaces between bars, equal spaces on the x- and y-axis, etc.)

Practice – Sharing Question #1c
Make two observations about the data based on the histogram you constructed. (1 min) 65 – 66 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1c from the Class Work handout. After students have shared their own answers, click to show desired answers. Inform students that the answers provided are just some (of many) possible answers. Ask students whose answers are not included to share their observations. Ask additional questions based on context. For example, If you pick a random tea out of a box, what are the odds it will be high in caffeine? Answer

Practice – Sharing Question #1c
Make two observations about the data based on the histogram you constructed. Most tea has between mg of caffeine. Seven types of tea have between 1-20 mg of caffeine. More than half of the tea has 40 mg or less of caffeine. About 20% of the tea has more than 40 mg of caffeine. There are not any teas that have 61 – 80 mg of caffeine. (1 min) 65 – 66 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #1c from the Class Work handout. After students have shared their own answers, click to show desired answers. Inform students that the answers provided are just some (of many) possible answers. Ask students whose answers are not included to share their observations. Ask additional questions based on context. For example, If you pick a random tea out of a box, what are the odds it will be high in caffeine?

Practice – Sharing Question #2
Based on the histogram, which statement must be true? A. No used car sold for $7,000. B. Exactly 5 of the used cars sold for $4,000. C. The most expensive used car sold for $11,999. D. Most of the used cars sold for less than $6,000. (1 min) 66 – 67 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #2 from the Class Work handout. Ask students to explain why they ruled out Answers A, B, and C. After students have shared their own answers, click to show desired answer. Answer

Based on the histogram, which statement must be true? A. No used car sold for $7,000. B. Exactly 5 of the used cars sold for $4,000. C. The most expensive used car sold for $11,999. D. Most of the used cars sold for less than $6,000. (1 min) 66 – 67 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #2 from the Class Work handout. Ask students to explain why they ruled out Answers A, B, and C. After students have shared their own answers, click to show desired answer.

The histogram below shows the scores for all the students who took a mathematics quiz. What percent of the students received a score of 80 or above? (1 min) 67 – 68 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #3 from the Class Work handout. The x-axis is not in the form of “intervals.” This may be a source of confusion for students. It might be helpful to have a discussion about it. Common error: Students will report answer as a whole number rather than as a percent. After students have shared their own answers, click to show desired answer. Answer

The histogram below shows the scores for all the students who took a mathematics quiz. What percent of the students received a score of 80 or above? 5 6 (1 min) 67 – 68 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #3 from the Class Work handout. The x-axis is not in the form of “intervals.” This may be a source of confusion for students. It might be helpful to have a discussion about it. Common error: Students will report answer as a whole number rather than as a percent. After students have shared their own answers, click to show desired answer. × = = 55% 5 + 6 = 11

Which age could be the median age of these club members? Explain your reasoning. A B C D. 44 (1 min) 68 – 69 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #4 from the Class Work handout. Common error: Students will choose B with the rationale that the median is the middle number and 31 is just about in the middle of 18 and 45. After students have shared their own answers, click to show desired answer. Answer

Which age could be the median age of these club members? Explain your reasoning. A B C D. 44 The median is the middle value in an ordered set of data. There are a total of 13 data points ( ) in this set of data. That means the 7th data point would be the median, which falls in the 32 – 38 age interval. (1 min) 68 – 69 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #4 from the Class Work handout. Common error: Students will choose B with the rationale that the median is the middle number and 31 is just about in the middle of 18 and 45. After students have shared their own answers, click to show desired answer.

Which age could be the median age of these club members? Explain your reasoning. A B C D. 44 Let’s prove it another way! (1 min) 69 – 70 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #4 from the Class Work handout. Common error: Students will choose B with the rationale that the median is the middle number and 31 is just about in the middle of 18 and 45. After students have shared their own answers, click to show desired answer. Answer

Which age could be the median age of these club members? Explain your reasoning. A B C D. 44 Let’s prove it another way! (1 min) 69 – 70 In-Class Notes Remind students to follow along on their handout, which they should use to take notes if they do not already have similar answers recorded from their Practice time. This slide reviews #4 from the Class Work handout. Common error: Students will choose B with the rationale that the median is the middle number and 31 is just about in the middle of 18 and 45. After students have shared their own answers, click to show desired answer.

Assessment: Online Quiz
How well do you understand histograms? Your class needs to pass the QUIZ to leave!! (5 min) 70 – 75 This online quiz is from a free site. The quiz could be given in many different ways – individually, partner, small group or as a whole class. Quiz could be printed as well (print directly from site if this is preferable). 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 on Histograms

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Displaying Numerical Data on Histograms

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Presentation on theme: "Displaying Numerical Data on Histograms"— Presentation transcript:

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