Displaying Numerical Data on Histograms 1. 2 Lesson ObjectiveLesson Objective: SWBAT display numerical data on a histogram. Student- Friendly Objective:

Displaying Numerical Data on Histograms

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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 (1 of 6)

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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.


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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 students3) Challenge work for advanced students4) Histograms homework6) 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.


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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

http://www.ixl.com/math/grade-6/create-histograms

www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-829635-8&chapter=9&lesson=1&headerFile=4&state

http://learnzillion.com/lessons/543-describe-attributes-of-a-data-set-by-analyzing-line-plots-histograms-and-box-plots

http://learnzillion.com/lessons/542-determine-the-number-of-observation-in-a-set-of-data-by-looking-at-histograms-and-line-plots


http://www.ixl.com/math/grade-6/create-histograms

http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-829635-8&chapter=9&lesson=1&headerFile=4&state






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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.

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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. (http://www.ehow.com/about_4708233_histograms.html#ixzz2Zcqyohe8)

Warm UpOBJECTIVE: SWBAT display numerical data on a histogram.Language Objective: SWBAT orally describe how to create a histogram.

Agenda

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Below are the 15 birth weights, in ounces, of all the Labrador Retriever puppies born at Kingston Kennels in the last three months.

a. Name an appropriate graph that could be used to summarize these birth weights. Explain your choice.

b. Describe the distribution of birth weights for the puppies using one measure of center (mean, median) or one measure of spread (range, IQR).

12 13 14 14 16 17 17 18 18 19 19 19 19 20 20


Agenda

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a. Name an appropriate graph that could be used to summarize these birth weights. Explain your choice.

12 13 14 14 16 17 17 18 18 19 19 19 19 20 20

Answer


Agenda

11


12 13 14 14 16 17 17 18 18 19 19 19 19 20 20

b. Describe the distribution of birth weights for the puppies using one measure of center (mean, median) or one measure of spread (range, IQR).

Answer


Agenda

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c. Use a measure of center to explain what the typical birth weight is for puppies.

12 13 14 14 16 17 17 18 18 19 19 19 19 20 20

Answer


Agenda

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Challenge: Find the Mean Absolute Deviation (MAD) of the 15 puppy weights.

12 13 14 14 16 17 17 18 18 19 19 19 19 20 20

Answer

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AgendaOBJECTIVE: 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)

5) Practice (I)– How Do You Read a Histogram? 10 mins (Partner)

4) Summary – Why Use a Histogram? (Whole Class) 5 mins

7) Assessment – Online Quiz (Whole Class) 5 mins

6) Practice (II)– Histogram Class Work 15 mins (Independent/Partner)

Agenda

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When we analyze data, what are we looking for?

Center

Spread(measure of

variation)

Shape

Median

Mean

Launch – Review Turn and Talk (30 sec)

Range

Interquartile Range

Mean Absolute Deviation

Today!

Launch Turn-and-talk

Agenda

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Puppy Weights Key: X – one puppy

12 13 14 15 16 17 18 19 20

X X

X X X

X X

X X X X

X X

Ounces

X X

Let’s go back to our line plot. Looking at the line plot, where do you see data clustered?

Scaffolding

Agenda

21

Puppy Weights

12 13 14 15 16 17 18 19 20

Ounces

Let’s go back to our box plot. Looking at the box plot, where do you see data clustered?

Scaffolding


Agenda

23

12 13 14 15 16 17 18 19 20

Ounces

Puppy Weights

12 13 14 15 16 17 18 19 20

X X

X X X

X X

X X X X

X X

X X

Let’s go back to both plots. How are the clusters in the line plot represented in the box plot?


Launch

Agenda

24

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?

Launch

Agenda

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It looks like this…

Launch

Agenda

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…and it is called…

Launch

Agenda

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…a histogram!


Agenda

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What is a histogram?

Launch Whole Class

Agenda

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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.

Word Bank

graph

intervals

bars

spaces

height

frequency

Explore

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Agenda

How was this histogram created?

Explore

31

Agenda

We start with a set of data.

62295512342027263012396

4830313630252967171538

Explore

32

Agenda

It is helpful to have the data ordered from...

least to

greatest!

62295512342027263012396

4830313630252967171538

Explore

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Agenda

Now we use our organized set of data to create a frequency table.

Age of People Attending a Movie

Age Ranges Tally Frequency

Definition

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67

Explore Turn-and-talk

35

Agenda

What should we use for our intervals, or our age ranges?

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



Scaffolding


37

Agenda

What should we use for our intervals, or our age ranges?

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

38

Agenda

What strategy should we use to tally our data?

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67




0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

Scaffolding

Explore

40

Agenda

What strategy should we use to tally our data?

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

Cross off each number and make a tally mark one at a

time!

Explore

41

Agenda

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

I

I

II

II

II

III

III I

I

III III

Explore

42

Agenda

Are we ready to complete the frequency column?

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

III

IIII

IIII IIIII III

III

Definition

Explore

44

Agenda

4 29

6 30

830

12 30 12

31 15

3417

36 20

38 25

39 26

55 27

62 29

67



0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

III

IIII

IIII IIIII III

III

3

4

6

8

0

1

2

45

Agenda

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.

Explore Think-Pair-Share

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.


46


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Agenda

Steps for creating a Frequency Table:

1) 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.

2) Make a tally mark for each datapoint next to the appropriate interval.

3) Write the frequency for each interval by totaling the number of tally marks for the interval.

Explore

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Agenda

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 0

50 – 59 I 1

60 – 69 II 2

Explore

Agenda


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

Here we have the x- and y-axis for our histogram.

49

Explore

Agenda


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

A Title and Labels!

What do we need to include to let the reader know what the graph is about?

50

Explore

51

Agenda

We have our x-axis labeled…

Ages of People Attending a Movie

Age

Num

ber o

f Peo

ple

(Fre

quen

cy)

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 0

50 – 59 I 1

60 – 69 II 2

Explore

52

Agenda

We need to be sure that we make equal spaces for our intervals!


Age

Num

ber o

f Peo

ple

(Fre

quen

cy)


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

Explore

53

Agenda

Notice that there are not any duplicate numbers on the x-axis!


Age

Num

ber o

f Peo

ple

(Fre

quen

cy)

0-9 10-19 20-29 30-39 40-49 50-59 60-69


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

Explore

54

Agenda


Age

Num

ber o

f Peo

ple

(Fre

quen

cy)

0-9 10-19 20-29 30-39 40-49 50-59 60-69

We have our y-axis labeled…

Notice the equal spaces!

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 0

50 – 59 I 1

60 – 69 II 2

Explore

55

Agenda

Notice that we have a scale on the y-axis – we are counting by 1’s


Age

Num

ber o

f Peo

ple

(Fre

quen

cy)

0-9 10-19 20-29 30-39 40-49 50-59 60-690

1

2

3

4

5

6

7

8

9


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

Explore

56

Agenda

Now we can put the bars on our histogram!


Age

Num

ber o

f Peo

ple

(Fre

quen

cy)

0-9 10-19 20-29 30-39 40-49 50-59 60-690

1

2

3

4

5

6

7

8

9


Age Ranges

Tally Frequency

0 – 9 III 3

10 – 19 IIII 4

20 – 29 IIII I 6

30 – 39 IIII III 8

40 – 49 0

50 – 59 I 1

60 – 69 II 2

3

4

6

8

0

1

2

Explore

57

Agenda

How does our histogram compare to the original histogram?

Explore: Review

58

Agenda

Data Frequency Table Histogram

Explore Small Group

59

Agenda

Minutes spent texting daily for 24 sixth grade students:

___Title

___Labels

___Equal intervals on both axes ___No spaces between bars___No duplicate #’s on either axis

Create a histogram with your group to represent the texting times.

0 0 2 3 5 810 12 15 18 19 2025 30 30 30 40 4560 75 80 90 90 120

Summary

60

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!

Agenda

http://www.online-stopwatch.com/

Summary

61

Agenda

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?

Scaffolding Hint Hint

Practice: Part I

64

Agenda

Create histograms

☐Interpret histograms

Now that we know how to create histograms, we need to make sure we know how to interpret them!

Practice: White Board Math

65

Agenda

On each of the following slides you will see a question about the related histogram.

Your job – after the question has been read aloud:

1) Read the question a second time to yourself (silently)2) Write your answer down on your white board3) Confer with a peer 4) Wait quietly as everyone finishes5) When you hear two claps, silently raise your white

board in the air

66

Agenda

What interval represents the most number of cars?


Answer

68

Agenda

How many cars passed through between 2:00 P.M. and 4:59 P.M.?


Answer

70

Agenda

How many months had six or more days of rain?


Answer

72

Agenda


Answer

What fraction of the months had less than 2 days of rain?

74

Agenda

How many bracelets have at least five beads?


Answer

76

Agenda

What percent of the bracelets have 4 beads or less?


Answer

78

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

A. 90–110, 111–130, 131–150

B. 91–110, 111–130, 131–150

C. 90–110, 110–130, 130–150

D. 81–100, 101–120, 121–140


Answer

80

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.


Sentence Starters

82

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.

Practice – Part II

83

Part 2 - (10 Min)

Work independently and check in with a partner to complete your class work.

1-Worksheet2-Share Out

In 10 minutes you will be asked to stop and share your answers!

Click on the timer!

Agenda

http://www.online-stopwatch.com/

http://www.online-stopwatch.com/countdown-timer/

http://www.online-stopwatch.com/countdown-timer/

Practice – Complete Class Work

84

Part 2 – (10 Min)

Agenda

Practice – Student Share Out

85

Part 3 – (5 Min)

Students share out work.

Classwork Questions

Agenda

Practice – Sharing Question #1a

86

Use intervals 1–20, 21–40, 41–60, 61–80, and 81–100 to make a frequency table.

Answer

Practice – Sharing Question #1b

88

Use the frequency table you created to construct a histogram.

Answer

Practice – Sharing Question #1c

90

Make two observations about the data based on the histogram you constructed.

Answer

Practice – Sharing Question #2

92

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.

Answer


94

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?

Answer


96

Which age could be the median age of these club members? Explain your reasoning.

A. 26 B. 31 C. 35 D. 44

Answer


98

Which age could be the median age of these club members? Explain your reasoning.

A. 26 B. 31 C. 35 D. 44

Let’s prove it another way!

Answer

Assessment: Online Quiz

100

Agenda

How well do you understand histograms?

Your class needs to pass the QUIZ

to leave!!


Documents

Displaying Numerical Data on Histograms 1. 2 Lesson ObjectiveLesson Objective: SWBAT display numerical data on a histogram. Student- Friendly Objective: