Displaying Numerical Data on
Histograms
1
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
2
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.
3
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
4
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
http://www.ixl.com/math/grade-6/create-histograms
www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07829635-8&chapter=9&lesson=1&headerFile=4&state
http://learnzillion.com/lessons/543-describe-attributes-of-a-data-set-byanalyzing-line-plots-histograms-and-box-plots
http://learnzillion.com/lessons/542-determine-the-number-ofobservation-in-a-set-of-data-by-looking-at-histograms-and-line-plots
5
Lesson Overview (5 of 6)
Before and After
6
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.
(http://www.ehow.com/about_4708233_histograms.html#ixzz2Zcqyo
he8)
7
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.
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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).
Agenda
8
20
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.
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13
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16
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a. Name an appropriate graph that could be used to summarize these birth weights.
Explain your choice.
Answer
9
Agenda
20
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.
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13
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14
16
17
17
18
18
19
19
19
19
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
11
Agenda
20
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.
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13
14
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16
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c. Use a measure of center to explain what the typical birth weight is for
puppies.
Answer
13
Agenda
20
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.
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Answer
15
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Agenda
20
Agenda
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?
(Whole Class/Small Group)
4) Summary – Why Use a Histogram? (Whole Class)
30 mins
5) Practice (I)– How Do You Read a Histogram?
(Partner)
10 mins
6) Practice (II)– Histogram Class Work
(Independent/Partner)
7) Assessment – Online Quiz (Whole Class)
15 mins
17
5 mins
5 mins
Launch – Review
Turn and Talk (30 sec)
When we analyze data, what are we looking for?
Center
Today!
Spread
(measure of
variation)
Shape
Median
Mean
Range
Interquartile Range
Mean Absolute
Deviation
Agenda
18
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
12
13
14
15
X
X
X
X
X
X
X
X
X
16
17
18
19
X
X
20
Ounces
Scaffolding
19
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
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13
14
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20
Ounces
Scaffolding
21
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
X
X
X
X
X
X
X
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20
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Ounces
Agenda
23
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?
Agenda
24
Launch
It looks like this…
Agenda
25
Launch
…and it is called…
Agenda
26
Launch
…a histogram!
Agenda
27
Launch
Turn-and-talk
What is a histogram?
Agenda
28
Launch
Whole Class
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
frequency
intervals
spaces
graph
bars
height
Agenda
29
Explore
How was this histogram created?
Agenda
30
Explore
We start with a set of data.
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29
55
12
34
20
27
26
30
12
39
6
4
8
30
31
36
30
25
29
67
17
15
38
Agenda
31
Explore
It is helpful to have the data ordered from...
62
29
55
12
34
20
27
26
30
12
39
6
4
8
30
31
36
30
25
29
67
17
15
38
least
to
greatest!
Agenda
32
Explore
Now we use our organized set of data to create a frequency table.
Age of People Attending
a Movie
4
29
Age Ranges
Definition
33
6
Tally
8
12
12
15
17
20
25
26
27
29
30
Frequency
30
30
31
34
36
38
39
55
62
67
Agenda
Explore
Turn-and-talk
What should we use for our intervals, or our age ranges?
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Scaffolding
35
Age of People Attending a Movie
Age Ranges
Tally
Frequency
Agenda
Explore
Turn-and-talk
What should we use for our intervals, or our age ranges?
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6
8
12
12
15
17
20
25
26
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29
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30
30
30
31
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36
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62
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Age of People Attending a Movie
Age Ranges
Tally
Frequency
0-9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
Agenda
37
Explore
Turn-and-talk
What strategy should we use to tally our data?
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6
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12
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15
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25
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30
30
30
31
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39
55
62
67
Scaffolding
38
Age of People Attending a Movie
Age Ranges
Tally
Frequency
0-9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
Agenda
Explore
What strategy should we use to tally our data?
4
6
8
12
12
15
17
20
25
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30
30
31
34
36
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39
55
62
67
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
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
Agenda
40
Explore
4
6
8
12
12
15
17
20
25
26
27
29
29
30
30
30
31
34
36
38
39
55
62
67
Age of People Attending a Movie
Age Ranges
Tally
0-9
I II
10 - 19
I III
20 - 29
IIII I
IIII III
30 - 39
Frequency
40 - 49
50 - 59
60 - 69
I
II
Agenda
41
Explore
Are we ready to complete the frequency column?
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8
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12
15
17
20
25
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30
30
30
31
34
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Definition
42
Age of People Attending a Movie
Age Ranges
Tally
0-9
III
10 - 19
IIII
20 - 29
IIII I
IIII III
30 - 39
Frequency
40 - 49
50 - 59
60 - 69
I
II
Agenda
Explore
4
6
8
12
12
15
17
20
25
26
27
29
29
30
30
30
31
34
36
38
39
55
62
67
Age of People Attending a Movie
Age Ranges
Tally
Frequency
0-9
III
3
10 - 19
IIII
4
20 - 29
IIII I
IIII III
6
30 - 39
0
40 - 49
50 - 59
60 - 69
8
I
II
1
2
Agenda
44
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.
Agenda
45
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.
Review the steps for
creating a Frequency
Table with the person
next to you.
Agenda
46
Explore
Think-Pair-Share
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 data
point next to the appropriate
interval.
3) Write the frequency for each
interval by totaling the number
of tally marks for the interval.
Agenda
47
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
0
50 – 59
I
1
60 – 69
II
2
Agenda
48
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
0
50 – 59
I
1
60 – 69
II
2
Agenda
49
Explore
What do we need to include to let the reader know what the
Age of People Attending a Movie graph is about?
Age
Ranges
Tally
0–9
III
3
10 – 19
IIII
4
20 – 29
IIII I
6
30 – 39
IIII III
8
40 – 49
Frequency
A Title and Labels!
0
50 – 59
I
1
60 – 69
II
2
Agenda
50
Explore
We have our x-axis labeled… What else do we need on the x-axis?
Age of People Attending a Movie
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
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
Age
Agenda
51
Explore
We need to be sure that we make equal spaces for our intervals!
Age of People Attending a Movie
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
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
Age
Agenda
52
Explore
Notice that there are not any duplicate numbers on the x-axis!
Age of People Attending a Movie
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
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
0-9
10-19 20-29 30-39 40-49 50-59 60-69
Age
Agenda
53
Explore
We have our y-axis labeled… what else do we need on the y-axis?
Age of People Attending a Movie
Tally
0–9
III
3
10 – 19
IIII
4
20 – 29
IIII I
6
30 – 39
IIII III
8
40 – 49
Frequency
0
50 – 59
I
1
60 – 69
II
2
Notice the equal
spaces!
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
0-9
10-19 20-29 30-39 40-49 50-59 60-69
Age
Agenda
54
Explore
Notice that we have a scale on the y-axis – we are counting by 1’s
Age of People Attending a Movie
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
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
9
8
7
6
5
4
3
2
1
0
0-9
10-19 20-29 30-39 40-49 50-59 60-69
Age
Agenda
55
Explore
Now we can put the bars on our histogram!
Age of People Attending a Movie
Tally
Frequency
0–9
III
33
10 – 19
IIII
44
20 – 29
IIII I
66
30 – 39
IIII III
88
40 – 49
00
50 – 59
I
11
60 – 69
II
22
Number of People (Frequency)
Age
Ranges
Ages of People Attending a Movie
9
8
7
6
5
4
3
2
1
0
0-9
10-19 20-29 30-39 40-49 50-59 60-69
Age
Agenda
56
Explore
How does our histogram compare to the original histogram?
Agenda
57
Explore: Review
Data
Frequency Table
Histogram
Agenda
58
Explore
Small Group
Minutes spent texting daily for 24 sixth grade students:
0
10
25
60
0
12
30
75
2
15
30
80
3
18
30
90
5
19
40
90
8
20
45
120
___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.
Agenda
59
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!
Agenda
60
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?
Scaffolding
61
Hint
Hint
Agenda
Practice: Part I
Create
histograms
☐Interpret
histograms
Now that we know how to create histograms, we need to
make sure we know how to interpret them!
Agenda
64
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:
1) Read the question a second time to yourself (silently)
2) Write your answer down on your white board
3) Confer with a peer
4) Wait quietly as everyone finishes
5) When you hear two claps, silently raise your white
board in the air
Agenda
65
Practice: White Board Math
What interval represents the most number of cars?
Answer
66
Agenda
Practice: White Board Math
How many cars passed through between 2:00 P.M. and
4:59 P.M.?
Answer
68
Agenda
Practice: White Board Math
How many months had six or more days of rain?
Answer
70
Agenda
Practice: White Board Math
What fraction of the months had less than 2 days of rain?
Answer
72
Agenda
Practice: White Board Math
How many bracelets have at least five beads?
Answer
74
Agenda
Practice: White Board Math
What percent of the bracelets have 4 beads or less?
Answer
76
Agenda
Practice: White Board Math
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
78
Agenda
Practice: White Board Math
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
80
Agenda
Practice: White Board Math
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.
Agenda
82
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
Click on the timer!
In 10 minutes you will be asked to stop and share your answers!
Agenda
83
Practice – Complete Class Work
Part 2 – (10 Min)
Agenda
84
Practice – Student Share Out
Part 3 – (5 Min)
Students share out work.
Classwork Questions
Agenda
85
Practice – Sharing Question #1a
Use intervals 1–20, 21–40, 41–60, 61–80, and 81–100 to make
a frequency table.
Answer
86
Practice – Sharing Question #1b
Use the frequency table you created to construct a histogram.
Answer
88
Practice – Sharing Question #1c
Make two observations about the data based on the histogram
you constructed.
Answer
90
Practice – Sharing Question #2
Based on the histogram, which statement must be true?
A.
B.
C.
D.
No used car sold for $7,000.
Exactly 5 of the used cars sold for $4,000.
The most expensive used car sold for $11,999.
Most of the used cars sold for less than $6,000.
Answer
92
Practice – Sharing Question #3
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
94
Practice – Sharing Question #4
Which age could be the median age
of these club members?
Explain your reasoning.
A.
B.
C.
D.
26
31
35
44
Answer
96
Practice – Sharing Question #4
Which age could be the median age
of these club members?
Explain your reasoning.
A.
B.
C.
D.
26
31
35
44
Let’s prove it another way!
Answer
98
Assessment: Online Quiz
How well do you understand histograms?
Your class needs to
pass the QUIZ
to leave!!
Agenda
100