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U n t er r i ch t spl a n
Anal y zing Dat a: M inimum,
M aximum, and Quart il e s (Ce l s ius )
Altersgruppe: 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 5 .16a, 5 .16c ,
6.15 b
Virginia - Mathematics Standards of Learning (2016): 5 .17 .a,
5 .17 .b, 5 .17 .d
Fairfax County Public Schools Program of Studies: 5 .16.a.1,
5 .16.a.2, 5 .16.a.3 , 5 .16.a.4 , 5 .16.c .1, 5 .16.c .2, 5 .16.c .3 ,
5 .16.c .4 , 6.15 .b.1, 6.15 .b.2
Online-Ressourcen: I n t he H e at o f t he M o me nt
Opening
T eacher
present s
St udent s
pract ice
Class
discussion
10
12
12
10
3
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e analyzing temperature data
P r ac t i c e finding the median and first and third quartiles
L e ar n a visual method to find the mean
De v e l o p statistical skills
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Ope ni ng | 10 min
Display the following problem:
Luke has 4 markers, Melissa has 10 markers, Nicholas has 6 markers, Olivia
has 3 markers, and Peter has 12 markers in their backpacks. What is the
m e a n number of markers?
Ask the students to calculate the answer in their notebooks.
When they are done working, ask : How do we find a mean?
To find a mean, we add all the values and then divide by the
number of values.
A sk : What is the mean here? How do we find it?
We add all the numbers and divide by 5, since there are 5 people.
The sum of the number of markers is 35, so when we divide by 5,
we get 7. The mean number of markers is 7.
A sk : What does a mean show?
A mean shows a central value of the data.
Display the following bar graph:
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S ay : This bar graph shows the number of markers each student has.
Let’s draw a line at 7, the mean.
Display the following bar graph:
A sk : How far below the line are the bars representing the number of
markers that Luke, Nicholas, and Olivia have?
Luke has 3 fewer markers than the mean, Nicholas has 1 fewer
marker, and Olivia has 4 fewer markers.
A sk : How far above the line are the bars representing the number of
markers that Melissa and Peter have?
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Melissa has 3 more markers than the mean, and Peter has 5 more
markers than the mean.
S ay : Consider the distances of the bars below the line compared to
the distances of the bars above the line. What do you notice?
Ask the students to discuss their observations with a partner.
When the students are done discussing, share. A sk : How do the
distances of the bars below the line compare to the distances of
the bars above the line?
The total distance below the line is 8 and the total distance
above the line is 8. If we add the spaces below the line we get the
same number as when we add the spaces above the line.
S ay : Yes. A mean is the number that shows how to fairly share all
the markers. If Melissa gave Luke 3 markers and if Peter gave
Nicholas 1 marker and Olivia 4 markers, then everyone would have 7
markers, the mean. We call the difference between the mean and the
data point a po si t i v e de v i at i o n if the data point is above the
mean and a ne gat i v e de v i at i o n if the data point is below the
mean. The mean occurs where the sum of the negative deviations
equals the sum of the positive deviations. Suppose we had made a
mistake and drawn the line at 8. How could we see that 8 is not the
mean?
Luke has 4 fewer markers than 8, Nicholas has 2 fewer markers,
and Olivia has 5 fewer markers. So the sum of the negative
deviations is 11. Melissa would have 2 more markers than 8 and
Peter would have 4 more markers than 8. So the sum of the
positive deviations is 6. Since the positive deviations do not
equal the negative deviations, then the line is set at the wrong
place, and 8 is not the mean.
T e ac he r pr e se nt s M at h game : I n t he H e at o f t he M o me nt B ar Gr aphs: C e l si us | 12 min
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Present Matific ’s episode I n t he H e at o f t he M o me nt - B ar
Gr aphs: C e l si us to the class, using the projector.
The goal of the episode is to collect data and then state the minimum,
maximum, median, first and third quartiles, and mean of that data.
S ay : Please read the instructions.
The instructions say, “Measure each city’s temperature and fill in
the table.”
Ask a student to come to the front of the room to move the
thermometer to the various cities and then enter their temperatures
in the table. When the table is complete, click
.
S ay : The episode is presenting a bar graph to represent the data.
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Let’s place the bars in order from shortest to longest.
Ask a student to come to the front of the room to arrange the bars
from shortest to longest.
S ay : Please read the question.
The question asks, “What is the minimum value?”
A sk : What is the lowest temperature in the bar graph?
Enter the number that the students suggest by clicking on the
.
If the answer is correct, the episode will proceed to the next question.
If the answer is incorrect, the question will wiggle.
The episode will proceed to ask about the maximum value, the
median, the first quartile, the third quartile, and the mean of the
data set. Remind the class of how to find the mean by moving the
green line up and down until the sum of the positive deviations is
equal to the sum of the negative deviations.
S t ude nt s pr ac t i c e M at h game : I n t he H e at o f t he M o me nt
- B ar Gr aphs: C e l si us | 12 min
Have the students play I n t he H e at o f t he M o me nt - B ar
Gr aphs: C e l si us on their personal devices. Circulate, answering
questions as necessary.
C l ass di sc ussi o n | 10 min
A sk : How do we find the median in a set of data?
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We order the data from smallest to greatest and then we choose
the middle number.
A sk : How do we find the first quartile?
Once the data is in order, we find the middle number of the lower
half of the data.
A sk : How do we find the third quartile?
Once the data is in order, we find the middle number of the upper
half of the data.
S ay : In the episode, there are always 11 cities. Why do you think
that the designers of the episode chose 11 cities?
Responses may vary. A possible response: With 11 cities, it is
easy to determine the median and the first and third quartiles.
Once the data is ordered, the median will be the sixth data point,
the first quartile will be the third data point, and the third quartile
will be the ninth data point.
S ay : Let’s look at a data set with 9 cities.
Display the following table:
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S ay : Let’s find the median and the first and third quartiles. What is
the first step?
We must put the data in order.
Ask a student to write the temperatures from smallest to largest on
the board.
6, 8, 10, 11, 12, 14, 15, 20, 22
A sk : What is the median? How do you know?
The median is 12 because it is the middle number.
A sk : What difficulty arises when we look for the first and third
quartiles?
The lower half of the data is 6, 8, 10, and 11. There are 4 data
points. There is no middle value. The same is true for the upper
half of the data. There are 4 data points, so there is no middle
value.
S ay : When this happens, we find the mean of the middle two data
points. We are looking at 6, 8, 10, and 11. The middle two numbers
are 8 and 10. So we average them to find the first quartile. What is
the first quartile?
The first quartile is 9, the average of 8 and 10.
A sk : What is the third quartile? How do we find it?
The third quartile is 17.5. The middle two numbers in the upper
half of the data are 15 and 20. When we average 15 and 20, we get
17.5.
S ay : Now let’s look at a data set with 10 cities.
Display the following table:
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S ay : Again, let’s find the median and the first and third quartiles.
Ask a student to write the temperatures from smallest to largest on
the board.
7, 7, 9, 10, 12, 14, 15, 16, 19, 23
A sk : What is the median? How do you know?
The median is 13. There is no middle number, because there are
10 cities, so we look at the fifth and sixth data points, 12 and 14,
and we average them.
S ay : Now let’s find the first quartile. List the values that are in the
lower half of the data.
7, 7, 9, 10, and 12
S ay : Yes, the lower half of the data is all the numbers below the
median. In this case, the median is not an actual data point, so we
use all the values below it. What is the first quartile? How do you
know?
The first quartile is 9 because it is the middle number of the
lower half of the data.
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A sk : What is the third quartile?
The third quartile is 16.
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C l o si ng | 3 min
S ay : The next day, Luke, Melissa, Nicholas, Olivia, and Peter again
count the number of markers they have in their backpacks. The
results are shown in the graph.
Display the following:
A sk : How can we tell that the mean of 5, 12, 7, 5, and 12 is not 9?
Ask the students to write down their responses. Collect their
responses to review later.
Luke, Nicholas, and Olivia all have fewer than 9 markers. Luke has
4 fewer markers, Nicholas has 2 fewer, Olivia has 4 fewer. So the
sum of the negative deviations is 4 plus 2 plus 4, or 10. Melissa
and Peter have more than 9 markers. They each have 12 markers, 3
more than 9. So the sum of the positive deviations is 3 plus 3, or
6. The sum of the negative deviations is 10, and the sum of the
positive deviations is 6. Because 10 is not equal to 6, the mean is
not 9.
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