Using the Mean as a Measure of Center Lesson 3 1.
-
Upload
abelard-arbogast -
Category
Documents
-
view
104 -
download
0
Transcript of Using the Mean as a Measure of Center Lesson 3 1.
![Page 1: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/1.jpg)
Using the Mean as a Measure of Center
Lesson 3
1
![Page 2: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/2.jpg)
Warm Up
OBJECTIVE: SWBAT understand the mean as a number that “evens out” or “balances” a distribution and recognize how the mean reacts to changes made to a data set.Language Objective: SWBAT write about what happens to the mean when a data set changes.
Agenda
2
The line plot below shows the number of hits made by each of 10 players on a baseball team during batting practice.
1. What was the median number of hits made by the players? Show or explainhow you got your answer.
2. Two additional players arrived at practice. The median number of hits increased. What could be the number of hits made by each of the two additional players? Show or explain how you got your answer.
Median: The middle number in an ordered set of data
10.5 hits
12 hits and 13 hits
![Page 3: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/3.jpg)
Launch – Review Turn and Talk (30 sec)
number of toppings students like on their pizzas
3
When we analyze data, what are we looking for?
Center
Spread
Shape
Median
Mean
Agenda
Today!
![Page 4: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/4.jpg)
Launch
Agenda
4
Six students in a middle-school class make a stack of cubes to show the number of letters in his or her name.
You can see from the stacks that the six names vary in length.
Arlene
Paul
Leo Al Joseph
Mia
![Page 5: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/5.jpg)
Launch - Review
Agenda
5
What is the median name length?
Arlene
Paul
Leo Al Joseph
Remember to order the data from least to greatest!
Mia
![Page 6: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/6.jpg)
Launch - Review
Agenda
6
What is the median name length?
Arlene
Paul
Leo Al
Joseph
Median = 3.5 letters
Mia
![Page 7: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/7.jpg)
Launch Partner
Agenda
7
1) Using cubes, make stacks like the ones shown below.
Arlene Paul Leo Al Joseph
2) Make the 6 stacks all the same height by moving the cubes around.
Mia
![Page 8: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/8.jpg)
Launch Whole Class
Agenda
8
How many cubes should be in each stack so that the heights are all the same?
Arlene Paul Leo Al Joseph Mia
![Page 9: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/9.jpg)
Launch Think-Pair-Share
Agenda
9
The stack height that you found represents the mean number of letters in the students’ names. How might you explain what the mean of a data set is?
Arlene Paul Leo Al Joseph Mia
Mean = 4 letters
![Page 10: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/10.jpg)
Launch Vocabulary
Agenda
10
The mean of a set of data is:
Arlene Paul Leo Al Joseph Mia
the balance point or average of a data set. It represents the value that each data point would take on if the total of the data values were redistributed equally.
![Page 11: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/11.jpg)
Launch Turn and talk (30 secs)
Agenda
11
Imagine the image below contains glasses of water. Explain to a friend how to find the mean amount of water.
![Page 12: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/12.jpg)
Launch Notes
Agenda
12
Miriam Luis Ben
What is the mean number of letters in the set of data below?
How can this cube be distributed evenly?
![Page 13: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/13.jpg)
Launch: First Names Small Group
Agenda
13
1) Create a stack of cubes to represent the letters in your own first name.
2) Line up your stack with those of your group members.
3) Find the mean number of letters in your group’s set of data by redistributing the cubes to make the stacks all the same height.
![Page 14: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/14.jpg)
Explore
Agenda
14
So I need to have cubes in my pocket every time I need to find the mean? Yikes! What if Wolfe+585 joined my group!He has 590 letters in his name!That is a lot of cubes to redistribute!
Adolph Blaine Charles David Earl Frederick Gerald Hubert Irvin John Kenneth Lloyd Martin Nero Oliver Paul Quincy Randolph Sherman Thomas Uncas Victor William Xerxes Yancy Zeus Wolfe schlegelstein hausenberger dorffvoraltern waren gewissenhaft schaferswessen schafewaren wohlgepflege und sorgfaltigkeit beschutzen von angreifen durch ihrraubgierigfeinde welche voraltern zwolftausend jahres vorandieerscheinen wander ersteer dem enschderraumschiff gebrauchlicht als sein ursprung von kraftgestart sein lange fahrt hinzwischen sternartigraum auf der suchenach diestern welche gehabt bewohnbar planeten kreise drehen sich und wohin der neurasse von verstandigmen schlichkeit konnte fortplanzen und sicher freuen anlebens langlich freude und ruhe mit nicht ein furcht vor angreifen von anderer intelligent geschopfs von hinzwischen sternartigraum, Senior
![Page 15: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/15.jpg)
Explore Small Group
Agenda
15
What happens if you don’t have cubes and you are asked to find the mean? How else could you find the mean?
Hints! -Count how many stacks you have at your table. -Count how many cubes you have altogether.
![Page 16: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/16.jpg)
Explore: How to Find the Mean Notes
Agenda
16
1) Add up all of the values in the data set.
Arlene Paul Leo Al Joseph
2) Divide the sum by how many values there are in the data set.
Mia 1 2 3 4 5 6
Mean = 4 letters
1
32
6
45
12
123
123
1234
123456
6 + 4 + 3 + 2 + 6 + 3 = 24
24 6 = 4÷246 = 4
![Page 17: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/17.jpg)
Explore Notes
Agenda
17
Miriam Luis Ben
1) Add up all of the values in the data set.
2) Divide the sum by how many values there are in the data set.
1 2 3
123
123456
6 + 4 + 3 = 13
1234
13 ÷ 3
133
![Page 18: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/18.jpg)
Explore – Class Challenge! Whole Class
Agenda
18
How would we calculate the mean number of letters in students’ names in our class?
1. Add up the number of letters in every student’s name
2. Divide the sum by the number of students in our class
Calculate
![Page 19: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/19.jpg)
Explore Think-Pair-Share
19
Agenda
What if Wolfe + 585 really did join our class?! How would that piece of data affect the average number of letters in students’ names?
Adolph Blaine Charles David Earl Frederick Gerald Hubert Irvin John Kenneth Lloyd Martin Nero Oliver Paul Quincy Randolph Sherman Thomas Uncas Victor William Xerxes Yancy Zeus Wolfe schlegelstein hausenberger dorffvoraltern waren gewissenhaft schaferswessen schafewaren wohlgepflege und sorgfaltigkeit beschutzen von angreifen durch ihrraubgierigfeinde welche voraltern zwolftausend jahres vorandieerscheinen wander ersteer dem enschderraumschiff gebrauchlicht als sein ursprung von kraftgestart sein lange fahrt hinzwischen sternartigraum auf der suchenach diestern welche gehabt bewohnbar planeten kreise drehen sich und wohin der neurasse von verstandigmen schlichkeit konnte fortplanzen und sicher freuen anlebens langlich freude und ruhe mit nicht ein furcht vor angreifen von anderer intelligent geschopfs von hinzwischen sternartigraum, Senior
Calculate
![Page 20: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/20.jpg)
20
Agenda
What if Justin joined our class instead of Wolfe + 585?! How would that affect the average number of letters in students’ names?
Explore Think-Pair-Share
Calculate
![Page 21: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/21.jpg)
Summary Think-Pair-Share
21
Agenda
Previously we discussed how the median reacts to changes made to a data set.
How does the mean react to changes made to a data set? Be prepared to explain your thinking.
![Page 22: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/22.jpg)
Practice
22
Part 1 - (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
![Page 23: Using the Mean as a Measure of Center Lesson 3 1.](https://reader033.fdocuments.in/reader033/viewer/2022051615/55204d6949795902118bf4b6/html5/thumbnails/23.jpg)
Practice – Student Share Out
23
Part 2 – (5 Min)
Students share out work.
Classwork Questions
Agenda