Math 6 Unit 7: Statistics Tasks Onlybhmsparnell.weebly.com/uploads/2/2/7/3/22730444/700... · 2019. 9. 8. · Math 6 Name: Date: Period: Statistics Unit – Entry Task Our Class 1

Math 6

Unit 7: Statistics

Tasks Only

Math 6 Name: Date: Period:

Statistics Unit – Entry Task

Our Class

1. What month were you born in?

2. How many siblings do you have?

3. What elementary school did you last attend?

4. What is your favorite subject at school?

5. How many total minutes do you spend each day doing homework?

6. How many total minutes do you spend each day watching

television or playing video games?

7. How tall are you (in centimeters)?

8. How many books are in your backpack right now?

Math 6


Question Number 1

Team Captain Resource Manager

Reporter/ Recorder

Facilitator

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Question Number 2


Reporter/ Recorder Facilitator

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Question Number 3


Reporter/ Recorder

Facilitator

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Question Number 4


Reporter/ Recorder

Facilitator

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e

Math 6


Question Number 5


Reporter/ Recorder

Facilitator

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Question Number 6


Reporter/ Recorder Facilitator

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ons

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Question Number 7


Reporter/ Recorder

Facilitator

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Question Number 8


Reporter/ Recorder

Facilitator

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Math 6


Our Class

“How would you describe who is in our class to a friend from another school?”

YOUR TASK: Work with your group to organize, analyze, and communicate the responses to one survey question for the entire class.

o Resource Managers – Travel clockwise around the room and collect the data for your group’s question number from all of the other groups in the class.

o You will have 15 minutes to organize and analyze the data for your group’s question. Team Captains – help manage time for your group.

o Prepare a 1-minute presentation (only one minute!) that uses your data to tell the story of our class. Include color-coding, labels and other technical writing tools strategically to show all the key information on your poster.

Math 6 Team: Date: Period:

Statistics Unit – Unit Project

Statistics Unit Project: Reaction Times

In this project, you will design an experiment where you explore a statistical question, gather data, represent your data in multiple ways, and make summary statements about what you learned about your classmates’ reaction times.

Part Topic Due Date

1 Select a statistical question to explore Design your experiment

2 Collect and organize your data Calculate the mean, median, and range of your data

3 Create a dot plot, histogram and box plot of your data Create a 5-number data summary of your data

4 Make summary statements about your data by describing shape and spread

5 Pick the best representation to describe your data Explain why your chosen representation is best

6 Present your project and results

Math 6


Statistics Unit Project: Reaction Times – Part 1

Today, you will select a statistical question to explore and design an experiment that will help you answer that question. As a class, we will construct a definition for statistical question.

! Go to http://nrich.maths.org/6044 and explore the different ways to

measure reaction times.

! Decide what question you want to explore as team and write it here:

! Describe in detail your team’s plan for your experiment. Be specific about how many trials you will allow each person try, how many total people you will test, and the options you would like to include.

Math 6



Today, you will collect your data and summarize your data using measures of center.

! Run your experiment according to your plan from Part 1.

! Record your data on a separate sheet of paper. Make sure that your data is organized and easy to read.

! Individual work: Calculate the mean, median, and range of your team’s data. Then, as a team compare values and come to consensus as to what the correct values are.

! Individual writing: If someone in your group made an error, describe the error and explain how to correct it. If no one in your group made an error, describe an error that you think is common and explain how to correct it.

Math 6



Today, you will create data displays to represent your experimental data.

! On a separate sheet of paper, each team member will create a dot plot,

histogram and box plot to describe your team’s data. Each team member should choose a different bin width or scale to use. For example, your Facilitator might choose a bin width of 2 for the histogram while your Team Captain might choose a bin width of 5. The Recorder/Reporter might scale by 2’s on the dot plot, while the Resource Manager might scale by 3’s.

! Include titles, labels, and other technical writing tools to make sure that your data displays show as much relevant information as possible. Be sure to label the mean and the 5-number data summary on the appropriate data displays.

Math 6



Today, you will summarize your data using statements describing shape and spread, and analyze the affect any outliers have on your data. You will also decide which representation to include in your final report to best describe your data.

! Individual writing: Make summary statements about your data by

describing the shape and the spread. Include the significance of your observation. For example, Our data shows a wide spread, which means that _____.

! Individual writing: Describe any outliers that in your data. Do the outliers affect your data? Why or why not? If you have no outliers, pick a value that would be an outlier and describe how it will affect the data.

! Individual writing: Which measure of center better describes your data: mean or median? How did you come to your decision?

! Individual writing: Which representation do you think best describes your data? Consider the type of data display as well as the bin width or scale. Why is your chosen representation the best one?

Math 6



Today, you will prepare for your group presentation.

! As a group, decide how to structure your presentation. Your team’s final

report should include:

o The statistical question you explored and the answer to your question

o Support your answer to your question by referring to the representation that best displays your data and by sharing the different summary statements that your team came up with about measures of center, shape, spread, outliers, and the 5-number data summary.

o The story of how you came to the answer to your question, including any new questions that came up along the way, or initial misunderstandings about your data (For example: At first we thought that _____, but when we looked more closely at the box plot, we noticed that ____.)

! Decide which group member is presenting the different parts of your final report. Remember, every group member must make a mathematical contribution to the presentation. Write down and practice what you will say.

Statistics Unit – Lesson Series 1 Adapted from MARS 2000 Pencils: Grade 6

1!


Pencils

Roberto puts seven pencil boxes on a table. No box has more than 9 pencils inside, and some boxes may be empty. The mean number of pencils in the boxes is 4, the median is 4, and the mode is 6.

YOUR TASK: Use the information above to help you answer the questions below.

1. Find the total number of pencils. Show or explain your reasoning.

2. Gloria says that the numbers of pencils in the boxes is 0, 1, 2, 2, 4, 5, 9. Gloria is not correct. Show or explain two reasons why you know that she is not correct.

3. How many pencils are in each of the seven boxes? Show and explain your reasoning.

4. Is this the only possible answer? If yes, justify your answer. If no, find another arrangement.

Student Materials Mean, Median, Mode, and Range S-1 © 2013 MARS, Shell Center, University of Nottingham

Penalty Shoot-Out 1. The bar chart represents the outcome of a penalty shoot-out competition.

Each person in the competition was allowed six shots at the goal. The graph shows, for example, that four people only scored one goal with their six shots.

a. How many people were involved in the shoot-out? Show how you obtain your answer.

b. Complete the table with values for the Mean, Median, Mode, and Range of scores. Explain how you calculate each answer.

Mean score

----------

Median score

----------

Mode score

----------

Range of scores

----------

1 2 3 4 5 6Score

Frequency

12345678

0


2. There is another penalty shoot-out. Use the table of results to draw a possible bar chart of the scores:

Mean score 3

Median score 3.5

Mode score 4

Range of scores 4

Show all your work.

1 2 3 4 5 6Score

Frequency

12345678

0


Card Set: Statistics Tables

S1

Mean score 3 Median score 4 Mode score 4

Range of scores 3

S2


Range of scores

S3 Mean score 3

Median score 2 Mode score

Range of scores 5

S4


Range of scores 4

S5


Range of scores 3

S6

Mean score Median score 3 Mode score 3

Range of scores 4


Card Set: Statistics Tables (continued)

S7


Range of scores 3

S8

Mean score

Median score 2

Mode score 2

Range of scores 4

S9

Mean score 3 Median score Mode score 2

Range of scores 3

S10

Mean score 3 Median score Mode score 1

Range of scores 4

S11

Mean score 3 Median score 3 Mode score

Range of scores 5

S12


Range of scores

Mean, Median, Mode, and Range Projector Resources:

Sharing Posters

1. One person from each group visit a different group and look carefully at their matched cards.

2. Check the cards and point out any cards you think are incorrect. You must give a reason why you think the card is incorrectly matched or completed, but do not make changes to the card.

3. Return to your original group, review your own matches and make any necessary changes using arrows to show if card needs to move.

P-4


Boy Bands 1. The bar chart represents the scores from a quiz.

Children were asked to name six boy bands in 30 seconds. Each score represents the number of correctly named bands.

a. How many children were involved in the quiz? Show how you obtain your answer.

b. Complete the table with values for the Mean, Median, Mode, and Range of scores. Explain how you calculate each answer.

Mean score

----------

Median score

----------

Mode score

----------

Range of scores

----------

1 2 3 4 5 6Score

Frequency

12345678

0


2. The results of another quiz question is shown in the table below. Draw a possible bar chart of the scores:

Mean score 4

Median score 3.5

Mode score 3

Range of scores 4

Show all your work.

1 2 3 4 5 6Score

Frequency

12345678

0

© CPM Educational Program Core Connections, Course 1

Lesson 8.1.2 Resource Page

Jumping Frog Jubilee Contest Data

2008

Frog Name Jump Length (inches) Skeeter Eater 231.5

Warped 230

Greg Crome Dome 229

R.G. 227

The Well Ain’t Dry 221.5

Winner 220.5

7 lb 8 oz. Baby 217

Delbert Sr 216.5

2009

Frog Name Jump Length (inches) For the Sign 252

Alex Frog 236.5

Shakit 231.5

Six-Mile Shooter 226.75

Spare the Air Every Day 223.25

Hooper 223.25

Jenifer’s Jumper 222.25

Dr. Frog 185.25

Statistics Unit – Lesson Series 2 1


5-Number Data Summary Fill in the missing information for each data set.

Problem 1

The owner of a super market recorded the number of customers who came into his store each hour in a day. The numbers of customers are 0, 2, 5, 4, 7, 6, 5, 4, and 1. Min:%_______%% Max:%________%

Q1:%________%% Q3:%________%

Median:%________%

Problem 2

Your teacher randomly selected some quizzes from each class to score and wants to get a sense of how most students did. The scores are 80, 92, 95, 70, 88, 60, 76, 82, 74, 64, 98, 90, 88 and 81.

Min:%_______%% Max:%________%

Q1:%________%% Q3:%________%

Median:%________

Problem 3

Jerome wants to know how many books he and his friends have read during this school year. The numbers of books they read are 12, 17, 10, 24, 18, 31, 17, 21, 20, 14, 30, 5 and 25.

Min:%_______%% Max:%________%

Q1:%________%% Q3:%________%

Median:%________

Problem 4

A zookeeper at the Oakland Zoo wanted to know the typical weight of hummingbirds that live at the zoo. She weighed 10 hummingbirds and recorded the following weights in grams: 7, 5, 6.2, 6.53, 4.37, 7.2, 4.9, 3.1, 6.8, and 3.75.

%

Min:%_______%% Max:%________%

Q1:%________%% Q3:%________%

Median:%________

Statistics Unit – Lesson Series 2 2

Problem 5

The heights of basketball players at Alliance Academy are represented in the histogram below. Their coach wants to know how to best describe the heights of his players.

Min:%_______%% Max:%________%

Q1:%________%% Q3:%________%

Median:%________%

Problem 6

Latanya is working on a project where she is gathering information on the shoe lengths of her classmates. She recorded 9 measurements in centimeters, but misplaced her notes. She found the paper where she recorded the 5-number data summary of her data, but needs help recreating the list of shoe lengths. The shoe lengths, rounded to the nearest centimeter, are: ____, ____, ____, ____, ____, ____, ____, ____ and ____.

%

Min:%%%%20% % Max:%%%%28%

Q1:%%%%%%23% % Q3:%%%%%%26%

Median:%%%%%25%%

Challenge:

• Is it possible to add one number to the data set without changing the 5-number data summary? If so, how? If not, why not? What about adding more than one number?

Learning Log:

• Why do you think mean and mode are not included in the 5-number data summary?

© CPM Educational Program Core Connections, Course 1

Lesson 8.1.4 Resource Page High-Temperature Data

City 1975 (°F) 2000 (°F) 1 Anchorage, AK 13 33 2 Spokane, WA 52 44 3 Billings, MT 62 44 4 Juneau, AK 29 45 5 Bangor, ME 53 48 6 Bellingham, WA 52 53 7 Albuquerque, NM 67 53 8 Denver, CO 60 54 9 Portland, OR 57 54

10 Seattle, WA 54 54 11 Boston, MA 60 56 12 New York, NY 56 58 13 Duluth, MN 55 60 14 Bismarck, ND 66 61 15 Baltimore, MD 61 62 16 Washington, D.C. 62 62 17 Philadelphia, PA 59 62 18 El Paso, TX 83 65 19 Lansing, MI 55 66 20 Phoenix, AZ 77 67 21 San Francisco, CA 67 67 22 Sacramento, CA 71 68 23 Los Angeles, CA 71 69 24 Raleigh, NC 63 70 25 Des Moines, IA 72 73 26 Kansas City, MO 73 74 27 Chicago, IL 60 75 28 Oklahoma City, OK 76 76 29 Louisville, KY 70 76 30 Topeka, KS 74 77 31 Atlanta, GA 66 79 32 Orlando, FL 79 82 33 Baton Rouge, LA 81 84 34 Honolulu, HI 84 85 35 New Orleans, LA 80 86

1975

2000

Statistics Unit – Expert Task Adapted from CPM, Course 1, Lesson 8.1.5

1!


Ms. Anderson’s Class

!Ms. Anderson’s math class has taken a test and she wants to find a good way to share the results so that students understand how the class did. The test scores for the class are: 78, 62, 91, 51, 55, 93, 76, 82, 65, 85, 79, 83, 55, and 72.

Decide which representation Ms. Anderson should use to display the data: a histogram, a box plot, or a dot plot. Your final product should include:

! An A+ Histogram, Box Plot, and Dot Plot.

! Technical writing tools to help others understand your representations.

! A written explanation to justify which representation is the best to answer Ms. Anderson’s question: “What did the class score on the last test?”

! At least 2 reasons as to why you did not choose a different representation.

! 3 summary statements about how the class did that are supported by your representation, including information about mean and/or a 5-number data summary.

!


Statistics Unit – Lesson Series 3 Adapted from Statistics, by Freedman, Pisani and Purves

Warm-Up: Shape and Spread

If you trace the top of the bars in a histogram, you would get sketches like the ones below. These sketches represent math test scores of three

different classes.

Which class did the best on the test? Explain how you made your decision.

1st Period 2nd Period 3rd Period


Statistics Unit – Lesson Series 3 Adapted from Statistics, by Freedman, Pisani and Purves !

Shape and Spread Earlier in the unit, we looked at information that described our class. Now let’s look at data for people who live in Oakland. The sketches below represent histograms for some of this data, but the titles got lost. Part 1 Match each graph with the title that best describes the data shown. Explain your reasoning using academic vocabulary from this unit, including:

! Range ! Median ! Minimum ! Maximum

! Mean ! symmetrical / not

symmetrical

Include two summary statements for each graphical representation:

• The shape of this representation means that _____. • The spread of this representation means that _____.

Resource Managers: When everyone on your team agrees on and can explain your answers, call your teacher to explain your matches and summary statements. Part 2 How can we describe the shape and spread of a box plot?

" Draw a box plot that might represent the same data as each sketch of a histogram.

" How is the shape and spread of the box plots different from the

shape and spread of the sketches of histograms?

" What kinds of information are easier to view in each data representation?


Statistics Unit – Lesson Series 3 Adapted from Statistics, by Freedman, Pisani and Purves !

Titles:

a Heights of All Members of Households Where Both Parents are Less Than 24 Years Old

b Heights of Married Couples

c Heights of All People

d Heights of All Cars

Sketches of Histograms:

1

2

3

4

Documents

Math 6 Unit 7: Statistics Tasks Onlybhmsparnell.weebly.com/uploads/2/2/7/3/22730444/700... · 2019. 9. 8. · Math 6 Name: Date: Period: Statistics Unit – Entry Task Our Class 1