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U1 Variability in Data
T1
Compare and Contrast
Statistical vs. a non-statistical question
T1
Discussion
What do the questions in your "statistical questions column" have in common?
What do the questions in your "non-statistical questions column" have in common?
What is the difference between the two types of questions?
T1
Summarize
A statistical question anticipates varied answers (variability). Example: What are the favorite colors of students in the school?
A non-statistical question has a single, definite answer. Example: How many days are in the month of March?
T1
Direct Instruction
The answers to a statistical question are called data. Data is information such as facts and numbers that can be used to analyze something or make decisions.
There are two kinds of data:
Discrete data is data you can count. It only has specific, separate values, like whole numbers. For example, the number of students in a class or how many pets someone has. You can’t have 2.5 students or 3.7 pets!
Continuous data is data that can take any value within a range. It’s like measuring something that can be in between numbers, like how tall someone is or the temperature outside. You can have 5.3 feet or 72.8 degrees.
Examples of both kinds of data:
T1
Create
In your notebook, create two statistical questions.
The answers to one of the questions will result in discrete data (whole numbers).
The answers to the other question will result in continuous data (parts of a whole).
T1
Discuss (2 min)
Refer to yesterday's assignment, the questions you wrote in your notebook, and share one of the statistical questions you created.
T1
Entry Ticket (5 min)
On the blank side, write: First name, last name, U1T1
What is the difference between a statistical question and a non-statistical question?
T1
Launch
Write on the board:
Introduce the two types of data: discrete (whole numbers) and continuous (whole numbers and parts of a whole)
T1
Vertical Collaboration
You and your group are going to create statistical questions for a REAL SURVEY that we will be using to get to know each other.
Work with your group to create at least four statistical questions that will allow you to collect both kinds of data.
T1
Share
One person from your group, go to Google Classroom > our class > Classwork.
Click the link to share your group's two favorite statistical questions -- one that will result in discrete data (whole numbers) and another that will result in continuous data (whole numbers and parts of a whole)
T1
Feedback
In a moment, I will pass yesterday's entry ticket back to you.
The first thing you want to do is glue it into your notebook. It is one of your learning archives.
Secondly, let's review some Level 3 work and discuss. If you scored a 1 or a 2, you are welcome to revise your original answer -- but I encourage you to leave your original answer (don't erase it, simply put a line through it and write your revised answer above, below or next to it)
T1
Class Info
I do make mistakes! Please check PowerSchool to verify that the number on your entry ticket is the same number I entered in PowerSchool.
T1
Survey
Great job of creating statistical questions yesterday! I used your submissions to create our Get to Know Your Class Survey Part 1.
Click the link below to answer the first set of questions.
* Bonus: how do you know that the questions in this survey are statistical questions?
T1
Share
T2
Launch
Show the data we collected. Read the data out loud (to emphasize that it doesn't make sense when read out loud)
Informally re-survey and record the data in a dot plot. As them what the min. max. and most is. Emphasize that this is much easier to "see"
T2
Vertical Collaboration
How many people were surveyed? How many people have 3 pets? How many have 1 pet?
Make a dot plot that shows the number of siblings. Identify the min, max and most.
Make a dot plot that shows the number of boxes sold. Identify the min, max and most.
T2
Summarize
A dot plot is a type of graph that is based on a number line. Each dot represents an individual data point. It makes it easier to see the data.
How to make a dot plot (a.k.a line plot):
1. Identify min. and max. (range)
2. Create a number line that represents the range of the data
3. For each data point, make a dot (or x) -- neatly spaced -- above the number
4. When finished, count the number of items in the data set and verify that you made the number of dots
T2
My Responsibilities
1. Make notes for your forgetful selves
2. In your notebook, use the data sets below to create a dot plot. Then identify the min, max, and most.
A. Daily high temperatures: 71, 72, 74, 72, 72, 68, 71, 67, 68, 71, 68, 72, 76, 75, 72, 73, 68, 69, 69, 73, 74, 76, 72, 74
B. Number of tornadoes: 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 6, 0, 0
C. Length of summer camps in days: 7, 7, 12, 10, 5, 10, 5, 7, 10, 9, 7, 9, 6, 10, 5, 8, 7, 8
D. Estimates of room lengths: 10, 13, 15, 16, 17, 11, 13, 15, 16, 17, 12, 14, 15, 16, 18, 12, 14, 15, 17, 18, 13, 14, 15, 17, 25
3. When you don't understand, look at textbook examples (review the pages prior to the CYUQs) or search
T2
Discuss (2 min)
How did the CYUQs go yesterday?
T2
Vertical Collaboration
Work with your group to create a dot plot that displays data from our class' survey.
T3
Launch
Model how to create a histogram with ranges of ten based on ages at a graduation party (10 items) 12, 30, 37, 22, 41, 45, 5, 35, 38, 13
What is the frequency of grades between 60 and 80?
How many students have shoe sizes between 10 and 11?
T3
Vertical Collaboration
Work with your group to create a histogram for the following data:
Points scored in a weekend tournament (15 values) 7, 42, 19, 33, 31, 48, 25, 4, 39, 21, 2, 34, 36, 28, 9
T3
Summarize
A histogram is a type of bar graph that organizes data into equal buckets (ranges). In addition to helping us to see the data, it makes it easy to see the frequency distribution.
To create a histogram:
1. Based on the data, determine the size of the buckets (ranges): 5, 10, 15, ... ?
2. Setup a graph with the buckets (ranges) on the x-axis and the frequency on the y-axis (remember to write labels)
3. Place each data point in the correct bucket (range)
Bar graph vs histogram:
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → Do in your notebook. You chose where you want to start. Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
p877: 13, 14, 15, 16, 17; p875: 2, 3, 4, 5 (Volume 2 Ch12-2)
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T3
Follow up
When making a histogram:
Be sure your columns are straight
Be sure to label the y-axis "frequency" and add a label to the x-axis that describes what the data represents
Each bucket must have the same range (i.e. if you go by 10's, all ranges are by 10's)
Another way to show the range is to write it below the "bucket"
When making your histogram, be sure your buckets hold more than one number (a dot plot already goes by 1's)
T3
Vertical Collaboration
Work with your group to create a histogram for the following data:
Age of people at a birthday party (20 values) 42, 5, 28, 34, 12, 56, 18, 25, 3, 47, 13, 44, 9, 39, 30, 22, 47, 2, 23, 8
Time it took to run a mile (minutes and seconds) (12 values) 6:45, 7:12, 8:03, 6:38, 7:50, 9:01, 8:27, 6:55, 7:18, 8:10, 9:30, 7:45
T3
My Responsibilities
CYUQs: In your notebook, create a histogram for the two data sets (below). Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
Minutes spent doing math homework (25 values) 11, 53, 47, 44, 3, 31, 55, 19, 50, 6, 38, 22, 28, 59, 2, 49, 14, 41, 12,
33, 16, 35, 13, 48, 29
Rainfall amounts (inches) (15 values) 22.3, 18.5, 27.9, 24.7, 22.1, 16.8, 26.5, 19.7, 21.4, 20.9, 17.4, 25.1, 23.6, 21.5, 30.0
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T3
Compare and Contrast
Dot Plot
Histogram
This is what students noticed:
A
Part 1
It's time to use what you've learned to represent our data visually.
When you receive your worksheet, neatly write your first and last name in the corner above the lists of data.
Create one dot plot and one histogram (each based on a different data set). INCLUDE LABELS.
when making your number lines, use a ruler to make the spacing (intervals) the same
Use pencil ONLY. Write neatly.
* If you were absent or lost your paper, pick one of the following and print a single page from your class period:
A
Submit
If you have not turned in your dot plot and histogram, please put it in the basket in the back of the room.
T4
Launch
Display and write on the following:
We are "Number Ninjas" - chopping up numbers
Page 1: model counting to the middle, circle exact numbers and write a question mark between others. Ask about patterns
Page 2: After: how could we prove that we are correct? (number line)
Page 3: Goal: force using a number line to prove what number is in the middle. Think pair share # 8 and #6 -- and ask if someone can prove it
Page 4: model counting to middle, circling, and then "calculating" mid. Any patterns? 10, 11 (mid #) & 8, 9 (none) & 6, 7 (mid #) & 4, 5 (none)
Page 5 After: look at these! What did we just do? (broke the data into 4 equal groups). NOTICE that all of the data sets were ordered!!!! Now you do it in groups.
T4
Vertical Collaboration
Work with your group to divide the data into 4 equal parts:
2, 4, 4, 7, 9, 11, 13, 15, 16, 18, 19
13, 7, 4, 18, 9, 4, 16, 2, 11, 15, 6
3, 5, 5, 8, 10, 12, 14, 16, 17, 19
T4
Summarize
To divide a data set into four equal parts:
First, make sure the data is in order from least to greatest!
Second, find the middle of the data set by counting from the ends toward the middle (number ninja)
Next, find the middle of the lower half: count from the left and middle (number ninja)
Last, find the middle of the upper half: count from the right and middle (number ninja)
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → Divide each data set into four equal parts. Do in your notebook. You chose where you want to start.
1, 3, 5, 5, 8, 10, 14, 17, 19
2, 4, 4, 7, 9, 11, 13, 15, 17, 18
1, 3, 5, 5, 7, 9, 12, 14, 14, 18, 19
14, 7, 3, 12, 8, 14, 5, 10, 6
9, 3, 15, 7, 12, 3, 18, 6, 11, 14
8, 14, 3, 11, 6, 14, 2, 9, 5, 17, 10
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Revise
The first part of your Unit 1 Projects look GREAT. It was a solid start. Let's take a moment to review the checklist together (below). Please compare your work and, if needed, make improvements.
1. Use a ruler for your histogram's rows and columns (90 degree angles, vertical and horizontal lines)
2. Include labels (1 for the dot plot, 2 for the histogram)
3. Verify that your histogram does not have any gaps between columns
4. Shade your histogram in a way that makes it easier to see the data (every other column)
5. Verify that your histogram has realistic buckets (ranges) -- not too big
Click below to see a Level 3 project:
T4
Review
Divide the data into 4 equal parts. Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
2, 3, 4, 7, 9, 11, 11, 11, 18
12, 7, 3, 18, 5, 9, 12, 2, 16, 8
A
Glue & Review
Glue your Dot Plot & Histogram (showing your Level 3 work) into your notebook. It is one of your learning archives.
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Launch
Setup: Today we are going to take our data sets -- divided into QUARTERS -- and use them to make a box plot
Start with this data: 17, 18, 19, 20, 21, 23, 23, 26, 28 (Minutes spent doing chores) and divide it into four equal groups
Make a number line (skip count)
Think out loud while marking the dots above min, max and Q1, Q2, Q3. Draw the whiskers and make the box
Turn and talk: what did I do first, second, third?
T4
Vertical Collaboration
For each of the following data sets, make a box-plot.
2, 7, 7, 7, 8, 9, 13, 14, 18
3, 5, 6, 8, 9, 10, 10, 13, 14, 19
2, 3, 4, 7, 9, 11, 11, 11, 18
T4
Summarize
A box plot, or box and whisker plot, is a graphical tool that displays the distribution of a dataset using 5 numbers: the minimum, maximum, Q1, Q2, and Q3
Steps for making a box plot:
1. Order the data from least to greatest and divide the ordered data into 4 equal parts (number ninja)
2. Create a number line (with correct spacing) that starts with the min and ends with the max
3. Make dots above the number line that represent the min, max, Q1, Q2, and Q3.
4. Make a box around Q1, Q2, and Q3. Draw whiskers to the min and max.
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → For each of the following data sets, make a box-plot. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you need help, get help. And if someone else needs help, give help.
9, 10, 12, 13, 14, 15, 17, 17, 20
16, 20, 21, 22, 22, 24, 24, 26, 27
5, 6, 7, 8, 9, 11, 12, 12, 15
18, 19, 20, 20, 21, 23, 24, 27
45, 42, 50, 44, 47, 42, 53, 49, 46, 54
35, 44, 38, 32, 46, 41, 35, 48, 40, 37
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Entry Ticket (5 min)
On the blank side, write: First name, last name, 12T4
For the past eleven days, Alice kept track of the number of minutes she practiced the violin.
9, 10, 12, 13, 15, 15, 17, 20, 24, 25, 30
Create a box and whisker plot to display the data.
T4
Extend
Click the link below. Make a box-plot for each of the four data sets. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you need help, get help. And if someone else needs help, give help.
T4
Small Group Reteaching
T4
Feedback
In a moment, I will pass yesterday's entry ticket back to you.
The first thing you want to do is glue it into your notebook. It is one of your learning archives.
Secondly, let's review some Level 3 work and discuss. If you scored a 1 or a 2, you are welcome to revise your original answer -- but I encourage you to leave your original answer (don't erase it, simply put a line through it and write your revised answer above, below or next to it)
T5
Introduction
The purpose of displaying data using a line plot, histogram, or box plot is so you can SEE the data visually. When you have a long list of numbers, it is hard to make sense of what is happening.
Once we have a line plot, histogram, or box plot; it is much easier to describe (make sense) the data. We can:
A. Identify trends and understand patterns
B. Predict the likelihood of seeing a value or range of values in the future
C. Make informed (more intelligent) decisions
T5
Discussion
Describe the shape of the data distributions.
T5
Direct Instruction
Here are a list of common descriptions: "The data ..."
"is centered at... " or "has a cluster at..."
"has gaps at... " or "has peaks at... "
"is symmetric" or "is not symmetric"
"is skewed to the right (or left)"
"has a min of... and max of... which means a range of.... "
"has x values"
* I printed the list for you to glue into your math notebook
T5
Direct Instruction
Vocabulary words and phrases for describing the distribution of a data set:
Cluster: where the data is grouped close together
Gap: a gap in the data where there are no values
Peak: most frequently occurring value (Bimodal data has two distinct peaks)
Range: how far apart the data points in a distribution are from each other. * The range is one way to describe the variability of the data
Shape: The overall pattern of the data, which can be symmetric (evenly balanced, like a bell curve) or skewed
T5
Direct Instruction
Skewed data is data that isn't spread out evenly, creating a "tail" or slant on one side when you look at the display.
- Left Skew (Negatively Skewed): The tail of the graph points to the left.
- Right Skew (Positively Skewed): The tail of the graph points to the right.
T5
Guided Practice
Use the sentence starters and vocabulary words to describe the distributions.
T5
My Responsibilities
1. Glue the sentence starters and vocabulary into your notebook.
2. CYUqs → Use your sentence starters and vocabulary to describe each of the data sets. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
p897: 9, 10, 12a, 12b; p895: 1, 2; p894: 2 (Volume 2)
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Direct Instruction
Uniform Distribution vs Symmetric Distribution
T5
Review
Use the sentence starters and vocabulary words to describe the distributions.
A
Unit Test is This Week
Thursday
A
Graphic Organizer
Today you will receive the graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, our vertical collaboration tasks, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Knowledge Application
What’s the Story in Our School?
Use the worksheet to guide you as you create a statistical question, collect data, display it three different ways, and summarize your findings.
A
Q & A
Knowledge Application Project reminder: only one question
A yes or no question is not a statistical question (because it doesn't anticipate enough variability). Also, you can't put yes and no on a number line (so it won't work for the three data displays we learned)
A question like, "What color is your hair?" is a statistical question but you can't put hair color on a number line (and all three of our data displays use a number line).
If you want to use a dot plot to get the data for making your box and whisker plot, remember that each x (or dot) is a data point. Be sure to write them all down!
Use the lines that are provided to create the spacing on your number lines (don't make lines between the given lines)
When making your histogram, be sure your buckets hold more than one number (Your dot plot already goes by 1's)
A
Directions
Finish your Unit 1 Graphic Organizer (Due tomorrow) and your "What's the story at our school?" Knowledge Application Project (Due Friday)
Both activities are designed to help you prepare for tomorrow's test.
If you need help, get help. If someone else needs help, give help.
A
Prepare
Tonight: spend at least 15 minutes reading over your graphic organizer. If something on it confuses you, look back at your notes, my notes, Google it, or ask a friend. Then make changes and update your graphic organizer. Be sure to bring it tomorrow for the test.
A
Test
Unit
A
Test Directions
Take out something to write with. If you would like, you may use your graphic organizer. No phones, smart watches, or other electronic devices.
When you get the test, be sure to read and follow the directions.
Do your best. Show your thinking. I will use your work to determine where you are in terms of your understanding on the key learning target(s).
When finished, put your test (with your name on it) and graphic organizer in the basket in the front. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Great job!
After reviewing your assessments, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
A
Retake Day
We have a retake day scheduled for 9/18.
This is what you need to know about retakes:
A
Q & A
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find someone whose work shows a Level 3 or 4. Compare and contrast your work and their work. Discuss what you notice. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
A
Directions
Today is a quiet, individual work day. The goal is for you to review a topics from Unit 1.
Take out your Chromebook, math notebook, and something to write with.
Click the link below to go to go to Delta Math. The first step will be to create an account. Sign up with Google. Use your school Google Account. After you create it, you will need to close Delta Math and open it again, this time signing in with your school Google Account.
Open and complete the Unit 1 Review. Start with any one of the four topics. When finished, choose another. If you don't finish in class, spend up to 20 minutes at home -- but stop after that :-)
When needed, use your notebook and pencil to work out your thinking.
Why, How, and What
In order to make sense of the world (DI1), students will model with mathematics (SMP4) and use appropriate tools strategically (SMP5) while reasoning with data (CC1).
Description
Investigate real world data sources, ask questions of data, start to understand variability - within data sets and across different forms of data, consider different types of data, and represent data with different representations. (p33)
Standards
- 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
- 6.SP.5 5. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- Source:
- 2013 CACC Math Content Standards
T1
Compare and Contrast
Statistical vs. a non-statistical question
T1
Discussion
What do the questions in your "statistical questions column" have in common?
What do the questions in your "non-statistical questions column" have in common?
What is the difference between the two types of questions?
T1
Summarize
A statistical question anticipates varied answers (variability). Example: What are the favorite colors of students in the school?
A non-statistical question has a single, definite answer. Example: How many days are in the month of March?
T1
Direct Instruction
The answers to a statistical question are called data. Data is information such as facts and numbers that can be used to analyze something or make decisions.
There are two kinds of data:
Discrete data is data you can count. It only has specific, separate values, like whole numbers. For example, the number of students in a class or how many pets someone has. You can’t have 2.5 students or 3.7 pets!
Continuous data is data that can take any value within a range. It’s like measuring something that can be in between numbers, like how tall someone is or the temperature outside. You can have 5.3 feet or 72.8 degrees.
Examples of both kinds of data:
T1
Create
In your notebook, create two statistical questions.
The answers to one of the questions will result in discrete data (whole numbers).
The answers to the other question will result in continuous data (parts of a whole).
T1
Discuss (2 min)
Refer to yesterday's assignment, the questions you wrote in your notebook, and share one of the statistical questions you created.
T1
Entry Ticket (5 min)
On the blank side, write: First name, last name, U1T1
What is the difference between a statistical question and a non-statistical question?
T1
Launch
Write on the board:
Introduce the two types of data: discrete (whole numbers) and continuous (whole numbers and parts of a whole)
T1
Vertical Collaboration
You and your group are going to create statistical questions for a REAL SURVEY that we will be using to get to know each other.
Work with your group to create at least four statistical questions that will allow you to collect both kinds of data.
T1
Share
One person from your group, go to Google Classroom > our class > Classwork.
Click the link to share your group's two favorite statistical questions -- one that will result in discrete data (whole numbers) and another that will result in continuous data (whole numbers and parts of a whole)
T1
Feedback
In a moment, I will pass yesterday's entry ticket back to you.
The first thing you want to do is glue it into your notebook. It is one of your learning archives.
Secondly, let's review some Level 3 work and discuss. If you scored a 1 or a 2, you are welcome to revise your original answer -- but I encourage you to leave your original answer (don't erase it, simply put a line through it and write your revised answer above, below or next to it)
T1
Class Info
I do make mistakes! Please check PowerSchool to verify that the number on your entry ticket is the same number I entered in PowerSchool.
T1
Survey
Great job of creating statistical questions yesterday! I used your submissions to create our Get to Know Your Class Survey Part 1.
Click the link below to answer the first set of questions.
* Bonus: how do you know that the questions in this survey are statistical questions?
T1
Share
T2
Launch
Show the data we collected. Read the data out loud (to emphasize that it doesn't make sense when read out loud)
Informally re-survey and record the data in a dot plot. As them what the min. max. and most is. Emphasize that this is much easier to "see"
T2
Vertical Collaboration
How many people were surveyed? How many people have 3 pets? How many have 1 pet?
Make a dot plot that shows the number of siblings. Identify the min, max and most.
Make a dot plot that shows the number of boxes sold. Identify the min, max and most.
T2
Summarize
A dot plot is a type of graph that is based on a number line. Each dot represents an individual data point. It makes it easier to see the data.
How to make a dot plot (a.k.a line plot):
1. Identify min. and max. (range)
2. Create a number line that represents the range of the data
3. For each data point, make a dot (or x) -- neatly spaced -- above the number
4. When finished, count the number of items in the data set and verify that you made the number of dots
T2
My Responsibilities
1. Make notes for your forgetful selves
2. In your notebook, use the data sets below to create a dot plot. Then identify the min, max, and most.
A. Daily high temperatures: 71, 72, 74, 72, 72, 68, 71, 67, 68, 71, 68, 72, 76, 75, 72, 73, 68, 69, 69, 73, 74, 76, 72, 74
B. Number of tornadoes: 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 0, 6, 0, 0
C. Length of summer camps in days: 7, 7, 12, 10, 5, 10, 5, 7, 10, 9, 7, 9, 6, 10, 5, 8, 7, 8
D. Estimates of room lengths: 10, 13, 15, 16, 17, 11, 13, 15, 16, 17, 12, 14, 15, 16, 18, 12, 14, 15, 17, 18, 13, 14, 15, 17, 25
3. When you don't understand, look at textbook examples (review the pages prior to the CYUQs) or search
T2
Discuss (2 min)
How did the CYUQs go yesterday?
T2
Vertical Collaboration
Work with your group to create a dot plot that displays data from our class' survey.
T3
Launch
Model how to create a histogram with ranges of ten based on ages at a graduation party (10 items) 12, 30, 37, 22, 41, 45, 5, 35, 38, 13
What is the frequency of grades between 60 and 80?
How many students have shoe sizes between 10 and 11?
T3
Vertical Collaboration
Work with your group to create a histogram for the following data:
Points scored in a weekend tournament (15 values) 7, 42, 19, 33, 31, 48, 25, 4, 39, 21, 2, 34, 36, 28, 9
T3
Summarize
A histogram is a type of bar graph that organizes data into equal buckets (ranges). In addition to helping us to see the data, it makes it easy to see the frequency distribution.
To create a histogram:
1. Based on the data, determine the size of the buckets (ranges): 5, 10, 15, ... ?
2. Setup a graph with the buckets (ranges) on the x-axis and the frequency on the y-axis (remember to write labels)
3. Place each data point in the correct bucket (range)
Bar graph vs histogram:
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → Do in your notebook. You chose where you want to start. Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
p877: 13, 14, 15, 16, 17; p875: 2, 3, 4, 5 (Volume 2 Ch12-2)
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T3
Follow up
When making a histogram:
Be sure your columns are straight
Be sure to label the y-axis "frequency" and add a label to the x-axis that describes what the data represents
Each bucket must have the same range (i.e. if you go by 10's, all ranges are by 10's)
Another way to show the range is to write it below the "bucket"
When making your histogram, be sure your buckets hold more than one number (a dot plot already goes by 1's)
T3
Vertical Collaboration
Work with your group to create a histogram for the following data:
Age of people at a birthday party (20 values) 42, 5, 28, 34, 12, 56, 18, 25, 3, 47, 13, 44, 9, 39, 30, 22, 47, 2, 23, 8
Time it took to run a mile (minutes and seconds) (12 values) 6:45, 7:12, 8:03, 6:38, 7:50, 9:01, 8:27, 6:55, 7:18, 8:10, 9:30, 7:45
T3
My Responsibilities
CYUQs: In your notebook, create a histogram for the two data sets (below). Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
Minutes spent doing math homework (25 values) 11, 53, 47, 44, 3, 31, 55, 19, 50, 6, 38, 22, 28, 59, 2, 49, 14, 41, 12,
33, 16, 35, 13, 48, 29
Rainfall amounts (inches) (15 values) 22.3, 18.5, 27.9, 24.7, 22.1, 16.8, 26.5, 19.7, 21.4, 20.9, 17.4, 25.1, 23.6, 21.5, 30.0
T3
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T3
Compare and Contrast
Dot Plot
Histogram
This is what students noticed:
A
Part 1
It's time to use what you've learned to represent our data visually.
When you receive your worksheet, neatly write your first and last name in the corner above the lists of data.
Create one dot plot and one histogram (each based on a different data set). INCLUDE LABELS.
when making your number lines, use a ruler to make the spacing (intervals) the same
Use pencil ONLY. Write neatly.
* If you were absent or lost your paper, pick one of the following and print a single page from your class period:
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Submit
If you have not turned in your dot plot and histogram, please put it in the basket in the back of the room.
T4
Launch
Display and write on the following:
We are "Number Ninjas" - chopping up numbers
Page 1: model counting to the middle, circle exact numbers and write a question mark between others. Ask about patterns
Page 2: After: how could we prove that we are correct? (number line)
Page 3: Goal: force using a number line to prove what number is in the middle. Think pair share # 8 and #6 -- and ask if someone can prove it
Page 4: model counting to middle, circling, and then "calculating" mid. Any patterns? 10, 11 (mid #) & 8, 9 (none) & 6, 7 (mid #) & 4, 5 (none)
Page 5 After: look at these! What did we just do? (broke the data into 4 equal groups). NOTICE that all of the data sets were ordered!!!! Now you do it in groups.
T4
Vertical Collaboration
Work with your group to divide the data into 4 equal parts:
2, 4, 4, 7, 9, 11, 13, 15, 16, 18, 19
13, 7, 4, 18, 9, 4, 16, 2, 11, 15, 6
3, 5, 5, 8, 10, 12, 14, 16, 17, 19
T4
Summarize
To divide a data set into four equal parts:
First, make sure the data is in order from least to greatest!
Second, find the middle of the data set by counting from the ends toward the middle (number ninja)
Next, find the middle of the lower half: count from the left and middle (number ninja)
Last, find the middle of the upper half: count from the right and middle (number ninja)
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → Divide each data set into four equal parts. Do in your notebook. You chose where you want to start.
1, 3, 5, 5, 8, 10, 14, 17, 19
2, 4, 4, 7, 9, 11, 13, 15, 17, 18
1, 3, 5, 5, 7, 9, 12, 14, 14, 18, 19
14, 7, 3, 12, 8, 14, 5, 10, 6
9, 3, 15, 7, 12, 3, 18, 6, 11, 14
8, 14, 3, 11, 6, 14, 2, 9, 5, 17, 10
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
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Revise
The first part of your Unit 1 Projects look GREAT. It was a solid start. Let's take a moment to review the checklist together (below). Please compare your work and, if needed, make improvements.
1. Use a ruler for your histogram's rows and columns (90 degree angles, vertical and horizontal lines)
2. Include labels (1 for the dot plot, 2 for the histogram)
3. Verify that your histogram does not have any gaps between columns
4. Shade your histogram in a way that makes it easier to see the data (every other column)
5. Verify that your histogram has realistic buckets (ranges) -- not too big
Click below to see a Level 3 project:
T4
Review
Divide the data into 4 equal parts. Check your work with the students around you and if you need help, get help. And if someone else needs help, give help.
2, 3, 4, 7, 9, 11, 11, 11, 18
12, 7, 3, 18, 5, 9, 12, 2, 16, 8
A
Glue & Review
Glue your Dot Plot & Histogram (showing your Level 3 work) into your notebook. It is one of your learning archives.
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Launch
Setup: Today we are going to take our data sets -- divided into QUARTERS -- and use them to make a box plot
Start with this data: 17, 18, 19, 20, 21, 23, 23, 26, 28 (Minutes spent doing chores) and divide it into four equal groups
Make a number line (skip count)
Think out loud while marking the dots above min, max and Q1, Q2, Q3. Draw the whiskers and make the box
Turn and talk: what did I do first, second, third?
T4
Vertical Collaboration
For each of the following data sets, make a box-plot.
2, 7, 7, 7, 8, 9, 13, 14, 18
3, 5, 6, 8, 9, 10, 10, 13, 14, 19
2, 3, 4, 7, 9, 11, 11, 11, 18
T4
Summarize
A box plot, or box and whisker plot, is a graphical tool that displays the distribution of a dataset using 5 numbers: the minimum, maximum, Q1, Q2, and Q3
Steps for making a box plot:
1. Order the data from least to greatest and divide the ordered data into 4 equal parts (number ninja)
2. Create a number line (with correct spacing) that starts with the min and ends with the max
3. Make dots above the number line that represent the min, max, Q1, Q2, and Q3.
4. Make a box around Q1, Q2, and Q3. Draw whiskers to the min and max.
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUQs → For each of the following data sets, make a box-plot. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you need help, get help. And if someone else needs help, give help.
9, 10, 12, 13, 14, 15, 17, 17, 20
16, 20, 21, 22, 22, 24, 24, 26, 27
5, 6, 7, 8, 9, 11, 12, 12, 15
18, 19, 20, 20, 21, 23, 24, 27
45, 42, 50, 44, 47, 42, 53, 49, 46, 54
35, 44, 38, 32, 46, 41, 35, 48, 40, 37
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Entry Ticket (5 min)
On the blank side, write: First name, last name, 12T4
For the past eleven days, Alice kept track of the number of minutes she practiced the violin.
9, 10, 12, 13, 15, 15, 17, 20, 24, 25, 30
Create a box and whisker plot to display the data.
T4
Extend
Click the link below. Make a box-plot for each of the four data sets. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you need help, get help. And if someone else needs help, give help.
T4
Small Group Reteaching
T4
Feedback
In a moment, I will pass yesterday's entry ticket back to you.
The first thing you want to do is glue it into your notebook. It is one of your learning archives.
Secondly, let's review some Level 3 work and discuss. If you scored a 1 or a 2, you are welcome to revise your original answer -- but I encourage you to leave your original answer (don't erase it, simply put a line through it and write your revised answer above, below or next to it)
T5
Introduction
The purpose of displaying data using a line plot, histogram, or box plot is so you can SEE the data visually. When you have a long list of numbers, it is hard to make sense of what is happening.
Once we have a line plot, histogram, or box plot; it is much easier to describe (make sense) the data. We can:
A. Identify trends and understand patterns
B. Predict the likelihood of seeing a value or range of values in the future
C. Make informed (more intelligent) decisions
T5
Discussion
Describe the shape of the data distributions.
T5
Direct Instruction
Here are a list of common descriptions: "The data ..."
"is centered at... " or "has a cluster at..."
"has gaps at... " or "has peaks at... "
"is symmetric" or "is not symmetric"
"is skewed to the right (or left)"
"has a min of... and max of... which means a range of.... "
"has x values"
* I printed the list for you to glue into your math notebook
T5
Direct Instruction
Vocabulary words and phrases for describing the distribution of a data set:
Cluster: where the data is grouped close together
Gap: a gap in the data where there are no values
Peak: most frequently occurring value (Bimodal data has two distinct peaks)
Range: how far apart the data points in a distribution are from each other. * The range is one way to describe the variability of the data
Shape: The overall pattern of the data, which can be symmetric (evenly balanced, like a bell curve) or skewed
T5
Direct Instruction
Skewed data is data that isn't spread out evenly, creating a "tail" or slant on one side when you look at the display.
- Left Skew (Negatively Skewed): The tail of the graph points to the left.
- Right Skew (Positively Skewed): The tail of the graph points to the right.
T5
Guided Practice
Use the sentence starters and vocabulary words to describe the distributions.
T5
My Responsibilities
1. Glue the sentence starters and vocabulary into your notebook.
2. CYUqs → Use your sentence starters and vocabulary to describe each of the data sets. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
p897: 9, 10, 12a, 12b; p895: 1, 2; p894: 2 (Volume 2)
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Direct Instruction
Uniform Distribution vs Symmetric Distribution
T5
Review
Use the sentence starters and vocabulary words to describe the distributions.
A
Unit Test is This Week
Thursday
A
Graphic Organizer
Today you will receive the graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, our vertical collaboration tasks, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Knowledge Application
What’s the Story in Our School?
Use the worksheet to guide you as you create a statistical question, collect data, display it three different ways, and summarize your findings.
A
Q & A
Knowledge Application Project reminder: only one question
A yes or no question is not a statistical question (because it doesn't anticipate enough variability). Also, you can't put yes and no on a number line (so it won't work for the three data displays we learned)
A question like, "What color is your hair?" is a statistical question but you can't put hair color on a number line (and all three of our data displays use a number line).
If you want to use a dot plot to get the data for making your box and whisker plot, remember that each x (or dot) is a data point. Be sure to write them all down!
Use the lines that are provided to create the spacing on your number lines (don't make lines between the given lines)
When making your histogram, be sure your buckets hold more than one number (Your dot plot already goes by 1's)
A
Directions
Finish your Unit 1 Graphic Organizer (Due tomorrow) and your "What's the story at our school?" Knowledge Application Project (Due Friday)
Both activities are designed to help you prepare for tomorrow's test.
If you need help, get help. If someone else needs help, give help.
A
Prepare
Tonight: spend at least 15 minutes reading over your graphic organizer. If something on it confuses you, look back at your notes, my notes, Google it, or ask a friend. Then make changes and update your graphic organizer. Be sure to bring it tomorrow for the test.
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Test
Unit
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Test Directions
Take out something to write with. If you would like, you may use your graphic organizer. No phones, smart watches, or other electronic devices.
When you get the test, be sure to read and follow the directions.
Do your best. Show your thinking. I will use your work to determine where you are in terms of your understanding on the key learning target(s).
When finished, put your test (with your name on it) and graphic organizer in the basket in the front. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
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Great job!
After reviewing your assessments, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
A
Retake Day
We have a retake day scheduled for 9/18.
This is what you need to know about retakes:
A
Q & A
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find someone whose work shows a Level 3 or 4. Compare and contrast your work and their work. Discuss what you notice. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
A
Directions
Today is a quiet, individual work day. The goal is for you to review a topics from Unit 1.
Take out your Chromebook, math notebook, and something to write with.
Click the link below to go to go to Delta Math. The first step will be to create an account. Sign up with Google. Use your school Google Account. After you create it, you will need to close Delta Math and open it again, this time signing in with your school Google Account.
Open and complete the Unit 1 Review. Start with any one of the four topics. When finished, choose another. If you don't finish in class, spend up to 20 minutes at home -- but stop after that :-)
When needed, use your notebook and pencil to work out your thinking.