Illustrative Mathematics Unit 6.8, Lesson 1: Got Data?

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Illustrative Math
Grade 6

Lesson 1: Got Data?

Let’s explore different kinds of data.

Illustrative Math Unit 6.8, Lesson 1 (printable worksheets)

Lesson 1 Summary

The following diagram shows the difference between categorical and numerical data.

Lesson 1.1 Dots of Data

Here is a dot plot for a data set.

1. Determine if each of the following would be an appropriate label to represent the data in the dot plot. Be prepared to explain your reasoning.
   a. Number of children per class.
   b. Distance between home and school, in miles.
   c. Hours spent watching TV each day.
   d. Weight of elephants, in pounds.
   e. Points received on a homework assignment.
   
2. Think of another label that can be used with the dot plot.
   a. Write it below the scale of the dot plot. Be sure to include the unit of measurement.
   b. In your scenario, what does one dot represent?
   c. In your scenario, what would a data point of 0 mean? What would a data point of 3 1/4 mean?
   

• See Video for Whole Lesson

Scroll down the page for the solutions to the “Are you ready for more?” section.

Lesson 1.2 Surveying the Class

Here are some survey questions. Your teacher will explain which questions can be used to learn more about the students in your class and how the responses will be collected. The data that your class collects will be used in upcoming activities.

1. How long does it usually take you to travel to school? Answer to the nearest minute.
   
2. How do you travel to school on most days? Choose one.

• Walk
• Bike
• Scooter or skateboard
• Car
• School bus
• Public transport
• Other
  

3. How tall are you without your shoes on? Answer to the nearest centimeter.
   
4. What is the length of your right foot without your shoe on? Answer to the nearest centimeter.
   
5. What is your arm span? Stretch your arms open, and measure the distance from the tip of your right hand’s middle finger to the tip of your left hand’s middle finger, across your back. Answer to the nearest centimeter.
   
6. How important are the following issues to you? Rate each on a scale from 0 (not important) to 10 (very important).
   a. Reducing pollution
   b. Recycling
   c. Conserving water
   
7. Do you have any siblings? _____ Yes _____ No
   
8. How many hours of sleep per night do you usually get when you have school the next day? Answer to the nearest half hour.
   
9. How many hours of sleep per night do you usually get when you do not have school the next day? Answer to the nearest half hour.
   
10. Other than traveling from school, what do you do right after school on most days?
    

• Have a snack
  
• Do homework
  
• Read a book
  
• Talk on the phone
  
• Practice a sport
  
• Do chores
  
• Use the computer
  
• Participate in an extracurricular activity
  

11. If you could meet one of these celebrities, who would you choose?
    

• A city or state leader
  
• A champion athlete
  
• A movie star
  
• A musical artist
  
• A best-selling author
  

12. Estimate how much time per week you usually spend on each of these activities. Answer to the nearest quarter of an hour.
    a. Playing sports or doing outdoor activities
    b. Using a screen for fun (watching TV, playing computer games, etc.)
    c. Doing homework
    d. Reading
    

Lesson 1.3 Numerical and Categorical Data

The list of survey questions in the activity earlier can help you complete these exercises.

1. The first survey question about travel time produces numerical data. Identify two other questions that produce numerical data. For each, describe what was measured and its unit of measurement.
   a. Question #: ______
   What was measured:
   Unit of measurement:
   b. Question #: ______
   What was measured:
   Unit of measurement:
   
2. The second survey question about travel method produces categorical data. Identify two other questions that produce categorical data. For each, describe what characteristic or feature was being studied.
   a. Question #: ______
   Characteristic being studied:
   b. Question #: ______
   Characteristic being studied:
   
3. Think about the responses to these survey questions. Do they produce numerical or categorical data? Be prepared to explain how you know.
   a. How many pets do you have?
   b. How many years have you lived in this state?
   c. What is your favorite band?
   d. What kind of music do you like best?
   e. What is the area code of your school’s phone number?
   f. Where were you born?
   g. How much does your backpack weigh?
   
4. Name two characteristics you could investigate to learn more about your classmates. Make sure one would give categorical data and the other would give numerical data.
   

Are you ready for more?

Priya and Han collected data on the birth months of students in their class. Here are tables showing their records for the same group of students.
This table shows Priya’s records.

Jan	Apr	Jan	Feb	Oct	May	June	July	Aug	Aug
Sep	Jan	Feb	Mar	Apr	Nov	Nov	Dec	Feb	Mar

This table shows Han’s records.

1	4	1	2	10	5	6	7	8	8
9	1	2	3	4	11	11	12	2	3

1. How are their records alike? How are they different?

• Show Answers

  They are both recording the birth months of students in their class.

2. What kind of data—categorical or numerical—do you think the variable “birth month” produces? Explain how you know.

• Show Answers

  “Birth Month” is categorical data.
  Even though Han’s records are numbers they are not quantities or measurements but labels to represent the months.

Glossary Terms

categorical data
A set of categorical data has values that are words instead of numbers.
For example, Han asks 5 friends to name their favorite color. Their answers are: blue, blue, green, blue, orange.

dot plot
A dot plot is a way to represent data on a number line. Each time a value appears in the data set, we put another dot above that number on the number line.
For example, in this dot plot there are three dots above the 9. This means that three different plants had a height of 9 cm.

numerical data
A set of numerical data has values that are numbers.
For example, Han lists the ages of people in his family: 7, 10, 12, 36, 40, 67.

Lesson 18 Practice Problems

1. Tyler asked 10 students at his school how much time in minutes it takes them to get from home to school. Determine if each of these dot plots could represent the data Tyler collected. Explain your reasoning for each dot plot.
   
2. Here is a list of questions. For each question, decide if the responses will produce numerical data or categorical data and give two possible responses.
   a. What is your favorite breakfast food?
   b. How did you get to school this morning?
   c. How many different teachers do you have?
   d. What is the last thing you ate or drank?
   e. How many minutes did it take you to get ready this morning—from waking up to leaving for school?
   
3. a. Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.
   b. Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.
   
4. Triangle DEF has vertices D = (-4,-4), E = (-2,-4), and F = (-3,-1).
   a. Plot the triangle in the coordinate plane and label the vertices.
   b. Name the coordinates of 3 points that are inside the triangle.
   c. What is the area of the triangle? Show your reasoning.
   

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