# Collecting & Organizing Data

## Overview

Students collect data to answer questions about a typical sixth grade student. Students collect data about themselves, working in pairs to measure height, arm span, etc. Students discuss characteristics they would like to know about sixth grade students, adding these topics to a preset list. Data are collected and organized such that there is a class data set for each topic for future use. Students are asked to think about how this data could be represented and organized.

# Key Concepts

For data to be useful, it must be collected in a consistent and accurate way. For example, for height data, students must agree on whether students should be measured with shoes on or off, and whether heights should be measured to the nearest inch, half inch, or centimeter.

# Goals and Learning Objectives

- Gather data about sixth grade students.
- Consider how data are collected.

# List of Questions

# Lesson Guide

Review the list of questions on the student screen:

- How tall are you (to the nearest inch)?
- How far can you jump (to the nearest inch)?
- How high can you reach (to the nearest inch)?
- How long is your foot (to the nearest half inch)?
- How many hours a week do you watch television?
- How many letters are in your first name?

Remember to add additional student-written questions from Lesson 1.

# Mathematics

Ask students to think about how the data should be collected, and how the method of collection could affect the results. Give them a minute or two to discuss this in pairs.

Discuss with the class that everybody must collect the data the same way. Following the same procedure and being accurate in measuring will improve the validity of the data.

- Ask students why it's important to collect the data in the same way. (Possible answer: Collecting data differently will lead to different answers.)
- For each question, briefly discuss how the data should be collected. (Examples: For the number of letters in their first name, should students use their full name or the name they are usually called—e.g., Chris vs. Christopher?)
- Some topics may be left ambiguous intentionally, to see how students interpret the question. (Example: When calculating how many hours a week students watch television, do they also count videos on the computer?)

ELL: This is a good opportunity for students to practice their math reasoning skills. It is also an opportunity for the instructor to model a think aloud about how the data should be collected.

## Opening

# List of Questions

Look at the list of questions.

Today you will collect data for each question. First you will collect data about yourself, and then the class will combine the collected data.

- As you collect the data, think about where you might fit into the overall class data for each question. For which categories do you think you match the typical characteristics for a sixth grade student?
- Discuss with your partner how you could collect data for each question and why it is important that everyone in the class collects data in the same way.

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will collect data that they will use to help define the characteristics of a typical sixth grade student.

## Opening

Collect data that you will use to help define the characteristics of a typical sixth grade student.

# Collect Data

# Lesson Guide

Divide students into pairs, so that students can assist each other in measuring. For the sake of accuracy and management, it would be helpful to have tape measures and chalk set up in designated areas ahead of time for any student questions that require these materials. Students can reach up and mark an outside wall with chalk, then measure their reach height. When students are finished collecting their data, have them add their individual data to a class data sheet that is accessible to all students

SWD: Provide students with disabilities a template to record their data. This will help them record accurate data around their statistical question. Check for understanding by asking students to state how they will be recording their numerical data in terms of measurement.

# Mathematics

As students work, they should think about what might be a typical answer for each question, and if their measurements are typical. They should also be thinking about measuring accurately and honestly.

# Interventions

**Students are recording inaccurate measurements.**

- What does it mean to measure to the nearest inch?
- If a measurement is between inch marks, how do you decide what to record?
- Is this how the rest of the class is recording this measurement?

**Students do not specify units of measurement.**

- For which questions should your answers have units?
- Why is it important to give the units when your answer is a measurement?

# Answers

- Answers will vary. Students should be using consistent units in their measurements.

## Work Time

# Collect Data

Work with a partner to answer all of the questions. Enter your data in your Notebook. Be careful to measure as accurately as possible. For the second question, record the best of three tries.

- How tall are you (to the nearest inch)?
- How far can you jump (to the nearest inch)?
- How high can you reach (to the nearest inch)?
- How long is your foot (to the nearest half inch)?
- How many hours a week do you watch television?
- How many letters are in your first name?
- Write and answer your own question.

Add the data you collected to the class data as directed by your teacher.

## Hint:

Remember that it is important that everyone in the class collects the data in the same way. Ask your teacher if you are not sure how to find or record the data for a question.

# What is Typical?

# Lesson Guide

Students will look back at the questions they answered and the data the class collected and consider for which questions it is easier to decide what is typical and for which questions it is more difficult to decide what is typical.

# Mathematical Practices

**Mathematical Practice 5: Use appropriate tools strategically.**

- Students must be careful to make their measurements consistently and in the same manner as the rest of the class.

# Interventions

**Student doesn’t understand why it might be easier to find a typical value for some data compared to other data.**

- Does the data have a big difference between the smallest number and the largest number?
- Does the data have a small difference between the smallest number and the largest number?
- Is your data spread out?
- Does your data have a lot of data points in a small range of numbers?

# Answers

- Answers will vary.
- Answers will vary. Possible answer: It will be easy to decide what is typical for how tall a sixth grade student is because most of us are similar in height.
- Answers will vary. Possible answer: It will be harder to decide what is typical for how far a 6th grade student can jump because some people can jump really far and others can't.
- Discussions will vary.

## Work Time

# What is Typical?

In future lessons you will use the data that the class collected to determine what is typical for a sixth grade student for each question. However, the way that you determine what is typical may differ, depending on the question.

Look back at the list of questions and the data you and the class collected.

- Do you think it will be easier to decide what is typical for some questions versus other questions?
- If so, for which questions do you think it will be easier?
- For which questions do you think it will be more difficult? Why?
- Discuss your thinking with a partner.

# Prepare a Presentation

# Lesson Guide

Students will prepare a presentation to share with their classmates.

# Preparing for Ways of Thinking

Review student’s statistical questions and measurement methods and choose several to bring up during Ways of Thinking.

Look for a variety of different questions, and also look for students who have good explanations of how they chose their question.

Look for students who have already formed opinions about the measures of center of their data.

# Challenge Problem

## Answers

- Answers will vary. Possible answer: Take the middle data point as representative of the data set.

## Work Time

# Prepare a Presentation

- Prepare a presentation that explains how you made your measurements and how you chose your own question.

# Challenge Problem

- If every single person in the class has a different arm span, how could you determine what the typical arm span is?

# Make Connections

# Lesson Guide

Have students share the methods they used to make their measurements. Have students who did the Challenge Problem share their answers.

ELL: Encourage students to verbalize their explanations. Allow students to speak in small groups to gain confidence prior to the discussion.

# Mathematical Practices

**Mathematical Practice 6: Attend to precision.**

- Discuss the differences between methods, and whether the different methods can produce data that is comparable.

# Mathematics

Now that the data have been collected, they will be compiled into sets containing measurements from all students.

Encourage students to think of ways to make sense of the data and how they can decide what is typical for each set of data. Ask questions like:

- Now that we have data sets on various topics, how can we make sense of the data?
- How can the data be organized?
- Is there a way to visually display the data?

Explain to students that they will analyze the data they have collected. To do that, they will spend the next few days looking at tools that they can use for this purpose.

## Performance Task

# Ways of Thinking: Make Connections

Take notes about:

- The ways that your classmates made their measurements. How do their methods compare to your methods?
- Your classmates’ ideas about for which questions it will be easier or more difficult to determine what is typical. How do their ideas compare to yours?

## Hint:

As your classmates present, ask questions such as:

- How did you take a measurement to answer the question?
- Do you think it will be easy or difficult to determine what is typical for this question? Why do you think so?

# Collecting Data

# A Possible Summary

The way data are collected can affect how they are interpreted. It is important that the data are collected accurately and in a consistent way. If data are not collected accurately, then the results are not valid.

## Formative Assessment

# Summary of the Math: Collecting Data

Write a summary of what you learned about collecting data.

## Hint:

Check your summary.

- Did you give reasons for why it is important to collect data accurately and in a consistent way?

# Reflect on Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to find out what students learned about collecting data or what statistical question they would like to find the answer to.

In addition, explain to students that during the unit they will be doing a project in which they choose a statistical question to answer. They need to start thinking about topics they might be interested in, or a statistical question they'd like to answer. They will choose groups and a topic in the next lesson.

ELL: Make sure that ELLs are clear about the purpose of the discussion and are able to participate (even if their pace or the accuracy of their contributions is lower than that of English-native students). Have students discuss what they learned and re-phrase the summary in their own words.

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful.

**What I learned about collecting data is …**

**I would like to find the answer to the statistical question …**