Unit 2.11: Data and Graphs

Big Idea:

Categorical and numerical data can be collected, recorded, and organized. There are various ways to represent, display, describe, and interpret data using tables and graphs.

Teacher-facing pages are green

Student-facing pages are white

notes for teachers are in the speaker notes

Core Math to Emphasize:

• There are different ways to organize data (information).
• Organization can obscure or make clear answers to questions about data.
• Data can be gathered and organized into a picture graph to help us understand the data.

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New Learning:

Re-engagement:

• In Grade 1 students collected data in up to 3 categories and organized it in a variety of ways.
• They answered questions about data that involve addition and comparison of numbers.

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• Students draw picture and bar graphs to represent categorical data with up to four categories.
• Students use Information from the graphs to solve simple put-together,
• take-apart, and compare problems.

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Categorical Data and Measurement Data

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Elementary students learn about two types of data: Categorical Data and Measurement Data.

Categorical Data (Grades K-3)

Categorical data comes from sorting objects into categories—for example, sorting a jumble of alphabet blocks to form two stacks, a stack for vowels and a stack for consonants. In this case there are two categories (Vowels and Consonants). In grades K-3 students make increasingly sophisticated picture and bar graphs to represent and analyze such data.

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In 1st grade, students started organizing data in different ways and comparing them, asking which way makes the data easier to interpret. This may have included informal picture graphs. In Grade 2 students are formally introduced to picture graphs. They create them directly from data and from tally tables, and use them to answer questions about the data. They also learn to create and use Bar Graphs. In Grade 3 they will scale these graphs - so that each icon or line on a graph might represent more than one instance.

Measurement Data (Grades 2-5)

Numerical data which comes from taking measurements can be represented by line plots. For example, if every child in a class measures the span of their hand to the nearest centimeter, a set of measurement data is obtained. Students have been developing important ideas about length measurement since Unit 2.2, Measuring Length. In this unit, they use these measurements to create line plots.

YouCubed Data Talks are math talks about data with K-16 samples. They can inspire us to use real world data. Some sources include the NY Times Learning Network especially What’s Going on with this Graph?

Guidance for the 2020-2021 school year is to eliminate lessons on generating or organizing measurement data into line plots. If you choose to introduce this concept, here are some activities you may use:

Options for Activities with Measurement Line Plots

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Line plots:

• Balloon Pop is a game in Toy Theatre that gives students practice making line plots with whole numbers. https://toytheater.com/balloon-pop/

Re-engagement with measurement:

• Measuring - go for a virtual walk and measure objects using whole numbers.

Guidance for the 2020-2021 school year is to eliminate lessons on generating or organizing measurement data into line plots. If you choose to introduce this concept, here are some activities you may use:

Options for Activities with Measurement Line Plots

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Math Talks: What do you notice? What do you wonder?

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Guidance for the 2020-2021 school year is to eliminate lessons on generating or organizing measurement data into line plots. If you choose to introduce this concept, here are some activities you may use:

Technology Resources & Independent Practice

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• Fuzz Bugs Students sort “fuzz bugs” into different categories and then answer quantitative questions based on the pictograph created by the sorting.
• Balloon Pop Line Plot Game Students pop balloons and keep track of their score on a line plot.
• Fruit Fall Students catch falling fruit and then graph the number they caught in a pictograph and answer questions about the graph.
• These tools allow you to make a bar graph online:
• Create a Graph and Bar Graph Maker
• They may be challenging for 2nd graders to use, but could be used for a whole class demonstration.
• YouCubed Data Talks are math talks about data with K-16 samples. They can inspire us to use real world data. Some sources include the NY Times Learning Network especially What’s Going on with this Graph?
• These videos contain general information about the three types of graphs in this unit:
• Picture Graph
• Bar Graphs
• Line Plots

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Suggested Lesson Sequence: 4 lessons to be taught over 2 weeks (May 17 - 28)

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Description: Students gather categorical data about their classmates. They organize it into tally tables and represent it with picture and bar graphs. They generate statements and questions about the data in the tables and graphs.

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• Lesson 1: Entry Task & LS 1 Day 1 - Seesaw Lesson 1 - Favorite Fruit

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• Lesson 2: LS 1 Day 2 - Seesaw Lesson 2 - Pets

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• Lesson 3: LS 1 Day 3 - Seesaw Lesson 3 - Favorite Ice Cream

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• Lesson 4: Apprentice Task - Seesaw Lesson 4 - Our Pets

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Synchronous and Asynchronous Teaching Options:

Use a combination of Synchronous and Asynchronous approaches

Optional Routines

• Continue the “Number of Days in School” routine. See Number of Days in School (Spanish) for ideas.
• Continue the “Skip Counting” routines. See Counting Routines for further instructions
• Continue Clock Routines: The Math Clock can be used by the teacher for time review, Daily Schedule or Skip Counting Routines. Review the sequence of activities of the day and the time each one starts.
• Data Routines. See the Data Routine slides for a description of how to incorporate this routine into your lessons.

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Student PDFs

2.11 Classwork .S. .C.

2.11 Homework .S. .C.

* .S. = Spanish Student Page .C. = Chinese Student Page

Daily Routine: Number of Days in School

Objective: To build one-to-one correspondence, lay the foundation for an understanding of place value, and give students a concrete sense of the magnitude of numbers up to 180 and their relationship to the passage of time.

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See the Number of Days in School (Spanish) slides for a description of how to incorporate this routine into your lessons.

Skip Counting Routine: Counting Routine

Objective: To practice counting in groups. This builds number sense by elucidating patterns such as odd/even; it brings out patterns in addition and subtraction.

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Skip counting has been an important routine since the beginning of the year. Your class may have already ventured past 100 during this routine. If not, you will do so now.

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In this unit, students formally go beyond 100. This routine is used as a warm-up for a number of lessons in this unit.

See the Skip Counting Routine Teacher page for the skip counting emphasized in this unit.

Materials: Interactive 1000 Chart base-10 blocks, Completed Thousand Chart BLM, a class number line (see Number Talks.)

Use the slider to make the board go beyond 100.

Daily Schedule

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Description: In 2nd grade, students learn to tell time to the nearest 5 minutes. The Daily Schedule will help students see how the events of the day align with these times. The Daily Schedule should be proportional, so that students begin to notice that the length of time spent on an activity can be seen on the schedule.

Objective: To provide opportunities for students to develop their sense of time. This important routine has helped build students’ sense of time and clock literacy since the beginning of the year

Half Hour Schedule BLM .S. .C

Daily Schedule Activity Cards BLM .S. .C

Routine: Review the sequence of activities of the day and the time each one starts. Note that in 1st grade, students read time to the half hour.

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Reading time to the nearest 5 minutes is new in 2nd grade

Number of the Day Routine

Objective: To focus attention on a single number to build understanding and recognition, and to help students grow in the ways they think about numbers and operations by sharing ideas with their peers about how to represent numbers.

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Present students with a number. They generate a variety of representations of the number, including drawings, equations, and visual models. This can be done mentally, with paper and pencil, or on virtual white boards or the provided Jamboard. Work does not have to be limited to equations, but can include:

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• Composition/decomposition
• Relationships to other numbers
• Real-world examples
• Using drawings and/or visual models

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Types of numbers can be adapted to the grade level and unit content.

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Reflections questions may include “What do you notice/wonder?” or “What is similar/different between representations?

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Use Jamboard Number of the Day (Spanish) to record or have students record representations.

Jamboard Number of the Day TEMPLATE

Make a copy and write your number of the day

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Number of the Day

This routine was introduced in Unit 2.3 and has been part of the Math Routines since then. Until now, students focused on 2-digit numbers. In this unit, you will extend the routine to numbers greater than 100.

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Frequency: Daily or Weekly

Objective: To help students grow in the ways they think about numbers and operations.

Materials: Base-10 blocks, Completed Thousand Chart BLM, a class number line

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Directions:

Present students with a number. They generate a variety of representations of the number, including drawings, equations, and examples. This can be done mentally or with paper and pencil. Work can include:

• Composition/decomposition
• Relationships to other numbers
• Real-world examples
• Using models

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Variations for this routine can be found here. Start with friendly numbers (multiples of 10, then 5 and/or 2) greater than 100. Gradually make the numbers more challenging.

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Questions to ask:

• Is it odd or even?
• Can you put it into groups?
• Can you skip count to it?
• What number is 10 more? 10 less? 5 more? 5 less?

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Number of the Day

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Routine: Data Routine

Objective: The Data Routine has both social and a math objectives:

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Social

• Students build community by sharing about themselves - their person, lives, interests, & preferences - learning about their classmate’s, finding and celebrating their similarities and differences
• Students build community by recognizing their shared environment (e.g. weather)

Math

• Students develop their understanding of categorical and measurement data (see progression of standards in the following slides and here) as they:
• Formulate questions
• Collect data
• Organize and display the data
• Analyze the data, and
• Interpret the results
• Students apply other important math ideas from all domains

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See the Data Routine slides for a description of how to incorporate this routine into your lessons.

2.11 Lesson 1: Entry Task

& LS 1 Day 1

Whole Class or Groups:

• Students describe and define data.
• Collect data from their class about their favorite fruit on Favorite Fruit Jamboard.
• Discuss how to organize the data to make it easier to notice things.

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Independent work: Seesaw Lesson 1 - Favorite Fruit

• Organize the data in a way that makes it easier to notice things about the class' favorite fruits.

There are different ways to organize data (information). Organization can obscure or make clear answers to questions about data. Data can be gathered and organized into a picture graph to help us understand the data.

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Whole Class or Groups: Look at student work or premade samples and discuss.

Core Math to Emphasize:

• There are different ways to organize data (information).
• Organization can obscure or make clear answers to questions about data.
• Data can be gathered and organized into a picture graph to help us understand the data.

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Math Norms

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Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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What is data?

Enoch: Bus

Angelly: Car

Helene: Car

Andrew: Walk

Milo: Bike

Chelsea: Car

Kei: Bus

Amaya: Walk

Vinh: Car

Yongjie: Bus

Data is a collection of information about our world.

We can collect data about our class.

Which one is your favorite fruit?

Favorite Fruit Jamboard

Here is data from another class:

What do you notice?

How could we organize the data to make it easier to notice things?

Here are some ways to organize the data:

What do you notice?

A picture graph is a way to organize data so we can easily find information:

What information can we find out from these graphs?

1 2 3 4 5 6 7

oranges

apples

pears

grapes

We can label our graph with a title, the categories, and a scale (numbers).

oranges

apples

pears

grapes

7

6

5

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Favorite Fruit

Favorite Fruit

2.11 Lesson 2: LS 1 Day 2

Whole Class or Groups: Math Talk

• Collect data from their class about pets they have or want and organize it on Pets Jamboard.
• Show data from another class, show how to make it a bar graph.

Independent work: Seesaw Lesson 2 - Pets

• Use the bar graph to answer each question about this class’s pets.

Picture graphs and bar graphs show categorical data. The graphs can be analyzed and used to answer questions about the data.

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Whole Class or Groups:

Look at student work or premade samples and discuss.

Core Math to Emphasize:

• Categorical data can be collected, recorded, and organized into picture graphs or bar graphs.
• The graphs can help answer questions about the data.
• Picture graphs and bar graphs can show the same information in different ways.

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Math Norms

28

Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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Math Talk

What do you notice? What do you wonder?

We can collect data about our class.

Which kind of pet do you have or want? (choose one)

Pets Jamboard

No Pet

Here is data from another class:

What do you notice?

We can change this picture graph into a bar graph:

What do you notice?

How are they alike? How are they different?

How many more students have or want a dog than a fish?

What does this remind you of?

How many more students have or want a dog than a fish?

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[--How many more--]

We can use tape diagrams to answer questions about comparing data on a graph.

How many students have or want a pet?

What does this remind you of?

How many students have or want a pet?

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We can use tape diagrams to answer questions about putting together data on a graph.

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[------------------How many altogether------------------]

2.11 Lesson 3: LS 1 Day 3

Whole Class or Groups: Math Talk

• Collect data from their class about favorite ice cream flavors and organize it on Ice Cream Flavors Jamboard.
• Show data from another class as a tally table.
• What do you notice? What questions could you ask that use comparing or putting together?

Independent work: Seesaw Lesson 3 - Favorite Ice Cream

• Create a picture graph and a bar graph using information from the tally chart about this class’ favorite ice cream flavors.
• Write a statement about about the data (I notice…) and a question about the data that can be answered by comparing or putting together.

Categorical data can be gathered using tally marks in a table. Tally tables, picture graphs, and bar graphs can show the same information in different ways.

Whole Class or Groups:

Look at student work or premade samples and discuss.

Core Math to Emphasize:

• Categorical data can be gathered using tally marks in a table.
• Tally tables, picture graphs, and bar graphs can show the same information in different ways.

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Math Norms

43

Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

​

SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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Math Talk

What do you notice? What do you wonder?

We can collect data about our class.

Which one is your favorite ice cream flavor?

Favorite Ice Cream Jamboard

Here is data from another class:

What do you notice?

What questions could you ask about comparing or putting together?

What was challenging about making the graphs?

How can you prove these statements using the graph?

6 people like chocolate ice cream best.

The fewest people like chocolate chip ice cream best.

More people like vanilla ice cream than strawberry.

How can you answer these questions using the graph?

How many fewer people like strawberry than vanilla?

How many students answered the question?

2.11 Lesson 4: Apprentice Task

Whole Class or Groups: Math Talk

• What do you remember about picture graphs and bar graphs?
• What do you remember about using a tally chart to make graphs?
• What do you remember about using a graph to ask and answer questions?
• Tell students that today they are going to look at data from another class and make a graph out of it.

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Independent work: Seesaw Lesson 4 - Apprentice Task Our Pets, Apprentice Task Our Pets .S. .C.

Read the directions for each task or problem. Use the tools to represent and solve the problems on each page.

Our Pets: Bar graphs can be used to represent categorical data and can help to answer questions about the data.

Whole Class or Groups: Our Pets Rubric Teacher

Bring the class together and discuss the graph and the questions. Compare the results from your class with the example in the Apprentice Task. How are they similar? How are they different?

Core Math to Emphasize:

• Tally tables can be used to gather and organize data.
• Information from tally tables can be used to make bar graphs.
• Both tally tables and bar graphs represent categorical data.
• Both tally tables and bar graphs can be used to answer questions about data.

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The Apprentice Task can be used as an assessment of categorical data.

Math Talk

What do you notice? What do you wonder?

What do you remember about picture graphs and bar graphs?

What do you remember about using a tally chart to make graphs?

What do you remember about using a graph to ask and answer questions?

How many more/fewer students… ?

I notice...

How many students… altogether?

Our Pets

Sam asked his classmates: “If you could only have one pet, what would it be?” He made a tally table to show the answers. Complete the table with the total of each animal.

Use the information in the tally table to fill in the bar graph.

Use the information in the graph to answer questions. Show how you know.

Pets Jamboard

How is the data about pets alike? How is it different?