MA.3.DP.1.2

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Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems.

Clarifications

Clarification 1: Problems include the use of data in informal comparisons between two data sets in the same units.

 Clarification 2: Data displays can be represented both horizontally and vertically.

Clarification 3: Circle graphs are limited to showing the total values in each category.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Data Analysis and Probability
Standard: Collect, represent and interpret numerical and categorical data.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Bar Graph 
  • Categorical Data 
  • Circle Graph 
  • Whole Number

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to interpret data displayed in scaled pictographs, circle graphs, scaled bar graphs and line plots. Like MA.3.DP.1.1, the purpose of this benchmark builds on data interpretation skills from Grades 1 and 2. In Grade 1, students interpreted data represented with tally marks and pictographs, and in Grade 2, students also interpreted data represented in pictographs and bar graphs. Additionally, students solved addition and subtraction problems using the data representations. 
  • In Grade 3, students will interpret categorical data represented in scaled pictographs and bar graphs, whole-number numerical data represented in line plots, and whole-number category totals in circle graphs (e.g., instead of percentages). To interpret the represented data, they will solve one- and two-step problems from a given data set or compare two data sets in the same units (MTR.5.1). 
  • Instruction should include opportunities for students to interpret their own numerical and categorical data (MTR.7.1). 
  • Students could use addition, subtraction, multiplication or division to solve the problems. This benchmark should be taught with MA.3.DP.1.1 (collecting and representing data) (MTR.2.1, MTR.4.1, MTR.5.1).

 

Common Misconceptions or Errors

  • Students may confuse the values in scaled pictographs and bar graphs. They should always utilize the given key when determining frequency of each category.

 

Strategies to Support Tiered Instruction

  • Instruction includes opportunities to determine the values in a scaled pictograph, pointing out the importance of paying close attention to the key of the pictograph. The key outlines how much each of the pictures on the graph will represent. Students connect multiplication strategies to this concept. Instruction includes opportunities to practice counting by 2s, 5s, and 10s, to be successful with this benchmark. To help students see the connection between the key and what each picture represents, a bar diagram may be helpful. 
    • Instruction includes opportunities to determine the values in a scaled pictograph, pointing out the importance of paying close attention to the key of the pictograph. The key outlines how much each of the pictures on the graph will represent. Students connect multiplication strategies to this concept. Instruction includes opportunities to practice counting by 2s, 5s, and 10s, to be successful with this benchmark. To help students see the connection between the key and what each picture represents, a bar diagram may be helpful. 

    • For example, students use the key for the pictograph and a bar model to determine the number of sunny days in August.

pictograph and a bar model to determine the number of sunny days in August.

 

Instructional Tasks

Instructional Task 1 

The pictographs show favorite subjects in third and fourth grades at Palm Elementary School. 

pictographs show favorite subjects in third and fourth grades

  • Part A. Write an equation that shows how many fourth graders chose reading as their favorite subject. 
  • Part B. How many third graders chose social studies as their favorite subject? 
  • Part C. How many more students prefer math in third grade than fourth grade?

 

Instructional Items

Instructional Item 1 

John surveys his classmates about their favorite foods, as shown in the bar graph. How many more classmates chose pizza as their favorite food than classmates who chose salad? 

bar graph

Instructional Item 2 

Molly surveys her class about their favorite ice cream flavors, as shown in the circle graph. How many students picked a favorite ice cream flavor other than vanilla? 

pie chart

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.DP.1.AP.2a: Interpret data with whole-number values represented with tables, pictographs or bar graphs to solve one-step “how many more” and “how many less” problems.
MA.3.DP.1.AP.2b: Interpret data with whole-number values represented with scaled pictographs or scaled bar graphs. For scaled pictographs, symbols used may only represent quantities of 2, 5 or 10 and only whole symbols may be used. For scaled bar graphs, intervals may only represent quantities of 2, 5 or 10.
MA.3.DP.1.AP.2c: Explore interpreting data with whole-number values represented with line plots.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessment

Collecting Cans for Recycling:

Students answer questions about a scaled bar graph.

Type: Formative Assessment

Lesson Plans

U.S. Symbols Construction:

Students will interpret and make comparisons of construction start and end dates and heights of U.S. symbols. Students will solve one- and two-step word problems based on the data. 

Type: Lesson Plan

Graph the Election 2:

Students will conduct an election and learn about the structure and functions of the government. With election data, students will represent data and graph the data. Math and Civics are in this integrated lesson plan.

Type: Lesson Plan

Fractions and Civics 3:

Students will conduct surveys, tally results, and represent the data on graphs. In this lesson, students will also represent data in fractions, equivalent fractions and learn how citizens demonstrate civility, cooperation, volunteerism and other civic virtues. Math and Civics are integrated in this lesson plan.

Type: Lesson Plan

How Many Years?:

Students will discuss what they know about individuals who represent the U.S. or Florida and interpret data including important dates in the lives of these individuals. Students will use the data to solve one and two-step word problems in this integrated lesson.  

Type: Lesson Plan

U.S. Images Data Sort:

Students will determine ways to categorize images of symbols, individuals and documents that represent the United States to create a table of their data. Using the table students will create a scaled pictograph in this integrated lesson plan.

Type: Lesson Plan

Help, Collect, Plot!:

In this lesson plan, students will collect numerical data on a school-based food drive and represent and interpret the the data using line plots.  The students will demonstrate volunteerism by donating to the community. 

 

Type: Lesson Plan

I Vote, You Vote, We Vote:

In this lesson, students will analyze voting data and perform mathematical procedures to determine the answer to specific questions. Students will compare the population of the community vs. the number of votes counted. Students will discuss the contribution each citizen is making when voting and the effects on the results when citizens do not vote.

Type: Lesson Plan

Going to the Dogs?:

In this integrated lesson plan, students will use their knowledge of collecting and interpreting data as they participate in a hypothetical election based on the controversy of whether or not their community should have a leash law. Students will be given background knowledge of the differences between state and local governments, and how laws are enacted, in particular, “leash laws” for dogs. The students will vote, tally the results, and use a frequency table to create a bar graph determining the range, title, and labels. Students will then interpret the election results while answering one- and two-step problems based on their bar graphs while demonstrating their knowledge of different levels of government and the importance of voting in local elections.

 

Type: Lesson Plan

Food Drive:

A data table is given listing class donations to a food drive. Students interpret the data and answer questions using addition and subtraction. Students discuss the importance of, volunteerism and ways that they can help their community.

Type: Lesson Plan

Raising the Bar:

Students will create and interpret bar graphs using tally mark data from a table. Students will also discuss and understand the implications of our civic duty to vote, and how this affects data for polls and decision-making, in this integrated lesson plan.

Type: Lesson Plan

Florida Fish Aquarium Challenge:

This task involves having students look at three different fish tank sizes and determine, using a data list, which fish will fit in these fish tanks based on their size. They will also need to look at other characteristics to determine how to group the fish together. Students will have to either multiply, divide or add repeatedly in order to find different solutions on how to place the fish in each tank size.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

X Marks the Spot!:

In this lesson, students will make multiple measurements and record the measurements on a line plot.

Type: Lesson Plan

This Is My Country:

Students will collect and represent categorical data (countries or states/districts of birth of third graders) on a scaled bar graph using an appropriate title, labels, and units. They will interpret and discuss the data by writing and solving one-step problems. It is suggested the students later use this same data to create a scaled pictograph and then compare the two representations.

Type: Lesson Plan

Animal Habitat MEA:

Animal Habitat MEA is where the students will help a pet store choose which habitat they should buy to house their snake and lizard families. The students will solve an open-ended problem and give details on the process that they used to solve the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Picking Pets:

Using information about the needs of different animals, students will help choose which pet would be best to purchase for a classroom.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Cars for Sale MEA:

Students will compare multi-digit numbers to create a procedure for choosing the best car for Edward Easy to buy for his driving school. They will have to weigh quantitative and qualitative factors to determine the best car to purchase. Students will present their recommendations and the steps to the procedure they created in writing and orally.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Original Student Tutorials

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Type: Original Student Tutorial

Bar Graph Jones and the Pyramid of Pi:

Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Making Connections Between Partitioning Circles and Circle Graphs:

Unlock an effective teaching strategy for connecting partitioning circles and circle graphs in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Growing Bean Plants:

This task adds some rigor to the activity, by collecting actual growth data, providing practice for students in measuring and recording length measurements. Centimeters are an appropriate unit for these measurements, as they provide a good level of precision for these measurements, while being easy enough for students to handle.

Type: Problem-Solving Task

The Longest Walk:

After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.

Type: Problem-Solving Task

Hand Span Measures:

The size of the hand makes a difference in some sports that involve throwing or catching and some activities such as playing the piano. Hand span is a measure that has been used for many years. By placing the hand on the edge of a piece of paper and marking the tips of the thumb and little finger, the student can measure a straight line. This is a better method than placing the hand directly on the ruler. Discuss rounding conventions. This could be used as a class activity, or students could gather and plot data on separate line plots from different age groups.

Type: Problem-Solving Task

STEM Lessons - Model Eliciting Activity

Animal Habitat MEA:

Animal Habitat MEA is where the students will help a pet store choose which habitat they should buy to house their snake and lizard families. The students will solve an open-ended problem and give details on the process that they used to solve the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Cars for Sale MEA:

Students will compare multi-digit numbers to create a procedure for choosing the best car for Edward Easy to buy for his driving school. They will have to weigh quantitative and qualitative factors to determine the best car to purchase. Students will present their recommendations and the steps to the procedure they created in writing and orally.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Florida Fish Aquarium Challenge:

This task involves having students look at three different fish tank sizes and determine, using a data list, which fish will fit in these fish tanks based on their size. They will also need to look at other characteristics to determine how to group the fish together. Students will have to either multiply, divide or add repeatedly in order to find different solutions on how to place the fish in each tank size.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Picking Pets:

Using information about the needs of different animals, students will help choose which pet would be best to purchase for a classroom.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

MFAS Formative Assessments

Collecting Cans for Recycling:

Students answer questions about a scaled bar graph.

Original Student Tutorials Mathematics - Grades K-5

Bar Graph Jones and the Pyramid of Pi:

Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.

STEM Civics Tutorials and Videos - Grades K-12

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Type: Original Student Tutorial

Bar Graph Jones and the Pyramid of Pi:

Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.

Type: Original Student Tutorial

Problem-Solving Task

The Longest Walk:

After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Growing Bean Plants:

This task adds some rigor to the activity, by collecting actual growth data, providing practice for students in measuring and recording length measurements. Centimeters are an appropriate unit for these measurements, as they provide a good level of precision for these measurements, while being easy enough for students to handle.

Type: Problem-Solving Task

The Longest Walk:

After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.

Type: Problem-Solving Task

Hand Span Measures:

The size of the hand makes a difference in some sports that involve throwing or catching and some activities such as playing the piano. Hand span is a measure that has been used for many years. By placing the hand on the edge of a piece of paper and marking the tips of the thumb and little finger, the student can measure a straight line. This is a better method than placing the hand directly on the ruler. Discuss rounding conventions. This could be used as a class activity, or students could gather and plot data on separate line plots from different age groups.

Type: Problem-Solving Task