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Clarifications
Clarification 1: Within this benchmark, the expectation is to complete a representation or construct a representation from a data set.Clarification 2: Instruction includes the connection between multiplication and the number of data points represented by a bar in scaled bar graph or a scaled column in a pictograph.
Clarification 3: Data displays are represented both horizontally and vertically.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Bar Graph
- Categorical Data
- Whole Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to represent numerical and categorical data using tables, scaled pictographs, scaled bar graphs, or line plots, using appropriate titles, tables, and units. Though there are many skills included in this benchmark, students bring background knowledge from Grades 1 and 2 when they collected, categorized and represented data in tables, pictographs, and bar graphs. In Grade 2, students were expected to represent data with appropriate titles, labels and units.- Before instruction begins, teachers should provide students with opportunities of reading and solving problems using scaled graphs before being asked to draw one. These skills will assist students with determining what they already know. This will save instructional time that can be focused on the Grade 3 extensions explained in the next paragraph (MTR.3.1).
- Instruction should include opportunities for students to collect and display their own numerical and categorical data (MTR.7.1).
- In Grade 3, two extensions of previous understandings about collecting and representing data occur. First, categorical data represented in pictographs and bar graphs are scaled. Students use their understanding of multiplication to read the data representations appropriately. Second, students represent numerical data in line plots, which shows the frequency of data on a number line (MTR.2.1).
- During instruction, it is important to remind students that scales on graphs should begin with 0.
- Because the expectation is to represent data with whole-number values, number lines do not need to be partitioned into fractional parts. Students will represent fractional values beginning in Grade 4.
- During instruction, it is important that students have the opportunity to display data horizontally and vertically. Their work with GR.1.1 will be beneficial in making graphs that are accurate representations.
Common Misconceptions or Errors
- Students may confuse which types of data (categorical or numerical) can be displayed with a data representation. In Grades 1 and 2, students graphed frequency of categorical data in pictographs and bar graphs. Representing frequency in numerical data graphed via line plots is a new expectation in Grade 3. During instruction, expect students to justify the representations they choose based on the data collected.
- Students tend to count each square as one for intervals on bar graphs that are not single units.
Strategies to Support Tiered Instruction
- Instruction includes how to decide which way to display data (numerical vs. categorical). The teacher provides examples of when to use pictographs and bar graphs, and when to use line plots. o For example, students measure the lengths of pencils to the nearest inch. Because the students are finding a numerical measurement, this data would be graphed on a line plot.
- Instruction includes how to decide which way to display their data (numerical vs.
categorical). The teacher provides examples of when to use pictographs and bar graphs, and when to use a line plot. Also, the teacher provides instruction regarding how numerical data refers to data that is in the form of numbers and categorical data is a type of data that is divided into groups.
- For example, categorical data could be favorite colors, types of pets at home, or hair color. Types of numerical data could be ages of students, numbers of siblings at home, or the results of the measurement of objects.
- Instruction includes opportunities to count the correct intervals on a scaled bar graph. The teacher provides instruction for identifying the scale and showing students how to read the bars according to the scale.
Instructional Tasks
Instructional Task 1
The data below shows the ages of students in an art class and their favorite colors.
- Part A. Represent the ages of the students in the art class using a line plot.
- Part B. Represent the favorite colors of the students in an art class using a scaled pictograph.
Instructional Items
Instructional Item 1
Rebecca surveyed the ages of kids visiting a movie theater and displayed the data using a line plot. The customers’ ages are below. Which line plot correctly displays the data that Rebecca collected?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Virtual Manipulative
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will compare different nutritional content of chicken nuggets from many restaurants presented in bar graphs. They will factor in the calories, total fat, and sodium information about the nuggets to create a procedure for ranking the nuggets from healthiest to least healthy.
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
In this Model Eliciting Activity, MEA, students will determine what two snacks should be placed in the school vending machines because the district is asking for healthier and tastier snacks. Factors to consider are calories, fat, protein, sugar, student comments, and cost.
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
Students are asked to sort a set of data and create a scaled bar graph using their sorted data.
Students make a line plot from a set of measurement data that includes measurements to the nearest whole centimeter.
Students make a line plot from a set of measurement data that includes measurements to the nearest fourth of an inch.
Students make a line plot from a set of measurement data that includes measurements to the nearest whole inch.
Students make a line plot displaying measurements found in Part One of this task.
STEM Civics Tutorials and Videos - Grades K-12
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.
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
Original Student Tutorials
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
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
In this video Sam-1 introduces a Model Eliciting Activity (MEA) challenge. Students will take their prior experiences from the properties unit and apply their knowledge of investigating sea turtle nesting temperatures.
Students will develop a hypothesis, design an experiment, and support their reasoning to determine how to best study different methods for cooling sea turtle nesting areas.
Type: Original Student Tutorial
In this video, students will make observations based on the property of size, specifically length. Students will learn about the metric and customary measurement systems and use line plots to organize and sort data.
Type: Original Student Tutorial
Problem-Solving Tasks
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
The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
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
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
The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.
Type: Problem-Solving Task
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
