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# Standard #: MA.3.DP.1.1

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Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units.

### 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.

### General Information

Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Date Adopted or Revised: 08/20
Status: State Board Approved

### 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 $\frac{\text{1}}{\text{2}}$ 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.

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

 Course Number1111 Course Title222 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

 Access Point Number Access Point Title MA.3.DP.1.AP.1a Sort and represent categorical data (up to four categories) with whole-number values using tables, pictographs or bar graphs. Select appropriate title, labels and units. MA.3.DP.1.AP.1b Explore representing numerical data with whole-number values using line plots.

#### Formative Assessments

 Name Description Measuring our Pencils Line Plot Students make a line plot from a set of measurement data that includes measurements to the nearest whole inch. Measuring our Pencils – Part Two Students make a line plot from a set of measurement data that includes measurements to the nearest fourth of an inch. Measuring Hand Spans Line Plot Students make a line plot from a set of measurement data that includes measurements to the nearest whole centimeter. The Teacher’s Shoe - Part Two Students make a line plot displaying measurements found in Part One of this task. Lunch Orders Students are asked to create a scaled bar graph from a given set of data. Flowers in the Garden Students are asked to create a pictograph from a given set of data. Favorite After School Activity Students are asked to sort a set of data and create a scaled bar graph using their sorted data.

#### Lesson Plans

 Name Description 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. Your Vote Counts, Math in Civics I This lesson will introduce and give students practice, voting collecting data, and creating graphs. The lesson will help students to recognize how to organize data and that it is every citizen’s responsibility to vote. Students will see first-hand what happens when everyone does not get to vote. Math and Civics are integrated into this 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. Elementary School Food Drive- Analyzing Data Students will then analyze a set of data from a school food drive scenario and complete a bar graph. Students will also use the data to discuss what items are important to be included in a food drive and how food drives are driven by volunteers in this integrated lesson plan. This lesson is Part 1 of 3 math lesson integrating the importance of volunteering in a food drive. Voting and Volunteerism Students will participate as a voter in their classroom community in an election about which school service project they could do. They will represent and interpret their voting data in various types of graphs, such as scaled bar graphs and scaled pictographs. After interpreting the data, they will recognize that as a responsible citizen, it is their civic duty to participate in the election process to have a voice in the outcome. 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. 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. 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. Rampin' It Up Students will use their knowledge of properties of materials and measurement of length to determine how the properties of different surfaces affect the distance traveled by a toy car. X Marks the Spot! In this lesson, students will make multiple measurements and record the measurements on a line plot. 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. How Far Does It Roll? In this lesson, students will roll ping pong balls down a ramp and record whole-number measurements for the roll distance.  Students will represent this data by creating a line plot.

#### Original Student Tutorials

 Name Description 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. 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.

#### Perspectives Video: Teaching Idea

 Name Description Using Manipulatives to Create Stem and Leaf Plots Unlock an effective teaching strategy for teaching stem and leaf plots in this Teacher Perspectives video for educators.

 Name Description 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. 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. Classroom Supplies 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. 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.

#### Virtual Manipulative

 Name Description KidsZone: Create a Graph Create bar, line, pie, area, and xy graphs.

#### Original Student Tutorials

 Name Description 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. 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.