Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Bar Graph
- Categorical Data
- Whole Number
Purpose and Instructional StrategiesThe 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 Task 1The 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 Item 1Rebecca 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.