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Clarifications
Clarification 1: Graphical representations are limited to histograms, bar charts, circle graphs, line plots, box plots and stem-and-leaf plots.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Bar Graph
- Box Plot
- Categorical
- Data Circle
- Graph
- Histogram
- Line Plot
- Stem-and-Leaf Plot
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 6, students created box plots and histograms to represent numerical data. In grade 7, students must choose and create an appropriate graphical representation for a given numerical or categorical data set. In grade 8, students will construct a scatter plot or a line graph for a given set of bivariate numerical data.- Students were introduced to bar charts (bar graphs) in grade 3, students may need to be reintroduced to this graphical representation.
- Graphical representations of categorical data sets are helpful for showing trends that can be analyzed and making comparisons of categories, among different items, or items over time periods. They visually show the mode of the data and, at a quick glance, show categories in a set of data that dominate others. Depending on the graphical representation chosen, either the frequency (number of items) or relative frequency (percentage) for each category can be illustrated.
- Histograms (for numerical data) and box plots (for categorical data) work well in grouping large sets of data to be easily compared, but do not allow viewers access to each individual data point if needed for other calculations such as the mean.
- Circle graphs are not ideal when too many categories are included as it is difficult to distinguish the difference in sizes of the sectors. Bar graph (or bar charts) make a similar comparison but the heights of the bars make the comparison more easily distinguishable.
- Stem-and-leaf plots and line plots are useful in displaying the shape of a numerical data set, easily identifying the mode and outliers, and they contain all of the values in the data set allowing for additional calculations such as the mean. They are not ideal when there is a large volume of data since it is time consuming to create and becomes difficult to read or interpret.
Common Misconceptions or Errors
- Students may not distinguish between histograms (numerical data) and bar charts, also called bar graphs (categorical data).
Strategies to Support Tiered Instruction
- Instruction includes displaying histograms and bar charts side by side and allow students to compare and contrast each one to help them understand the difference between the two, and what information we can learn from each one.
- Teacher provides a graphic organizer for each type of data display for students to reference in the future.
- Teacher co-creates examples of both bar graphs and histograms with students, explaining step-by-step how to create them and how/why they are different.
Instructional Tasks
Instructional Task 1 (MTR.2.1)The following data shows the grams of protein in 21 protein bars.
- Part A. Create two different graphical representations of the data using histograms, bar charts, circle graphs, line plots, box plots or stem-and-leaf plots.
- Part B. Compare and contrast the two displays and determine which is more appropriate. Explain your reasoning.
Instructional Items
Instructional Item 1Select an appropriate type of display for each of the following situations.
- the salaries of all 40 employees at a small company
- the salaries of all 250 people at a mid-sized company
- the distribution of colors in a bag of colored candies
- the number of siblings students in the 7th grade class have
*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
3D Modeling
Lesson Plans
Problem-Solving Task
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will analyze and compare data for various products sold in a joke shop to make recommendations on the best, and worst, products. Students will apply weighted averages, ratios, percentages, and proportions to perform calculations that support their recommendations as well as create graphical representations to help make sense of and compare the data.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Student Resources
Problem-Solving Task
The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Task
The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.
Type: Problem-Solving Task
