# MA.7.DP.1.4

Use proportional reasoning to construct, display and interpret data in circle graphs.

### Clarifications

Clarification 1: Data is limited to no more than 6 categories.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Circle Graph
• Data
• Proportional Relationships

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students worked with solving problems using ratio relationships. In grade 7, students apply their knowledge of ratios to solve problems involving proportions, including using proportional reasoning to construct, display and interpret categorical data in circle graphs. In high school, students will select an appropriate method to represent data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.
• Circle graphs can be used to show how categories represent part of a whole, or compositions. Totals are represented as percentages totaling 100%, which illustrates the percentage breakdown of items and visually represents a comparison. Circle graphs are not effective, however, when there are too many categories.
• Students should be able to identify strengths and limitations in showcasing data within a circle graph.

• Instruction begins with data sets out of 100 to allow for easier calculations of percentages.
• Students should brainstorm how they might split up their circle into the needed percentages (MTR.5.1).
• For example, students can slice a circle into 4 equal parts to show students the 4 right angles at the center which total 360°. Then emphasize using proportional relationships to determine the central angle sizes needed based on the percentage size of each “slice” of the circle.
• Students should collect their own data with which to create a circle graph (MTR.7.1).
• For example, have students count colored candy/snacks or survey other students in the room about their favorite color, favorite sport or favorite genre of music/movies.
• Use protractors or online software to assist in creating circle graphs accurately.

### Common Misconceptions or Errors

• Students may incorrectly use the percent of a category for the central angle degrees instead of finding the degrees by using a proportion.
• Students may incorrectly round or make other errors in calculations that will lead to the circle graph sections not totaling 100%.

### Strategies to Support Tiered Instruction

• Teacher models several examples to work through with students, showing how to set up the proportion to find the central angle degrees, referencing patterns for students to discuss.
• For example, if students need to determine the angle measure that corresponds to 21%, the proportion below can be used.
$\frac{\text{21}}{\text{100}}$ = $\frac{\text{x}}{\text{360}}$
• Teacher models and works through several problems while discussing aloud how to properly round when having to total to 100%, reinforcing to students to work through the problems carefully as to not make computation errors.
• Teacher models using computer-based software to create circle graphs to verify how to properly round.
• Teacher provides students with fill in the blank examples working from percent of a category using proportions to find the central angle degrees.
• Teacher provides several completed examples of problems where rounding was needed for students to reference while working through multiple problems together.
• For students incorrectly using a protractor, provide students with a circle and allow them to measure sections then find the percent.
• Teacher models using fraction circle manipulatives to support converting fractions to percentages.

A group of friends has been given \$800 to host a party. They must decide how much money will be spent on food, drinks, paper products, music and decorations.
• Part A. As a group, develop two options for the friends to choose from regarding how to spend their money. Decide how much to spend in each area and create a circle graph for each option to represent your choices.
• Part B. Mikel presented the circle graph below with his recommendations on how to spend the money. How much did he choose to spend on food and drinks? How much did he choose to spend on music?

### Instructional Items

Instructional Item 1
Circle Point High School surveyed its students to determine which mode of transportation they use to get to and from school. Create and label a circle graph based on the results given below.

*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.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.DP.1.AP.4: Use proportional reasoning to interpret data in a pie chart.

## Related Resources

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

## Lesson Plans

The Watergate Effect part 3:

Students will create a circle graph to display categorical data of the public presidential approval rates after the Supreme Court Case United States v. Nixon. Students will graph results independently and compare them to the circle graphs created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926) and the Watergate Effect Part 2 Lesson (Resource ID#: 210122) to discuss the trend of the data over the entirety of the Supreme Court case.

Type: Lesson Plan

The Watergate Effect part 2:

Students will create a circle graph to display categorical data of the public presidential approval rates during the Supreme Court Case United States v. Nixon. Students will graph results in pairs/groups and compare them to the circle graph created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926).

Type: Lesson Plan

Create a Circle Graph to Represent Percentages:

Students will compare each region's percentage of seats in the U.S. House of Representatives to other regions and the whole. Students will calculate central angle degrees and create a circle graph to represent the percentages. The civics standard will be the real-world example used to apply the concept of displaying data to the Legislative Branch of government in this integrated lesson plan.

Type: Lesson Plan

The Watergate Effect Part 1:

Students will create a circle graph to display categorical data of the public presidential approval rates of Richard Nixon before the Supreme Court Case United States v. Nixon. Students will calculate percentages and central angle degrees to graph results in pairs/groups and analyze the results in this integrated lesson plan.

Type: Lesson Plan

Use Circle Graphs to Analyze International Organizations:

Students will analyze international organizations using proportional reasoning to construct circle graphs while examining the purpose of international organizations and the United States’ participation in this integrated lesson plan.

Type: Lesson Plan

Graphing Data:

This is lesson 2 in a mini unit of 3 lessons. Students will analyze data collected from students, teachers, and principals to decide whether cell phone usage should be allowed in the classroom. They will be receiving data from fictional surveys of teachers and principals. Students will use the given data to choose and create an appropriate graphical representation.

Type: Lesson Plan

Introduction to Voting and Graphing Data:

The students will vote on whether cell phones should be allowed in the classroom or not. They will use this data to select the appropriate way of graphing the results. The teacher will give sample data from other teachers and principals for students to review. The correlation will be relating students to local voting in this integrated lesson plan.

Type: Lesson Plan

## Student Resources

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## Parent Resources

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