Ohio Resource Center
Assessments
NAEP Assessment Item, Grade 8: Estimate Using a Circle Graph
Discipline
Mathematics
5, 6, 7, 8
Professional Commentary

Students are asked to estimate the number of radios represented by a 37° sector of a circle. They have the option of using a calculator. This multiple-choice question is a sample test item used in grades 8 and 12 in the 1992 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 1992-8M12, No. 4. (sw)

Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (5–7)
D.
Use models and pictures to relate concepts of ratio, proportion and percent.
I.
Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.
1.
Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
13.
Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
5.
Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
13.
Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 = 2 and 4.23 x 5.8 25.
14.
Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
7.
Solve problems using the appropriate form of a rational number (fraction, decimal or percent).
Geometry and Spatial Sense Standard
Benchmarks (5–7)
E.
Use proportions to express relationships among corresponding parts of similar figures.
1.
Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.
Data Analysis and Probability Standard
Benchmarks (5–7)
A.
Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.
Benchmarks (8–10)
A.
Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
1.
Read, construct and interpret frequency tables, circle graphs and line graphs.
1.
Read, construct and interpret line graphs, circle graphs and histograms.
2.
Select, create and use graphical representations that are appropriate for the type of data collected.
1.
Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.
1.
Use, create and interpret scatterplots and other types of graphs as appropriate.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (6–8)
understand and use ratios and proportions to represent quantitative relationships;
Compute fluently and make reasonable estimates
Expectations (3–5)
develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
Expectations (6–8)
understand and use ratios and proportions to represent quantitative relationships;
develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results;
develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (6–8)
understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (3–5)
use geometric models to solve problems in other areas of mathematics, such as number and measurement;
Expectations (6–8)
understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
Data Analysis and Probability Standard
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Expectations (6–8)
select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.