Ohio's Academic Content Standards in Mathematics

By the end of grade 10

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Number, Number Sense and Operations Standard
Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Indicators for grade 10 1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct as a hypotenuse or on a number line. (ORC Resources) 2. Explain the meaning of the nth root. (ORC Resources) 3. Use factorial notation and computations to represent and solve problem situations involving arrangements. (ORC Resources) 4. Approximate the nth root of a given number greater than zero between consecutive integers when n is an integer; e.g., the 4th root of 50 is between 2 and 3. (ORC Resources)

Measurement Standard
Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools, and technologies. Indicators for grade 10 1. Explain how a small error in measurement may lead to a large error in calculated results. (ORC Resources) 2. Calculate relative error. (ORC Resources) 3. Explain the difference between absolute error and relative error in measurement. (ORC Resources) 4. Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare "accurate to the nearest foot" when measuring the height of a person versus when measuring the height of a mountain. (ORC Resources) 5. Determine the measures of central and inscribed angles and their associated major and minor arcs. (ORC Resources)

Geometry and Spatial Sense Standard
Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems. Indicators for grade 10 1. Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter); and d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle). (ORC Resources) 2. Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane. (ORC Resources) 3. Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including: a. prove the Pythagorean Theorem; b. prove theorems involving triangle similarity and congruence; c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; and d. test a conjecture using basic constructions made with a compass and straightedge or technology. (ORC Resources) 4. Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. (ORC Resources) 5. Construct congruent or similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. (ORC Resources) 6. Identify the reflection and rotation symmetries of two- and three-dimensional figures. (ORC Resources) 7. Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software. (ORC Resources) 8. Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. (ORC Resources) 9. Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable. (ORC Resources) 10. Solve problems involving chords, radii, and arcs within the same circle. (ORC Resources)

Patterns, Functions and Algebra Standard
Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. Indicators for grade 10 1. Define function formally and with f(x) notation. (ORC Resources) 2. Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range. (ORC Resources) 3. Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height. (ORC Resources) 4. Use algebraic representations and functions to describe and generalize geometric properties and relationships. (ORC Resources) 5. Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions. (ORC Resources) 6. Solve equations and inequalities having rational expressions as coefficients and solutions. (ORC Resources) 7. Solve systems of linear inequalities. (ORC Resources) 8. Graph the quadratic relationship that defines circles. (ORC Resources) 9. Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. (ORC Resources) 10. Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. (ORC Resources) 11. Solve real-world problems that can be modeled, using systems of linear equations and inequalities. (ORC Resources) 12. Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis. (ORC Resources)

Data Analysis and Probability Standard
Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. Indicators for grade 10 1. Describe measures of center and the range verbally, graphically and algebraically. (ORC Resources) 2. Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology. (ORC Resources) 3. Display bivariate data where at least one variable is categorical. (ORC Resources) 4. Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot. (ORC Resources) 5. Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present. (ORC Resources) 6. Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread. (ORC Resources) 7. Model problems dealing with uncertainty with area models (geometric probability). (ORC Resources) 8. Differentiate and explain the relationships between the probability of an event and the odds of an event, and compute one given the other. (ORC Resources)