February 1st - Episode 18 of the
Ohio Treasure Chest Podcast
is now online.
Click here to access it now!
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February 1st - Episode 18 of the
Ohio Treasure Chest Podcast |
Home -
Math -
Grade 10
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Below are the indicators for
Grade 10. Click on the numbers in the left-hand column
to access resources in the following categories:
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| Number, Number Sense and Operations | |||||
| 1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct square root of 2 as a hypotenuse or on a number line. | |||||
| 2. Explain the meaning of the nth root. | |||||
| 3. Use factorial notation and computations to represent and solve problem situations involving arrangements. | |||||
| 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. | |||||
| Measurement | |||||
| 1. Explain how a small error in measurement may lead to a large error in calculated results. | |||||
| 2. Calculate relative error. | |||||
| 3. Explain the difference between absolute error and relative error in measurement. | |||||
| 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. | |||||
| 5. Determine the measures of central and inscribed angles and their associated major and minor arcs. | |||||
| Geometry and Spatial Sense | |||||
| 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, circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle). |
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| 2. Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane. | |||||
| 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; d. test a conjecture using basic constructions made with a compass and straightedge or technology. |
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| 4. Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. | |||||
| 5. Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. | |||||
| 6. Identify the reflection and rotation symmetries of two- and three-dimensional figures. | |||||
| 7. Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software. | |||||
| 8. Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. | |||||
| 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. | |||||
| 10. Solve problems involving chords, radii and arcs within the same circle. | |||||
| Patterns, Functions and Algebra | |||||
| 1. Define function formally and with f(x) notation. | |||||
| 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. | |||||
| 3. Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height. | |||||
| 4. Use algebraic representations and functions to describe and generalize geometric properties and relationships. | |||||
| 5. Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions. | |||||
| 6. Solve equations and inequalities having rational expressions as coefficients and solutions. | |||||
| 7. Solve systems of linear inequalities. | |||||
| 8. Graph the quadratic relationship that defines circles. | |||||
| 9. Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. | |||||
| 10. Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. | |||||
| 11. Solve real-world problems that can be modeled, using systems of linear equations and inequalities. | |||||
| 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. | |||||
| Data Analysis and Probability | |||||
| 1. Describe measures of center and the range verbally, graphically and algebraically. | |||||
| 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. | |||||
| 3. Display bivariate data where at least one variable is categorical. | |||||
| 4. Identify outliers on a data display; e.g., use interquartile range to identify outliers on a box-and-whisker plot. | |||||
| 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. | |||||
| 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. | |||||
| 7. Model problems dealing with uncertainty with area models (geometric probability). | |||||
| 8. Differentiate and explain the relationship between the probability of an event and the odds of an event, and compute one given the other. | |||||