Academic Content Standards

Geometry
10th grade Academic Content Standards

These are what we will be studying this year

Number, Number Sense and Operations Standard

____ 1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct 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 is an integer; e.g., the 4th root
of 50 is between 2 and 3.

Measurement Standard

____ 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 Standard

____ 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).

____ 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.

____ 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 Standard

____ 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 Standard
____ 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.


Ideally we will do
1st semester  (19 indicators) :
Number, Number Sense and Operations Standards
Measurement Standards
Geometry and Spatial Sense Standards

2nd semester (20 indicators) :
Data Analysis and Probability Standards
Patterns, Functions and Algebra Standards