Geometry

10

^{th}grade Academic Content StandardsThese 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

*n*th root.____ 3. Use factorial notation and computations to represent and solve problem situations involving arrangements.

____ 4. Approximate the

*n*th root of a given number greater than zerobetween consecutive integers when

*n*is an integer; e.g., the 4th rootof 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

1

^{st}semester (19 indicators) :**Number, Number Sense and Operations Standards**

**Measurement Standards**

**Geometry and Spatial Sense Standards**

2

^{nd}semester (20 indicators) :**Data Analysis and Probability Standards**

**Patterns, Functions and Algebra Standards**