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Georgia Math Standards - 9th Grade
MathScore aligns to the Georgia Math Standards for 9th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Georgia Math Standards at other levels.
Algebra
MM1A1 Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.a. Represent functions using function notation.
b. Graph the basic functions f(x) = xn, where n = 1 to 3, f(x) = x , f(x) = |x|, and f(x) = 1/x. (Nonlinear Functions )
c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.
d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior. (Domain and Range , Quadratic X-Intercepts , Quadratic Zero Equations , Quadratic Formula )
e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.
f. Recognize sequences as functions with domains that are whole numbers.
g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.
h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.
i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).
MM1A2 Students will simplify and operate with radical expressions, polynomials, and rational expressions.
a. Simplify algebraic and numeric expressions involving square root. (Simplifying Algebraic Expressions 2 , Roots Of Exponential Expressions , Simplifying Radical Expressions )
b. Perform operations with square roots. (Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
c. Add, subtract, multiply, and divide polynomials. (Foil Method , Polynomial Fraction Simplification )
d. Expand binomials using the Binomial Theorem. (Foil Method )
e. Add, subtract, multiply, and divide rational expressions.
f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.
- (x + y)2 = x2 + 2xy + y2
- (x - y)2 = x2 - 2xy + y2
- (x + y)(x - y) = x2- y2
- (x + a)(x + b) = x2 + (a + b)x + ab
- (x + y)3 = x3 + 3 x2y + 3xy2 + y3
- (x - y)3 = x3 - 3x2y + 3xy2 – y3
MM1A3 Students will solve simple equations.
a. Solve quadratic equations in the form ax2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable. (Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
b. Solve equations involving radicals such as √x + b = c, using algebraic techniques.
c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x2 + bx + c = 0.
d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.
Geometry
MM1G1 Students will investigate properties of geometric figures in the coordinate plane.a. Determine the distance between two points.
b. Determine the distance between a point and a line.
c. Determine the midpoint of a segment.
d. Understand the distance formula as an application of the Pythagorean theorem.
e. Use the coordinate plane to investigate properties of and verify conjecture related to triangles and quadrilaterals.
MM1G2 Students will understand and use the language of mathematical argument and justification.
a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.
b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.
MM1G3 Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
a. Determine the sum of interior and exterior angles in a polygon. (Triangle Angles , Quadrilateral Angles , Triangle Angles 2 , Solving For Angles , Polygon Angles )
b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.
Data Analysis
MM1D1 Students will determine the number of outcomes related to a given event.a. Apply the addition and multiplication principles of counting.
MM1D2 Students will use the basic laws of probability.
a. Find the probabilities of mutually exclusive events. (Probability 2 )
b. Find the probabilities of dependent events. (Object Picking Probability )
c. Calculate conditional probabilities.
d. Use expected value to predict outcomes.
MM1D3 Students will relate samples to a population.
a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.
b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.
c. Understand that a random sample is used to improve the chance of selecting a representative sample.
MM1D4 Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).
Process Skills
MM1P1 Students will solve problems (using appropriate technology).a. Build new mathematical knowledge through problem solving. (Many topics align to this standard)
b. Solve problems that arise in mathematics and in other contexts. (Integer Word Problems )
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
MM1P2 Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjecture.
c. Develop and evaluate mathematical arguments and proofs.
MM1P3 Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
MM1P4 Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics. (Train Problems , Mixture Word Problems , Work Word Problems )
MM1P5 Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
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