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AI.1. Number Sense and Algebraic Operations - The student will use expressions and equations to model number relationships. AI.1.1. Equations and Formulas AI.1.1.a. Translate word phrases and sentences into expressions and equations and vice versa.
AI.1.1.b. Solve literal equations involving several variables for one variable in terms of the others.
AI.1.1.c. Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.
AI.1.1.d. Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent.
AI.1.2. Expressions AI.1.2.b. Simplify polynomials by adding, subtracting or multiplying.
AI.2. Relations and Functions - The student will use relations and functions to model number relationships. AI.2.1. Relations and Functions AI.2.1.b. Distinguish between relations and functions. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AI.2.2. Linear Equations and Graphs AI.2.2.a. Solve linear equations by graphing or using properties of equality.
AI.2.2.c. Slope AI.2.2.c.I. Calculate the slope of a line using a graph, an equation, two points or a set of data points.
AI.2.2.c.II. Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.
AI.2.2.d. Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points.
AI.2.2.e. Match equations to a graph, table, or situation and vice versa.
AI.2.3. Linear Inequalities and Graphs AI.2.3.a. Solve linear inequalities by graphing or using properties of inequalities.
AI.2.3.b. Match inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.
AI.2.4. Solve a system of linear equations by graphing, substitution or elimination.
AI.3. Data Analysis, Probability and Statistics - The student will use data analysis, probability and statistics to formulate and justify predictions from a set of data. AI.3.1. Data Analysis AI.3.1.b. Make valid inferences, predictions, and/or arguments based on data from graphs, tables, and charts.
AI.3.1.c. Solve two-step and three-step problems using concepts such as probability and measures of central tendency.
AI.3.2. Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data.
AII.2. Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. AII.2.2. Systems of Equations AII.2.2.b. Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.
AII.3. Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data. AII.3.1. Analysis of Collected Data Involving Two Variables AII.3.1.a. Interpret data on a scatter plot using a linear, exponential, or quadratic model/equation.
AII.3.2. Measures of Central Tendency and Variability AII.3.2.a. Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average).
AII.3.2.b. Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation).
AII.3.3. Identify and use arithmetic and geometric sequences and series to solve problems. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
G.2. Properties of 2-Dimensional Figures - The student will use the properties and formulas of geometric figures to solve problems. G.2.2. Line and Angle Relationships G.2.2.a. Use the angle relationships formed by parallel lines cut by a transversal to solve problems.
G.2.2.b. Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs.
G.2.2.c. Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.
G.2.3. Polygons and Other Plane Figures G.2.3.a. Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).
G.2.3.d. Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each.
G.2.4. Similarity G.2.4.a. Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs.
G.2.4.b. Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.
G.2.5. Congruence G.2.5.b. Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.
G.4. Properties of 3-Dimensional Figures - The student will use the properties and formulas of geometric figures to solve problems. G.4.1. Polyhedra and Other Solids G.4.1.a. Identify, describe, and analyze polyhedra (for example, regular, decahedral).
G.4.2. Similarity: Use ratios of similar 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.
G.5. Coordinate Geometry - The student will solve problems with geometric figures in the coordinate plane. G.5.1. Find the distance between two points; the midpoint of a segment; and calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.
PS1.1. Apply a wide variety of problem-solving strategies (identify a pattern, use equivalent representations) to solve problems from within and outside mathematics.
PS1.2. Identify the problem from a described situation, determine the necessary data and apply appropriate problem-solving strategies.
PS2.3. Analyze mathematical definitions and discover generalizations through investigations. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
PS3.1. Use various types of logical reasoning in mathematical contexts and real-world situations.
PS3.2. Prepare and evaluate suppositions and arguments.
PS3.3. Verify conclusions, identify counterexamples, test conjectures, and justify solutions to mathematical problems.
PS3.4. Justify mathematical statements through proofs.
PS4.1. Link mathematical ideas to the real world (e.g., statistics helps qualify the confidence we can have when drawing conclusions based on a sample).
PS4.3. Use mathematics to solve problems encountered in daily life.