| Knowledge of Algebra, Patterns, and Functions: Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships. |
| Patterns and Functions
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Identify, describe, extend, and create patterns, functions and sequences |
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Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph
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Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
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Determine whether relationships are linear or nonlinear when represented in words, in a table, symbolically, or in a graph
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| Expressions, Equations, and Inequalities
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Write, simplify, and evaluate expressions |
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Write an algebraic expression to represent unknown quantities
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Evaluate an algebraic expression
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Evaluate numeric expressions using the order of operations
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Simplify algebraic expressions by combining like terms
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Identify, write, solve, and apply equations and inequalities |
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Write equations or inequalities to represent relationships
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Solve for the unknown in a linear equation
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Solve for the unknown in an inequality
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Identify or graph solutions of inequalities on a number line
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Identify equivalent equations
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Apply given formulas to a problem-solving situation
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| Numeric and Graphic Representations of Relationships
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Locate points on a number line and in a coordinate plane |
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Graph linear equations in a coordinate plane
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Analyze linear relationships |
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Determine the slope of a graph in a linear relationship
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| Knowledge of Geometry: Students will apply the properties of one-, two-, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects. |
| Properties of Plane Geometric Figures
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Analyze the properties of plane geometric figures |
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Identify and describe geometric relationships between angles formed when parallel lines are cut by a transversal.
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Identify and describe the relationship among the parts of a right triangle
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Analyze geometric relationships |
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Determine the measurements of angles formed by parallel lines cut by a transversal
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Apply right angle concepts to solve real-world problems
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| Representation of Geometric Figures
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Represent plane geometric figures |
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Draw quadrilaterals
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Construct perpendicular line segments
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Construct triangles
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| Congruence and Similarity
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Apply the properties of similar polygons |
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Determine similar parts of polygons
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| Transformations
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Analyze a transformation on a coordinate plane |
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Identify, describe, and plot the results of multiple transformations on a coordinate plane
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| Knowledge of Measurement: Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements. |
| Applications in Measurement
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Estimate and apply measurement formulas |
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Estimate and determine the circumference or area of a circle
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Estimate and determine area of a composite figure
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Estimate and determine the volume of a cylinder
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Analyze measurement relationships |
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Use proportional reasoning to solve measurement problems
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| Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. |
| Sample Space
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Determine the number of outcomes
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| Theoretical Probability
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Determine the probability of an event comprised of no more than 2 independent events |
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Express the probability of an event as a fraction, a decimal, or a percent
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Determine the probability of a second event that is dependent on a first event of equally likely outcomes |
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Express the probability as a fraction, a decimal, or a percent
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| Experimental Probability
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Analyze the results of a survey or simulation |
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Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent
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| Knowledge of Number Relationships and Computation/Arithmetic: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. |
| Knowledge of Number and Place Value
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Apply knowledge of rational numbers and place value |
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Read, write, and represent rational numbers
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Compare, order, and describe rational numbers with and without relational symbols (<, >, =)
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| Number Computation
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Analyze number relations and compute |
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Add, subtract, multiply and divide integers
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Calculate powers of integers and square roots of perfect square whole numbers
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Identify and use the laws of exponents to simplify expressions
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Use properties of addition and multiplication to simplify expressions
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Estimate the square roots of whole numbers
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Analyze ratios, proportions, and percents |
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Determine unit rates
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Determine or use percents, rates of increase and decrease, discount, commission, sales tax, and simple interest in the context of a problem
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Solve problems using proportional reasoning
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