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Arkansas Standards - Grade 8 Math
The state of Arkansas has prescribed that students of Grade 8 Math master certain topics. The topics are listed below. Each of these topics/strands are covered in TenMarks, helping students refresh their knowledge, as well as learn as they practice - resulting in mastery.
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Standard MA.1.TDM: Students will use matrices to analyze data to solve real-world problems.
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MA.1.TDM.1 Collect and interpret data in a matrix and perform operations to solve real-world problems, with and without technology
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MA.1.TDM.2 Solve real-world problems involving systems of linear equations using matrices (e.g., inverses, augmented, Cramer??s rule)
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MA.1.TDM.3 Find and use the inverse of a matrix to solve real-world problems (e.g., cryptology)
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MA.1.TDM.4 Organize and use transition matrices to solve probability problems that link present events to future events, with or without technology (e.g., consumer trends, polling trends, board games, weather trends)
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Standard OP.2.TDM: Students will use various techniques to solve optimization problems.
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OP.2.TDM.1 Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible region
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OP.2.TDM.2 Model and solve real-world problems using linear programming (e.g., maximum profit/minimal cost, investments, agriculture, manufacturing, banking)
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OP.2.TDM.3 Interpret the meaning of the minimum or maximum value in terms of the objective function
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OP.2.TDM.4 Model and solve real-world problems involving optimization of area and volume
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Standard ME.3.TDM: Students will apply various measurement techniques to solve real-world problems.
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ME.3.TDM.1 Solve problems using dimensional analysis (factor-label method) (e.g., construction, medical, metric, standard to metric, rate conversions)
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ME.3.TDM.2 Use sine, cosine, and tangent ratios to determine lengths of sides and angle measures of right triangles for real-world problems (e.g., angles of elevation and depression and various distances)
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ME.3.TDM.3 Use laws of sine and cosine to determine lengths of sides, measures of angles, and area of triangles for realworld problems (e.g., Heron??s formula)
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ME.3.TDM.4 Calculate the area of two-dimensional composite figures
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ME.3.TDM.5 Calculate the surface area and volume of three-dimensional composite figures
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Standard EF.4.TDM: Students will extend algebraic skills to solve real-world problems involving exponential/logarithmic functions.
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EF.4.TDM.1 Draw and recognize the graphs of logarithmic and exponential functions, with and without appropriate technology
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EF.4.TDM.2 Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equations
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EF.4.TDM.3 Use the change of base formula to simplify and evaluate logarithmic expressions, using technology
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EF.4.TDM.4 Recognize and apply properties of exponential functions to solve real-world problems (e.g., compound interest, amortization, annuities, appreciation, depreciation)
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EF.4.TDM.5 Recognize and apply properties of logarithmic functions to solve real-world problems (e.g., Richter scale pH, decibel scale, bacterial growth, radioactive decay, Newton??s Law of Cooling)
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Standard DA.5.TDM: Students will analyze data using various statistical tools.
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DA.5.TDM.1 Read, interpret, and analyze graphical representations of data used in various contexts (e.g., science reasoning, newspaper graphs)
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DA.5.TDM.2 Identify biases that affect the validity of a data set
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DA.5.TDM.3 Collect, analyze, and compare data sets using five-number summary
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DA.5.TDM.4 Investigate and analyze the characteristics of normal and skewed distributions
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DA.5.TDM.5 Determine and interpret the measures of spread of a data set (e.g., standard deviation, range, percentiles, variance)
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Standard LSM.1.TFM: Students will examine linear systems and matrices and their applications.
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LSM.1.TFM.1 Use matrices (e.g., row-echelon form, Gauss-Jordan method, inverses) to solve systems of linear equations, with or without technology
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LSM.1.TFM.2 Find and use the inverse of a matrix to solve real-world problems (e.g., cryptology)
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LSM.1.TFM.3 Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible region
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LSM.1.TFM.4 Model and solve real-world problems using linear programming (e.g., maximum profit/minimal cost, investments, agriculture, manufacturing, banking)
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LSM.1.TFM.5 Interpret the meaning of the minimum or maximum value in terms of the objective function
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Standard ST.2.TFM: Students will operate with sets and use set theory to solve problems.
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ST.2.TFM.1 Define sets using set-builder notation
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ST.2.TFM.2 Use correct terminology to describe relationships between sets in various contexts
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ST.2.TFM.3 Perform set operations such as union and intersection, complement, and Cartesian product
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ST.2.TFM.4 Use Venn diagrams to explore relationships and patterns and to make arguments about relationships between sets, including real-world situations
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ST.2.TFM.5 Use a truth table to draw conclusions about a statement
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ST.2.TFM.6 Judge the validity of arguments and give counterexamples to disprove statements
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Standard CT.3.TFM: Students will use combinatorial reasoning to find numbers of outcomes and related probabilities.
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CT.3.TFM.1 Use fundamental counting principles of addition and multiplication to solve problems
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CT.3.TFM.2 Evaluate expressions indicating permutations or combinations, with and without technology
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CT.3.TFM.3 Evaluate expressions involving distinguishable permutations
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CT.3.TFM.4 Distinguish between and use permutations and combinations to solve problems
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CT.3.TFM.5 Calculate probabilities of mutually exclusive events, independent events, and dependent events
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CT.3.TFM.6 Construct and examine Pascal??s triangle
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CT.3.TFM.7 Develop and use the binomial theorem
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CT.3.TFM.8 Use combinations to find a specified term in a binomial expansion
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Standard S.4.TFM: Students will compute and analyze data using various statistical tools, with appropriate technology.
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S.4.TFM.1 Collect data using random sampling
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S.4.TFM.2 Calculate and interpret statistical problems using measures of central tendencies and graphs
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S.4.TFM.3 Analyze and compare data sets using five-number summary, graphically and numerically
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S.4.TFM.4 Investigate and analyze the characteristics of normal and skewed distributions
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S.4.TFM.5 Determine and interpret measures of variation of a data set, with or without technology
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Standard F.5.TFM: Students will solve real-world problems involving financial decision making.
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F.5.TFM.1 Read and interpret graphs related to finance
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F.5.TFM.2 Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equations
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F.5.TFM.3 Solve real-world problems involving
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F.5.TFM.3.a compound interest
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Content Standard 1: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.
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LA.1.AI.1 Evaluate algebraic expressions, including radicals, by applying the order of operations
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LA.1.AI.2 Translate word phrases and sentences into expressions, equations, and inequalities, and vice versa
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LA.1.AI.3 Apply the laws of (integral) exponents and roots.
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LA.1.AI.4 Solve problems involving scientific notation, including multiplication and division.
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LA.1.AI.5 Perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives
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LA.1.AI.6 Simplify algebraic fractions by factoring
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LA.1.AI.7 Recognize when an expression is undefined
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LA.1.AI.8 Simplify radical expressions such as 3/(square root of 7)
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LA.1.AI.9 Add, subtract, and multiply simple radical expressions like 3(square root of 20) + 7(square root of 5) and 4(square root of 5) * 2(square root of 3)
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Content Standard 2: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities and systems of equations and solve with fluency.
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SEI.2.AI.1 Solve multi-step equations and inequalities with rational coefficients
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SEI.2.AI.2 Solve systems of two linear equations
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SEI.2.AI.3 Solve linear formulas and literal equations for a specified variable
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SEI.2.AI.4 Solve and graph simple absolute value equations and inequalities
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SEI.2.AI.5 Solve real world problems that involve a combination of rates, proportions and percents
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SEI.2.AI.6 Solve problems involving direct variation and indirect (inverse) variation to model rates of change
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SEI.2.AI.7 Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem)
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SEI.2.AI.8 Communicate real world problems graphically, algebraically, numerically and verbally
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Content Standard 3: Students will analyze functions by investigating rates of change, intercepts, and zeros.
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LF.3.AI.1 Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data
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LF.3.AI.2 Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data
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LF.3.AI.3 Know and/or use function notation, including evaluating functions for given values in their domain
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LF.3.AI.4 Identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs
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LF.3.AI.5 Interpret the rate of change/slope and intercepts within the context of everyday life
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LF.3.AI.6 Calculate the slope given
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LF.3.AI.6.b the graph of a line
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LF.3.AI.6.c the equation of a line
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LF.3.AI.7 Determine by using slope whether a pair of lines are parallel, perpendicular, or neither
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LF.3.AI.8 Write an equation in slope-intercept, point-slope, and standard forms given
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LF.3.AI.8.b a point and y-intercept
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LF.3.AI.8.c x-intercept and y-intercept
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LF.3.AI.8.d a point and slope
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LF.3.AI.8.e a table of data
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LF.3.AI.8.f the graph of a line
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LF.3.AI.9 Describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa
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Content Standard 4: Students will compare the properties in the family of functions.
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NLF.4.AI.1 Factoring polynomials
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NLF.4.AI.2 Determine minimum, maximum, vertex, and zeros, given the graph
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NLF.4.AI.3 Solve quadratic equations using the appropriate methods with and without technology
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NLF.4.AI.4 Recognize function families and their connections including vertical shift and reflection over the x-axis
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NLF.4.AI.5 Communicate real world problems graphically, algebraically, numerically and verbally
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Content Standard 5: Students will compare various methods of reporting data to make inferences or predictions.
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DIP.5.AI.1 Construct and use scatter plots and line of best fit to make inferences in real life situations
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DIP.5.AI.2 Use simple matrices in addition, subtraction, and scalar multiplication
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DIP.5.A1.3 Construct simple matrices for real life situations
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DIP.5.AI.4 Determine the effects of changes in the data set on the measures of central tendency
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DIP.5.AI.5 Use two or more graphs (i.e., box-and- whisker, histograms, scatter plots) to compare data sets
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DIP.5.AI.6 Construct and interpret a cumulative frequency histogram in real life situations
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DIP.5.AI.7 Recognize linear functions and non-linear functions by using a table or a graph
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DIP.5.AI.8 Compute simple probability with and without replacement
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DIP.5.AI.9 Recognize patterns using explicitly defined and recursively defined linear functions
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DIP.5.AI.10 Communicate real world problems graphically, algebraically, numerically and verbally
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DIP.5.AI.11 Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusions
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DIP.5.AI.12 Recognize when arguments based on data confuse correlation with causation
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Content Standard 1: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.
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LA.1.AI.1 Evaluate algebraic expressions, including radicals, by applying the order of operations
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LA.1.AI.2 Translate word phrases and sentences into expressions, equations, and inequalities, and vice versa
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LA.1.AI.4 Solve problems involving scientific notation, including multiplication and division.
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LA.1.AI.6 Simplify algebraic fractions by factoring
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LA.1.AI.7 Recognize when an expression is undefined
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Content Standard 2: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities and systems of equations and solve with fluency.
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SEI.2.AI.1 Solve multi-step equations and inequalities with rational coefficients
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SEI.2.AI.2 Solve systems of two linear equations
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SEI.2.AI.3 Solve linear formulas and literal equations for a specified variable
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SEI.2.AI.4 Solve and graph simple absolute value equations and inequalities
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SEI.2.AI.5 Solve real world problems that involve a combination of rates, proportions and percents
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SEI.2.AI.6 Solve problems involving direct variation and indirect (inverse) variation to model rates of change
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SEI.2.AI.7 Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem)
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SEI.2.AI.8 Communicate real world problems graphically, algebraically, numerically and verbally
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Content Standard 3: Students will analyze functions by investigating rates of change, intercepts, and zeros.
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LF.3.AI.1 Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data
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LF.3.AI.2 Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data
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LF.3.AI.3 Know and/or use function notation, including evaluating functions for given values in their domain
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LF.3.AI.4 Identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs
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LF.3.AI.5 Interpret the rate of change/slope and intercepts within the context of everyday life
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LF.3.AI.6 Calculate the slope given
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LF.3.AI.6.b the graph of a line
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LF.3.AI.6.c the equation of a line
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LF.3.AI.7 Determine by using slope whether a pair of lines are parallel, perpendicular, or neither
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LF.3.AI.8 Write an equation in slope-intercept, point-slope, and standard forms given
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LF.3.AI.8.b a point and y-intercept
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LF.3.AI.8.c x-intercept and y-intercept
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LF.3.AI.8.d a point and slope
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LF.3.AI.8.e a table of data
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LF.3.AI.8.f the graph of a line
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LF.3.AI.9 Describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa
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Content Standard 4: Students will compare the properties in the family of functions.
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Content Standard 4: Students will compare the properties in the family of functions.
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Content Standard 5: Students will compare various methods of reporting data to make inferences or predictions.
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DIP.5.AI.1 Construct and use scatter plots and line of best fit to make inferences in real life situations
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DIP.5.AI.2 Use simple matrices in addition, subtraction, and scalar multiplication.
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DIP.5.AI.3 Construct simple matrices for real life situations
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DIP.5.AI.5 Use two or more graphs (i.e., box-and-whisker, histograms, scatter plot) to compare data sets
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DIP.5.AI.6 Construct and interpret a cumulative frequency histogram in real life situations
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DIP.5.AI.7 Recognize linear functions and non-linear functions by using a table or graph
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DIP.5.AI.8 Compute simple probability with and without replacement
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DIP.5.AI.9 Recognize patterns using explicitly defined and recursively defined linear functions
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DIP.5.AI.11 Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusions
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DIP.5.AI.12 Recognize when arguments based on data confuse correlation with causation
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Content Standard 1: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.
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LA.1.AI.1 Evaluate algebraic expressions, including radicals, by applying the order of operations
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LA.1.AI.3 Apply the laws of (integral) exponents
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LA.1.AI.4 Solve problems involving scientific notation, including multiplication and division
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LA.1.AI.5 Perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives
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LA.1.AI.6 Simplify algebraic fractions by factoring
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LA.1.AI.8 Simplify radical expressions such as 3/(square root of 7)
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LA.1.AI.9 Add, subtract, and multiply simple radical expressions like 3(square root of 20) + 7(square root of 5) and 4(square root of 5) * 2(square root of 3)
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Content Standard 2: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities and systems of equations and solve with fluency.
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SEI.2.AI.2 Solve systems of two linear equations
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SEI.2.AI.2.a numerically (from a table or guess and check)
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SEI.2.AI.2.b algebraically (including the use of manipulatives)
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SEI.2.AI.2.d technologically
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SEI.2.AI.4 Solve and graph simple absolute value equations and inequalities
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SEI.2.AI.8 Communicate real world problems graphically, algebraically, numerically and verbally
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Content Standard 3: Students will analyze functions by investigating rates of change, intercepts, and zeros.
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Content Standard 3: Students will analyze functions by investigating rates of change, intercepts, and zeros.
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Content Standard 4: Students will compare the properties in the family of functions.
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NLF.3.AI.1 Factoring polynomials
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NLF.3.AI.2 Determine minimum, maximum, vertex, and zeros, given the graph
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NLF.3.AI.3 Solve quadratic equations using the appropriate methods with and without technology
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NLF.3.AI.4 Recognize function families and their connections including vertical shift and reflection over the x-axis
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NLF.3.AI.5 Communicate real world problems graphically, algebraically, numerically and verbally
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Content Standard 5: Students will compare various methods of reporting data to make inferences or predictions.
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DIP.5.AI.4 Determine the effects of changes in the data set on the measures of central tendency
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DIP.5.AI.5 Use two or more graphs (box-and- whisker, histograms, scatter plots to compare data sets
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DIP.5.AI.6 Construct and interpret a cumulative frequency histogram in real life situations
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DIP.5.AI.7 Recognize linear functions and non-linear functions by using a table or a graph
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DIP.5.AI.8 Compute simple probability with and without replacement
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DIP.5.AI.9 Recognize patterns using explicitly defined and recursively defined linear functions
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DIP.5.AI.10 Communicate real world problems graphically, algebraically, numerically and verbally.
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DIP.5.AI.11 Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusions
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DIP.5.AI.12 Recognize when arguments based on data confuse correlation with causation
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Content Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.
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LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations
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LG.1.G.2 Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles
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LG.1.G.3 Describe relationships derived from geometric figures or figural patterns
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LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines
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LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel
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LG.1.G.6 Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180? , and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it??s length
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Content Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.
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T.2.G.1 Apply congruence (SSS ??) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification
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T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)
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T.2.G.3 Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems
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T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems
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T.2.G.5 Use the special right triangle relationships (30?-60?-90? and 45?-45?-90?) to solve problems
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T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression
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T.2.G.7 Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression
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Content Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.
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M.3.G.1 Calculate probabilities arising in geometric contexts
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M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms
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M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes
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M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)
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M.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions
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Content Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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R.4.G.1 Explore and verify the properties of quadrilaterals
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R.4.G.2 Solve problems using properties of polygons:
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R.4.G.2.a sum of the measures of the interior angles of a polygon
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R.4.G.2.b interior and exterior angle measure of a regular polygon or irregular polygon
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R.4.G.2.c number of sides or angles of a polygon
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R.4.G.3 Identify and explain why figures tessellate
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R.4.G.4 Identify the attributes of the five Platonic Solids
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R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles
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R.4.G.6 Solve problems using inscribed and circumscribed figures
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R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects
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R.4.G.8 Draw, examine, and classify cross-sections of three-dimensional objects
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R.4.G.9 Explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate
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Content Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
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CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines
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CGT.5.G.2 Write the equation of a line parallel to a line through a given point not on the line
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CGT.5.G.3 Write the equation of a line perpendicular to a line through a given point
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CGT.5.G.4 Write the equation of the perpendicular bisector of a line segment
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CGT.5.G.5 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)
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CGT.5.G.6 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle
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CGT.5.G.7 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane
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Content Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.
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LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations
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LG.1.G.2 Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles
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LG.1.G.3 Describe relationships derived from geometric figures or figural patterns
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LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines
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LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel
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LG.1.G.6 Give justification for conclusions reached by deductive reasoning State and prove key basic theorems in geometry (i.e., Pythagorean theorem, the sum of the measures of the angles of a triangle is 180?, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length
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Content Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.
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T.2.G.1 Apply congruence (SSS ??) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification
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T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)
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T.2.G.3 Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems
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T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems
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T.2.G.7 Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths, including angles of elevation and angles of depression
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Content Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.
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M.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions
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Content Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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R.4.G.1 Explore and verify the properties of quadrilaterals
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R.4.G.2 Solve problems using properties of polygons:
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R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects
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R.4.G.9 Explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate
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Content Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
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CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines
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CGT.5.G.2 Write the equation of a line parallel to a line through a given point not on the line
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CGT.5.G.3 Write the equation of a line perpendicular to a line through a given point
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CGT.5.G.4 Write the equation of the perpendicular bisector of a line segment
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CGT.5.G.5 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)
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Content Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.
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LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations
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LG.1.G.6 Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., Pythagorean theorem, the sum of the measures of the angles of a triangle is 180?, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
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Content Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.
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T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems
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T.2.G.5 Use the special right triangle relationships (30?-60?-90? and 45?-45?-90?) to solve problems
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T.2.G.6 Using trigonometric ratios(sine, cosine, tangent), determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression
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T.2.G.7 Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression
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Content Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.
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M.3.G.1 Calculate probabilities arising in geometric contexts
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M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms
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M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes
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M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)
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M.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions
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Content Standard 4: Students will analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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R.4.G.3 Identify and explain why figures tessellate
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R.4.G.4 Identify the attributes of the five Platonic Solids
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R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles
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R.4.G.6 Solve problems using inscribed and circumscribed figures
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R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects
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R.4.G.8 Draw, examine, and classify cross-sections of three-dimensional objects
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R.4.G.9 Explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate
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Content Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
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CGT.5.G.5 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)
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CGT.5.G.6 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle
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CGT.5.G.7 Draw and interpret the results of transformations and transformations on figures in the coordinate plane
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CGT.5.G.7.c rotations (90?, 180?, clockwise and counterclockwise about the origin)
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CGT.5.G.7.d dilations (scale factor)
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Content Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.
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LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations
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LG.1.G.6 Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., Pythagorean theorem, the sum of the measures of the angles of a triangle is 180?, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
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Content Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.
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T.2.G.1 Apply congruence (SSS ??) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification
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T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)
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T.2.G.3 Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems
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T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems
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T.2.G.5 Use the special right triangle relationships (30?-60?-90? and 45?-45?-90?) to solve problems
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T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression
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T.2.G.7 Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression
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Content Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.
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M.3.G.1 Calculate probabilities arising in geometric contexts
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M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms
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M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes
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M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)
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M.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions
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Content Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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R.4.G.1 Explore and verify the properties of quadrilaterals
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R.4.G.2 Solve problems using properties of polygons:
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R.4.G.2.a sum of the measures of the interior angles of a polygon
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R.4.G.2.b interior and exterior angle measure of a regular polygon or irregular polygon
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R.4.G.2.c number of sides or angles of a polygon
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R.4.G.3 Identify and explain why figures tessellate
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R.4.G.4 Identify the attributes of the five Platonic Solids
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R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles
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R.4.G.6 Solve problems using inscribed and circumscribed figures
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R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects
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R.4.G.8 Draw, examine, and classify cross-sections of three-dimensional objects
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R.4.G.9 Explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate
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|
Content Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
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CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines
|
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CGT.5.G.2 Write the equation of a line parallel to a line through a given point not on the line
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CGT.5.G.3 Write the equation of a line perpendicular to a line through a given point
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CGT.5.G.4 Write the equation of the perpendicular bisector of a line segment
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CGT.5.G.5 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)
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CGT.5.G.6 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle
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CGT.5.G.7 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane
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Content Standard 1: Students will represent and analyze mathematical situations and properties using patterns, relations, functions and algebraic symbols.
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RF.1.AII.1 Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function
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RF.1.AII.2 Evaluate, add, subtract, multiply, and divide functions and give appropriate domain and range restrictions
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RF.1.AII.3 Determine the inverse of a function (Graph, with and without appropriate technology, functions and their inverses)
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RF.1.AII.4 Analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial)
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RF.1.AII.5 Graph, with and without appropriate technology, functions defined as piece-wise and step
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RF.1.AII.6 Recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion)
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RF.1.AII.7 Investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum)
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RF.1.AII.8 Use basic properties of frequency and amplitude to solve problems
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RF.1.AII.9 Apply the concepts of functions to real world situations
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Content Standard 2: Students will analyze and apply various methods to model, graph and solve linear and absolute value equations and inequalities.
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LEI.2.AII.1 Solve, with and without appropriate technology, absolute value equations and inequalities written in one or two variables, and graph solutions.
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LEI.2.AII.2 Solve, with and without appropriate technology, systems of linear equations with two variables and graph the solution set
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LEI.2.AII.3 Develop and apply, with and without appropriate technology, the basic operations and properties of matrices (associative, commutative, identity, and inverse)
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LEI.2.AII.4 Solve, with and without appropriate technology, systems of linear equations with three variables using algebraic methods, including matrices
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LEI.2.AII.5 Apply, with or without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programming
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Content Standard 3: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve quadratic equations.
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QEF.3.AII.1 Perform computations with radicals
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QEF.3.AII.2 Extend the number system to include the complex numbers
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QEF.3.AII.3 Analyze and solve quadratic equations with and without appropriate technology by
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QEF.3.AII.3.c extracting the square root
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QEF.3.AII.3.d completing the square
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QEF.3.AII.3.e using the quadratic formula
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QEF.3.AII.4 Derive the quadratic formula and use it to solve equations
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QEF.3.AII.5 Develop and analyze, with and without appropriate technology, quadratic relations
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QEF.3.AII.6 Apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needed
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Content Standard 4: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.
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PRF.4.AII.1 Determine the factors of polynomials by
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PRF.4.AII.1.a using factoring techniques including grouping and the sum or difference of two cubes
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PRF.4.AII.1.b using long division
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PRF.4.AII.1.c using synthetic division
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PRF.4.AII.2 Analyze and sketch, with and without appropriate technology, the graph of a given polynomial function, determining the characteristics of domain and range, maximum and minimum points, end behavior, zeros, multiplicity of zeros, y-intercept, and symmetry
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PRF.4.AII.3 Write the equation of a polynomial function given its roots
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PRF.4.AII.4 Identify the equation of a polynomial function given its graph or table
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PRF.4.AII.5 Identify the characteristics of graphs of power functions of the form f(x) = ax to the n power, for negative integral values of n, including domain, range, end behavior, and behavior at x = 0, and compare these characteristics to the graphs of related positive integral power functions
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PRF.4.AII.6 Simplify, add, subtract, multiply, and divide with rational expressions
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PRF.4.AII.7 Establish the relationship between radical expressions and expressions containing rational exponents
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PRF.4.AII.8 Simplify variable expressions containing rational exponents using the laws of exponents
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Content Standard 5: Students will graph exponential functions and relate them to logarithms. They will solve real world problems using exponential functions.
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ELF.5.AII.1 Recognize the graphs of exponential functions distinguishing between growth and decay
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ELF.5.AII.2 Graph exponential functions and identify key characteristics: domain, range, intercepts, asymptotes, and end behavior
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ELF.5.AII.3 Identify the effect that changes in the parameters of the base have on the graph of the exponential function
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ELF.5.AII.4 Recognize and solve problems that can be modeled using exponential functions
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ELF.5.AII.5 Establish the relationship between exponential and logarithmic functions
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ELF.5.AII.6 Evaluate simple logarithms using the definition
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ELF.5.AII.7 Use properties of logarithms to manipulate logarithmic expressions
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Content Standard 6: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real world problems.
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DAP.6.AII.1 Find regression line for scatter plot, using appropriate technology, and interpret the correlation coefficient
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DAP.6.AII.2 Interpret and use the correlation coefficient to assess the strength of the linear relationship between two variables
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DAP.6.AII.3 Find the quadratic curve of best fit using appropriate technology
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DAP.6.AII.4 Identify strengths and weaknesses of using regression equations to approximate data
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DAP.6.AII.5 Compute and explain measures of spread (range, percentiles, variance, standard deviation)
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DAP.6.AII.6 Describe the characteristics of a Gaussian normal distribution
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Smartest Way to Practice Math
TenMarks is the smartest way to practice and learn math online. Experience our interactive worksheets that engage students.
Personalized program, mapped to state standards
Interactive worksheets with hints and video lessons
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