Florida

AR Algebraic Reasoning

• MA.912.AR.2 Write, solve and graph linear equations, functions and inequalities in one and two variables.

  • MA.912.AR.2.5 Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine constraints in terms of the context.

    • Set-builder notation (A2)
    • Interval notation (A2)
    • Interpret the slope and y-intercept of a linear function (A2)
    • Slope-intercept form: write an equation from a word problem (A2)
    • Domain and range of linear functions: word problems (A2)

• MA.912.AR.5 Write, solve and graph exponential and logarithmic equations and functions in one and two variables.

  • MA.912.AR.5.3 Given a mathematical or real-world context, classify an exponential function as representing growth or decay.

    • Exponential growth and decay (A2-Z.9)

  • MA.912.AR.5.4 Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.

    • Write exponential functions from tables and graphs (A2)
    • Write exponential functions: word problems (A2-Z.3)
    • Exponential growth and decay: word problems (A2-Z.10)

  • MA.912.AR.5.5 Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.

    • Exponential functions over unit intervals (A2-Z.6)
    • Describe linear and exponential growth and decay (A2-Z.8)

  • MA.912.AR.5.6 Given a table, equation or written description of an exponential function, graph that function and determine its key features.

    • Domain and range of exponential functions (A2-Z.1)
    • Graph exponential functions (A2-Z.4)
    • Match exponential functions and graphs (A2-Z.5)

F Functions

• MA.912.F.1 Understand, compare and analyze properties of functions.

  • MA.912.F.1.6 Compare key features of linear and nonlinear functions each represented algebraically, graphically, in tables or written descriptions.

    • Compare linear and exponential growth (A2)

  • MA.912.F.1.8 Determine whether a linear, quadratic or exponential function best models a given real-world situation.

    • Write linear and exponential functions: word problems (A1-AA.5)
    • Identify linear and exponential functions (A2-Z.7)
    • Identify linear and quadratic functions from tables (A2)

FL Financial Literacy

• MA.912.FL.3 Describe the advantages and disadvantages of short-term and long-term purchases.

  • MA.912.FL.3.1 Compare simple, compound and continuously compounded interest over time.

  • MA.912.FL.3.2 Solve real-world problems involving simple, compound and continuously compounded interest.

    • Simple interest: word problems (A2)
    • Compound interest: find the balance (A2)
    • Continuously compounded interest: find the balance or principal (A2)

  • MA.912.FL.3.4 Explain the relationship between simple interest and linear growth. Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.

GR Geometric Reasoning

• MA.912.GR.1 Prove and apply geometric theorems to solve problems.

  • MA.912.GR.1.6 Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.

    • Congruence statements and corresponding parts (G-K.1)
    • Solve problems involving corresponding parts (G-K.2)
    • Identify congruent figures (G-K.3)
    • Ratios in similar figures (G-M.1)
    • Similarity statements (G-M.2)
    • Identify similar figures (G-M.3)
    • Side lengths and angle measures in similar figures (G-M.4)
    • Similar triangles and indirect measurement (G-M.5)
    • Perimeters of similar figures (G-M.6)
    • Similarity and altitudes in right triangles (G-M.13)
    • Areas of similar figures (G-M.14)
    • Prove proportions or angle congruences using similarity (G-M.16)
    • Proofs involving similarity in right triangles (G-M.17)
    • Area and perimeter of similar figures (G-S.12)

• MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.

  • MA.912.GR.2.4 Determine symmetries of reflection, symmetries of rotation and symmetries of translation of a geometric figure.

    • Line symmetry (G-J.1)
    • Rotational symmetry (G-J.2)
    • Draw lines of symmetry (G-J.3)
    • Count lines of symmetry (G-J.4)

• MA.912.GR.4 Use geometric measurement and dimensions to solve problems.

  • MA.912.GR.4.3 Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.

    • Perimeter and area: changes in scale (G-S.13)
    • Surface area and volume: changes in scale (G-U.15)
    • Perimeter, area, and volume: changes in scale (G-U.16)

  • MA.912.GR.4.4 Solve mathematical and real-world problems involving the area of two-dimensional figures.

    • Area of rectangles and squares (G-S.2)
    • Area of parallelograms and triangles (G-S.3)
    • Area of trapezoids (G-S.4)
    • Area of regular polygons (G-S.6)
    • Area and circumference of circles (G-S.9)
    • Area of compound figures (G-S.10)
    • Area between two shapes (G-S.11)

  • MA.912.GR.4.5 Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.

    • Volume of prisms and cylinders (G-U.8)
    • Volume of pyramids and cones (G-U.9)
    • Volume of spheres (G-U.10)
    • Surface area and volume review (G-U.17)
    • Calculate density, mass, and volume (G-V.9)

  • MA.912.GR.4.6 Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.

    • Surface area of prisms and cylinders (G-U.4)
    • Surface area of pyramids and cones (G-U.5)
    • Surface area of spheres (G-U.6)
    • Surface area and volume review (G-U.17)

T Trigonometry

• MA.912.T.1 Define and use trigonometric ratios, identities or functions to solve problems.

  • MA.912.T.1.2 Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.

    • Pythagorean theorem (G-P.1)
    • Trigonometric ratios: find a side length (G-Q.12)
    • Trigonometric ratios: find an angle measure (G-Q.13)
    • Solve a right triangle (G-Q.14)
    • Trigonometric ratios: word problems (G-Q.15)

DP Data Analysis and Probability

• MA.912.DP.1 Summarize, represent and interpret categorical and numerical data with one and two variables.

  • MA.912.DP.1.1 Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.

    • Create bar graphs, line graphs, and histograms (A2)

  • MA.912.DP.1.2 Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.

    • Interpret stem-and-leaf plots (A2)
    • Box plots (A2)
    • Interpret a scatter plot (A2)
    • Interpret bar graphs, line graphs, and histograms (A2)
    • Interpret circle graphs (A2)

• MA.912.DP.2 Solve problems involving univariate and bivariate numerical data.

  • MA.912.DP.2.1 For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.

    • Identify an outlier and describe the effect of removing it (A2-SS.5)
    • Mean and median (A1)

  • MA.912.DP.2.4 Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.

    • Write equations for lines of best fit (A2)
    • Interpret lines of best fit: word problems (A2)
    • Find the equation of a regression line (A2-TT.4)
    • Interpret regression lines (A2-TT.5)
    • Analyze a regression line of a data set (A2-TT.6)

  • MA.912.DP.2.9 Fit an exponential function to bivariate numerical data that suggests an exponential association. Use the model to solve real-world problems in terms of the context of the data.

    • Exponential regression (A2-TT.7)

• MA.912.DP.4 Use and interpret independence and probability.

  • MA.912.DP.4.1 Describe events as subsets of a sample space using characteristics, or categories, of the outcomes, or as unions, intersections or complements of other events.

    • Sample spaces for compound events (G)

  • MA.912.DP.4.2 Determine if events A and B are independent by calculating the product of their probabilities.

    • Identify independent events (G-AA.10)

  • MA.912.DP.4.3 Calculate the conditional probability of two events and interpret the result in terms of its context.

    • Find conditional probabilities (G-AA.11)

  • MA.912.DP.4.4 Interpret the independence of two events using conditional probability.

    • Independence and conditional probability (G-AA.13)

  • MA.912.DP.4.5 Given a two-way table containing data from a population, interpret the joint and marginal relative frequencies as empirical probabilities and the conditional relative frequencies as empirical conditional probabilities. Use those probabilities to determine whether characteristics in the population are approximately independent.

  • MA.912.DP.4.6 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

    • Independence and conditional probability (G-AA.13)

  • MA.912.DP.4.7 Apply the addition rule for probability, taking into consideration whether the events are mutually exclusive, and interpret the result in terms of the model and its context.

    • Find probabilities using the addition rule (G-AA.15)

  • MA.912.DP.4.8 Apply the general multiplication rule for probability, taking into consideration whether the events are independent and interpret the result in terms of the context.

    • Probability of independent and dependent events (G-AA.4)

  • MA.912.DP.4.9 Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.

    • Outcomes of compound events (G-AA.2)
    • Identify independent and dependent events (G-AA.3)
    • Probability of independent and dependent events (G-AA.4)
    • Counting principle (G-AA.5)

  • MA.912.DP.4.10 Given a mathematical or real-world situation, calculate the appropriate permutation or combination.

    • Permutation and combination notation (G-AA.7)
    • Find probabilities using combinations and permutations (G-AA.8)
    • Combinations and permutations: word problems (A2)

LT Logic and Discrete Theory

• MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

  • MA.912.LT.4.1 Translate propositional statements into logical arguments using propositional variables and logical connectives.

  • MA.912.LT.4.2 Determine truth values of simple and compound statements using truth tables.

    • Truth tables (G-A.7)

  • MA.912.LT.4.3 Identify and accurately interpret "if…then," "if and only if," "all" and "not" statements. Find the converse, inverse and contrapositive of a statement.

    • Identify hypotheses and conclusions (G-A.1)
    • Conditionals (G-A.3)
    • Negations (G-A.4)
    • Converses, inverses, and contrapositives (G-A.5)
    • Biconditionals (G-A.6)

  • MA.912.LT.4.4 Represent logic operations, such as AND, OR, NOT, NOR and XOR, using logical symbolism to solve problems.

    • Truth values (G-A.8)

  • MA.912.LT.4.5 Determine whether two propositions are logically equivalent.

  • MA.912.LT.4.9 Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.

  • MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.

    • Counterexamples (G-A.2)

• MA.912.LT.5 Apply properties from Set Theory to solve problems.

  • MA.912.LT.5.1 Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.

    • Sets, subsets, and complements (A1-G.1)

  • MA.912.LT.5.4 Perform the set operations of taking the complement of a set and the union, intersection, difference and product of two sets.

    • Sets, subsets, and complements (G)
    • Unions and intersections of sets (A2)

  • MA.912.LT.5.5 Explore relationships and patterns and make arguments about relationships between sets using Venn Diagrams.

    • Use Venn diagrams to solve problems (G)

  • MA.912.LT.5.6 Prove set relations, including DeMorgan's Laws and equivalence relations.