Introductory Mathematics

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1 Introductory Mathematics Identify subsets of the real number system Estimate and compute with rational Grade 7: 1.02 numbers Compare, order, and convert among Grade 6: 1.03 fractions, decimals (terminating and nonterminating), and percents Solve problems involving percent of Grade 7: 1.01 increase and percent of decrease Use scientific notation to express large Grade 6: 1.06 numbers and numbers less than one. Express in standard form numbers given in scientific notation Use rules of exponents. Grade 6: Solve problems involving exponents and Grade 6: 1.05, 1.06 scientific notation Estimate the square root of a number Introductory Mathematics: 1.01 between two consecutive integers; using a calculator, find the square root of a number to the nearest tenth Determine the absolute value of a number Identify, explain, and apply the Grade 6: 5.01 commutative, associative, and distributive properties, inverses, and identities in algebraic expressions Simply algebraic expressions. Grade 6: Analyze problem situations, select Introductory Mathematics: 1.02 appropriate strategies, and use an organized approach to solve multi-step 2.01 Find the surface area of rectangular solids Grade 7: 2.02 and cylinders Use models to explore the relationship of Grade 7: 2.02 the volume of a cone to a cylinder and a pyramid to a prism with the same base and height. p. 1

2 2.03 Find the volume of prisms, cylinders, Grade 7: 2.02 pyramids, and cones, with and without models Use the Pythagorean Theorem to solve Introductory Mathematics: Determine the effect on volume of solid Introductory Mathematics: 2.01 figures when one or more dimension is changed Solve problems related to similar and Grade 7: 3.03 congruent figures Locate, give the coordinates of, and graph plane figures which are the results of rotations (multiples of 90 o ). Graph plane figures which are similar to a given figure (dilations) Identify and draw 3-dimensional figures from different perspectives (top, side, front, corner) Build 3-dimensional figures from drawings giving various views Select appropriate units and tools for measurement tasks; determine precision and check for reasonableness of results Use formulas in problem-solving situations Solve one and two step linear equations and inequalities Graph a linear equation by determining ordered pairs. Locate ordered pairs which satisfy a given linear inequality. Grade 6: 3.03 Introductory Mathematics: 2.05 Grade 7: 3.01 Grade 7: 3.01 Grade 6: 2.01 Grade 7: 5.04 Grade 6: 5.03 Grade 7: 5.03 Introductory Mathematics: Investigate the concept of slope. Introductory Mathematics: 4.01c 3.05 Describe, extend, analyze and create a wide Grade 5: 5.01 variety of geometric and numerical patterns, such as Pascal's triangle or the Fibonacci sequence Interpret and construct box plots. Grade 7: Collect data involving two variables and Introductory Mathematics: 3.01 display on a scatter plot; interpret results; identify positive and negative relationships. p. 2

3 4.03 Interpret the mean, explain its sensitivity to Grade 7: 4.02, 4.03, 4.04 extremes, and explain its use in comparison with the median and the mode Evaluate arguments based on data. Investigate random vs.biased sampling Find the probability of independent and Grade 6: 4.05 dependent events Make predictions based on theoretical Grade 6: 4.04 probabilities and experimental results. Algebra I: 4.01a, b, c 3.02 Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions Identify misuses of statistical and numerical data. Algebra I: 3.02, 3.05, Develop an understanding of function. a) Translate among verbal, tabular, graphic, and algebraic representations of functions. b) Identify relations and functions as linear or nonlinear. c) Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation. d) Interpret and compare properties of linear functions from tables, graphs, or equations. Algebra I: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y- intercept. Algebra I: Solve problems using linear equations and inequalities; justify symbolically and graphically. Algebra I: 3.08b 4.04 Solve problems using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots. p. 3

4 Algebra I 1.01 Operate with real numbers to solve a variety of Grade 8: 1.01, 5.04 Algebra 1: 1.01a 1.02 Operate with polynomials. Algebra 1: 1.01b 1.03 Factor polynomials. Algebra 1: 1.01c 2.01 Use formulas and algebraic expressions (from science, geometry, statistics, etc.) to solve 2.02 Describe, extend, and express algebraically a wide variety of geometric patterns Translate word phrases and sentences into expressions and equations and vice versa Identify properties and relationships of data in tables, graphs, and equations Define and distinguish between relations and functions, dependent and independent variables, domain and range Graph and interpret in the context of the problem, relations and functions on the coordinate plane. Include linear equations and inequalities, quadratics, and exponentials Determine and use slopes of linear relationships to solve 3.06 Write the equation of and graph linear relationships given relevant information Investigate and determine the effects of changes in slope and intercepts on the graph and equation of a line. Grade 6: 5.02 Grade 7: 5.04 Algebra 1: 1.02 Algebra 1: 4.01a p. 4 Grade 7: 5.02 Algebra 1 Grade 7: 5.01 Algebra 1: 4.01a Grade 8: 5.01 Algebra 1 Algebra 1: 4.01, 4.02, 4.03, 4.04 Grade 8: 5.01, 5.02, 5.03 Algebra 1: 4.01 Grade 8: 5.02, 5.03 Algebra 1: 4.01 Grade 8: 5.01, 5.02, 5.03 Algebra 1: Use linear equations or inequalities to solve Grade 8: 5.03 Algebra 1: Use systems of linear equations or inequalities in two Algebra 1: 4.03 variables to solve 3.10 Graph quadratic functions. Algebra 1: Use quadratic equations to solve Algebra 1: Use formulas and graphs to solve problems involving Algebra 1: 4.04 exponential functions Use matrices to display and interpret data. Algebra 1: 3.01

5 4.02 Recognize and identify linear and non-linear data. Grade 8: 5.01b 4.03 Create and use linear models based on real data. Grade 8: 4.02 Algebra 1: 3.03 Algebra II: 1.02f 1.03 Model and solve problems using direct variation. Geometry: Find the lengths and midpoints of segments to solve Geometry: 3.01, Use the parallelism or perpendicularity of lines and segments to solve Algebra II: Operate (addition, subtraction, scalar multiplication) with matrices to solve p. 5

6 Geometry Select appropriate operations and solve a variety of Geometry application problems using real numbers Identify, name, and draw sets of points, such as line, ray, Geometry segment, and plane Identify the coordinates of a point in a plane or in space. Grade 6: Find the length and the midpoint of a segment in two or Algebra 1: 2.01 three dimensions to solve problems 2.04 Use inductive reasoning and the tools of construction to Geometry reach conclusions Use the structure (definitions, postulates, theorems, Geometry: 2.01, 2.02, 2.03, 2.04 properties of equality and inequality) of deductive reasoning to solve 2.06 Write and interpret conditional statements including the Geometry: 2.01 converse, inverse, and contrapositive Write direct (two-column, paragraph, or flow) and Geometry: 2.02, 2.03 indirect proofs Use properties, definitions, and theorems of angles and Geometry: 2.02 lines to solve problems and write proofs Use properties, definitions, and theorems of polygons to Geometry: 2.03b solve 2.10 Recognize, identify, and model regular and non-regular Geometry: 2.04 polyhedra Use coordinate geometry to confirm properties of Geometry: 2.03 polygons Develop and use properties of quadrilaterals to solve Geometry: 2.03b problems and write proofs Develop and use properties of triangles to solve problems Geometry: 2.03a and write proofs Investigate and use properties of triangles to solve Geometry: 2.03a problems and write proofs Apply properties of right triangles to solve Grade 8: 3.02 Geometry: Develop and use properties of circles to solve problems Geometry: 2.03d and write proofs. p. 6

7 2.17 Apply properties of circles to solve Geometry: 2.03d 2.18 Use spheres to solve problems related to the definition of Geometry: 2.04 a sphere and sets of points related to the sphere Use formulas to solve problems Geometry: Use slopes to determine if two lines are parallel or Algebra 1: 2.02 perpendicular Write the equation of a line parallel or perpendicular to a Algebra 1: 2.02 given line through a given point. 3.03Transform (translate, reflect, rotate, dilate) polygons in Geometry: 3.01 the coordinate plane; describe the transformation in simple algebraic terms Use length, area, and volume to solve problems Geometry: 1.03 involving probability. Algebra 2: 4.04 Advanced Mathematics: Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to describe the transformation of polygons in the coordinate plane. p. 7

8 Algebra II Operate with numbers to solve Algebra 2: 1.01, 1.02, Operate with algebraic expressions to solve Algebra 2: 1.03, Write the equations in standard form of circles and Algebra 2: 2.09 parabolas; graph Graph ellipses and hyperbolas given the equations. Pre-Calculus: Describe graphically, algebraically and verbally realworld Algebra 2 phenomena as functions; identify the independent and dependent variables Translate among graphic, algebraic, and verbal Algebra 2 representations of relations Graph relations and functions and find the zeros of Algebra 2 functions Find the composition and inverse of functions. Algebra 2: Use quadratic equations and inequalities to solve Algebra 2: Find and interpret the maximum and minimum values and Algebra 2: 2.02 the intercepts of a quadratic function Use polynomial equations (up to 4th degree) to solve 3.08 Find zeros, intercepts, and approximate the turning points of polynomial functions; describe them in the context of the problem. Algebra 2: 2.02, 2.06 (no 4 th degree polynomials) Algebra 2: 2.02, Write a polynomial equation given its solutions. Algebra 2: 2.02, Use rational equations to solve Algebra 2: Use equations which contain radical expressions to solve Algebra 2: Use systems of two or more equations to solve Algebra 2: Use linear programming (systems of three or more inequalities) to solve 3.14 Use equations and inequalities with absolute value to solve 3.15 Write and graph exponential functions of the form f(x) = ab x. Algebra 2: 2.10 Algebra 2: 2.08 Algebra 2: 2.03 p. 8

9 3.16 Recognize as inverses the exponential and logarithmic Algebra 2: 1.01 functions Use logarithmic and exponential equations to solve Algebra 2: 1.01, Write and interpret an equation of a curve (linear, Algebra 2: 2.04 exponential, quadratic) which models a set of data Find the equation of the curve of best-fit (linear, Algebra 2: 2.04 exponential, quadratic) for a set of data. Interpret the constants, coefficients, and bases in the context of the data. Check the equation for goodness-of-fit and use the equation for predictions Use exponential equations of the form f(x) = (1+ r) x Algebra 2: 2.03 where r is given as a rate of growth or decay to solve 4.04 Operate with matrices to solve Algebra 2: 1.04 p. 9

10 Technical Mathematics Solve a variety of application problems using real Technical Mathematics 1 numbers; use calculators when appropriate Select and use measuring devices and appropriate Technical Mathematics 1: 2.01 units of measurement to solve 2.02 Compare measurements to specified tolerances. Technical Mathematics 1: Use significant digits to indicate accuracy of measurement Interpret and construct maps and scale drawings. Technical Mathematics 1: Solve vector problems using scale drawings. Recognize and indicate magnitude and direction Use formulas to solve Technical Mathematics 1: 1.01c, Solve for an unknown dimension or an unknown angle in both plane and solid shapes by creating models or diagrams. p. 10 Technical Mathematics 1: 1.01d, 2.03, Apply properties of right triangles to solve problems Technical Mathematics 1: Use slopes to determine if two lines are parallel or Algebra 1: 2.02 perpendicular Write the equation of a line parallel or perpendicular Algebra 1: 2.02 to a given line through a given point Graph relations and functions and find the zeros of Technical Mathematics 2: 2.01, 2.02 functions; use graphing calculators when appropriate Use quadratic equations and inequalities to solve Technical Mathematics 2: Use linear programming (systems of three or more Technical Mathematics 2: 2.04 inequalities) to solve 3.06 Solve problems involving direct and inverse Algebra 1: 1.03 (direct) variation Determine domain and range in relations and functions Use appropriate measures of central tendency (mean, mode, median) and variance (range, standard deviation) to describe and interpret sets of data Use an appropriate format (table, chart, graph, matrix) to present and analyze data. Technical Mathematics 2: 2.01, 2.02, 2.03, 2.04 Technical Mathematics 1: 1.01a

11 4.03 Use formulas for permutations and combinations to determine the number of ways an event can occur Determine the probability of independent and dependent events Apply algebraic and trigonometric concepts to confirm properties of geometric figures in the coordinate plane. Technical Mathematics 2: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms. Technical Mathematics 2: Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to describe the transformation of polygons in the coordinate plane. p. 11

12 Technical Mathematics Use logarithms and exponents to solve Technical Mathematics 2: Identify and draw to scale 3-dimensional figures from Technical Mathematics 1: 1.01d different perspectives (top, side, front, corner) Build 3-dimensional scale models from drawings given Technical Mathematics 1: 1.01d various views Identify the coordinates of a point in a plane or in Technical Mathematics space Find the length and the midpoint of a segment in two Algebra 1: 2.01 or three dimensions Use inductive reasoning and the tools of construction Technical Mathematics to reach conclusions Use the structure (definitions, postulates, theorems, Technical Mathematics 2: 1.01, 1.02 properties of equality and inequality) of deductive reasoning to solve 2.07 Write direct (two-column, paragraph, or flow) and indirect proofs Use properties and definitions of angles and lines to Technical Mathematics 2: 1.01 solve 2.09 Use properties and definitions of polygons to solve Technical Mathematics 2: 1.02c problems 2.10 Recognize, identify, and model regular polyhedra. Technical Mathematics 2: Use coordinate geometry to confirm properties of Technical Mathematics 1: 3.03 polygons Use properties and definitions of quadrilaterals Technical Mathematics 2: 1.02b (parallelograms, rectangles, rhombi, squares, trapezoids, kites) to solve 2.13 Use properties and definitions of triangles to solve Technical Mathematics 2: 1.02a 2.14 Investigate and use properties of triangles to solve Technical Mathematics 1: Develop and use properties of circles to solve Technical Mathematics 2: 1.02d 2.16 Apply properties of circles to solve Technical Mathematics 2: 1.02d p. 12

13 3.01 Transform (translate, reflect, rotate, dilate) polygons in Technical Mathematics 1: 3.02 the coordinate plane; describe the transformation in simple algebraic terms Describe graphically, algebraically and verbally realworld phenomena as functions; interpret the independent Technical Mathematics 2: 2.01, 2.02 and dependent variables Solve systems of two or more equations. Technical Mathematics 2: Solve problems using combined and joint variation Write and graph exponential functions of the form Technical Mathematics 2: 2.02 f(x) = ab x Use length, area, and volume to solve problems Technical Mathematics 1: 2.03 involving probability Write and interpret an equation of a curve (linear, exponential, quadratic) which models a set of data Find the equation of the curve of best-fit (linear, exponential, quadratic) for a set of data. Interpret the constants, coefficients, and bases in the context of the data. Check the equation for goodness-of-fit and use the equation for predictions Use exponential equations of the form f(x) = (1+ r) x, where r is given as a rate of growth or decay, to solve Technical Mathematics 1: 1.01b Technical Mathematics 2: 2.03 Technical Mathematics 2: 2.03 Technical Mathematics 2: Operate with matrices to solve Technical Mathematics 1: 3.03 Technical Mathematics 2: 2.04 p. 13

14 Discrete Mathematics Solve problems involving election methods: Discrete Mathematics: 2.03b Plurality, Run-off, Sequential Run-off, Borda, Condorcet Solve problems involving weighted voting, voting Discrete Mathematics: 2.03c power, and winning coalitions Solve problems involving estate division. Discrete Mathematics: 2.03d 1.04 Solve problems involving continuous fair division. Discrete Mathematics: 2.03d 1.05 Solve problems involving apportionment: Discrete Mathematics: 2.03a including, but not limited to, Hamilton, Jefferson, Hill, Webster, Adams, Quota (Balinski and Young) Define the terms associated with a graph (edges, Discrete Mathematics: 1.02 vertices, degree, paths, circuits, connected, disconnected, and trees) Represent problem situations using finite graphs and Discrete Mathematics: 1.01, 1.02 adjacency matrices Find the critical path(s) using PERT (Program and Discrete Mathematics: 1.02 Evaluation Review Technique) 2.04 Find an Euler circuit or path, if it exists. Discrete Mathematics: Find a Hamiltonian circuit or path, if it exists. Discrete Mathematics: Solve problems involving Euler and Hamiltonian Discrete Mathematics: 1.02 circuits Find the minimum-cost spanning tree for a given Discrete Mathematics: 1.02 graph Incorporate graph coloring to solve real-world Discrete Mathematics: 2.01e problems using the four color theorem and chromatic numbers Use binary expression trees to solve problems in Discrete Mathematics: 2.01e Polish and reverse Polish notation Solve problems involving bin packing Solve problems requiring matrix operations. Discrete Mathematics: Use recursive relations to solve Discrete Mathematics: Verify explicit (closed-form) definitions using Discrete Mathematics: 3.01e mathematical induction Find explicit (closed form) definitions using finite Discrete Mathematics: 3.01d differences and geometric or arithmetic formulas. p. 14

15 3.05 Use mixed recursion to solve problems involving Discrete Mathematics: 3.01 growth and decay Use sequences and series to solve Discrete Mathematics: Use Venn diagram to solve counting problems Discrete Mathematics: 2.01e involving intersection and union of sets Use basic laws of logic to solve more complicated Discrete Mathematics: 2.01e Venn diagram 4.03 Solve problems using addition and multiplication Discrete Mathematics: 2.02a principles Solve problems involving permutations and Discrete Mathematics: 2.02 combinations, including independent., dependent, mutually exclusive, and circular Use experimental probability and simulations for Discrete Mathematics: 2.02c probability models Find expected values and determine fairness. Discrete Mathematics: 2.02d 4.07 Identify discrete random variables and use them to Discrete Mathematics: 2.02e solve 4.08 Derive and apply the Binomial Probability Theorem. Discrete Mathematics: 2.02f Advanced Mathematics: Describe data to solve a) Apply and compare methods of data collection. b) Apply statistical principles and methods in sample surveys. c) Determine measures of central tendency and spread. d) Recognize, define, and use the normal distribution curve. e) Interpret graphical displays of data. f) Compare distributions of data. p. 15

16 Pre-Calculus (previously Advanced Mathematics) Convert points in two dimensions between Pre-Calculus: 2.05 rectangular and polar coordinate systems Operate with vectors in two and three Pre-Calculus: 1.03 dimensions to solve 1.03 Convert complex numbers between rectangular and polar forms; use DeMoivre's Theorem to find roots and powers of complex numbers Develop and use the trigonometric Pre-Calculus: 2.02 relationships to solve 2.02 Develop and use the Law of Sines and Law Pre-Calculus: 2.02 of Cosines to solve problems involving triangles and vectors Use coordinate geometry to describe solid Geometry: 3.02 figures Graph and use the basic functions (constant, Pre-Calculus: 1.01, 2.01, 2.04 linear, quadratic, cubic, square root, absolute value, reciprocal, rational, trigonometric, exponential, logarithmic, piecewise defined, and greatest integer) to solve 3.02 Graph and use the basic quadratic relations Pre-Calculus: 1.01, 1.02 (parabola, circle, ellipse, hyperbola) to solve 3.03 Use trigonometric and inverse trigonometric Pre-Calculus: 1.01, 2.02, 2.04 functions to solve 3.04 Use polar equations to solve Pre-Calculus: Use sequences and series to solve Pre-Calculus: Create and use mathematical models of Pre-Calculus: 2.03 linear, polynomial, exponential, trigonometric, power, and logarithmic functions to solve p. 16

17 4.03 Summarize distributions of univariate data to solve Advanced Functions and Modeling: 1.02 Discrete Mathematics: 2.01 AP Statistics: 1.01, 2.01, Use parametric equations to model and solve 2.08 Explore the limit of a function graphically, numerically, and algebraically. p. 17

18 Advanced Placement Statistics Summarize distributions of univariate data. AP Statistics: Interpret graphical displays of distributions of univariate data AP Statistics: 1.02, 2.01 (Dotplots, stemplots, histograms) Compare distributions of univariate data (dotplots, back-toback AP Statistics: 2.01, 2.02 stemplots, parallel boxplots) Analyze bivariate data. AP Statistics: Analyze catagorical data. AP Statistics: Understand and compare methods of data collection. AP Statistics: Understand principles, methods, and difficulties in sample AP Statistics: 3.03 surveys Understand principles, methods, and difficulties in designed AP Statistics: 3.04 experiments Understand and use probability. AP Statistics: Understand normal distributions. AP Statistics: Understand and simulate sampling distributions. AP Statistics: Understand the Central Limit Theorem and its importance. AP Statistics: Understand and construct confidence intervals. AP Statistics: Understand and perform tests of significance. AP Statistics: 3.10 p. 18

19 Advanced Placement Calculus Calculate limits (including one-sided AP Calculus: 1.01a limits) using algebra Find the slope of a curve at a point. AP Calculus: 2.02a 1.03 Find the derivative of basic functions, AP Calculus: 2.04a including X r, exponential, logarithmic, trigonometric, and inverse trigonometric Use basic rules for derivatives of sum, AP Calculus: 2.04b product and quotient of functions Use chain rule and implicit differentiation. AP Calculus: 2.04c 1.06 Evaluate definite integrals using basic AP Calculus: 3.01 properties Use the Fundamental Theorem to evaluate AP Calculus: 3.03a definite integrals Find the antiderivative of basic functions. AP Calculus: Find the antiderivative by substitution of AP Calculus: 3.02b variables Use implicit differentiation to find AP Calculus: 2.04c derivatives of inverse functions Use available technology to graph, analyze, AP Calculus: 1.02, 1.03 predict, and explain observed local and global behavior of functions Recognize asymptotes in terms of graphical AP Calculus: 1.02 behavior Apply geometric understanding of graphs AP Calculus: 1.03c of continuous functions (Intermediate Value Theorem, Extreme Value Theorem) Find the equation of tangent lines to a AP Calculus: 2.02b curve at a point and use it to approximate function values Apply Mean Value Theorem and identify AP Calculus: 2.03c its geometric consequences Use derivatives to analyze graphs of AP Calculus: 2.03 curves Evaluate Riemann sums. AP Calculus: 3.04c p. 19

20 2.08 Use the Fundamental Theorem to represent AP Calculus: 3.03b particular antiderivatives both graphically and analytically Describe asymptotic behavior in terms of AP Calculus: 1.02b limits involving infinity Compare relative magnitudes of functions AP Calculus: 1.02c and their rates of change Determine continuity of functions by use of AP Calculus: 1.03b limits Recognize definition of derivative. AP Calculus: Examine relationship between AP Calculus: 2.01c differentiability and continuity Find instantaneous rate of change as the AP Calculus: 2.02c limit of average rate of change Compare and interpret characteristics of AP Calculus: 2.05a graphs of f, f', and f'' Model a written description of a physical AP Calculus: 2.06 situation with a differential equation and viceversa Use derivatives to solve optimization AP Calculus: Use derivatives to model rates of change. AP Calculus: 2.06c 3.11 Interpret the derivative as a rate of change AP Calculus: 2.06e in varied applied contexts, including velocity, speed, and acceleration Interpret the definite integral as a limit of AP Calculus: 3.01b Riemann sums Recognize the definite integral of the rate AP Calculus: 3.01c of change of a quantity over an interval as the change of the quantity over the interval: p. 20

21 3.14 Use integrals to model physical, social, or AP Calculus: 3.04 economic situations. Specific applications should include finding the area of a region, the volume of a solid with known cross sections, the average value of a function, and the distance traveled by a particle along a line Find a specific antiderivative using initial AP Calculus: 3.04b conditions Solve separable differential equations and AP Calculus: 3.04h use them as models Estimate limits from graphs or tables of AP Calculus: 1.01b data Approximate rates of change from graphs AP Calculus: 2.02d and tables of values Approximate definite integrals numerically AP Calculus: 3.04c with Riemann sums and Trapezoidal Rule. p. 21

22 Integrated Mathematics Apply the laws of exponents to perform Integrated Mathematics 1: 1.01a operations on expressions with integral exponents Evaluate algebraic expressions including Grade 8: 1.01, 5.04 absolute value and radical expressions Solve problems using direct and inverse variation Identify, name, and draw sets of points, such as line, ray, segment, and plane 2.02 Identify the coordinates of a point in a plane or in space Use inductive reasoning and the tools of construction to reach conclusions Write and interpret conditional statements including the converse, inverse, and contrapositive Use properties and definitions of polygons to solve 2.06 Investigate and use properties of triangles to solve problems and write proofs Develop and use properties of triangles to solve problems and write proofs. Integrated Mathematics 2: 1.03 Integrated Mathematics 3: 1.04 Integrated Mathematics Grade 6: 3.04 Integrated Mathematics Integrated Mathematics Integrated Mathematics 3: 2.01 Integrated Mathematics 3: 2.03c Integrated Mathematics 3: 2.03a Integrated Mathematics 3: 2.03a 2.08 Use formulas to solve Integrated Mathematics 1: Translate word phrases and sentences into Integrated Mathematics expressions and equations and vice versa Identify properties and relationships of data in tables, graphs, and equations Define and distinguish between relations and functions, dependent and independent variables, domain and range Graph and interpret in the context of the problem, relations and functions on the coordinate plane. Include linear equations and inequalities, and exponentials. Grade 7: 5.02 Integrated Mathematics 1: 4.01a, 4.02a Grade 8: 5.01 Integrated Mathematics Integrated Mathematics 1: 4.01, 4.02, 4.03 p. 22

23 3.05 Determine and use slopes of linear relationships to solve 3.06 Write the equation of and graph linear relationships given relevant information Investigate and determine the effects of changes in slope and intercepts on the graph and equation of a line Use linear equations or inequalities to solve 3.09 Use systems of linear equations or inequalities in two variables to solve 3.10 Use formulas and graphs to solve problems involving exponential functions Use basic measures of central tendency (median, mean) and dispersion (range, standard deviation) to describe and analyze data Use length, area, and volume to solve problems involving probability Recognize and identify linear and nonlinear data Create and use linear models based on real data. Integrated Mathematics 3: 2.04 Integrated Mathematics 2: 4.01, 4.02, 4.03 Grade 8: 5.01, 5.02, 5.03 Integrated Mathematics 1: 4.01 Grade 8: 5.02, 5.03 Integrated Mathematics 1: 4.01 Grade 8: 5.01, 5.02, 5.03 Integrated Mathematics 1: 4.01 Grade 8: 5.03 Integrated Mathematics 1: 4.01 Integrated Mathematics 1: 4.03 Integrated Mathematics 2: 4.01 Integrated Mathematics 1: 4.02 Integrated Mathematics 2: 3.01 Integrated Mathematics 1: 3.02 Grade 8: 5.01b Integrated Mathematics 1: Use algebraic expressions, including iterative and recursive forms, to model and solve 2.02 Develop and apply properties of solids to solve 3.01 Use graph theory to model relationships and solve 3.02 Use theoretical and experimental probability to model and solve p. 23

24 Integrated Mathematics Operate with numbers to solve Integrated Mathematics 1.02 Operate with algebraic expressions to solve Integrated Mathematics 2: 1.01, Find the length and the midpoint of a Integrated Mathematics 2: 2.01 segment in two or three dimensions to solve 2.02 Use the structure (definitions, postulates, Integrated Mathematics 3 theorems, properties of equality and inequality) of deductive reasoning to solve 2.03 Write direct (two-column, paragraph, or Integrated Mathematics 3 flow) and indirect proofs Use coordinate geometry to confirm properties of polygons Transform (translate, reflect, rotate, dilate) polygons in the coordinate plane; describe the transformation in simple algebraic terms Use properties, definitions, and theorems related to angles and lines to solve problems and write proofs Use properties, definitions, and theorems related to quadrilaterals (parallelograms, rectangles, rhombi, squares, trapezoids, kites) to solve problems and write proofs Apply properties of right triangles to solve 3.01 Describe graphically, algebraically and verbally real-world phenomena as functions; identify the independent and dependent variables Graph relations and functions and find the zeros of functions. Integrated Mathematics 2 Integrated Mathematics 3 Integrated Mathematics 2: 2.04 Integrated Mathematics 3: 2.02 Integrated Mathematics 3: 2.03b Grade 8: 3.02 Integrated Mathematics 2: 2.03 Integrated Mathematics Integrated Mathematics 3.03 Use quadratic equations to solve Integrated Mathematics 2: 4.02 Integrated Mathematics 3: 3.02 p. 24

25 3.04 Find and interpret the maximum and Integrated Mathematics 2: 4.02 minimum values and the intercepts of a quadratic function; recognize the x-intercepts of the function as the solutions of the equation Use slopes to determine if two lines are Integrated Mathematics 2: 2.02 parallel or perpendicular Write the equation of a line parallel or Integrated Mathematics 2: 2.02 perpendicular to a given line through a given point Use systems of two or more equations to solve 3.08 Use linear programming (systems of three or more inequalities) to solve 3.09 Write and graph exponential functions of the form f(x) = a b x Define and use permutations and combinations in counting situations Perform experiments and compare theoretical and empirical results Calculate the expected value of an event; use expected value to solve Integrated Mathematics 2: 4.01 Integrated Mathematics 3: 3.01 Integrated Mathematics 2: 4.01 Integrated Mathematics 1: 4.02 Integrated Mathematics 1: 3.02 Integrated Mathematics 1: 3.02 Integrated Mathematics 1: Operate with matrices to solve Integrated Mathematics 2: 1.04 Integrated Mathematics 1: Model and solve problems using direct variation. Integrated Mathematics 1: Describe data to solve Integrated Mathematics 3: 4.01, Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve 4.03 Use power models to solve p. 25

26 Integrated Mathematics Use logarithms and exponents to solve Integrated Mathematics 3: Operate with algebraic expressions to solve Integrated Mathematics 3: 1.01, Use properties, definitions, and theorems Integrated Mathematics 3: 2.03d related to circles to solve problems and write proofs Apply properties of circles to solve Integrated Mathematics 3: 2.03a 2.03 Use spheres to solve problems related to Integrated Mathematics 1: 2.02 the definition of a sphere and sets of points related to the sphere Recognize, identify, and model regular and Integrated Mathematics 1: 2.02 non-regular polyhedra Use coordinate geometry to describe solid Integrated Mathematics 1: 2.02 figures Write the equations in standard form of Integrated Mathematics 4: 2.01 circles and parabolas and graph Graph ellipses and hyperbolas given the Integrated Mathematics 4: 2.01 equations Translate among graphic, algebraic, and Integrated Mathematics verbal representations of relations Find the composition and inverse of Integrated Mathematics 4: 4.03 functions Use equations, and inequalities with Integrated Mathematics 3: 3.04 absolute value to solve 3.04 Use polynomial equations (up to 4th Integrated Mathematics 4: 4.01 degree) to solve 3.05 Solve problems involving rational Integrated Mathematics 3: 3.03 equations Solve equations which contain radical Integrated Mathematics 2: 4.03 expressions Recognize as inverses the exponential and logarithmic functions. Integrated Mathematics 3: 1.03 Integrated Mathematics 4: 4.01 p. 26

27 3.08 Use logarithmic and exponential equations to solve 4.01 Write and interpret an equation of a curve (linear, exponential, quadratic) which models a set of data Find the equation of the curve of best-fit (linear, exponential, quadratic) for a set of data. Interpret the constants, coefficients, and bases in the context of the data. Check the equation for goodness-of-fit and use the equation for predictions Use exponential equations of the form f(x) = (1+ r) x where r is given as a rate of growth or decay to solve Integrated Mathematics 1: 2.04 Integrated Mathematics 2: 2.06 Advanced Mathematics: 2.02 Integrated Mathematics 2: 3.03, 3.04 Advanced Mathematics: 3.01d Integrated Mathematics 1: 4.02 Integrated Mathematics 4: 4.01 Integrated Mathematics 2: 3.02 Integrated Mathematics 2: 3.02 Integrated Mathematics 1: Use logic and deductive reasoning to draw conclusions and solve 2.02 Apply the properties, definitions, and theorems of angles and lines to solve problems and write proofs Use the law of sines and law of cosines to solve 3.01 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties Use quadratic functions and inequalities to model and solve problems; justify results Transform functions in two dimensions; describe the results algebraically and geometrically. p. 27

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