BUILT YOU. ACT Pathway. for

Transcription

1 BUILT for YOU

2 Think Through Math s is built to equip students with the skills and conceptual understandings of high school level mathematics necessary for success in college. This pathway progresses from pre-algebra and elementary algebra skills up through more sophisticated algebraic relationships. Linear, exponential and quadratic functions are interwoven so that students not only learn about each relationship individually, but also have an opportunity to compare them against one another and continually revisit each relationship in more complex ways. The pathway also takes students on a deep dive into probability concepts and geometric relationships. Detailed information can be found on the ACT website:

3 Ratios and Proportional Relationships and The Number System and The Number System and Geometry Using Proportions to Solve Problems Percent and Percent Change Identifying and Generating Equivalent Solving with the Distributive Property in Context Operations with Rational Numbers I Operations with Rational Numbers II Understanding Properties of Integer Exponents Applying Properties of Integer Exponents Approximating Values of Irrational Numbers Interpreting Numbers Written in Scientific Notation Operations with Numbers in Scientific Notation Pythagorean Theorem - Mixed Problems Pythagorean Theorem - Distance Formula AF 601 AF 601 AF 701 A 601 A 601 N 603 N 603 A 512 N 605 A 512 N 605 N 604 A 511 A 511 G 508 G 602 G 602 G 605 Solve word problems containing several rates, proportions, or percentages Solve word problems containing several rates, proportions, or percentages Solve complex arithmetic problems involving percent of increase or decrease or requiring integration of several concepts (e.g., using several ratios, comparing percentages, or comparing averages) Manipulate expressions and equations Manipulate expressions and equations Apply number properties involving positive/ negative numbers Apply number properties involving positive/ negative numbers Work problems involving positive integer exponents Apply properties of rational exponents Work problems involving positive integer exponents Apply properties of rational exponents Apply the facts that π is irrational and that the square root of an integer is rational only if that integer is a perfect square Work with scientific notation Work with scientific notation Given the length of two sides of a right triangle, find the third when the lengths are Pythagorean triples Use the Pythagorean theorem Use the Pythagorean theorem Use the distance formula 3

4 Creating Reasoning about and Inequalities Creating Reasoning about and Inequalities Writing and Solving Linear in One Variable Writing and Graphing Linear in Two or More Variables Solving Linear Inequalities in One Variable Graphing Linear Inequalities Modeling Exponential Relationships with, Inequalities, and Graphs Solving Systems of Linear A 502 AF 502 AF 503 A 503 A 601 A 602 A 603 AF 702 F 702 A 604 Solve real-world problems by using first-degree equations Build functions and write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) Match linear equations with their graphs in the coordinate plane Solve first-degree inequalities when the method does not involve reversing the inequality sign Manipulate expressions and equations Solve linear inequalities when the method involves reversing the inequality sign Match linear inequalities with their graphs on the number line Build functions and write expressions, equations, Build functions for relations that are exponential Solve systems of two linear equations Interpreting Functions Function Notation II F 505 Understand the concept of a function as having a well-defined output value at each valid input value F 507 Interpret statements that use function notation in terms of their context Interpreting Graphs of Linear and Exponential Functions in Context Understanding the Domain of a Function Rate of Change for Linear and Exponential Functions AF 603 AF 704 F 504 F 506 F 503 Interpret and use information from graphs in the coordinate plane Analyze and draw conclusions based on information from graphs in the coordinate plane Attend to the difference between a function modeling a situation and the reality of the situation Understand the concept of domain and range in terms of valid input and output, and in terms of function graphs Build functions and use quantitative information to identify graphs for relations that are proportional or linear 4

5 Building Functions Arithmetic with Polynomials and Rational The Real Number System Creating Transformations of Graphs of Linear and Exponential Functions Writing Linear and Exponential Functions from a Context AF 604 AF 705 AF 706 AF 602 AF 702 Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down Identify characteristics of graphs based on a set of or on a general equation such as y = ax² + c Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions Build functions and write expressions, equations, and inequalities for common algebra settings (e.g., distance to a point on a curve and profit for variable cost and demand) Build functions and write expressions, equations, Composite Functions AF 602 Build functions and write expressions, equations, and inequalities for common algebra settings (e.g., distance to a point on a curve and profit for variable cost and demand) F 604 Evaluate composite functions at integer values F 708 Write an expression for the composite of two simple functions Writing Geometric Sequences Using an Explicit Formula F 703 Exhibit knowledge of geometric sequences Writing Geometric Sequences Recursively Writing Arithmetic Sequences Explicitly and Recursively Adding and Subtracting Polynomials F 703 F 603 F 502 A 505 Exhibit knowledge of geometric sequences Find a recursive expression for the general term in a sequence described recursively Find the next term in a sequence described recursively Add, subtract, and multiply polynomials Multiplying polynomials A 505 Add, subtract, and multiply polynomials Using Rational N 605 Apply properties of rational exponents Exponents to Rewrite Modeling Quadratic AF 702 Build functions and write expressions, equations, Relationships with, Inequalities, and Graphs 5

6 Seeing Structure in Interpreting Functions Building Functions Interpreting Functions Reasoning about and Inequalities Interpreting Functions The Complex Number System Statistics and Probability Factoring Quadratic Sketching Graphs of Quadratic Functions in Context Writing Quadratic Functions from Their Graphs Rewriting Quadratics to Reveal Their Structure Using the Quadratic Formula Solving Quadratic Graphically Rational Functions and Their Graphs A 506 Identify solutions to simple quadratic equations A 507 Solve quadratic equations in the form (x + a)(x + b) = 0, where a and b are numbers or variables A 508 Factor simple quadratics (e.g., the difference of squares and perfect square trinomials) A 605 Solve quadratic equations G 609 Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) AF 702 Build functions and write expressions, equations, G 609 Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) AF 702 Build functions and write expressions, equations, G 609 Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) A 506 Identify solutions to simple quadratic equations A 605 A 506 Solve quadratic equations Identify solutions to simple quadratic equations A 513 Determine when an expression is undefined F 508 Find the domain of polynomial functions and rational functions F 602 Build functions for relations that are inversely proportional Logarithmic Functions F 707 Exhibit knowledge of logarithms Complex Number N 504 Exhibit some knowledge of the complex numbers Arithmetic N 606 Multiply two complex numbers Understanding the S 701 Distinguish between mean, median, and mode for Effects of Outliers on a list of numbers Mean and Median Compound Probability S 503 Compute straightforward probabilities for common situations Patterns of Association in Data S 502 S 702 Manipulate data from tables and charts Analyze and draw conclusions based on information from tables and charts, including twoway frequency tables 6

7 Interpreting Categorical and Quantitative Data Conditional Probability and the Rules of Probability Geometry Congruence Fitting Functions to Data Organizing Possible Outcomes of Events Understanding Independent and Dependent Events Understanding Conditional Probability Modeling Probability Situations Using Two- Way Frequency Tables Relating Probabilities of Unions and Intersections of Events Volume of Composite Solids Defining Transformations Rotational and Reflectional Symmetry F 701 S 506 S 603 S 604 S 605 S 606 S 704 S 604 S 605 S 704 S 504 S 602 S 702 S 604 S 605 S 704 G 405 G 607 G 608 G 502 Compare actual values and the values of a modeling function to judge model fit and compare Recognize that when a statistical model is used, model values typically differ from actual values Apply counting techniques Compute a probability when the event and/or sample space are not given or obvious Recognize the concepts of conditional and joint probability expressed in real-world contexts Recognize the concept of independence expressed in real-world contexts Exhibit knowledge of conditional and joint probability Compute a probability when the event and/or sample space are not given or obvious Recognize the concepts of conditional and joint probability expressed in real-world contexts Exhibit knowledge of conditional and joint probability Use Venn diagrams in counting Interpret and use information from tables and charts, including two-way frequency tables Analyze and draw conclusions based on information from tables and charts, including twoway frequency tables Compute a probability when the event and/or sample space are not given or obvious Recognize the concepts of conditional and joint probability expressed in real-world contexts Exhibit knowledge of conditional and joint probability Use geometric formulas when all necessary information is given Find the coordinates of a point reflected across a vertical or horizontal line or across y = x Find the coordinates of a point rotated 90 about the origin Count the number of lines of symmetry of a geometric figure What is Proof? G 704 Analyze and draw conclusions based on a set of Proving Theorems About Lines and Angles G 704 Analyze and draw conclusions based on a set of 7

8 Similarity, Right Triangles, and Trigonometry Congruence Similarity, Right Triangles, and Trigonometry Geometric Measurement and Dimension Expressing Geometric Properties with Problem Solving with Congruent Triangles Proving Theorems About Relationships in Triangles Proving Theorems About Parallelograms G 603 Apply properties of , , similar, and congruent triangles G 705 Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization G 704 Analyze and draw conclusions based on a set of G 704 Analyze and draw conclusions based on a set of Properties of Dilations I G 703 Use scale factors to determine the magnitude of a size change Problem Solving with Transformations and Similarity Proving Theorems About Similar Triangles Problem Solving with Similarity and Trigonometric Ratios Sine and Cosine of Complementary Angles Understanding Formulas for Curved Figures Problem Solving with Coordinates of Parallel and Perpendicular Lines G 705 G 704 G 509 G 604 G 509 G 601 G 606 Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization Analyze and draw conclusions based on a set of Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths Apply basic trigonometric ratios to solve righttriangle problems Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths Use relationships involving area, perimeter, and volume of geometric figures to compute another measure (e.g., surface area for a cube of a given volume and simple geometric probability) Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point The Number System Midpoint Practice G 511 Find the midpoint of a line segment Expressing Geometric Dividing a Segment G 511 Find the midpoint of a line segment Properties with Proportionally Using Coordinates to Find Perimeters and Areas G 605 Use the distance formula Circles Expressing Geometric Properties with Tangents, Chords, Radii and Angles in Circles Problem Solving with the Equation of a Circle G 701 G 609 Use relationships among angles, arcs, and distances in a circle Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) 8