Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Foundations of mathematics wikipedia , lookup
History of mathematical notation wikipedia , lookup
Laws of Form wikipedia , lookup
System of polynomial equations wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
Linear algebra wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
VersaTiles(R) Algebra 1 Grades: 7, 8 State: Georgia Common Core Standards Subject: Mathematics Publisher: ETA hand2mind Common Core Georgia Performance Standards Mathematics Grade 7 - Adopted 2011 STRAND / DOMAIN GA.CC.MP.7. Mathematical Practices The Standards for Mathematical Practice reflect various forms of expertise and mathematical habits of mind that students develop throughout their mathematics education. VersaTiles is designed to help students become more fluent and more efficient in various mathematical skills (e.g., computational algorithms, applications of formulae, mathematical vocabulary). While there will be opportunities for teachers to elicit evidence of the Standards for Mathematical Practice if they extend VersaTiles activities into class discussions, math journals, or other formats, the activities themselves are designed primarily as skill practice. Thus, the correlation presented here shows coverage of the mathematics content standards. STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.7.RP. Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real‐world and mathematical problems. MCC7.RP.2. Recognize and represent proportional relationships between quantities. EXPECTATION MCC7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 06 (Slippery Slopes) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 10 (Parallel and Perpendicular) EXPECTATION MCC7.RP.2c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.7.RP. Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real‐world and mathematical problems. MCC7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 22-23 (Making a Change) STRAND / DOMAIN CATEGORY / CLUSTER GA.CC.7.NS. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. STANDARD MCC7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. EXPECTATION MCC7.NS.1a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 05 (Name That Property) EXPECTATION MCC7.NS.1b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real‐world contexts. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 05 (Name That Property) STRAND / DOMAIN GA.CC.7.NS. The Number System CATEGORY / CLUSTER STANDARD Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. MCC7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. EXPECTATION MCC7.NS.2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 22-23 (Making a Change) EXPECTATION MCC7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 22-23 (Making a Change) STRAND / DOMAIN GA.CC.7.NS. The Number System CATEGORY / CLUSTER STANDARD Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. MCC7.NS.3. Solve real‐world and mathematical problems involving the four operations with rational numbers. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 22-23 (Making a Change) STRAND / DOMAIN GA.CC.7.EE. Expressions and Equations CATEGORY / CLUSTER STANDARD Use properties of operations to generate equivalent expressions. MCC7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 06 (The Distributive Property) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 05 (Monomial Times Polynomial) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 06 (Rats-FOILed Again!) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 07 (Multiplication Patterns) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 08 (Factors and GCF) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 09 (Patterns-They re Everywhere!) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 24 (More Factoring) STANDARD MCC7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 08-09 (Know the Situation) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 19 (Coming to Terms) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 20-21 (Ratios and Proportions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 08-09 (The Distance Formula) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 16-17 (Inverse Variation) VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 06-07 (Add and Subtract Matrices) VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 08-09 (Scalar Multiplication) STRAND / DOMAIN GA.CC.7.EE. Expressions and Equations CATEGORY / CLUSTER STANDARD Solve real‐life and mathematical problems using numerical and algebraic expressions and equations. MCC7.EE.3. Solve multi‐step real‐life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 22-23 (Making a Change) STRAND / DOMAIN GA.CC.7.EE. Expressions and Equations CATEGORY / CLUSTER STANDARD Solve real‐life and mathematical problems using numerical and algebraic expressions and equations. MCC7.EE.4. Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. EXPECTATION MCC7.EE.4a. Solve word problems leading to equations of the form pq + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) EXPECTATION MCC7.EE.4b. Solve word problems leading to inequalities of the form px + q > r or px = q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 11 (Out of Balance I) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 12 (Out of Balance II) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 13 (Multi-Stepper) STRAND / DOMAIN GA.CC.7.G. CATEGORY / CLUSTER STANDARD Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. MCC7.G.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 20-21 (Ratios and Proportions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) STRAND / DOMAIN GA.CC.7.SP. Statistics and Probability CATEGORY / CLUSTER STANDARD Use random sampling to draw inferences about a population. MCC7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 14-15 (Sampling and Bias) STANDARD MCC7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 14-15 (Sampling and Bias) STRAND / DOMAIN GA.CC.7.SP. Statistics and Probability CATEGORY / CLUSTER STANDARD Investigate chance processes and develop, use, and evaluate probability models. MCC7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 01 (Simple Probability) VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 20-21 (Compound Events) Common Core Georgia Performance Standards Mathematics Grade 8 - Adopted 2011 STRAND / DOMAIN GA.CC.MP.8. Mathematical Practices The Standards for Mathematical Practice reflect various forms of expertise and mathematical habits of mind that students develop throughout their mathematics education. VersaTiles is designed to help students become more fluent and more efficient in various mathematical skills (e.g., computational algorithms, applications of formulae, mathematical vocabulary). While there will be opportunities for teachers to elicit evidence of the Standards for Mathematical Practice if they extend VersaTiles activities into class discussions, math journals, or other formats, the activities themselves are designed primarily as skill practice. Thus, the correlation presented here shows coverage of the mathematics content standards. STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.8.NS. The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. MCC8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 11 (Wanting to Belong) STANDARD MCC8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 10 (Hip to Be Square) STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.8.EE. Expressions and Equations Work with radicals and integer exponents. MCC8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 10 (Hip to Be Square) STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.8.EE. Expressions and Equations Understand the connections between proportional relationships, lines, and linear equations. MCC8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance‐time graph to a distance‐time equation to determine which of two moving objects has greater speed. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 01 (Variables and Powers) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 01 (Relations, Domain, and Range) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 08 (Point and Slope) STANDARD MCC8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 06 (Slippery Slopes) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 10 (Parallel and Perpendicular) STRAND / DOMAIN CATEGORY / CLUSTER STANDARD GA.CC.8.EE. Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations. MCC8.EE.7. Solve linear equations in one variable. EXPECTATION MCC8.EE.7a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 14 (Dividing to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 15 (Multiplying to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) EXPECTATION MCC8.EE.7b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 14 (Dividing to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 15 (Multiplying to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) STRAND / DOMAIN GA.CC.8.EE. Expressions and Equations CATEGORY / CLUSTER STANDARD Analyze and solve linear equations and pairs of simultaneous linear equations. MCC8.EE.8. Analyze and solve pairs of simultaneous linear equations. EXPECTATION MCC8.EE.8a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 18-19 (Systems of Equations) EXPECTATION MCC8.EE.8b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 18-19 (Systems of Equations) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 22 (Solving by Substitution) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 23 (Elimination) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 24 (More Elimination) STRAND / DOMAIN GA.CC.8.F. CATEGORY / CLUSTER STANDARD Functions Define, evaluate, and compare functions. MCC8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 02-03 (Does It Function?) STANDARD MCC8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 09 (Standard Form) STRAND / DOMAIN GA.CC.8.F. CATEGORY / CLUSTER STANDARD Functions Use functions to model relationships between quantities. MCC8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 06 (Slippery Slopes) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 10 (Parallel and Perpendicular) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) STANDARD MCC8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 08-09 (Know the Situation) STRAND / DOMAIN GA.CC.8.G. CATEGORY / CLUSTER STANDARD Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. MCC8.G.1. Verify experimentally the properties of rotations, reflections, and translations: EXPECTATION MCC8.G.1a. Lines are taken to lines, and line segments to line segments of the same length. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) EXPECTATION MCC8.G.1b. Angles are taken to angles of the same measure. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) EXPECTATION MCC8.G.1c. Parallel lines are taken to parallel lines. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) STRAND / DOMAIN GA.CC.8.G. CATEGORY / CLUSTER STANDARD Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. MCC8.G.4. Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 10-11 (Similar Triangles) STRAND / DOMAIN GA.CC.8.G. CATEGORY / CLUSTER STANDARD Geometry Understand and apply the Pythagorean Theorem. MCC8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real‐world and mathematical problems in two and three dimensions. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 06 (Pythagorean Theorem) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 07 (Pythagorean Theorem) STANDARD MCC8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 08-09 (The Distance Formula) STRAND / GA.CC.8.SP. Statistics and Probability DOMAIN CATEGORY / CLUSTER STANDARD Investigate patterns of association in bivariate data. MCC8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 22-23 (Scatter Plots) STANDARD MCC8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 22-23 (Scatter Plots) © 2012, EdGate Correlation Services, LLC. All Rights reserved. VersaTiles(R) Algebra 1 Grades: 9-12 State: Georgia Common Core Standards Subject: Mathematics Publisher: ETA hand2mind Common Core Georgia Performance Standards Mathematics Grades 9-12 - Adopted 2011 STRAND / DOMAIN GA.CC.MP. Mathematical Practices The Standards for Mathematical Practice reflect various forms of expertise and mathematical habits of mind that students develop throughout their mathematics education. VersaTiles is designed to help students become more fluent and more efficient in various mathematical skills (e.g., computational algorithms, applications of formulae, mathematical vocabulary). While there will be opportunities for teachers to elicit evidence of the Standards for Mathematical Practice if they extend VersaTiles activities into class discussions, math journals, or other formats, the activities themselves are designed primarily as skill practice. Thus, the correlation presented here shows coverage of the mathematics content standards. STRAND / DOMAIN GA.CC.9-12.N. Number and Quantity CATEGORY / CLUSTER MCC9-12.N.Q. Quantities STANDARD Reason quantitatively and use units to solve problems. EXPECTATION MCC9‐12.N.Q.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 10 (Hip to Be Square) STRAND / DOMAIN GA.CC.9-12.N. Number and Quantity CATEGORY / CLUSTER MCC9-12.N.VM. Vector and Matrix Quantities STANDARD Perform operations on matrices and use matrices in applications. EXPECTATION MCC9‐12.N.VM.6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 02-03 (Introduction to Matrices) VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 04-05 (Arrays of Data) EXPECTATION MCC9‐12.N.VM.7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 08-09 (Scalar Multiplication) EXPECTATION MCC9‐12.N.VM.8. (+) Add, subtract, and multiply matrices of appropriate dimensions. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 06-07 (Add and Subtract Matrices) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.SSE. Seeing Structure in Expressions Interpret the structure of expressions STANDARD EXPECTATION MCC9‐12.A.SSE.1. Interpret expressions that represent a quantity in terms of its context. GRADE MCC9‐12.A.SSE.1a. Interpret parts of an expression, such as terms, factors, and coefficients. EXPECTATION VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 04 (Add or Subtract Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 05 (Monomial Times Polynomial) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 06 (Rats-FOILed Again!) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 07 (Multiplication Patterns) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 20 (Dividing Polynomials) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.SSE. Seeing Structure in Expressions STANDARD Interpret the structure of expressions EXPECTATION MCC9‐12.A.SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2). VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 06 (The Distributive Property) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 07 (Commuting and Associating) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 01 (Powerful Products) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 02 (Powerful Quotients) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 04 (Add or Subtract Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 10 (Factoring Trinomials I) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 11 (Factoring Trinomials II) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 12 (Factor Differences of Squares) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 13 (Perfect Squares) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 01 (Multiply & Divide Powers) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 02 (Go Ahead, Rationalize) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 03 (More with Radical Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 05 (Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 18 (Multiply Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 19 (Divide Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 20 (Dividing Polynomials) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 21 (More Rational Expressions I) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 22 (More Rational Expressions II) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 23 (Mixed and Complex) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.SSE. Seeing Structure in Expressions Write expressions in equivalent forms to solve problems STANDARD EXPECTATION MCC9‐12.A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. GRADE MCC9‐12.A.SSE.3a. Factor a quadratic expression to reveal the zeros of the function it defines. EXPECTATION VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 10 (Factoring Trinomials I) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 11 (Factoring Trinomials II) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 12 (Factor Differences of Squares) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 13 (Perfect Squares) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 24 (More Factoring) GRADE MCC9‐12.A.SSE.3c. Use the properties of exponents to transform expressions for exponential EXPECTATION functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 04 (Radical Equations) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomials STANDARD EXPECTATION MCC9‐12.A.APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 04 (Add or Subtract Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 05 (Monomial Times Polynomial) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 06 (Rats-FOILed Again!) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 07 (Multiplication Patterns) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / MCC9-12.A.APR. Arithmetic with Polynomials and Rational Expressions CLUSTER Rewrite rational expressions STANDARD EXPECTATION MCC9‐12.A.APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 05 (Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 18 (Multiply Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 19 (Divide Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 20 (Dividing Polynomials) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 21 (More Rational Expressions I) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 22 (More Rational Expressions II) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 23 (Mixed and Complex) EXPECTATION MCC9‐12.A.APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 18 (Multiply Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 19 (Divide Rational Expressions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 21 (More Rational Expressions I) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 22 (More Rational Expressions II) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 23 (Mixed and Complex) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.CED. Creating Equations STANDARD Create equations that describe numbers or relationships EXPECTATION MCC9‐12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) EXPECTATION MCC9‐12.A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 08 (Point and Slope) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 14-15 (Identifying Parabolas) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 16-17 (The Graph Shows It) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) EXPECTATION MCC9‐12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non‐viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) EXPECTATION MCC9‐12.A.CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 18 (Solving for "y") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 24 (Solving Literal Equations) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.REI. Reasoning with Equations and Inequalities STANDARD Understand solving equations as a process of reasoning and explain the reasoning EXPECTATION MCC9‐12.A.REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 14 (Dividing to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 15 (Multiplying to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 15 (It s Absolute) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 18 (Make It Square) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 19 (Using the Quadratic Formula) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 04 (Radical Equations) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 24 (Solve Rational Equations) EXPECTATION MCC9‐12.A.REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 24 (Solve Rational Equations) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.REI. Reasoning with Equations and Inequalities Solve equations and inequalities in one variable STANDARD EXPECTATION MCC9‐12.A.REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 14 (Dividing to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 15 (Multiplying to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 11 (Out of Balance I) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 12 (Out of Balance II) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 13 (Multi-Stepper) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.REI. Reasoning with Equations and Inequalities STANDARD Solve equations and inequalities in one variable EXPECTATION MCC9‐12.A.REI.4. Solve quadratic equations in one variable. GRADE MCC9‐12.A.REI.4a. Use the method of completing the square to transform any quadratic EXPECTATION equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 18 (Make It Square) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 19 (Using the Quadratic Formula) GRADE MCC9‐12.A.REI.4b. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square EXPECTATION roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 18 (Make It Square) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 19 (Using the Quadratic Formula) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.REI. Reasoning with Equations and Inequalities Solve systems of equations STANDARD EXPECTATION MCC9‐12.A.REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 23 (Elimination) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 24 (More Elimination) EXPECTATION MCC9‐12.A.REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 18-19 (Systems of Equations) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 22 (Solving by Substitution) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 23 (Elimination) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 24 (More Elimination) STRAND / DOMAIN GA.CC.9-12.A. Algebra CATEGORY / CLUSTER MCC9-12.A.REI. Reasoning with Equations and Inequalities STANDARD Represent and solve equations and inequalities graphically EXPECTATION MCC9‐12.A.REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 14-15 (Identifying Parabolas) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 16-17 (The Graph Shows It) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) EXPECTATION MCC9‐12.A.REI.11. Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 18-19 (Systems of Equations) EXPECTATION MCC9‐12.A.REI.12. Graph the solutions to a linear inequality in two variables as a half‐plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half‐planes. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 16-17 (Inequalities in Two Variables) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 20-21 (Systems of Inequalities) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.IF. Interpreting Functions STANDARD Understand the concept of a function and use function notation EXPECTATION MCC9‐12.F.IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 02-03 (Does It Function?) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.IF. Interpreting Functions STANDARD Interpret functions that arise in applications in terms of the context EXPECTATION MCC9‐12.F.IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 08-09 (Know the Situation) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 14-15 (Identifying Parabolas) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 16-17 (The Graph Shows It) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) EXPECTATION MCC9‐12.F.IF.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person‐hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 01 (Relations, Domain, and Range) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.IF. Interpreting Functions STANDARD Analyze functions using different representations EXPECTATION MCC9‐12.F.IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. GRADE MCC9‐12.F.IF.7a. EXPECTATION Graph linear and quadratic functions and show intercepts, maxima, and minima. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 14-15 (Identifying Parabolas) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 16-17 (The Graph Shows It) GRADE MCC9‐12.F.IF.7d. EXPECTATION (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) GRADE MCC9‐12.F.IF.7e. EXPECTATION Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.IF. Interpreting Functions STANDARD Analyze functions using different representations EXPECTATION MCC9‐12.F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. GRADE MCC9‐12.F.IF.8a. EXPECTATION Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 18 (Make It Square) GRADE MCC9‐12.F.IF.8b. EXPECTATION Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 04 (Radical Equations) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.IF. Interpreting Functions STANDARD Analyze functions using different representations EXPECTATION MCC9‐12.F.IF.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 01 (Variables and Powers) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 01 (Relations, Domain, and Range) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 08 (Point and Slope) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.BF. Building Functions STANDARD Build a function that models a relationship between two quantities EXPECTATION MCC9‐12.F.BF.1. Write a function that describes a relationship between two quantities. GRADE MCC9‐12.F.BF.1a. Determine an explicit expression, a recursive process, or steps for EXPECTATION calculation from a context. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 12 (Writing Equations) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1617 (Inverse Variation) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.BF. Building Functions STANDARD Build new functions from existing functions EXPECTATION MCC9‐12.F.BF.4. Find inverse functions. GRADE MCC9‐12.F.BF.4a. Solve an equation of the form f(x) = c for a simple function f that has an EXPECTATION inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x‐1) for x ≠ 1. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 13 (Solving for "x") VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 14 (Dividing to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 15 (Multiplying to Solve) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 16 (Solving Equations) VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 17 (Equation Practice) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 15 (It s Absolute) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 18 (Make It Square) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 19 (Using the Quadratic Formula) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 04 (Radical Equations) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 24 (Solve Rational Equations) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.LE. Linear, Quadratic, and Exponential Models STANDARD Construct and compare linear, quadratic, and exponential models and solve problems EXPECTATION MCC9‐12.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. GRADE MCC9‐12.F.LE.1a. Prove that linear functions grow by equal differences over equal intervals EXPECTATION and that exponential functions grow by equal factors over equal intervals. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 01 (Relations, Domain, and Range) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 09 (Standard Form) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 10 (Parallel and Perpendicular) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 20-21 (Exponential Functions) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 22-23 (Growth and Decay) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 04 (Radical Equations) GRADE MCC9‐12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per EXPECTATION unit interval relative to another. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) GRADE MCC9‐12.F.LE.1c. EXPECTATION Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 04-05 (Linear Functions) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.LE. Linear, Quadratic, and Exponential Models STANDARD Construct and compare linear, quadratic, and exponential models and solve problems EXPECTATION MCC9‐12.F.LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input‐output pairs (include reading these from a table). VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 07 (Find the Function) VersaTiles(R) Algebra 1, Book 3 (Polynomials & Nonlinear Functions), page 03 (Polynomials) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.LE. Linear, Quadratic, and Exponential Models STANDARD Interpret expressions for functions in terms of the situation they model EXPECTATION MCC9‐12.F.LE.5. Interpret the parameters in a linear or exponential function in terms of a context. VersaTiles(R) Algebra 1, Book 1 (Expressions & Equations), page 08-09 (Know the Situation) STRAND / DOMAIN GA.CC.9-12.F. Functions CATEGORY / CLUSTER MCC9‐12.F.TF. Trigonometric Functions STANDARD Extend the domain of trigonometric functions using the unit circle EXPECTATION MCC9‐12.F.TF.3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π ‐ x, π + x, and 2π ‐ x in terms of their values for x, where x is any real number. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 12 (Off on a Tangent) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 13 (Sine and Cosine Ratios) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1415 (Trigonometric Ratios) STRAND / DOMAIN GA.CC.9-12.G. Geometry CATEGORY / CLUSTER MCC9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations STANDARD EXPECTATION MCC9‐12.G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1011 (Similar Triangles) STRAND / DOMAIN GA.CC.9-12.G. Geometry CATEGORY / CLUSTER MCC9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Prove theorems involving similarity STANDARD EXPECTATION MCC9‐12.G.SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1011 (Similar Triangles) STRAND / DOMAIN GA.CC.9-12.G. Geometry CATEGORY / MCC9-12.G.SRT. Similarity, Right Triangles, and Trigonometry CLUSTER Define trigonometric ratios and solve problems involving right triangles STANDARD EXPECTATION MCC9‐12.G.SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 12 (Off on a Tangent) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 13 (Sine and Cosine Ratios) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1415 (Trigonometric Ratios) EXPECTATION MCC9‐12.G.SRT.7. Explain and use the relationship between the sine and cosine of complementary angles. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 13 (Sine and Cosine Ratios) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1415 (Trigonometric Ratios) EXPECTATION MCC9‐12.G.SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 06 (Pythagorean Theorem) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 07 (Pythagorean Theorem) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 12 (Off on a Tangent) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 13 (Sine and Cosine Ratios) VersaTiles(R) Algebra 1, Book 4 (Radicals & Rational Functions), page 1415 (Trigonometric Ratios) STRAND / DOMAIN GA.CC.9-12.G. Geometry CATEGORY / CLUSTER MCC9-12.G.GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraically STANDARD EXPECTATION MCC9‐12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 08 (Point and Slope) VersaTiles(R) Algebra 1, Book 2 (Linear Functions), page 10 (Parallel and Perpendicular) STRAND / DOMAIN GA.CC.9-12.S. Statistics and Probability CATEGORY / CLUSTER MCC9-12.S.ID. Interpreting Categorical and Quantitative Data STANDARD Summarize, represent, and interpret data on two categorical and quantitative variables EXPECTATION MCC9‐12.S.ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. GRADE MCC9‐12.S.ID.6b. Informally assess the fit of a function by plotting and analyzing residuals. EXPECTATION VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 22-23 (Scatter Plots) GRADE MCC9‐12.S.ID.6c. Fit a linear function for a scatter plot that suggests a linear association. EXPECTATION VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 22-23 (Scatter Plots) STRAND / DOMAIN GA.CC.9-12.S. Statistics and Probability CATEGORY / CLUSTER MCC9-12.S.CP. Conditional Probability and the Rules of Probability STANDARD Understand independence and conditional probability and use them to interpret data EXPECTATION MCC9‐12.S.CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 01 (Simple Probability) STRAND / DOMAIN GA.CC.9-12.S. Statistics and Probability CATEGORY / CLUSTER MCC9-12.S.CP. Conditional Probability and the Rules of Probability STANDARD Use the rules of probability to compute probabilities of compound events in a uniform probability model EXPECTATION MCC9‐12.S.CP.7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 20-21 (Compound Events) EXPECTATION MCC9‐12.S.CP.8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 20-21 (Compound Events) EXPECTATION MCC9‐12.S.CP.9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. VersaTiles(R) Algebra 1, Book 5 (Data Analysis & Probability), page 20-21 (Compound Events) © 2012, EdGate Correlation Services, LLC. All Rights reserved.