Arithmetic With Polynomials And Rational Expressions 
HSA.APR: Perform Arithmetic Operations On Polynomials 
HSA.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. 
Rewrite Rational Expressions 
HSA.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. 
Congruence 
HSG.CO: Experiment With Transformations In The Plane 
HSG.CO.1  Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 
Expressions And Equations 
6.EE: Reason About And Solve OneVariable Equations And Inequalities. 
6.EE.5  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 
8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations. 
8.EE.8.a  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. 
Work With Radicals And Integer Exponents. 
8.EE.1  Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 
Functions 
8.F: Define, Evaluate, And Compare Functions. 
8.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.1 
Geometry 
8.G: Understand Congruence And Similarity Using Physical Models, Trans Parencies, Or Geometry Software. 
8.G.2  Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 

8.G.4  Understand that a twodimensional 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. 
Interpreting Functions 
HSF.IF: Understand The Concept Of A Function And Use Function Notation 
HSF.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). 
Measurement And Data 
4.MD: Geometric Measurement: Understand Concepts Of Angle And Measure Angles. 
4.MD.5  Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: 
Number And Operations In Base Ten 
1.NBT: Understand Place Value. 
1.NBT.2  Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: 
Use Place Value Understanding And Properties Of Operations To Add And Subtract. 
1.NBT.4  Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 
2.NBT: Use Place Value Understanding And Properties Of Operations To Add And Subtract. 
2.NBT.5  Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 

2.NBT.6  Add up to four twodigit numbers using strategies based on place value and properties of operations. 

2.NBT.7  Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4 
3.NBT.2  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 
5.NBT: Perform Operations With MultiDigit Whole Numbers And With Decimals To Hundredths. 
5.NBT.5  Fluently multiply multidigit whole numbers using the standard algorithm. 

5.NBT.6  Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 

5.NBT.7  Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
Understand The Place Value System. 
5.NBT.1  Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 
4.NBT: Generalize Place Value Understanding For MultiDigit Whole Numbers. 
4.NBT.1  Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 
Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic. 
4.NBT.4  Fluently add and subtract multidigit whole numbers using the standard algorithm. 

4.NBT.5  Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 
Number And Operations—Fractions 
5.NF: Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. 
5.NF.1  Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 
3.NF: Develop Understanding Of Fractions As Numbers. 
3.NF.1  Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 

3.NF.3.a  Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 
Operations And Algebraic Thinking 
1.OA: Add And Subtract Within 20. 
1.OA.6  Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 
Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction. 
1.OA.4  Understand subtraction as an unknownaddend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. 
Work With Addition And Subtraction Equations. 
1.OA.7  Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 
2.OA: Add And Subtract Within 20. 
2.OA.2  Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two onedigit numbers. 
3.OA: Multiply And Divide Within 100. 
3.OA.7  Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. 
Understand Properties Of Multiplication And The Relationship Between Multiplication And Division. 
3.OA.6  Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
K.OA: Understand Addition As Putting Together And Adding To, And Under Stand Subtraction As Taking Apart And Taking From. 
K.OA.5  Fluently add and subtract within 5. 
Ratios And Proportional Relationships 
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. 
6.RP.1  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 

6.RP.2  Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 
7.RP: Analyze Proportional Relationships And Use Them To Solve RealWorld And Mathematical Problems. 
7.RP.2  Recognize and represent proportional relationships between quantities. 
Reasoning With Equations And Inequalities 
HSA.REI: Represent And Solve Equations And Inequalities Graphically 
HSA.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). 
Similarity, Right Triangles, And Trigonometry 
HSG.SRT: Apply Trigonometry To General Triangles 
HSG.SRT.11  (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 
Define Trigonometric Ratios And Solve Problems Involving Right Triangles 
HSG.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. 
Statistics And Probability 
6.SP: Develop Understanding Of Statistical Variability. 
6.SP.2  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 
The Complex Number System 
HSN.CN: Perform Arithmetic Operations With Complex Numbers. 
HSN.CN.1  Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. 
Use Complex Numbers In Polynomial Identities And Equations. 
HSN.CN.9  (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. 
The Number System 
6.NS: Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers. 
6.NS.5  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 

6.NS.6  Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 

6.NS.6.b  Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

6.NS.7  Understand ordering and absolute value of rational numbers. 

6.NS.7.c  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of –30 dollars, write –30 = 30 to describe the size of the debt in dollars. 
Compute Fluently With MultiDigit Numbers And Find Common Factors And Multiples. 
6.NS.2  Fluently divide multidigit numbers using the standard algorithm. 
8.NS: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers. 
8.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. 
Trigonometric Functions 
HSF.TF: Extend The Domain Of Trigonometric Functions Using The Unit Circle 
HSF.TF.1  Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 
Model Periodic Phenomena With Trigonometric Functions 
HSF.TF.6  (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. 
Vector And Matrix Quantities 
HSN.VM: Perform Operations On Matrices And Use Matrices In Applications. 
HSN.VM.10  (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. 

HSN.VM.9  (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. 
Perform Operations On Vectors. 
HSN.VM.4.c  Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise. 