# Special Program: Algebra Ready to Teach

# Algebra Ready to Teach

An Educeri Digital Textbook that covers foundational skills for success with High School Algebra.

### Use Addition Strategies

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

ACMNA055(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.61.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).

1.NBT.41.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit 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 two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

2.OA.22.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

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### Use Subtraction Strategies

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

ACMNA055(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.61.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).

2.OA.22.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

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### Use Multiplication Strategies

(E) Represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

3.4.F(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.G(G) Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

4.4.D(D) Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

(Y2) Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)

ACMNA075(Y4) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

ACMNA076(Y4) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

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 one-digit numbers.

3.NBT.33.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4.NBT.54.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 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.

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### Use Division Strategies

(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.J(J) Determine a quotient using the relationship between multiplication and division

3.5.B(B) Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

5.3.C(C) Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

(Y2) Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)

ACMNA075(Y4) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

ACMNA076(Y4) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

ACMNA101(Y5) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3.OA.73.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 one-digit numbers.

5.NBT.65.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit 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.

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### Fluently Add and Subtract

(G) Apply properties of operations to add and subtract two or three numbers.

2.4.A(A) Recall basic facts to add and subtract within 20 with automaticity

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

ACMNA055(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

Algebra Textbook Chapter 1

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### Fluently Multiply

(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

4.4.B(B) Determine products of a number and 10 or 100 using properties of operations and place value understandings

(Y3) Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

ACMNA075(Y4) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4.NBT.54.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 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.

Algebra Textbook Chapter 1

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### Fluently Divide

(J) Determine a quotient using the relationship between multiplication and division

4.4.F(F) Use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

(Y3) Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

ACMNA075(Y4) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

ACMNA121(Y5) Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121)

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### Add, Subtract, Multiply, and Divide in Algebra Problems

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.36.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

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### Evaluate Expressions

(E) Describe the meaning of parentheses and brackets in a numeric expression

5.4.F(F) Simplify numerical expressions that do not involve exponents, including up to two levels of grouping

5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.25.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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### Describe Algebra Expressions

(Y7) Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)

ACMNA177(Y7) Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

6.EE.2.A Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

6.EE.2.B6.EE.2.B Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

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### Combine Like Terms

(A) Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

6.7.D(D) Generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.46.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

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### Distribute

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.46.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

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### Simplify Expressions (Distribute and Combine Like Terms)

(Y8) Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)

ACMNA192(Y8) Simplify algebraic expressions involving the four operations (ACMNA192)

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

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### Substitute and Evaluate

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### Describe Equations and Inequalities

(B) Distinguish between expressions and equations verbally, numerically, and algebraically

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.

6.EE.86.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

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### Use Inverse Operations (Subtract to Zero)

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### Solve Inequalities Using Additive Inverse

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### Use Inverse Operations (Divide to One)

(A) Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

6.10.A(A) Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts

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### Solve Inequalities Using Multiplicative Inverse

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### Solve Inequalities Using Additive and Multiplicative Inverse

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### Solve Inequalities (Simplify then Inverse Operations)

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### Combine Positive and Negative Terms

(C) Represent integer operations with concrete models and connect the actions with the models to standardized algorithms

6.3.D(D) Add, subtract, multiply, and divide integers fluently

7.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.

7.NS.1.D7.NS.1.D Apply properties of operations as strategies to add and subtract rational numbers.

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### Multiply and Divide Positive and Negative Terms

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.2.A7.NS.2.A 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.

7.NS.2.B7.NS.2.B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2.C7.NS.2.C Apply properties of operations as strategies to multiply and divide rational numbers.

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### Cross Multiplication

7.RP.2 Recognize and represent proportional relationships between quantities.

7.RP.2.C7.RP.2.C 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.

HSA.REI.2HSA.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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### Solve Equations using Square Roots

(Y9) Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212)

ACMNA241(Y10) Solve simple quadratic equations using a range of strategies (ACMNA241)

HSA.REI.4 Solve quadratic equations in one variable.

HSA.REI.4.BHSA.REI.4.B Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square 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.

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### Equations with No Solutions and Infinite Solutions

(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

A1.3.F(F) Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

A1.5.A(A) Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

(Y8) Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

ACMNA237(Y10) Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology (ACMNA237)

8.EE.7 Solve linear equations in one variable.

8.EE.7.A8.EE.7.A 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).

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### Graph Equation Solutions (Straight Lines)

(B) Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5.C(C) Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

HSA.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSA.REI.10HSA.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).

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### Graph Equation Solutions (Curves)

(C) Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

A1.7.A(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

HSA.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSA.REI.10HSA.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).

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### Evaluate and Graph Linear and Quadratic Functions

(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

A1.7.A(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

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### Distinguish Between Functions and Non-Functions

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### Characteristics of Linear Functions

(A) Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1)

A1.3.C(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

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### Determine if Linear Equations and Functions are Equal

(B) Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

A1.3.C(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

8.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 = s2 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.

HSA.REI.10HSA.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).

HSF.IF.7HSF.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.*

HSF.IF.7.AHSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.

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### Find Intercepts of Linear Functions and Equations

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### Write Linear Equations in Slope-Intercept Form

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### Convert Linear Equations in Standard Form to Slope-Intercept Form

(Y8) Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

ACMNA235(Y10) Solve problems involving linear equations, including those derived from formulas (ACMNA235)

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

HSF.IF.8HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF.LE.2HSF.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).

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### Find the Solution type of Systems of Linear Equations

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

8.EE.8.A8.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.

8.EE.8.B8.EE.8.B 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.

HSA.REI.10HSA.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.

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### Find the Solution of a System of Linear Equations

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

8.EE.8.A8.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.

8.EE.8.B8.EE.8.B 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.

HSA.REI.11HSA.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.

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### Analyze Systems of Linear Equations Using a Calculator

(F) Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

A1.5.C(C) Solve systems of two linear equations with two variables for mathematical and real-world problems.

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

8.EE.8.A8.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.

8.EE.8.C8.EE.8.C Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

HSA.REI.11HSA.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.

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### Solve Inequalities Using a Negative Multiplicative Inverse

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### Check Solutions to a Linear Inequality

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### Identify Graphs of Linear Inequalities

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### 8.4 Graph Linear Inequalities

(B) Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points

A1.3.D(D) Graph the solution set of linear inequalities in two variables on the coordinate plane

(Y10) Solve linear inequalities and graph their solutions on a number line (ACMNA236)

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

HSA.REI.12HSA.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.

HSF.IF.8HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

8.4 Graph Linear Inequalities

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### Use Exponent Rules to Multiply

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.

HSA.APR.1HSA.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.

Lesson 9.2

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### Simplify Polynomials

Lesson 9.4

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### Rewrite Special Pattern Polynomials

(F) Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

A2.7.E(E) Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

Lesson 9.5

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### Use Exponent Rules to Simplify Expressions with Fractions

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.

HSA.APR.6HSA.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.

Lesson 9.6

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### 10.1 Identify Intercepts and Vertex of a Quadratic Function Graph

10.1 Identify Intercepts and Vertex of a Quadratic Function Graph

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### 10.2 Analyze Quadratic Function Forms

(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

HSF.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.*

HSF.IF.7.AHSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF.IF.8HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

10.2 Analyze Quadratic Function Forms

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### 10.6 Write Quadratic Functions in Vertex Form

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

HSA.SSE.3.BHSA.SSE.3.B Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

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### Solve Quadratic Equations Using an Online Calculator

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### Analyze the Types of Data in a Data Set

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### Analyze Scatter Plots

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### Interpret the Correlation Between two Quantitative Variables

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### Identify Geometric Notation

(A) Distinguish between undefined terms, definitions, postulates, conjectures, and theorems

G.5.A(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

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### Distinguish Between Rigid Motions

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### Translate a Shape

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### Reflect a Shape

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### Rotate a Shape

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### Congruent Triangles using Rigid Motions

(B) Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

G.6.C(C) Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles