ALGEBRA 2 AND HONORS ALGEBRA 2 Grades 9 10 11 12

Algebra 2 And Honors Algebra 2 Grades 9 10 11 12-Free PDF

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ten computation focusing on properties of operations particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi digit integers and. division of polynomials with long division of integers Students identify zeros of polynomials. including complex zeros of quadratic polynomials and make connections between zeros of. polynomials and solutions of polynomial equations The unit culminates with the fundamental. theorem of algebra A central theme of this unit is that the arithmetic of rational expressions is. governed by the same rules as the arithmetic of rational numbers. Critical Area 2 Building on their previous work with functions and on their work with. trigonometric ratios and circles in Geometry students now use the coordinate plane to extend. trigonometry to model periodic phenomena, Critical Area 3 In this unit students synthesize and generalize what they have learned about a. variety of function families They extend their work with exponential functions to include. solving exponential equations with logarithms They explore the effects of transformations on. graphs of diverse functions including functions arising in an application in order to abstract the. general principle that transformations on a graph always have the same effect regardless of the. type of the underlying function They identify appropriate types of functions to model a situation. they adjust parameters to improve the model and they compare models by analyzing. appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as the process of choosing and using mathematics and statistics to. analyze empirical situations to understand them better and to make decisions is at the heart of. this unit The narrative discussion and diagram of the modeling cycle should be considered when. knowledge of functions statistics and geometry is applied in a modeling context. Critical Area 4 In this unit students see how the visual displays and summary statistics they. learned in earlier grades relate to different types of data and to probability distributions They. identify different ways of collecting data including sample surveys experiments and. simulations and the role that randomness and careful design play in the conclusions that can be. Common Core State Standards for Mathematics Appendix A page 37. Expressions, An expression is a record of a computation with numbers symbols that represent numbers. arithmetic operations exponentiation and at more advanced levels the operation of evaluating a. function Conventions about the use of parentheses and the order of operations assure that each. expression is unambiguous Creating an expression that describes a computation involving a. general quantity requires the ability to express the computation in general terms abstracting from. specific instances Reading an expression with comprehension involves analysis of its underlying. structure This may suggest a different but equivalent way of writing the expression that exhibits. some different aspect of its meaning For example p 0 05p can be interpreted as the addition of. a 5 tax to a price p Rewriting p 0 05p as 1 05p shows that adding a tax is the same as. multiplying the price by a constant factor Algebraic manipulations are governed by the. properties of operations and exponents and the conventions of algebraic notation At times an. expression is the result of applying operations to simpler expressions For example p 0 05p is. the sum of the simpler expressions p and 0 05p Viewing an expression as the result of operation. on simpler expressions can sometimes clarify its underlying structure A spreadsheet or a. computer algebra system CAS can be used to experiment with algebraic expressions perform. complicated algebraic manipulations and understand how algebraic manipulations behave. Equations and inequalities, An equation is a statement of equality between two expressions often viewed as a question. asking for which values of the variables the expressions on either side are in fact equal These. values are the solutions to the equation An identity in contrast is true for all values of the. variables identities are often developed by rewriting an expression in an equivalent form The. solutions of an equation in one variable form a set of numbers the solutions of an equation in. two variables form a set of ordered pairs of numbers which can be plotted in the coordinate. plane Two or more equations and or inequalities form a system A solution for such a system. must satisfy every equation and inequality in the system An equation can often be solved by. successively deducing from it one or more simpler equations For example one can add the same. constant to both sides without changing the solutions but squaring both sides might lead to. extraneous solutions Strategic competence in solving includes looking ahead for productive. manipulations and anticipating the nature and number of solutions Some equations have no. solutions in a given number system but have a solution in a larger system For example the. solution of x 1 0 is an integer not a whole number the solution of 2x 1 0 is a rational. number not an integer the solutions of x2 2 0 are real numbers not rational numbers and. the solutions of x2 2 0 are complex numbers not real numbers The same solution techniques. used to solve equations can be used to rearrange formulas For example the formula for the area. of a trapezoid A b1 b2 2 h can be solved for h using the same deductive process. Inequalities can be solved by reasoning about the properties of inequality Many but not all of. the properties of equality continue to hold for inequalities and can be useful in solving them. Connections to Functions and Modeling, Expressions can define functions and equivalent expressions define the same function Asking. when two functions have the same value for the same input leads to an equation graphing the. two functions allows for finding approximate solutions of the equation Converting a verbal. description to an equation inequality or system of these is an essential skill in modeling. Honors Algebra 2, Students successfully completing the Honors Algebra 2 course designation will cover the same.
standards below with greater depth In addition there are community service career exploration. and research project components required,Algebra 2 Enhancement. The Algebra 2 Enhancement course is designed to lend effective support to students concurrently. enrolled in Algebra 2 Using the Response to Intervention RtI model the Enhancement course. is a Tier 2 Intervention aimed at students who are at risk in mathematics It allows for rapid. response to student difficulties and provides opportunities for additional time spent on daily. targets intensity of instruction explicitly teaching and moving from the concrete to the abstract. frequent response from students and feedback from teachers as well as strategic teaching using. data to direct instruction Students are placed in the Enhancement course based on test scores. teacher parent request and academic achievement These students are enrolled in Algebra 2. Students receive elective credit for the Enhancement course. Number and Quantity Content Standards,Domain The Complex Number System N. Cluster Perform arithmetic operations with complex numbers. 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, I can define and apply the properties of the imaginary number i. I can write a complex number in the form of a bi where a and b are real numbers. 2 Use the relation i2 1 and the commutative associative and distributive properties to add. subtract and multiply complex numbers, I can add subtract and multiply expressions involving complex numbers. I can apply the commutative associative and distributive properties to simplify. expressions involving complex numbers, Cluster Use complex numbers in polynomial identities and equations.
7 Solve quadratic equations with real coefficients that have complex solutions. I can solve quadratic equations that have complex solutions. 8 Extend polynomial identities to the complex numbers. I can apply polynomial identities such as factoring to simplify expressions involving. complex numbers, 9 Know the Fundamental Theorem of Algebra show that it is true for quadratic polynomials. I can apply the Fundamental Theorem of Algebra to polynomial functions. Algebra Content Standards,Domain Seeing Structure in Expressions A. Cluster Interpret the structure of expressions, 1 Interpret expressions that represent a quantity in terms of its context. a Interpret parts of an expression such as terms factors and coefficients. I can distinguish parts of an expression such as terms factors and coefficients. b Interpret complicated expressions by viewing one or more of their parts as a single entity. I can analyze complicated expressions by viewing one or more of their parts as a single. 2 Use the structure of an expression to identify ways to rewrite it. I can use the structure of an expression to reconstruct it in different forms. Cluster Write expressions in equivalent forms to solve problems. 4 Derive the formula for the sum of a finite geometric series when the common ratio is not 1. and use the formula to solve problems, I can write a formula for the sum of a finite geometric series. I can solve problems using a formula for the sum of a finite geometric series. Domain Arithmetic with Polynomials and Rational Expressions A. Cluster Perform arithmetic operations on polynomials. 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, I can demonstrate that polynomials are closed under the operations of integers.
Cluster Understand the relationship between zeros and factors of polynomials. 2 Know and apply the Remainder Theorem For a polynomial p x and a number a the. remainder on division by x a is p a so p a 0 if and only if x a is a factor of p x. I can divide polynomials and apply the Remainder Theorem using multiple strategies. 3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to. construct a rough graph of the function defined by the polynomial. I can identify zeros of a polynomial function and use them to graph the polynomial. Cluster Use polynomial identities to solve problems. 4 Prove polynomial identities and use them to describe numerical relationships. I can apply and prove polynomial identities and use them to describe numerical. relationships, 5 Know and apply the Binomial Theorem for the expansion of x y n in powers of x and y for a. positive integer n where x and y are any numbers with coefficients determined for example. by Pascal s Triangle,I can apply the Binomial Theorem. Cluster Rewrite rational expressions, 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, I can simplify and rewrite rational expressions in different forms. 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, I can simplify rational expressions using addition subtraction multiplication and.
division by nonzero rational expressions,Domain Creating Equations A. Cluster Create equations that describe numbers or relationships. 1 Create equations and inequalities in one variable and use them to solve problems from a. variety of contexts e g science history and culture including those of Montana American. I can compose and construct equations from a variety of contexts. 2 Create equations in two or more variables to represent relationships between quantities graph. equations on coordinate axes with labels and scales. I can create equations in two or more variables to represent relationships between. quantities, I can graph equations in two or more variables on the coordinate axes with labels and. 3 Represent constraints by equations or inequalities and by systems of equations and or. inequalities and interpret solutions as viable or nonviable options in a modeling context. I can write algebraic expressions and or equations to represent constraints. I can interpret solutions as viable or non viable for a problem situation. 4 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving. I can solve an equation or formula for a variable, Domain Reasoning with Equations and Inequalities A. Cluster Understand solving equations as a process of reasoning and explain the reasoning. 2 Solve simple rational and radical equations in one variable and give examples showing how. extraneous solutions may arise, I can solve simple rational and radical equations in one variable. I can distinguish between an actual solution and an extraneous solution. Cluster Represent and solve equations and inequalities graphically. 11 Explain why the x coordinates of the points where the graphs of the equations y f x and. ALGEBRA 2 AND HONORS ALGEBRA 2 Grades 9 10 11 12 Unit of Credit 1 Year Prerequisite Geometry Course Overview Domains Seeing Structure in Expressions Arithmetic

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