ROSLYN PUBLIC SCHOOLS INTEGRATED ALGEBRA CURRICULUM. Day(s) Topic Textbook Workbook Additional Worksheets

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1 I. Review 1 and 2 Review p Screening Test 2. Review sheet

2 II. Real Numbers A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas. 1 Review of the real number system p Properties of real numbers p47-54 p32-34 Commutative Distributive Associative Identity Inverse Zero 3 Closure p45-47 p and 5 Binary Tables 1. binary tables.notebook 6 Rules of Exponents p p52-54 Zero and negative exponents Product of powers (a m ) (a n ) Power of a product (ab) n Powers raised to a power (a m ) n Quotient of powers Power of a quotients (a/b) n 7 Scientific Notation p p Mathematical systems (4 sheets)

3 III. Linear Equations A.A.1 Translate a quantitative verbal phrase into an algebraic expression A.A.2 Write a verbal expression that matches a given mathematical expression A.A.3 Distinguish the difference between an algebraic expression and an algebraic equation A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable A.A.22 Solve all types of linear equations in one variable A.A.23 Solve literal equations for a given variable 1 and 2 Translating verbal, written and algebraic phrases Represent words with mathematical expressions and equations (and vice versa) Distinguish between algebraic expressions and equations Write expressions and equations to represents a situation p p63-70

4 Days Topic Textbook Workbook Additional Worksheets 3 and 4 Solving linear equations One and two steps equations with one unknown (including fractions and decimals) *combine like terms *Distributive property *Variables on both sides of the equal sign Determine whether a value is a solution to a given equation p p Solving literal equations p p86-89 evaluating formulas 6 Number word problems p133 Number problems 7 and 8 Consecutive integer problems Consecutive integer problems 9 Perimeter word problems p138 Perimeter problems 10 Coin and stamp problems p Coin problems 11 and 12 Motion Problems p141 Motion problems 13 Review of all word problems Mixed set of verbal problems

5 IV. Linear Inequalities A.A.21 A.A.24 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable Solve linear inequalities in one variable 1 Translating verbal, written and algebraic phrases involving inequalities p (translating) p89-94 Graph inequalities on a number line Disjunction (or) Conjunction (and) 2 Solving linear inequalities with one variable Multiplying or dividing by a negative number Multistep 3 Compound Inequalities Solving Graphing p (graphing) p p Inequalities 2. Writing and solving inequalities 4 Word problems involving inequalities p160 p95-96

6 V. Graphing Linear Equations and Inequalities ROSLYN PUBLIC SCHOOLS A.A.32 A.A.33 A.A.34 A.A.35 A.A.36 A.A.37 A.A.38 A.A.39 A.A.40 A.G.3 A.G.6 Graph the Explain slope as a rate of change between dependent and independent variables Determine the slope of a line, given the coordinates of two points on the line Write the equation of a line, given its slope and the coordinates of a point on the line Write the equation of a line, given the coordinates of two points on the line Write the equation of a line parallel to the x- or y-axis Determine the slope of a line, given its equation in any form Determine if two lines are parallel, given their equations in any form Determine whether a given point is on a line, given the equation of the line Determine whether a given point is in the solution set of a system of linear inequalities Determine when a relation is a function, by examining ordered pairs and inspecting graphs relations Graph linear inequalities 1 and 2 Review of the coordinate plane system and terminology Introduction to functions Definition Vertical line test Recognize a function Domain/range Input/output 3 Graphing a line from a table of values p p Identifying the domain and range of a function Lesson 4.2 Practice B Determine if a point lies on a line

7 4 Slope definition Finding the slope from a graph Determining the slope using the slope formula Identify the four slope types Graphing horizontal and vertical lines 5 Finding the x- and y-intercepts algebraically and graphically 6 Graphing a line using the slope-intercept method p p p369 Finding the x- and y-intercepts p Lesson 5.1 Practice A Identify the slope and y-intercept from an equation Write the equation of a line in slope-intercept form from a graph 7 and 8 Write the equation of a line given the slope and a point on the line p Practice B Practice B Write the equation of a line passing through two given points on the line Write the equation of a line from a table of values 9 and 10 Determine if two lines are parallel or perpendicular given their equations in any form p p and 12 Write the equation of the line parallel to or perpendicular to a given line and passing through a given point Graphing linear inequalities on the coordinate plane p p Why Did the Three Pigs Leave Home?

8 VI. Systems of Linear Equations and Inequalities A.A.7 A.A.10 A.A.40 A.G.7 Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables Solve systems of two linear equations in two variables algebraically (See A.G.7) Determine whether a given point is in the solution set of a system of linear inequalities Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10) 1 and 2 Solving systems of linear equations graphically and checking p p What Were the Headlines After a Mad Scientist Trained Two Eggs to Attack a Candy Store With Sharp Sticks? 3 and 4 Solving systems of linear equations algebraically using substitution 5 and 6 Solving systems of linear equations using combinations/elimination 7 Solving verbal problems involving systems of linear equations 8 Solving systems of linear inequalities graphically p p Practice 7-2 p p Practice 7-3 p Practice 7-4 p p Determine if a point is in the solution of a system of linear inequalities

9 VII. Polynomials A.A.12 A.A.13 Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only. Add, subtract, and multiply monomials and polynomials 1 Add and subtract polynomials p p Multiply polynomials Polynomial by monomial Binomial by binomial (FOIL) Polynomial by polynomial p p99-111

10 VIII. Factoring A.A.19 A.A.20 Identify and factor the difference of two perfect squares Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) 1 and 2 Factoring using the GCF method p p Double Cross 3 Factoring the difference of two squares DOTS p p G-4 4 and 5 Factoring trinomials in the form of ax 2 +bx+c p p G-3 where a=1 6 Factoring trinomials in the form of ax 2 +bx+c p p G-3 where a 1 7 Factoring Completely p p G-5

11 IX. Quadratic Equations A.A.8 A.A.11 A.A.27 A.A.28 Analyze and solve verbal problems that involve quadratic equations Solve a system of one linear and one quadratic equation in two variables, where only factoring is required Note: The quadratic equation should represent a parabola and the solution(s) should be integers. Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression A.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10 ) A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph A.G.8 Find the roots of a parabolic function graphically Note: Only quadratic equations with integral solutions. A.G.9 Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers. A.G.10 Determine the vertex and axis of symmetry of a parabola, given its graph (See A.A.41) Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value. 1-3 Solve quadratic equations algebraically through factoring Rewrite quadratic equations in standard form 4 and 5 Graph a quadratic from a table of values p p p p Unit 7 Patterns/Functions (6 pages) Use the graph and the formulas to determine the axis of symmetry, vertex, and maximum or minimum Determine the roots of a quadratic equation from its graph 6 and 7 Solve verbal problems involving quadratics p G-8 2. G-9 3.Quadratic Word Problems

12 8 Solve linear-quadratic systems graphically p p Unit 7 Patterns/Functions: Solving Quadratic/Linear Pairs of Equations Graphically 9 and 10 Solve linear-quadratic systems algebraically p p Worksheet Unit 7 Patterns/Functions: Solving Quadratic/Linear Pairs of Equations Algebraically

13 X. Other Non-Linear Functions A.A.9 Analyze and solve verbal problems that involve exponential growth and decay A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph 1-4 Graph and identify exponential functions Solve word problems involving exponential functions (including compound interest problems) 5 Graph and identify absolute value functions p p p p Algebra 1- Exponential Growth and Decay 2. Lesson 8.5 Practice B 6 Distinguish between the graphs of different functions 1. Integrated Algebra Practice: Families of Functions 2. FUNCTIONS: Families of Functions

14 XI. Rational Expressions and Equations A.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no remainder A.A.15 Find values of a variable for which an algebraic fraction is undefined A.A.16 Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms A.A.17 Add or subtract fractional expressions with monomial or like binomial denominators A.A.18 Multiply and divide algebraic fractions and express the product or quotient in simplest form A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable. A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations 1 Find the value(s) for which the fraction is p540 p undefined 2 Simplify rational expressions through factoring p p (including factoring out -1) 3-5 Multiplying and dividing rational expressions p p Adding and subtracting rational expressions with like and unlike denominators 9-11 Solving fractional equations by crossmultiplication and by multiplying by the LCD p p p p

15 XII. Ratios, Proportions and Percents A.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percent (decrease/increase and discount), and proportionality/direct variation A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable. A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations A.M.1 Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail) A.M.2 Solve problems involving conversions within measurement systems, given the relationship between the units A.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure 1 and 2 Simplify ratios p p Calculate unit rates Converting unit rates Solving proportions 3 and 4 Percent problems involving tax, simple interest, sale price, commission, gratuities and increase/decrease p p and 6 Relative error and percent error p p Direct Variation p p

16 XIII. Radicals and Right Triangles A.R.6 Use mathematics to show and understand physical phenomena (e.g., find the height of a building if a ladder of a given length forms a given angle of elevation with the ground) A.N.2 Simplify radical terms (no variable in the radicand) A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form A.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides A.A.43 Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle A.A.44 Find the measure of a side of a right triangle, given an acute angle and the length of another side A.A.45 Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides 1 Simplifying radicals p p Adding and subtracting radicals p p Multiplying radicals p p Dividing radicals p p Using the Pythagorean theorem to determine if a triangle is a right triangle and to find the missing side of a right triangle p p and 7 Intro to trigonometry Solving basic problems involving the sine, cosine and tangent functions p , p Word problems involving the angle of depression and angle of elevation p p Algebra 1 Angle of Elevation/Depression 2. Practice 11-6

17 XIV. Plane and Solid Geometry A.G.1 Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only). A.G.2 Use formulas to calculate volume and surface area of rectangular solids and cylinders 1 Find the perimeter and area of triangles, parallelograms, rectangles, rhombuses, squares, trapezoids, circles, semi-circles, and quarter-circles 1. Area of Polygons # Area of Circles 3. Circumference 2 Shaded area problems p p Surface of rectangular solids and cylinders p p Surface Area #1 and 2 4 Volume of rectangular prisms and cylinders p p

18 XV. Set Theory A.RP.11 Use a Venn diagram to support a logical argument A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagrams A.CM.3 Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form A.R.2 Recognize, compare, and use an array of representational forms A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form A.A.30 Find the complement of a subset of a given set, within a given universe A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets) 1 and 2 Set-builder and interval notation Review of the real number system Comparing Notations 3 and 4 Intersection and union of sets, venn diagrams p71-74 p54-58 Numbers Operations and Properties

19 XVI. Probability A.S.18 Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces A.S.19 Determine the number of elements in a sample space and the number of favorable events A.S.20 Calculate the probability of an event and its complement A.S.21 Determine empirical probabilities based on specific sample data A.S.22 Determine, based on calculated probability of a set of events, if: o some or all are equally likely to occur o one is more likely to occur than another o whether or not an event is certain to happen or not to happen A.S.23 Calculate the probability of: o a series of independent events o a series of dependent events o two mutually exclusive events o two events that are not mutually exclusive 1 and 2 Sample space p p Simple probability Counting principle 3 and 4 Conditional probability p p Probability of independent and dependent events 5 and 6 Permutations and factorials p P

20 XVII. Statistics and Regression A.S.1 Categorize data as qualitative or quantitative A.S.2 Determine whether the data to be analyzed is univariate or bivariate A.S.3 Determine when collected data or display of data may be biased A.S.4 Compare and contrast the appropriateness of different measures of central tendency for a given data set A.S.5 Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data A.S.6 Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box and-whisker plot A.S.7 Create a scatter plot of bivariate data A.S.8 Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line A.S.9 Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-andwhisker plot A.S.10 Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions A.S.11 Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles A.S.12 Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none) A.S.13 Understand the difference between correlation and causation A.S.14 Identify variables that might have a correlation but not a causal relationship A.S.15 Identify and describe sources of bias and its effect, drawing conclusions from data A.S.16 Recognize how linear transformations of one-variable data affect the data s mean, median, mode, and range A.S.17 Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation 1 and 2 Categorizing data p p Measures of central tendency 3 Histograms and cumulative frequency histograms 4 and 5 Percentiles p p p p Box and whisker plots

21 6 Drawing conclusions from data p p and 8 Scatter plots and lines of best fit p p Integrated Algebra Practice: Scatter Plots #1 2. Integrated Algebra Practice: Scatter Plots #2

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