Course Title: Honors Algebra Course Level: Honors Textbook: Algebra 1 Publisher: McDougall Littell

Transcription

1 Course Title: Honors Algebra Course Level: Honors Textbook: Algebra Publisher: McDougall Littell The following is a list of key topics studied in Honors Algebra. Identify and use the properties of operations on real numbers. Simplify numerical expressions using the order of operations. Translate English phrases to algebraic expressions. Solve, graph, and write linear equations. Solve and graph linear inequalities. Solve systems of linear equations and inequalities. Simplify expressions involving exponents and roots. Solve and graph quadratic equations. Add, subtract, multiply, and divide polynomials. Factor polynomials. Use ratios, proportions, and percents to solve real-life Simplify, add, subtract, multiply, and divide Explore linear, exponential, quadratic, and rational functions. Explore measures of central tendency and data displays. Explore operations and equations with radicals. Apply algebraic concepts to solve real-life Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page Adopted by the School Committee on /7/03

2 Evaluate variable expressions and model real-life situations. Evaluate expressions involving exponents and model real-life situations. Use order of operations to evaluate algebraic expressions. Use a calculator to evaluate real-life expressions. Check and solve simple equations and inequalities, including real-life situations. Translate verbal phrases into algebraic expressions. Use a verbal model to write an algebraic equation or inequality to solve a real-life problem. Use tables and graphs of organized data, including real-life situations. Identify a function and make an input-output table. 8.P. Evaluate simple algebraic expressions for given variable values. p N.7 Extend the order of operations to include positive integer exponents. p N.7 Extend the order of operations to include positive integer exponents. p N.7 Extend the order of operations to include positive integer exponents. p. 8-0.N. 8.P.4 8.D. 6.P.4 Use properties of the real number system to judge the validity of equations and inequalities, to prove or disprove statements, and to justify every step in a sequential argument. Create and use symbolic expressions and relate them to verbal representations. Select create, interpret, and utilize various tabular and graphical representations of data. Represent real-life situations and mathematical relationships with concrete models, tables, graphs, and rules in words with symbols, e.g., input-output tables. p p p p p Write an equation for a real-life p function. Graph and compare real numbers 0.N. Represent numerical relationships on a number line. p and find opposites and absolute Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page Adopted by the School Committee on /7/03

3 values. Add real numbers and use addition to solve real-life Subtract real numbers and use subtraction to solve real-life Organize data in a matrix and add and subtract matrices. Multiply real numbers and use multiplication to solve real-life Use the Distributive Property and simplify expressions by combining like terms. Divide real numbers and use division to solve real-life Find the probability and odds of an event. Solve linear equations using addition or subtraction and apply them to real-life situations. Solve linear equations using multiplication or division and apply them to real-life situations. Use two or more transformations to solve an equation and apply the equations to real-life situations. Collect variables on one side of an equation and apply these equations Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 3 Adopted by the School Committee on /7/03 8.N. Select and use appropriate operations addition, subtraction, multiplication, division, and positive integer exponents to solve problems with rational numbers. p N. Select and use appropriate operations addition, subtraction, p multiplication, division, and positive integer exponents to solve problems with rational numbers. 0.P.8 Add, subtract, and multiply matrices p N. 0.N. 8.N. 8.D.4 Select and use appropriate operations addition, subtraction, multiplication, division, and positive integer exponents to solve problems with rational numbers. Recognize and apply the associative, distributive, and commutative properties. Select and use appropriate operations addition, subtraction, multiplication, division, and positive integer exponents to solve problems with rational numbers. Use tree diagrams, tables, organized lists, basic combinatorics, and area models to compute probabilities for events. p p p p. 4-0 p p p p

4 to real-life Draw a diagram to help understand real-life problems and check answers. Find exact and approximate solutions to equations with decimals and apply them to real-life Solve a formula or literal equation for one of its variables. 0.P.7 0.P.6 Describe, generalize, and model linear, exponential, and power functions to investigate real-world situations. variables using algebraic methods, models, and/or graphs. Apply the associative, commutative, distributive, identity, and inverse properties to isolate a variable. p p p Rewrite an equation in function 0.P. Describe, complete, extend, analyze, generalize, and create a wide p. 76- form. variety of patterns, including functions. 79 Use rates, ratios, and percents to 8.N.3 Use ratios and proportions in the solution of problems involving rate p. 80- model and solve real-life of change. 86 Plot points in a coordinate plane and 8.D. Select, create, interpret, and utilize various graphical p. 03- use a scatter plot. representations of data. 09 Graph a linear equation using a table 0.P. Graph linear equations by plotting points. p. 0- of values. 7 Graph horizontal and vertical lines. 0.P. Graph linear equations by plotting points. p. 3-7 Find the intercepts of the graph of a 8.P.0 Compare rates of change and x- and y-intercepts of linear patterns. p. 8- linear equation and use intercepts to sketch a graph of a line. 4 Find slope using two points and interpret slope as a constant rate of change. Write linear equations that represent direct variation. Graph a linear equation in slopeintercept form and use the form to 8.P.5 0.P. Identify the slope of a line as a constant rate of change. p P.7 Solve everyday problems that can be modeled using direct variation. p P. Use slope and y-intercept to graph a line and demonstrate an understanding of the relationship. interpret real-life situations. Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 4 Adopted by the School Committee on /7/03 p

5 Identify if a relation is a function and use functional notation to solve Use slope-intercept form to write an equation of a line and to model a real-life situation. Use the slope and a point to write an equation of a line and to make predictions about real-life situations. Use two points to write an equation of a line given two points and use the equation to model a real-life situation. Find a linear equation that approximates a set of data points, and use scatter plots to determine positive, negative, or no correlation. Use point-slope form to write a linear equation and use the equation to model a real-life situation. Transform a linear equation into standard form and use it to model real-life situations. Determine whether a linear model is appropriate and use it to make reallife predictions. 0.P. Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including functions. 0.P. 0.P. 0.P. 0.P. 0.P. 0.P. 0.P. Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including functions. Find a linear equation describing a line from a graph or a geometric Find a linear equation describing a line from a graph or a geometric Find a linear equation describing a line from a graph or a geometric Find a linear equation describing a line from a graph or a geometric Find a linear equation describing a line from a graph or geometric Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including linear functions. p p p Graph and solve linear inequalities Set up and solve linear inequalities using algebraic methods. p in one variable. 339 Use linear inequalities to model and Set up and solve linear inequalities using algebraic models. p solve real-life 345 Write, solve and graph compound 0.P.7 Describe, generalize, and model linear, exponential, and power p Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 5 Adopted by the School Committee on /7/03 p p p p p. 35-3

6 inequalities and use them to model functions to investigate real-world situations. 35 real-life situations. Solve absolute value equations. 0.P.6 Solve equations including absolute value. p Solve absolute value inequalities. 0.P.6 Solve inequalities involving absolute value. p Graph a linear inequality in two 0.P.7 Apply graphic methods to solutions of p variables. 36 Model a real-life situation using a 0.P.7 Apply graphic methods to solutions of p. 36- linear inequality in two variables. 367 Make and use a stem and leaf plot to 8.D. Select, create, interpret, and utilize various graphical p put data in order. representations of data including stem-and-leaf plots. 369 Find the mean, median, and mode of 8.D.3 Find, describe and interpret measures of central tendency. p data. 374 Draw, read, and interpret a box and 8.D. Select, create, interpret and utilize various graphical representations p whisker plot of real-life data. of data, including box- and-whisker plots. 38 Solve a system of linear equations by 0.P.8 Solve problems that can be modeled using a system of linear p graphing. 404 Solve a system of linear equations by 0.P.8 Solve problems that can be modeled using a system of linear p substitution. 40 Solve a system of linear equations by 0.P.8 Solve problems that can be modeled using a system of linear p. 4- linear combinations. 47 Identify linear systems as having 0.P.8 Solve problems that can be modeled using a system of linear p. 45- one, no, or infinitely many solutions. 43 Write and use a linear system as a 0.P.8 Solve problems that can be modeled using a system of linear p real-life model. 43 Solve a system of linear inequalities 0.P.8 Solve problems that can be modeled using a system of linear p. 43- by graphing. 433 Use a system of linear inequalities to 0.P.8 Solve problems that can be modeled using a system of linear p model a real-life situation. 438 Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 6 Adopted by the School Committee on /7/03

7 Use properties of exponents to multiply exponential expressions. Use the division properties of exponents to evaluate powers and simplify expressions. Use the division properties of exponents to find a probability. Use scientific notation to express large and small numbers and perform operations with numbers in scientific notation. Use scientific notation to solve reallife Write, use, and graph models for exponential growth. Write, use, and graph models for exponential decay. Evaluate and approximate square roots. Solve a quadratic equation by finding square roots. Use properties of radicals to simplify radicals. Use quadratic equations to model real-life situations. Sketch the graph of a quadratic function. 0.N. Simplify numerical expressions including those with integer exponents. 0.N. Simplify numerical expressions including those with integer exponents. 0.P. 8.N.4 8.N.4 0.P.7 0.P.7 0.N.3 0.N.3 0.N. 0.P.7 0.P. Simplify numerical expressions including those with integer exponents. Represent numbers in scientific notation, and use them in calculations and Represent numbers in scientific notation, and use them in calculations and Describe, generalize, and model linear, exponential, and power functions to investigate real-world situations. Describe, generalize, and model linear, exponential, and power functions to investigate real-world situations. Find the approximate value for solutions to problems involving square roots and cube roots. Find the approximate value for solutions to problems involving square roots and cube roots. Simplify numerical expressions including those with integer exponents. Solve everyday problems that can be modeled using quadratic functions. Describe, complete, and create a variety of patterns, including quadratic functions. p p p p p p p p p p p p Use the quadratic formula to solve a quadratic equation, including real- 0.P.5 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. life models. Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 7 Adopted by the School Committee on /7/03 p

8 Find the number of solutions of a quadratic equation by using the discriminant and apply to real-life problems Add and subtract polynomials and use them to model real-life situations. Multiply two polynomials and apply to real-life situations. Use special product patterns for the product of a sum and difference and for the square of a binomial and apply them to real-life models. 0.P.5 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. p Solve polynomial equations in 0.P.5 Find solutions to quadratic equations. p factored form. 60 Factor a quadratic expression of the 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p form x + bx + c. 609 Factor a quadratic expression of ax 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p bx + c. 68 Use special product patterns to factor 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p. 69- quadratic polynomials. 64 Use the distributive property to 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p. 65- factor a polynomial. 63 Use factoring to solve quadratic and 0.P.5 Find solutions to quadratic equations. p polynomial equations. 63 Solve and use proportions in real-life 0.P.5 Find solutions to quadratic equations. p Solve and use percent in real-life 8.N.3 Use ratios and proportions in the solution of problems involving rate p of change. 655 Use direct and inverse variation., and 0.P.7 Describe, generalize, and model linear, exponential, and power p solve real-life functions to investigate real-world situations. 663 Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 8 Adopted by the School Committee on /7/03 0.P.3 Add, subtract, multiply and divide polynomials. p P.3 Add, subtract, multiply, and divide polynomials. p P.3 Add, subtract, multiply, and divide polynomials. p

9 Simplify 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p Multiply and divide rational 0.P.4 Simplify rational algebraic expressions by factoring. p expressions. 675 Add and subtract rational 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p expressions. 68 Divide a polynomial by a monomial 0.P.4 Demonstrate facility in symbolic manipulation of polynomial and p or binomial factor, including long 689 division. Solve rational equations..p.8 Solve a variety of equations, including those with rational p Add, subtract, multiply and divide radical expressions and use them to model real-life situations. Solve a radical equation and apply them to real-life Use the Pythagorean Theorem and its converse. expressions. 698.N. Simplify numerical expressions with powers and roots. p P. Solve everyday problems that can be modeled using square roots. p G.4 Demonstrate an understanding of the Pythagorean Theorem and p apply it to the solutions of 744 Grade 8, Algebra Honors Scituate Public Schools PreK- Math Curriculum Page 9 Adopted by the School Committee on /7/03