Assessment Anchors and Eligible Content Aligned to the Algebra 1 Pennsylvania Core Standards

Transcription

1 Assessment Anchors and Eligible Content Aligned to the Algebra 1 Pennsylvania Core Standards MODULE 1 A1.1.1 ASSESSMENT ANCHOR Operations and Linear Equations & Inequalities Demonstrate an understanding of rational and irrational numbers. DESCRIPTOR ELIGIBLE CONTENT I CAN Learn Lesson # I CAN Learn Lesson Title A Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents). A Compare and/or order any real numbers. Note: Rational and irrational may be mixed. HA1-025 Comparing and Ordering Real Numbers A Apply number theory concepts to show relationships between real numbers in problem-solving settings. A A Simplify square roots. Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. HA1-490 HA1-492 HA1-335 MPA-027 Simplifying Square Roots Simplifying Square and Cube Roots Finding the LCD of Rational Expressions and Changing Fractions to Equivalent Fractions Finding the Greatest Common Factor MPA-030 Finding Least Common Multiple of Two or More Numbers

2 A Use exponents, roots, and/or absolute values to solve problems. A Simplify/evaluate expressions involving properties/laws of exponents, roots, and/ or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. MPA-013 Using Powers and Exponents in Expressions HA1-810 Simplifying Expressions Using the Multiplication Properties of Exponents HA1-815 Simplifying Expressions with Negative and Zero Exponents HA1-818 Simplifying Expressions Using the Division Properties of Exponents HA1-065 Evaluating Expressions Containing Exponents HA1-860 Using the Laws of Exponents A Use estimation strategies in problem solving situations. A Use estimation to solve problems. MPA-005 Estimating Products and Quotients Using Patterns MPA-017 Rounding Decimals and Estimating Computations Using Decimals MPA-033 Estimating Computations with Fractions and Mixed Numbers MPA-065 Estimating Square Roots

3 A Simplify expressions involving polynomials. A Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. HA1-075 Simplifying Algebraic Expressions by Combining Like Terms HA1-076 Basic Distributive Property HA1-085 Simplifying Expressions Using the Properties of Real Numbers HA1-079 Using a Concrete Model to Simplify Algebraic Expressions HA1-090 Simplifying Expressions Using the Property of -1 HA1-080 Simplifying and Evaluating Algebraic Expressions Containing Grouping Symbols HA1-220 Identifying and Multiplying Monomials HA1-225 Dividing Monomials and Simplifying Expressions Having an Exponent of Zero HA1-230 Raising a Monomial or Quotient of Monomials to a Power HA1-240 Identifying the Degree of Polynomials and Simplifying by Combining Like Terms HA1-245 Adding and Subtracting Polynomials HA1-920 Simplifying Algebraic Expressions Using the Distributive Property HA1-255 Multiplying Two Binomials Using the FOIL Method HA1-260 Squaring a Binomial and Finding the Product of a Sum and Difference

4 A Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax2 + bx + c where a is equal to 1 after factoring out all monomial factors. HA1-265 Writing a Number in Prime Factorization and Finding the Greatest Common Factor HA1-270 Factoring the Greatest Common Monomial Factor from a Polynomial HA1-271 Factoring Trinomials and Differences of Squares Using Algebra Tiles HA1-275 Factoring the Difference Between Two Squares and Perfect Trinomial Squares HA1-276 Factoring Sums and Differences of Cubes HA1-280 Factoring x² + bx + c When c is Greater Than Zero HA1-285 Factoring x² + bx + c When c is Less Than Zero HA1-290 Factoring ax² + bx + c HA1-291 Factoring Quadratic Expressions Using the Graphing Calculator HA1-295 Factoring by Removing a Common Factor and Grouping HA1-300 Factoring a Polynomial Completely HA1-802 Factoring A Simplify/reduce a rational algebraic HA1-315 Defining Rational Expressions and Determining the Restricted Values HA1-320 Simplifying Rational Expressions HA1-325 Multiplying Rational Expressions HA1-330 Dividing Rational Expressions HA1-335 Finding the LCD of Rational Expressions and Changing Fractions to Equivalent Fractions HA1-340 Adding and Subtracting Rational Expressions

5 A1.1.2 HA1-345 HA1-350 HA1-335 ASSESSMENT ANCHOR Adding and Subtracting Polynomials and Rational Expressions Simplifying Complex Fractions Finding the LCD of Rational Expressions and Changing Fractions to Equivalent Fractions Linear Equations DESCRIPTOR ELIGIBLE CONTENT I CAN Learn Lesson # I CAN Learn Lesson Title A Write, solve, and/or graph linear equations using various methods. A Write, solve, and/or apply a linear equation (including problem situations). HA1-115 Using the Addition and Subtraction Properties for Equations HA1-120 Using the Multiplication and Division Properties for Equations HA1-124 Using a Concrete Model to Solve One- and Two- Step Equations HA1-125 Solving Equations Using More Than One Property HA1-140 Solving Equations by Combining Like Terms HA1-144 Using a Concrete Model to Solve Equations with Variables on Both Sides HA1-145 Solving Equations with Variables on Both Sides HA1-360 Expressing Ratios in Simplest Form and Solving Equations Involving Proportions HA1-382 Solving Linear Equations Using the Graphing Calculator HA1-449 Applying Inductive and Deductive Reasoning HA1-150 Writing an Equation to Solve Word Problems HA1-155 Writing an Equation to Solve Consecutive Integer Problems HA1-160 Writing an Equation to Solve Distance, Rate, and Time Problems HA1-362 Solving Work Problems

6 HA1-472 Solving Mixture Problems HA1-165 HA1-170 HA1-380 HA1-385 HA1-398 HA1-401 HA1-394 HA1-405 HA1-410 HA1-395 Using Equations to Solve Percent Problems Solving Percent of Change Problems Graphing Linear Equations Finding the Slope of a Line from its Graph or from the Coordinates of Two Points Graphing Linear Equations Using Slope and y-intercept or Slope and a Point How Variations of "m" and "b"; Affect the Graph of y = mx + b Interchanging Linear Equations Between Standard Form and Slope-Intercept Form Determining an Equation of a Line Given the Slope and Coordinates of One Point Determining an Equation of a Line Given the Coordinates of Two Points Finding the Equation of a Line Parallel or Perpendicular to a Given Line A Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only. HA1-115 Using the Addition and Subtraction Properties for Equations HA1-120 Using the Multiplication and Division Properties for Equations HA1-124 Using a Concrete Model to Solve One- and Two- Step Equations HA1-125 Solving Equations Using More Than One Property HA1-140 Solving Equations by Combining Like Terms HA1-144 Using a Concrete Model to Solve Equations with Variables on Both Sides HA1-145 Solving Equations with Variables on Both Sides

7 A Interpret solutions to problems in the context of the problem situation. Note: Linear equations only. HA1-360 HA1-155 HA1-160 Expressing Ratios in Simplest Form and Solving Equations Involving Proportions Writing an Equation to Solve Consecutive Integer Problems Writing an Equation to Solve Distance, Rate, and Time Problems HA1-362 Solving Work Problems HA1-472 Solving Mixture Problems HA1-165 Using Equations to Solve Percent Problems HA1-170 Solving Percent of Change Problems HA1-455 Solving Systems of Linear Equations by Graphing HA1-460 Solving Systems of Linear Equations by the Substitution Method HA1-465 Solving Systems of Linear Equations by the Addition/Subtraction Method HA1-470 Solving Systems of Linear Equations by the Multiply/Add/Subtract Method HA1-806 Solving Systems of Linear Equations Using the Graphing Calculator A Write, solve, and/or graph systems of linear equations using various methods. A Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. HA1-455 Solving Systems of Linear Equations by Graphing HA1-460 Solving Systems of Linear Equations by the Substitution Method

8 HA1-465 Solving Systems of Linear Equations by the Addition/Subtraction Method HA1-470 Solving Systems of Linear Equations by the Multiply/Add/Subtract Method A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. HA1-806 HA1-455 HA1-460 Solving Systems of Linear Equations Using the Graphing Calculator Solving Systems of Linear Equations by Graphing Solving Systems of Linear Equations by the Substitution Method HA1-465 Solving Systems of Linear Equations by the Addition/Subtraction Method HA1-470 Solving Systems of Linear Equations by the Multiply/Add/Subtract Method A Write, solve, and/or graph linear inequalities using various methods. A Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). HA1-806 HA1-200 HA1-205 Solving Systems of Linear Equations Using the Graphing Calculator Combined Inequalities Solving Combined Inequalities A Identify or graph the solution set to a linear inequality on a number line. HA1-185 Solving Inequalities Using the Addition and Subtraction Properties HA1-190 Solving Inequalities Using the Multiplication and Division Properties HA1-195 Solving Inequalities Using More Than One Property

9 A Interpret solutions to problems in the context of the problem situation. Note: Linear inequalities only. HA1-185 Solving Inequalities Using the Addition and Subtraction Properties HA1-190 Solving Inequalities Using the Multiplication and Division Properties HA1-195 Solving Inequalities Using More Than One Property A A Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. HA1-415 Graphing Linear Inequalities with Two Variables HA1-416 Graphing Linear Inequalities with Two Variables Using the Graphing Calculator HA1-475 Graphing the Solution Set of a System of Linear Inequalities A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. HA1-870 HA1-415 HA1-416 Solving Problems with Systems of Linear Equations and Inequalities Graphing Linear Inequalities with Two Variables Graphing Linear Inequalities with Two Variables Using the Graphing Calculator HA1-475 Graphing the Solution Set of a System of Linear Inequalities HA1-870 Solving Problems with Systems of Linear Equations and Inequalities

10 MODULE 2 Linear Functions and Data Organizations A1.2.1 ASSESSMENT ANCHOR Functions A DESCRIPTOR Analyze and/or use patterns or relations. A ELIGIBLE CONTENT Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. I CAN Learn Lesson # MPA-270 I CAN Learn Lesson Title Generating Algebraic Expressions from Patterns of Models HA1-447 HA1-448 Identifying Number Patterns Finding the nth Term of a Pattern A Determine whether a relation is a function, given a set of points or a graph. MPA-103 Distinguishing Between Relations and Functions HA1-437 Identifying Relations as Functions A Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). HA1-438 Finding the Domain and Range of Functions HA1-867 Identifying Domain and Range of Relations Given Graphs, Tables, or Sets of Ordered Pairs A Interpret and/or use linear functions and their equations, graphs, or tables. A Create, interpret, and/or use the equation, graph, or table of a linear function. HA1-441 Applications of Functions and Relations Involving Distance, Rate, and Time HA1-442 Interpreting Graphs of Functions in Real-Life Situations

11 A1.2.2 A DESCRIPTOR Describe, compute, and/or use the rate of change (slope) of a line. A Translate from one representation of a linear function to another (i.e., graph, table, and equation). ASSESSMENT ANCHOR ELIGIBLE CONTENT Identify, describe, A and/or use constant rates of change. A Apply the concept of linear rate of change (slope) to solve problems. HA1-955 Analyzing Linear Functions HA1-960 HA1-402 I CAN Learn Lesson # HA1-955 HA1-398 HA1-401 HA1-955 HA1-960 Real-World Applications of Linear Functions Translating Among Multiple Representations of Functions I CAN Learn Lesson Title Analyzing Linear Functions Coordinate Geometry Graphing Linear Equations Using Slope and y-intercept or Slope and a Point How Variations of m and b Affect the Graph of y = mx + b Analyzing Linear Functions Real-World Applications of Linear Functions

12 A Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line. Note: Linear equation may be in pointslope, standard, and/or slopeintercept form. HA1-380 Graphing Linear Equations HA1-385 Finding the Slope of a Line from its Graph or from the Coordinates of Two Points HA1-398 Graphing Linear Equations Using Slope and y-intercept or Slope and a Point HA1-401 How Variations of "m" and "b"; Affect the Graph of y = mx + b HA1-394 Interchanging Linear Equations Between Standard Form and Slope-Intercept Form HA1-405 Determining an Equation of a Line Given the Slope and Coordinates of One Point HA1-410 Determining an Equation of a Line Given the Coordinates of Two Points HA1-405 Determining an Equation of a Line Given the Slope and Coordinates of One Point HA1-410 Determining an Equation of a Line Given the Coordinates of Two Points A Determine the slope and/or y-intercept represented by a linear equation or graph. HA1-955 Analyzing Linear Functions HA1-960 Real-World Applications of Linear Functions

13 HA1-401 How Variations of "m" and "b"; Affect the Graph of y = mx + b HA1-405 Determining an Equation of a Line Given the Slope and Coordinates of One Point HA1-410 Determining an Equation of a Line Given the Coordinates of Two Points A Analyze and/or interpret data on a scatter plot. A Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. HA1-965 Determining the Best-Fitting Line MPA-132 Interpreting and Creating Scatterplots HA1-605 Interpreting the Correlation Coefficient of a Linear Fit HA1-965 Determining the Best-Fitting Line ASSESSMENT ANCHOR A1.2.3 Data Analysis DESCRIPTOR ELIGIBLE CONTENT I CAN Learn Lesson # I CAN Learn Lesson Title A Use measures of dispersion to describe a set of data. A Calculate and/or interpret the range, quartiles, and interquartile range of data. HA1-540 Finding the Mean, Median, and Mode from Data and Frequency Distribution Tables HA1-541 Analyzing Data Using the Measures of Central Tendency and the Range MPA-097 Constructing Box-and-Whisker Plots HA1-555 Computing the Range, Variance, and Standard Deviation of a Set of Data

14 A Use data displays in problem-solving settings and/or to make predictions. A Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation. HA1-877 Drawing Inferences and Making Predictions from Tables and Graphs MPA-092 Reading and Interpreting Bar, Line, and Circle Graphs MPA-098 Making Predictions from Graphs and Choosing the Correct Graph MPA-099 Making Predictions from Graphs and Choosing the Correct Graph A Analyze data, make predictions, and/or answer questions based on displayed data (box-andwhisker plots, stemand-leaf plots, scatter plots, measures of central tendency, or other representations). HA1-545 Using Frequency Tables HA1-540 Finding the Mean, Median, and Mode from Data and Frequency Distribution Tables HA1-541 Analyzing Data Using the Measures of Central Tendency and the Range HA1-965 Determining the Best-Fitting Line HA1-605 Interpreting the Correlation Coefficient of a Linear Fit HA1-885 Histograms and the Normal Distribution HA1-555 Computing the Range, Variance, and Standard Deviation of a Set of Data HA1-877 Drawing Inferences and Making Predictions from Tables and Graphs MPA-096 Constructing Stem-and-Leaf Plots MPA-097 Constructing Box-and-Whisker Plots

15 MPA-131 Interpreting and Creating Histograms MPA-132 Interpreting and Creating Scatterplots MPA-835 Using Measures of Central Tendency MPA-836 Using Measures of Variation A Make predictions using the equations or graphs of best-fit lines of scatter plots. HA1-965 Determining the Best-Fitting Line HA1-605 Interpreting the Correlation Coefficient of a Linear Fit MPA-132 Interpreting and Creating Scatterplots A Apply probability to practical situations. A Find probabilities for compound events (e.g., fi nd probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. HA1-605 HA1-879 HA1-560 Interpreting the Correlation Coefficient of a Linear Fit Applying Counting Techniques to Permutations and Combinations Determining Probability of an Event and Complementary Event from a Random Experiment HA1-555 Computing the Range, Variance, and Standard Deviation of a Set of Data MPA-090 Finding the Probability of Simple Real-Life Events MPA-112 Constructing Sample Spaces for Compound Events (Dependent and Independent) MPA-113 Finding the Probability of Compound Events Through Experimentation MPA-114 Finding the Odds of Events and Experimental Probability from a Math Model