Keystone Exams: Algebra I Assessment Anchors and Eligible Content. Pennsylvania

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1 Keystone Exams: Algebra I Assessment Anchors and Pennsylvania Algebra STANDARDS MODULE 1 Operations and Linear Equations & Inequalities ASSESSMENT ANCHOR A1.1.1 Operations with Real Numbers and Expressions 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. A Simplify square roots (e.g., 24 = 2 6). P7 Example P8 Exercises P10 #13-#18 AE P8 Check Your Understanding 615 #1-#9 Example 612 Extra Practice 837 Mid-Chapter Quiz 629 #8, #9, #14 Practice and Problem Solving 615 #17-#34 Practice Test 661 #6-#10 Standardized Test Example 614 Study Guide and Review 657 #18-#25 AE 613 Codes used for Teacher Edition pages are the initial caps of headings on that page.

2 A Apply number theory concepts to show relationships between real numbers in problem solving settings. A Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. 471 Check Your Understanding 472 Example 471 Extra Practice 832 Mid-Chapter Quiz 492 #6-#8 Practice and Problem Solving Practice Test 517 #5-#8 Real-World Example 472 Study Guide and Review 514 #15-#18 AE 472; DI 474 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. Check Your Understanding 105 #1-#3, 404, 412 Example 103, 402, 403, 408, 409, 411 Extra Practice Practice and Problem Solving 106 #13-#21, 405, 413 Practice Test 463 #1-#6 Standardized Test Practice 466 #1, #2 Study Guide and Review 460 AE 103, 402 A Use estimation strategies in problem solving situations. A Use estimation to solve problems. Problem-Solving Handbook 812 Real-World Example 163 Study Tip P18 TNT 163 Keystone Exams: Algebra I 2 Algebra 1

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. 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. A Simplify/reduce a rational algebraic expression. Check Your Understanding 435, 441, 450 Example 433, 434, 439, 441, 447, 448 Explore Extra Practice 831 Practice and Problem Solving 436, 442, 450 Practice Test 463 #14-#22 Real-World Example 435, 449 Study Guide and Review 461 #37-#41, 462 AE 434, 440, 448; DI 435, 441, 448 Check Your Understanding 489 Example 486, 487 Explore Extra Practice 833 Key Concept 485 Mid-Chapter Quiz 492 #20-#22 Practice and Problem Solving 489 Practice Test 517 #18, #19 Standardized Test Practice 491 #52, 520 #4 Study Guide and Review 515 #31-#34 AE 486; DI 486 Check Your Understanding 687 Example 684, 685, 686, 687 Extend 691 Key Concept 685 Practice and Problem Solving 688 AE 686, FMC 686 Keystone Exams: Algebra I 3 Algebra 1

4 A1.1.2 Linear Equations A Write, solve, and/or graph linear equations using various methods. A Write, solve, and/or apply a linear equation (including problem situations). A Use and/or identify an algebraic property to justify any step in an equation solving process. Note: Linear equations only. A Interpret solutions to problems in the context of the problem situation. Note: Linear equations only. Check Your Understanding 77, 86, 93 Example 75, 83, 84, 85, 91 Explore 81-82, 90 Practice and Problem Solving 78, 86-87, Real-World Example 76, 85, 92 Standardized Test Practice 89 AE 76, 84, 92; DI 77, 92; TNT 77 Check Your Understanding 19 Example 17, 19 83, 84 Key Concept 16, 17, 18, 83, 84 Practice and Problem Solving Real-World Example 18 AE 17, 18, 19, 84; DI 18 Check Your Understanding 86 #16, #17, 93 #8 Mixed Problem Solving 846 Practice and Problem Solving 86 #42, #43, #62-#71, 94 #23, #40, #41, #51, #52, 101 #38, #40 Real-World Example 85, 92 Standardized Test Practice 89 AE 85, 92 Keystone Exams: Algebra I 4 Algebra 1

5 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. A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. 333 Check Your Understanding 336, 344, 350, 357 Concept Summary 333 Example 334, 342, 343, 348, 349, 350 Extend Key Concept 342 Mid-Chapter Quiz 361 Practice and Problem Solving , , 352, 358 Real-World Example 335, 344, 350, 357 Standardized Test Practice 347 #32, 396 #1-#4, #6-#8 Study Guide and Review 389, 390 AE 334, 343, 349, 356; DI 343, 357 Check Your Understanding 336 #9, 345 #7, 351 #6, 357 #5, #6 Mixed Problem Solving 850 Practice and Problem Solving 337 #25, #26, #42, #43, 345 #23-#26, 352 #23, #30, #31, 358 #20, #25, #27 Real-World Example 335, 344, 350, 357 A1.1.3 Linear Inequalities 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). 304, 310 Check Your Understanding 306, 312 Example 304, 306, 310 Extra Practice 826 Practice and Problem Solving 306, 307, Practice Test 325 #12-#14, #17-#21 Real-World Example 305, 311 Standardized Test Practice 329 #9, #12, #14 Study Guide and Review 324 #31-#44 AE 305, 311; DI 308, 311 Keystone Exams: Algebra I 5 Algebra 1

6 A Identify or graph the solution set to a linear inequality on a number line. A Interpret solutions to problems in the context of the problem situation. Note: Limit to linear inequalities. 284 Check Your Understanding 286 #1-#8 Practice and Problem Solving 286 #12-#29 Check Your Understanding 286 #11, 293 #1, 298 #1, #2 Mixed Problem Solving 849 Practice and Problem Solving 286 #34-#40, 293 #10, #30-#34, #39, #40, 299 #35, #36, #39-#41 Real-World Example 285, 291, 296 A Write, solve, and/or graph systems of linear inequalities using various methods. A Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. Check Your Understanding 384 Example 382 Extra Practice 829 Practice and Problem Solving Practice Test 393 #22-#25 Real-World Example 383 Standardized Test Practice 396 #5 Study Guide and Review 392 #67-#71 AE 383, 384; DI 383 Check Your Understanding 384 #9 Mixed Problem Solving 850 Practice and Problem Solving 384 #25, #26, #36, #37 Real-World Example 383 A1.2.1 Functions A Analyze and/or use patterns or relations. A Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. The following page references can be expanded to include patterns to meet this objective. Example 39, 47 H.O.T. Problems 43 #41 Practice and Problem Solving 43 #37, 51 #48 Keystone Exams: Algebra I 6 Algebra 1

7 A Determine whether a relation is a function, given a set of points or a graph. A Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). Check Your Understanding 49 #1-#8 Example 45, 47 Extra Practice 817 Key Concept 45, 47 Practice and Problem Solving 50 #20-#25 Study Guide and Review 66 #65-#68 Study Tip 47 AE Check Your Understanding 41 #1, #2 Example 39 Practice and Problem Solving 41 #9-#14, 42 #27, #28 AE 39 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. A Translate from one representation of a linear function to another (i.e., graph, table, and equation). Check Your Understanding 49 #9, #10, 164 #9 Practice and Problem Solving 50 #45, #48, 164 #22, #23, #36, #37-#44 Real-World Example 163 Check Your Understanding 157 #9, #10 Example 155, 156 Extend 167 Practice and Problem Solving 157 #19, #20, #29-#34, #58 AE 156 Keystone Exams: Algebra I 7 Algebra 1

8 A1.2.2 Coordinate Geometry A Describe, compute, and/or use the rate of change (slope) of a line. A Identify, describe, and/or use constant rates of change. A Apply the concept of linear rate of change (slope) to solve problems. 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 point slope, standard, and/or slope intercept form. A Determine the slope and/or y intercept represented by a linear equation or graph. Check Your Understanding 175 #4, #5 Example 172 H.O.T. Problems 177 #49 Practice and Problem Solving 176 #20-#23 Study Tip 172 AE Check Your Understanding 175 Example 173, 174 Extra Practice 821 Mid-Chapter Quiz 179 #23, #24 Practice and Problem Solving Practice Test 205 #14 Standardized Test Practice 208 #3, #4, #12 Study Guide and Review 203 #27-#31 AE 173, 174; DI 174 Check Your Understanding 217 #1-#4, #11-#14, 227 #5-#8 Example 214, 224, 225 Practice and Problem Solving 218 #17-#22, #33-#36, #38-#43, #52-#57, 227 #10-#21, #25-#30 Real-World Example 217 Standardized Test Example 216 AE 215, 217, 225; DI 226 Check Your Understanding 175 #1, 227 Example 224 Extend H.O.T. Problems 229 #49 Practice and Problem Solving 176 #16, #17, 227 Standardized Test Practice 230 #53 Keystone Exams: Algebra I 8 Algebra 1

9 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. 246 Check Your Understanding 248 #3 Practice and Problem Solving 249 #8-#10 Practice Test 275 #20 Real-World Example 246 Study Guide and Review 273 #48 AE 246 A1.2.3 Data Analysis A Use measures of dispersion to describe a set of data. A Calculate and/or interpret the range, quartiles, and interquartile range of data. P38, P42 Concept Summary 757 Example P38, P42 Exercises P39 #9-#16, P43 #4, #5 Posttest P45 #70 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, measures of central tendency, or other representations. A Analyze data, make predictions, and/or answer questions based on displayed data (box andwhisker plots, stem and leaf plots, scatter plots, measures of central tendency, or other representations). A Make predictions using the equations or graphs of best fit lines of scatter plots. The following page references can be expanded to include predictions to meet this objective. P40-P43, Check Your Understanding 248 #3 Example P40, P41 Exercises P43 Practice and Problem Solving 249 #8-#11 Real-World Example 247 Study Tip 247 AE P41, 247 Check Your Understanding 248 #3 H.O.T. Problems 250 #16 Practice and Problem Solving 249 #8-#11 Practice Test 275 #20 Real-World Example 247 AE 247 Keystone Exams: Algebra I 9 Algebra 1

10 A STANDARDS Apply probability to practical situations. A Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. Check Your Understanding 775 Extra Practice 844 H.O.T. Problems 777 #34, #35 Key Concept 771 Practice and Problem Solving Real-World Example 771, 773 Standardized Test Practice 801 #14 Study Guide and Review 796 #25-#30 AE 772; DI 773 Keystone Exams: Algebra I 10 Algebra 1

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