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 MidChapter 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 MidChapter Quiz 492 #6#8 Practice and Problem Solving Practice Test 517 #5#8 RealWorld 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. ProblemSolving Handbook 812 RealWorld 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 RealWorld 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 MidChapter 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 8182, 90 Practice and Problem Solving 78, 8687, RealWorld 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 RealWorld 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 RealWorld 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 MidChapter Quiz 361 Practice and Problem Solving , , 352, 358 RealWorld 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 RealWorld 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 RealWorld 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 RealWorld 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 RealWorld 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 RealWorld 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 RealWorld 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 MidChapter 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 RealWorld 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 RealWorld 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. P40P43, Check Your Understanding 248 #3 Example P40, P41 Exercises P43 Practice and Problem Solving 249 #8#11 RealWorld 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 RealWorld 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 RealWorld 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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