MACMILLAN/McGRAW-HILL MATH CONNECTS and IMPACT MATHEMATICS TO WASHINGTON STATE MATHEMATICS STANDARDS ESSENTIAL ACADEMIC LEARNING REQUIREMENTS (EALRs) And GRADE LEVEL EXPECTATIONS (GLEs) / Edition, Copyright 2009
MACMILLAN/MCGRAW-HILL MATH CONNECTS and IMPACT MATHEMATICS, 2009 Washington and, 4.1. Core Content: Multi-digit multiplication (Numbers, Operations, Algebra) Students learn basic multiplication facts and efficient procedures for multiplying two- and three-digit numbers. They explore the relationship between multiplication and division as they learn related division and multiplication facts in the same fact family. These skills, along with mental math and estimation, allow students to solve problems that call for multiplication. Building on an understanding of how multiplication and division relate to each other, students prepare to learn efficient procedures for division, which will be developed in fifth grade. Multiplication of whole numbers is not only a basic skill, it is also closely connected to Core Content in this grade level on area, and this connection reinforces understanding of both concepts. Multiplication is also central to students study of many other topics in mathematics across the grades, including fractions, volume, and algebra. Performance Expectations Students are expected to: 4.1.A Quickly recall multiplication facts through 10 x 10 and the related division facts Math Connects: pp. 154-157, 160-162, 163, 175, 182, 184, 187, 310 IMPACT Mathematics: pp. T2C, T2D, T3, T4, T12 4.1.B Identify factors and multiples of a number. Math Connects: pp. 176B, 176-179, 180, 186, 187, 188 IMPACT Mathematics: pp. T5, T6 4.1.C Represent multiplication of a two-digit number by a twodigit number with place value models. Math Connects: pp. 273B, 273-275, 276A, 276B, 276-279, 280A, 280B, 282-283, 284B, 284-286, 287, 288A, 303, 305 IMPACT Mathematics: pp. T27, T28 4.1.D Multiply by 10, 100, and 1,000. Math Connects: pp. 161, 162, 188, 237B, 238, 239, 267, 273B, 273-275 IMPACT Mathematics: p. T21 4.1.E Compare the values represented by digits in whole numbers using place value. Math Connects: pp. 14G, 14H, 14-15, 16, 17A, 17B, 17-19, 20-21, 22B, 22-25, 26A, 29, 30, 31, 33, 44-45, 49, 50, 59 IMPACT Mathematics: pp. T27, T28 2
4.1.F Fluently and accurately multiply up to a three-digit number by one- and two-digit numbers using the standard multiplication algorithm. 4.1.G Mentally multiply two-digit numbers by numbers through 10 and by multiples of 10. 4.1.H Estimate products to approximate solutions to problems and determine reasonableness of answers. 4.1.I Solve single- and multi-step word problems involving multi-digit multiplication and verify the solutions. 4.1.J Solve single- and multi-step word problems involving division and verify the solutions. and, Math Connects: pp. 246-248, 249, 252-255, 258-261, 264, 265, 266, 267, 270, 273-275, 276-279, 282-283, 284-286, 287, 288-291, 296-298, 299, 301, 303-304, 305 IMPACT Mathematics: pp. T2C, T3, T4, T5, T7, T8, T11, T12 Math Connects: pp. 234H, 237B, 237-239, 240A, 240-241, 242B, 242-244, 245, 246A, 252-255, 263, 264, 273B, 273-275, 276A, 276B, 276-279, 280B, 288-289, 292-293, 301, 305 IMPACT Mathematics: pp. T3, T4, T21, T27, T28, T31 Math Connects: pp. 242-244, 245, 247, 252-253, 258-259, 262, 264, 276-279, 285, 288-289, 296-297, 300-301, 303 IMPACT Mathematics: pp. T3, T9, T10, T24C, T24D, T27, T28, T95 Math Connects: pp. 237, 238, 239, 240, 242, 243, 244, 252, 254, 258, 259, 260, 269, 273, 274, 275, 276, 277, 284, 285, 286, 288, 290, 296, 298 IMPACT Mathematics: pp. T2D, T7, T8, T12 Math Connects: pp. 148, 151, 152, 156, 160, 162, 313, 314, 315, 316, 318, 322, 323, 326, 327, 328, 332, 333, 334, 336, 337, 338, 341, 342, 343, 351, 355, LA2, LA3, LA4, LA5, LA6, LA7 IMPACT Mathematics: pp. T2, T2D, T7, T8, T9, T10, T12 4.2. Core Content: Fractions, decimals, and mixed numbers (Numbers, Algebra) Students solidify and extend their understanding of fractions (including mixed numbers) to include decimals and the relationships between fractions and decimals. Students work with common factors and common multiples as preparation for learning procedures for fraction operations in grades five and six. When they are comfortable with and knowledgeable about fractions, students are likely to be successful with the challenging skills of learning how to add, subtract, multiply, and divide fractions. 3
Performance Expectations Students are expected to: 4.2.A Represent decimals through hundredths with place value models, fraction equivalents, and the number line. 4.2.B Read, write, compare, and order decimals through hundredths. 4.2.C Convert a mixed number to a fraction and vice versa, and visually represent the number. 4.2.D Convert a decimal to a fraction and vice versa, and visually represent the number. 4.2.E Compare and order decimals and fractions (including mixed numbers) on the number line, lists, and the symbols <, >, or =. and, Math Connects: pp. 574, 576, 577-578, 579B, 579-581, 582A, 582-585, 586A, 588-589, 590A, 590-591, 593, 596-598, 599, 602-604, 605, 606, 607, 608, 609, 610, 611, 614, 616, 617, 628-629, 630, 636-637, 638, 645, 648 IMPACT Mathematics: pp. T45, T46, T46C, T46D, T47, T48, T49, T50, T51, T52, T55 Math Connects: pp. 574H, 579-581, 582-584, 590B, 590-592, 593, 594A, 597-599, 602, 603, 606, 607, 609, 611, 612, 613 IMPACT Mathematics: pp. T46C, T46D, T51, T52, T53, T54, T55 Math Connects: pp. 560-563, 570, 571, 572, 573 IMPACT Mathematics: pp. T53, T54 Math Connects: pp. 576, 577-578, 579B, 579-581, 582A, 582-585, 586A, 588-589, 590A, 593, 596-599, 602-604, 605, 607, 610, 611, R58-R59 IMPACT Mathematics: pp. T46C, T46D, T47, T48, T49, T50, T55, T56 Math Connects: pp. 588B, 588-589, 590A, 593, 596, 598, 599, 600-601, 602-604, 605, 608, 611 IMPACT Mathematics: pp. T46C, T46D, T51, T52, T53, T54 4.2.F Write a fraction equivalent to a given fraction. Math Connects: pp. 546-547, 548-551, 552, 553, 555, 566, 569, 571, 572-573, 597 IMPACT Mathematics: pp. T33, T34, T34C, T34D, T35, T36, T37, T38, T46D 4
and, 4.2.G Simplify fractions using common factors. Math Connects: Opportunities to address: pp. 546-547, 548-551, LA14B, LA14-LA17 IMPACT Mathematics: pp. T34C, T41, T42, T50 4.2.H Round fractions and decimals to the nearest whole number. 4.2.I Solve single- and multi-step word problems involving comparison of decimals and fractions (including mixed numbers), and verify the solutions. Math Connects: pp. 617-620, 621, 622-625, 633, 643, 644-645, 649, 650-651 IMPACT Mathematics: p. T56 Math Connects: pp. 537, 538, 540, 551, 552, 560, 563, 579, 583, 590, 602, 617, 618, 619, 622, 624, 630, 631, 632, 638, 639, 640 IMPACT Mathematics: pp. T38, T40, T52 4.3. Core Content: Concept of area (Geometry/Measurement, Algebra) Students learn how to find the area of a rectangle as a basis for later work with areas of other geometric figures. They select appropriate units, tools, and strategies, including formulas, and use them to solve problems involving perimeter and area. Solving such problems helps students develop spatial skills, which are critical for dealing with a wide range of geometric concepts. The study of area is closely connected to Core Content on multiplication, and connections between these concepts should be emphasized whenever possible. Performance Expectations Students are expected to: 4.3.A Determine congruence of two-dimensional figures. Math Connects: pp. 418B, 418-420, 421, 422A, 432, 433 IMPACT Mathematics: pp. T99, T100, T100C, T103, T104, T108 4.3.B Determine the approximate area of a figure using square units. Math Connects: pp. 436J, 460, 461, 462, 464-465, 476, 477, 479 IMPACT Mathematics: pp. T3, T57, T58, T58C, T58D, T59, T60, T61, T62, T63, T64, T65, T66, T80D 4.3.C Determine the perimeter and area of a rectangle using formulas, and explain why the formulas work. Math Connects: pp. 293, 436I, 436J, 436, 456B, 456-459, 460A, 460B, 460-462, 463, 464-465, 466A, 466-467, 472, 474, 475, 476, 477, 479 5
and, Continued from previous page IMPACT Mathematics: pp. T57, T58, T58C, T58D, T59, T60, T61, T62 4.3.D Determine the areas of figures that can be broken down into rectangles. 4.3.E Demonstrate that rectangles with the same area can have different perimeters, and that rectangles with the same perimeter can have different areas. 4.3.F Solve single- and multi-step word problems involving perimeters and areas of rectangles and verify the solutions. Math Connects: pp. 460B, 477, R67, R68, R69 IMPACT Mathematics: pp. T58, T58C, T62, T63, T64, T65, T66, T100D Math Connects: pp. 456B, 462, 464-465 IMPACT Mathematics: pp. T58C, T59, T60 Math Connects: pp. 446-447, 456, 457, 458, 460, 461, 462, 466-467, 477 IMPACT Mathematics: pp. T61, T62, T65 4.4. Additional Key Content (Geometry/Measurement, Algebra, Data/Statistics/Probability) Students use coordinate grids to connect numbers to basic ideas in algebra and geometry. This connection between algebra and geometry runs throughout advanced mathematics and allows students to use tools from one branch of mathematics to solve problems related to another branch. Students also extend and reinforce their work with whole numbers and fractions to describe sets of data and find simple probabilities. Students combine measurement work with their developing ideas about multiplication and division as they do basic measurement conversions. They begin to use algebraic notation while solving problems in preparation for formalizing algebraic thinking in later grades. Performance Expectations Students are expected to: 4.4.A Represent an unknown quantity in simple expressions, equations, and inequalities using letters, boxes, and other symbols. Math Connects: pp. 7, 31, 148, 149, 152, 156-157, 163, 168, 173, 182, 186, 187, 190, 193A, 193B, 193-195, 196-197, 198A, 198B, 198-201, 202A, 202, 207, 214B, 214-216, 217, 218A, 220-223, 224, 225, 228, 229, 230, 231, 239, 267, R56-R57 IMPACT Mathematics: pp. T13, T14, T22 6
4.4.B Solve single- and multi-step problems involving familiar unit conversions, including time, within either the U.S. customary or metric system. 4.4.C Estimate and determine elapsed time using a calendar, a digital clock, and an analog clock. 4.4.D Graph and identify points in the first quadrant of the coordinate plane using ordered pairs. 4.4.E Determine the median, mode, and range of a set of data and describe what each measure indicates about the data. and, Math Connects: pp. 252, 274, 277, 441-443, 444A, 444B, 444-445, 448-449, 450-452, 453, 455, 459, 473, 485, 486-489, 490-491, 498-500, 504-507, 528, R62-R63 IMPACT Mathematics: pp. T61, T67, T68D, T80, T80C, T81, T83 Math Connects: pp. 482I, 520B, 520-523, 524, 530, 531 IMPACT Mathematics: pp. T67, T68, T68C, T68D, T73, T74, T77, T78 Math Connects: pp. 392H, 406B, 406-408, 409, 412A, 415, 430, 435, R62-R63 IMPACT Mathematics: pp. T90, T95, T96 Math Connects: pp. 98B, 98-101, 102A, 105-107, 108A, 111, 133, 140, R73, R74-R75 IMPACT Mathematics: p. T91 4.4.F Describe and compare the likelihood of events. Math Connects: pp. 128B, 128-130, 131, 132, 138, 139, 140-141 4.4.G Determine a simple probability from a context that includes a picture. 4.4.H Display the results of probability experiments and interpret the results. Math Connects: pp. 122-123, 124-127, 128B, 128-130, 131, 138, 139, R76 Math Connects: pp. 124B, 124, 125, 126, 127, 128A, 128B, 130, 131, 138 4.5. Core Processes: Reasoning, problem solving, and communication Students in grade four solve problems that extend their understanding of core mathematical concepts such as multiplication of multi-digit numbers, area, probability, and the relationships between fractions and decimals as they make strategic decisions that bring them to reasonable solutions. Students use pictures, symbols, or mathematical language to explain the reasoning behind their decisions and solutions. They further develop their problem-solving skills by making generalizations about the processes used and 7
and, applying these generalizations to similar problem situations. These critical reasoning, problem-solving, and communication skills represent the kind of mathematical thinking that equips students to use the mathematics they know to solve a growing range of useful and important problems and to make decisions based on quantitative information. Performance Expectations Students are expected to: 4.5.A Determine the question(s) to be answered given a problem situation. Math Connects: pp. 26-27, 40-41, 42-43, 46, 48, 62-63, 76-77, 78-79, 86, 88, 102-103, 118-119, 120-121, 134, 137, 158-159, 164-165, 170-171, 183, 185, 202-203, 212-213, 218-219, 226, 230, 240-241, 250-251, 256-257, 263, 265, 280-281, 292-293, 294-295, 302, 304, 320-321, 330-331, 340-341, 348, 350, 366-367, 380-381, 382-383, 386, 388, 404-405, 416-417, 426-427, 430, 431, 446-447, 454-455, 466-467, 477, 502-503, 516-517, 518-519, 527, 529, 544-545, 558-559, 564-565, 568, 570, 586-587, 594-595, 600-601, 608, 609, 626-627, 634-635, 642-643, 646, 647 4.5.B Identify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem. Math Connects: pp. 26-27, 40-41, 46, 48, 62-63, 76-77, 86, 88, 102-103, 118-119, 134, 137, 158-159, 170-171, 183, 185, 202-203, 218-219, 226, 230, 240-241, 250-251, 263, 265, 280-281, 294-295, 302, 304, 320-321, 330-331, 348, 350, 366-367, 380-381, 386, 388, 404-405, 416-417, 430, 431, 446-447, 466-467, 477, 502-503, 518-519, 527, 529, 544-545, 564-565, 568, 570, 586-587, 594-595, 608, 609, 626-627, 634-635, 646, 647 8
4.5.C Identify missing information that is needed to solve a problem. 4.5.D Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem. 4.5.E Select and use one or more appropriate strategies to solve a problem and explain why that strategy was chosen. 4.5.F Represent a problem situation using words, numbers, pictures, physical objects, or symbols. Continued on next page and, Math Connects: pp. 202-203, 226 Math Connects: pp. 40-41, 48, 76-77, 88, 102-103, 118-119, 134, 137, 170-171, 185, 218-219, 230, 250-251, 265, 280-281, 294-295, 302, 304, 320-321, 330-331, 348, 350, 366-367, 380-381, 386, 388, 404-405, 416-417, 430, 431, 446-447, 466-467, 477, 502-503, 518-519, 527, 529, 544-545, 564-565, 568, 570, 586-587, 594-595, 608, 609, 626-627, 634-635, 646, 647 Math Connects: pp. 40-41, 48, 76-77, 88, 118-119, 137, 170-171, 185, 218-219, 230, 250-251, 265, 294-295, 304, 330-331, 350, 380-381, 388, 416-417, 431, 466-467, 477, 518-519, 529, 564-565, 570, 594-595, 609, 634-635, 647 Math Connects: pp. 26-27, 40-41, 42-43, 46, 48, 62-63, 76-77, 78-79, 86, 88, 102-103, 118-119, 120-121, 134, 137, 158-159, 164-165, 170-171, 183, 185, 202-203, 212-213, 218-219, 226, 230, 240-241, 250-251, 256-257, 263, 265, 280-281, 292-293, 294-295, 302, 304, 320-321, 330-331, 340-341, 348, 350, 366-367, 380-381, 382-383, 386, 388, 404-405, 416-417, 426-427, 430, 431, 446-447, 454-455, 466-467, 477, 502-503, 516-517, 518-519, 527, 529, 9
and, Continued from previous page 544-545, 558-559, 564-565, 568, 570, 586-587, 594-595, 600-601, 608, 609, 626-627, 634-635, 642-643, 646, 647 4.5.G Explain why a specific problem-solving strategy or procedure was used to determine a solution. 4.5.H Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. 4.5.I Summarize mathematical information, draw conclusions, and explain reasoning. Math Connects: pp. 40-41, 48, 76-77, 88, 118-119, 137, 170-171, 185, 218-219, 230, 250-251, 265, 294-295, 304, 330-331, 350, 380-381, 388, 416-417, 431, 466-467, 477, 518-519, 529, 564-565, 570, 594-595, 609, 634-635, 647 Math Connects: pp. 40-41, 48, 76-77, 88, 102-103, 118-119, 134, 137, 170-171, 185, 218-219, 230, 250-251, 265, 280-281, 294-295, 302, 304, 320-321, 330-331, 348, 350, 366-367, 380-381, 386, 388, 404-405, 416-417, 430, 431, 446-447, 466-467, 477, 502-503, 518-519, 527, 529, 544-545, 564-565, 568, 570, 586-587, 594-595, 608, 609, 626-627, 634-635, 646, 647 Math Connects: pp. 240-241, 263, 416-417, 502-503, 527, 594-595, 634-635, P2-P3, P4-P5, P6-P7, P8-P9 10
4.5.J Make and test conjectures based on data (or information) collected from explorations and experiments. and, Math Connects: pp. 62-63, 86, 123, 320-321, 348, 439-440, 448-449, 496-497 11