New York Math Test Houghton Mifflin Grade 4 Elementary Elements
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1 1. MATHEMATICAL REASONING Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument. A. use models, facts, and relationships to draw conclusions about mathematics and explain their thinking. Grade K Representative Pages: 42-45, , , , , , , , , Grade 1 Representative Pages: 11A-12, 19A-20, 25A-30, 57A-58, 71A-74, 125A- 128, 191A-196, 403A-406, 549A-552, 565A-568 Grade 2 Representative Pages: 17A-20, 71A-72, 159A-160, 199A-206, 255A-264, 385A-392, 475A-476, 515A-516, 555A-558, 563A-566 Grade 3 Representative Pages: 16-17, , , , , , , , , Grade 4 Representative Pages: 16-17, , , , , , , , , B. use patterns and relationships to analyze mathematical situations. Grade K 76-91, 92-95, , , , Grade 1 193A-194, 209A-214, 217A-218, 275A-276, 427A-428 Grade 2 27A-28, 83A-84, 91A-92, 285A-286, 505A-506, 575A-576 Grade , , , 301, , , Grade , , , , , , C. justify their answers and solution processes. Throughout the series, students discuss their strategies and solutions for the Problem Solving feature. Grade K Representative Pages: 42-45, 92-95, , , , , , , , Grade 1 Representative Pages: 35A-36, 77A-78, 131A-132, 159A-160, 231A-232, 283A-284, 363A-364, 431A-432, 527A-528, 581A-582 Grade 2 Representative Pages: 33A-34, 75A-76, 129A-130, 159A-160, 263A-264, 393A-394, 443A-444, 475A-476, 533A-534, 567A-568 Grade 3 Representative Pages: 64-65, 76-77, , , , , , , , Grade 4 Representative Pages: 70-71, 88-89, , , , , , , , (1)
2 D. use logical reasoning to reach simple conclusions. Throughout the series, students use logical reasoning to reach solutions for the Problem Solving feature. Grade K Representative Pages: 60-63, , , , , , , , , Grade 1 Representative Pages: 119A-120, 131A-132, 159A-160, 231A-232, 283A- 284, 329A-330, 419A-420, 431A-432, 459A-460, 581A-582 Grade 2 Representative Pages: 45A-46, 75A-76, 91A-92, 117A-118, 175A-176, 217A-218, 263A-264, 393A-394, 475A-476, 567A-568 Grade 3 Representative Pages: 76-77, , , , , , , , , Grade 4 Representative Pages: 26-27, 70-71, , , , , , , , NUMBER AND NUMERATION Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas. A. use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances. Grade K , , , , , , , Grade 1 191A-198, 201A-204, 371A-376, 455A-458, 467A-470, 475A-478 Grade 2 65A-68, 325A-336, , 505A-512 Grade 3 4-5, 16-17, 32-35, , , , Grade , , , , B. use concrete materials to model numbers and number relationships for whole numbers and common fractions, including decimal fractions. Grade K , , , , , , , , , Grade 1 191A-198, 201A-206, 371A-376 Grade 2 27A-28, 65A-68, 285A-286, 325A-336, 505A-512 Grade 3 4-5, 16-17, 32-35, , Grade 4 9, 16-17, , , (2)
3 C. relate counting to grouping and to place value. Grade K , , , , Grade 1 191A-198, 201A-206 Grade 2 67A-70, 507A-508, 513A-514 Grade , Grade 4 4-5, D. recognize the order of whole numbers and commonly used fractions and decimals. Grade K , Grade 1 229A-230, 373A-376 Grade 2 87A-88, 331A-332, 527A-530 Grade , , Grade 4 6-8, 20-22, , E. demonstrate the concept of percent through problems related to actual situations. Grade 3 Can be developed from material on fractions and decimals , Grade 4 Can be developed from material on fractions and decimals , OPERATIONS Students use mathematical operations and relationships among them to understand mathematics. A. add, subtract, multiply, and divide whole numbers. Grade K , , , Grade 1 9A-18, 25A-30, 55A-64, 71A-78, 97A-104, 111A-120, 125A-132, 251A- 260, 267A-272, 399A-408, 411A-420 Grade 2 13A-22, 29A-32, 199A-206, 223A-226, 255A-262, 269A-274, 363A-370, 373A-378, 383A-392 Grade , , , , , , , , , , , , , Grade , , , , , , , (3)
4 B. develop strategies for selecting the appropriate computational and operational method in problem-solving situations. Grade K Grade 1 77A-78, 283A-284, 431A-432, 581A-582 Grade 2 45A-46, 175A-176, 393A-394, 567A-568 Grade , , , , , , Grade , 78-83, , , , , , C. know single-digit addition, subtraction, multiplication, and division facts. Grade K , Grade 1 97A-108, 111A-120, 127A-128, 253A-258, 269A-272, 277A-280, 399A- 408, 411A-418, 425A-426 Grade 2 43A-44, 363A-366, 373A-376, 387A-390 Grade , , , , , , , , , , Grade , , D. understand the commutative and associative properties. Grade 1 31A-32, 99A-100, 125A-128, 257A-258, 275A-276, 407A-408 Grade 2 9A-10, 21A-22, 367A-368 Grade , , Grade , , , MODELING/MULTIPLE REPRESENTATION Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships. A. use concrete materials to model spatial relationships. Grade K , Grade 1 349A-352 Grade 2 307A-312, 315A-318 Grade , , , Grade , B. construct tables, charts, and graphs to display and analyze real-world data. Grade K 48-63, , , , Grade 1 153A-154, 157A-158, 167A-170, 261A-262, 557A-558 Grade 2 111A-114, 125A-126, 517A-518 Grade Grade , , (4)
5 C. use multiple representations (simulations, manipulative materials, and diagrams) as tools to explain the operation of everyday procedures. Grade K Representative Pages: , , , , , , Grade 1 Representative Pages: 19A-20, 25A-30, 71A-74, 113A-116, 259A-260, 315A-320, 327A-328, 403A-406, 515A-518, 549A-552 Grade 2 Representative Pages: 153A-160, 167A-176, 227A-228, 283A-284, 429A- 436, 439A-444, 463A-476, 481A-486, 531A-534, 579A-580 Grade , 68-75, 78-85, , , Grade , , , , D. use variables such as height, weight, and hand size to predict changes over time. Grade (line graphs) E. use physical materials, pictures, and diagrams to explain mathematical ideas and processes and to demonstrate geometric concepts. Grade K Representative Pages: , , , , , , , , , Grade 1 Representative Pages: 9A-12, 25A-30, 55A-58, 65A-66, 71A-74, 105A- 106, 259A-260, 353A-356, 359A-362, 369A-370 Grade 2 Representative Pages: 17A-20, 81A-82, 199A-206, 255A-264, 311A-312, 315A-318, 325A-336, 361A-362, 385A-392, 561A-566 Grade 3 Representative Pages: 16-17, , , , , , , , , Grade 4 Representative Pages: 16-17, , , , , , , , , MEASUREMENT Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. A. understand that measurement is approximate, never exact. Grade K , Grade 1 451A-454, 465A-466, 473A-474 Grade 2 413A-416, 454 (Enrichment) Grade , , , Grade , (5)
6 B. select appropriate standard and nonstandard measurement tools in measurement activities. Grade K , , Grade 1 453A-458, 467A-470, 475A-480 Grade 2 413A-420, 429A-436, 441A-444 Grade , , Grade , C. understand the attributes of area, length, capacity, weight, volume, time, temperature, and angle. Grade K , Grade 1 451A-458, 465A-470, 473A-480, 490 (Enrichment), 501A-506, 515A-516 Grade 2 417A-422, 429A-436, 439A-444, 463A-472 Grade , 78-83, , , , , , Grade , , , , D. estimate and find measures such as length, perimeter, area, and volume using both standard and nonstandard units. Grade K Grade 1 451A-458, 465A-470, 473A-480 Grade 2 413A-422, 433A-436 Grade , , , Grade , , , E. collect and display data. Grade K 48-59, Grade 1 153A-154, 157A-158, 167A-170, 261A-262, 557A-558 Grade 2 111A-114, 125A-126, 517A-518 Grade Grade , F. use statistical methods such as graphs, tables, and charts to interpret data. Grade K 48-63, Grade 1 153A-158, 165A-172, 527A-528, 557A-558 Grade 2 111A-118, 123A-130, 287A-288 Grade , , Grade , , (6)
7 6. UNCERTAINTY Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations. A. make estimates to compare to actual results of both formal and informal measurement. Grade K , Grade 1 451A-452, 465A-466, 473A-474 Grade 2 413A-416 Grade , , , Grade , B. make estimates to compare to actual results of computations. Grade K 430 (Activity Option), 434 (Activity Option) Grade 1 88 (Enrichment), 142 (Enrichment), 592 (Enrichment) Grade 2 215A-216, 275A-276, 577A-578 Grade , , Grade , , , , C. recognize situations where only an estimate is required. Grade K , , , , Grade 1 223A-224, 451A-452, 465A-466, 473A-474 Grade 2 215A-216, 275A-276, 413A-416, 577A-578 Grade , , , , , , Grade , 64-67, , , , D. develop a wide variety of estimation skills and strategies. Grade K , , , , 430 (Activity Option), 434 (Activity Option) Grade 1 88 (Enrichment), 142 (Enrichment), 223A-224, 451A-452, 465A-466, 473A-474, 592 (Enrichment) Grade 2 215A-216, 275A-276, 454 (Enrichment), 544 (Enrichment), 592 (Enrichment) Grade , 12-13, 24-27, , , , , , Grade , 24-25, 64-67, , , , (7)
8 E. determine the reasonableness of results. See Problem Solving features found throughout the series. Grade K Representative Pages: 42-45, , , , , , , , , Grade 1 Representative Pages: 35A-36, 77A-78, 119A-120, 131A-132, 171A-172, 283A-284, 431A-432, 459A-460, 479A-480, 581A-582 Grade 2 Representative Pages: 45A-46, 75A-76, 117A-118, 175A-176, 217A-218, 393A-394, 443A-444, 533A-534, 567A-568, 581A-582 Grade 3 Representative Pages: 12-13, 76-77, , , , , , , , Grade 4 Representative Pages: 36-37, 70-71, , , , , , , , F. predict experimental possibilities. Grade 1 377A-378 Grade 2 337A-338 Grade Grade G. make predictions using unbiased random samples. Grade 1 377A-378 Grade 2 337A-338 Grade Grade H. determine probabilities of simple events. Grade 1 377A-378 Grade 2 337A-338 Grade Grade (8)
9 7. PATTERNS/FUNCTIONS Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently. A. recognize, describe, extend, and create a wide variety of patterns. Grade K 76-95, , , Grade 1 193A-194, 209A-214, 217A-218, 363A-364, 374 Grade 2 65A-66, 83A-84, 91A-92, 319A-320, 505A-506, 553A-554, 561A-562 Grade , , , 301, , Grade , , , , , , B. represent and describe mathematical relationships. Grade K 76-91, 92-95, , , , Grade 1 125A-126, 275A-280, 425A-428, 575A-576 Grade 2 27A-28, 285A-286, 575A-576 Grade , , Grade , 70-71, , C. explore and express relationships using variables and open sentences. Grade K , , Grade 1 125A-128, 131A-132, 259A-260, 275A-280, 283A-284, 419A-420, 425A- 428, 431A-432, 575A-576 Grade 2 33A-34, 45A-46, 393A-394, 567A-568 Grade , , , , , , Grade , , , , D. solve for an unknown using manipulative materials. Grade K , , Grade 1 131A-132, 259A-260, , 581A-582 Grade 2 21A-22, 41A-42, 45A-46, 393A-394 Grade , , , , , , Grade , , , , E. use a variety of manipulative materials and technologies to explore patterns. Grade K 76-95, , , Grade 1 193A-194, 209A-214, 217A-218, 363A-364, 374 Grade 2 65A-66, 83A-84, 91A-92, 319A-320, 505A-506, 553A-554, 561A-562 Grade , , , 301, , Grade , , , , , , (9)
10 F. interpret graphs. Grade K 48-63, , , , Grade 1 155A-156, 165A-166, 169A-170, 171A-172 Grade 2 115A-116, 123A-124, 127A-130 Grade , Grade , , G. explore and develop relationships among two- and three-dimensional geometric shapes. Grade K , Grade 1 353A-356, 359A-362 Grade 2 307A-318 Grade , , Grade , , H. discover patterns in nature, art, music, and literature. Grade K Grade 1 209A (Two-Minute Math), 215B (Gifted and Talented), 374 (Problem Solving-Reasoning) Grade 2 319A-320 Grade 3 301, Grade (10)
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