New Jersey Core Curriculum Content Standards for Mathematics Grades K-6

Transcription

1 A Correlation of to the New Jersey Core Curriculum Content Standards for Mathematics Grades K-6 O/M-147

2 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the objectives of the New Jersey Core Curriculum Content Standards for Mathematics. Correlation page references are to the Teacher Edition, which contains facsimile Pupil Edition pages. Scott Foresman Addison Wesley Mathematics was carefully developed to reflect the specific needs of students and teachers at every grade level, while maintaining an overall primary goal: to have math make sense from every perspective. This program is based on scientific research that describes how children learn mathematics well and on classroom-based evidence that validates proven reliability. Reaching All Learners Scott Foresman Addison Wesley Mathematics addresses the needs of every student through structured instruction that makes concepts easier for students to grasp. Lessons provide step-by-step examples that show students how to think about and solve the problem. Built-in leveled practice in every lesson allows the teacher to customize instruction to match students abilities. Reaching All Learners, featured in the Teacher Edition, helps teachers meet the diverse needs of the classroom with fun and stimulating activities that are easy to incorporate directly into the lesson plan. Test Prep Scott Foresman - Addison Wesley Mathematics builds understanding through connections to prior knowledge, math strands, other subjects and the real world. It provides practice for maximum results and offers assessment in a variety of ways. Besides carefully placed reviews at the end of each Section, an important Test Prep strand runs throughout the program. Writing exercises prepare students for open-ended and short-or extended-response questions on state and national tests. Spiral review in a test format help students keep their test-taking skills sharp. Priority on problem solving: Problem-solving instruction is systematic and explicit. Reading connections help children with problem-solving skills and strategies for math. Reading for Math Success encourages students to use the reading skills and strategies they already know to solve math problems. Instructional Support In the Teacher Edition, the Lesson Planner provides an easy, at-a-glance planning tool. It identifies objectives, math understandings, focus questions, vocabulary, and resources for each lesson in the chapter. Professional Development at the beginning of each chapter in the Teacher Edition includes a Skills Trace as well as Math Background and Teaching Tips for each section in the chapter. Ancillaries help to reach all learners with practice, problem solving, hands-on math, language support, assessment and teacher support. Technology resources for both the student and the teacher provide a whole new dimension to math instruction by helping to create motivating and engaging lessons.

3 Table of Contents Standard Standard Standard Standard Standard

4 to the Content Standards for Mathematics Grades K- 6 STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS. Cumulative Progress Indicators By the end of Grade 2, students will: A. Number Sense 1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Whole numbers through hundreds Ordinals Proper fractions (denominators of 2, 3, 4, 8, 10) K: 53A-53B, 53-54, 55A-55B, 55-56, 57A-57B, 57-58, 59A-59B, 59-60, 69A-69B, 69-70, 77A-77B, 77-78, 79A-79B, 79-80, 81A-81B, 81-82, 83A-83B, 83-84, 85A-85B, 85-86, 93A-93B, 93-94, 103A-103B, , 105A-105B, , 107A-107B, , 109A-109B, , 111A-111B, , 215A-215B, , 289A- 289B, : 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18, 181A-181B, , 183A-183B, , 185A-185B, , 187A-187B, , 189A- 189B, , 241A-241B, , 267A-267B, : 81A-81B, 81-82, 83A-83B, 83-84, 85A-85B, 85-86, 95A-95B, 95-96, 101A-101B, , 103A-103B, , 269A-269B, , 271A-271B, , 273A- 273B, , 275A-275B, , 277A-277B, Demonstrate an understanding of whole number place value concepts. K: Preparation: 105A-105B, , 107A-107B, , 109A-109B, , 111A-111B, , 117A-117B, , 289A-289B, : 281A-281B, , 283A-283B, , 284A-284B, , 287A-287B, : 81A-81B, 81-82, 83A-83B, 83-84, 85A-85B, 85-86, 91A-91B,

5 3. Understand that numbers have a variety of uses. K: 133A-133B, , 135A-135B, , 137A-137B, , 139A-139B, , 145A-145B, , 149A-149B, , 153A-153B, , 161A- 161B, , 167A-167B, , 171A-171B, , 173A-173B, , 175A-175B, , 179A-179B, , 181A-181B, , 183A-183B, : 205A-205B, , 207A-207B, , 209A-209B, , 211A-211B, , 343A-343B, , 345A-345B, , 347A-347B, , 365A- 365B, , 383A-383B, : 291A-291B, , 293A-293B, , 295A-295B, , 341A-341B, , 363A-363B, Count and perform simple computations with coins. Amounts up to $1.00 (using cents notation) K: 179A-179B, , 181A-181B, , 183A-183B, , 187A-187B, : 331A-331B, , 333A-333B, , 335A-335B, , 337A-337B, , 343A-343B, , 345A-345B, , 347A-347B, : 109A-109B, , 111A-111B, , 113A-113B, , 115A-115B, , 117A-117B, , 119A-119B, , 121A-121B, Compare and order whole numbers. K: 63A-63B, 63-64, 65A-65B, 65-66, 87A-87B, 87-88, 89A-89B, 89-90, 91A-91B, 91-92, 121A-121B, : 29A-29B, 29-30, 31A-31B, 31-32, 297A-297B, , 301A-301B, : 15A-15B, 15-16, 91A-91B, 91-92, 399A-399B, , 409A-409B, B. Numerical Operations 1. Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems. Joining, separating, and comparing K: 225A-225B, , 227A-227B, , 229A-229B, , 231A-231B, , 235A-235B, , 237A-237B, , 245A-245B, , 247A- 247B, , 265A-265B, , 267A-267B, , 269A-269B, : 45A-45B, 45-46, 61A-61B, 61-62, 75A-75B, : 3A-3B, 3-4, 13A-13B, 13-14, 15A-15B,

6 2. Explore the meanings of multiplication and division by modeling and discussing problems. K: Preparation: 287A-287B, , 293A-293B, , 295A-295B, , 297A-297B, : Preparation: , , : 467A-467B, , 469A-469B, , 471A-471B, , 473A-473B, , 475A-475B, , 483A-483B, , 485A-485B, Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as "counting on" and "near doubles") and then commit them to memory. K: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A- 277B, : 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 97A-97B, 97-98, 103A-103B, , 105A-105B, , 107A-107B, , 125A-125B, , 127A- 127B, , 129A-129B, , 417A-417B, , 419A-419B, , 425A-425B, , 435A-435B, , 437A-437B, , 439A-439B, : 43A-43B, 43-44, 45A-45B, 45-46, 47A-47B, 47-48, 49A-49B, 49-50, 51A-51B, 51-52, 53A-53B, 53-54, 57A-57B, 57-58, 61A-61B, 61-62, 63A-63B, 63-64, 65A-65B, Construct, use, and explain procedures for performing addition and subtraction calculations with: Pencil-and-paper Mental math Calculator K: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A- 277B, : 417A-417B, , 419A-419B, , 425A-425B, , 435A-435B, , 437A-437B, , 439A-439B, ; 459A-459B, , 461A- 461B, , 463A-463B, , 465A-465B, , 471A-471B, , 473A-473B, , 475A-475B, , 477A-477B, : 135A-135B , 137A-137B, , 139A-139B, , 141A-141B, , 145A-145B, , 147A-147B, , 149A-149B, , 175A- 175B, , 177A-177B, , 179A-179B, , 181A-181B, , 185A-185B, , 187A-187B, , 189A-189B, , 191A-191B, , 193A-193B,

7 5. Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 2-digit numbers Subtraction of 2-digit numbers K: Preparation: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A-277B, : 459A-459B, , 461A-461B, , 463A-463B, , 465A-465B, , 471A-471B, , 473A-473B, , 475A-475B, , 477A- 477B, : 175A-175B, , 177A-177B, , 179A-179B, , 181A-181B, , 185A-185B, , 187A-187B, , 189A-189B, , 191A- 191B, , 193A-193B, Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers. K: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A- 277B, : 417A-417B, , 419A-419B, , 425A-425B, , 435A-435B, , 437A-437B, , 439A-439B, ; 459A-459B, , 461A- 461B, , 463A-463B, , 465A-465B, , 471A-471B, , 473A-473B, , 475A-475B, , 477A-477B, : 135A-135B , 137A-137B, , 139A-139B, , 141A-141B, , 145A-145B, , 147A-147B, , 149A-149B, , 175A- 175B, , 177A-177B, , 179A-179B, , 181A-181B, , 185A-185B, , 187A-187B, , 189A-189B, , 191A-191B, , 193A-193B, Check the reasonableness of results of computations. K: Preparation: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A-277B, : 141A-141B, , 439A-439B, : 175A-175B, , 177A-177B, , 179A-179B, , 181A-181B, , 185A-185B, , 187A-187B, , 189A-189B, , 191A- 191B, , 193A-193B, , 227A-227B,

8 8. Understand and use the inverse relationship between addition and subtraction. K: Preparation: , 273A-273B, , 275A-275B, , 277A-277B, : 137A-137B, , 139A-139B, , 141A-141B, , 435A-435B, , 437A-437B, , 439A-439B, , 2: 27A-27B, 27-28, 65A-65B, 65-66, 227A-227B, C. Estimation 1. Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set. K: 119A-119B, : 249A-249B, : 401A-401B, Determine the reasonableness of an answer by estimating the result of computations (e.g., is not 211). K: Preparation: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A-277B, : 141A-141B, , 439A-439B, : 175A-175B, , 177A-177B, , 179A-179B, , 181A-181B, , 185A-185B, , 187A-187B, , 189A-189B, , 191A- 191B, , 193A-193B, , 227A-227B, Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation. K: Preparation: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A-277B, : 141A-141B, , 249A-249B, , 439A-439B, : 141A-141B, , 149A-149B, , 191A-191B, , 229A-229B, , 429A-429B, , 445A-445B,

9 Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will: A. Number Sense 1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well). Whole numbers through hundred thousands Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line 3: 4A-4B, 4-5, 6A-6B, 6-7, 10A-10B, 10-11, 12A-12B, 12-13, 498A-498B, , 502A-502B, , 504A-504B, , 512A-512B, , 516A-516B, , 518A-518B, Demonstrate an understanding of whole number place value concepts. 3: 4A-4B, 4-5, 6A-6B, 6-7, 8A-8B, 8-9, 10A-10B, 10-11, 12A-12B, Identify whether any whole number is odd or even. 3: 24A-24B, 24-25, Explore the extension of the place value system to decimals through hundredths. 3: 564A-564B, , 566A-566B, Understand the various uses of numbers. Counting, measuring, labeling (e.g., numbers on baseball uniforms) 3: 4A-4B, 4-5, 36A-36B, 36-37, 192A-192B, , 464A-464B, , 468A- 468B, , 532A-532B, Compare and order numbers. 3: 18A-18B, 18-21, 22A-22B, 22-23, 506A-506B, , 568A-568B,

10 B. Numerical Operations 1. Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Addition and subtraction: joining, separating, comparing 3: 66A-66B, 66-69, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 94A-94B, 94-95, 96A-96B, Multiplication: repeated addition, area/array 3: 260A-260B, , 262A-262B, Division: repeated subtraction, sharing 3: 370A-370B, , 372A-372B, Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction"). 3: 276A-276B, , 280A-280B, , 282A-282B, , 286A-286B, , 288A-288B, , 292A-292B, , 316A-316B, , 318A- 318B, , 320A-320B, , 324A-324B, , 328A-328B, , 386A-386B, , 388A-388B, , 390A-390B, , 392A-392B, , 396A-396B, , 402A-402B, Construct, use, and explain procedures for performing whole number calculations with: Pencil-and-paper Mental math Calculator 3: 126A-126B, , 128A-128B, , 132A-132B, , 136A-136B, , 146A-146B, , 148A-148B, , 150A-150B, , 152A- 152B, , 156A-156B, , 162A-162B, , 166A-166B, Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 3-digit numbers 3: 128A-128B, , 132A-132B, Subtraction of 3-digit numbers 3: 150A-150B, , 152A-152B, Multiplication of 2-digit numbers by 1-digit numbers 3: 282A-282BM

11 5. Count and perform simple computations with money. Cents notation ( ) 3: 36A-36B, 36-39, 40A-40B, 40-41, 162A-162B, Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers. 3: 126A-126B, , 128A-128B, , 132A-132B, , 136A-136B, , 146A-146B, , 148A-148B, , 150A-150B, , 152A- 152B, , 156A-156B, , 162A-162B, , 166A-166B, Check the reasonableness of results of computations. 3: 80A-80B, 80-81, 82A-82B, 82-83, 86A-86B, 86-89, 90A-90B, 90-91, 94A-94B, 94-95, 96A-96B, 96-97, 98A-98B, , 160A-160B, C. Estimation 1. Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set. 3: Related material: 86A-86B, 86-89, 98A-98B, Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the result of computations. 3: 80A-80B, 80-81, 82A-82B, 82-83, 86A-86B, 86-89, 90A-90B, 90-91, 94A-94B, 94-95, 96A-96B, 96-97, 98A-98B, , 160A-160B, Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. 3: 160A-160B, Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable. 3: 80A-80B, 80-81, 82A-82B, 82-83, 86A-86B, 86-89, 90A-90B, 90-91, 94A-94B, 94-95, 96A-96B, 96-97, 98A-98B, , 160A-160B,

12 Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will: A. Number Sense 1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well). Whole numbers through millions Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line Decimals through hundredths 4: 4A-4B, 4-7, 8A-8B, 8-9, 28A-28B, 28-29, 34A-34B, 34-37, 500A-500B, , 502A-502B, , 504A-504B, , 624A-624B, Demonstrate an understanding of place value concepts. 4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11, 628A-628B, Demonstrate a sense of the relative magnitudes of numbers. 4: 16A-16B, 16-19, 522A-522B, , 524A-524B, , 534A-534B, , 630A-630B, Understand the various uses of numbers. Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor) 4: 28A-28B, 28-29, 190A-190B, , 464A-464B, , 468A-468B, , 588A-588B, , 652A-652B, Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number. 4: 4A-4B, 4-7, 28A-28B, 28-29, 500A-500B, , 502A-502B, , 516A- 516B, , 520A-520B, , 624A-624B, Compare and order numbers. 4: 16A-16B, 16-19, 522A-522B, , 524A-524B, , 534A-534B, , 630A-630B,

13 7. Explore settings that give rise to negative numbers. Temperatures below 0 o, debts Extension of the number line 4: 664A-664B, B. Numerical Operations 1. Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Addition and subtraction: joining, separating, comparing 4: 62A-62B, 62-63, 64A-64B, 64-65, 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, Multiplication: repeated addition, area/array 4: 124A-124B, , 128A-128B, , 132A-132B, , 136A-136B, Division: repeated subtraction, sharing 4: 146A-146B, , 148A-148B, , 150A-150B, , 152A-152B, Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction") and then commit them to memory. 4: 124A-124B, , 128A-128B, , 132A-132B, , 136A-136B, , 146A-146B, , 148A-148B, , 150A-150B, , 152A- 152B, Construct, use, and explain procedures for performing whole number calculations and with: Pencil-and-paper Mental math Calculator 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 270A-270B, , 274A-274B, , 332A-332B, , 336A-336B, , 380A- 380B, , 386A-386B, , 390A-390B,

14 4. Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 3-digit numbers Subtraction of 3-digit numbers 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, Multiplication of 2-digit numbers Division of 3-digit numbers by 1-digit numbers 4: 270A-270B, , 274A-274B, , 332A-332B, Construct and use procedures for performing decimal addition and subtraction. 4: 638A-638B, , 642A-642B, Count and perform simple computations with money. Standard dollars and cents notation 4: 76A-76B, 76-79, 286A-286B, , 340A-340B, , 392A-392B, Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers. 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 270A-270B, , 274A-274B, , 332A-332B, , 336A-336B, , 380A- 380B, , 386A-386B, , 390A-390B, Check the reasonableness of results of computations. 4: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71, 72A-72B, 72-73, 258A-258B, , 316A-316B, , 368A-368B, , 636A-636B, Use concrete models to explore addition and subtraction with fractions. 4: 562A-562B, , 564A-564B, , 568A-568B, , 574A-574B, , 578A-578B, Understand and use the inverse relationships between addition and subtraction and between multiplication and division. 4: 100A-100B, , 148A-148B, , 166A-166B,

15 C. Estimation 1. Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set. 4: Related material: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71, 72A-72B, 72-73, 258A-258B, , 316A-316B, , 368A-368B, , 636A-636B, Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the results of computations. 4: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71, 72A-72B, 72-73, 258A-258B, , 316A-316B, , 368A-368B, , 636A-636B, Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. 4: 600A-600B, Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable. 4: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71, 72A-72B, 72-73, 258A-258B, , 316A-316B, , 368A-368B, , 636A-636B, Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will: A. Number Sense 1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well). All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers All decimals 5: 26A-26B, 26-27, 84A-84B, 84-85, 394A-394B, , 398A-398B, , 400A-400B, , 404A-404B, Recognize the decimal nature of United States currency and compute with money. 5: 139, , 160A-160B, ,

16 3. Demonstrate a sense of the relative magnitudes of numbers. 5: 6A-6B, 6-7, 12A-12B, 12-13, 418A-418B, , 420A-420B, , 430A- 430B, Use whole numbers, fractions, and decimals to represent equivalent forms of the same number. 5: 410A-410B, , 412A-412B, , 416A-416B, , 426A-426B, Develop and apply number theory concepts in problem solving situations. Primes, factors, multiples 5: 162A-162B, , 164A-164B, Compare and order numbers. 5: 6A-6B, 6-7, 12A-12B, 12-13, 418A-418B, , 420A-420B, , 430A- 430B, B. Numerical Operations 1. Recognize the appropriate use of each arithmetic operation in problem situations. 5: 36A-36B, 36-37, 38A-38B, 38-39, 40A-40B, 40-41, 88A-88B, 88-91, 94A-94B, 94-97, 152A-152B, , 156A-156B, , 158A-158B, , 160A-160B, A-202B, , 214A-214B, , 218A-218B, , 224A- 224B, , 230A-230B, , 232A-232B, , 234A-234B, Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with: Pencil-and-paper Mental math Calculator 5: 38A-38B, 38-39, 40A-40B, 40-41, 460A-460B, , 462A-462B, , 464A-464B, , 466A-466B, , 472A-472B, , 474A-474B, , 476A-476B, , 478A-478B,

17 3. Use an efficient and accurate pencil-and-paper procedure for division of a 3- digit number by a 2-digit number. 5: 202A-202B, , 204A-204B, , 214A-214B, Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers. 5: 36A-36B, 36-37, 38A-38B, 38-39, 40A-40B, 40-41, 88A-88B, 88-91, 94A-94B, 94-97, 152A-152B, , 156A-156B, , 158A-158B, , 160A-160B, A-202B, , 214A-214B, , 218A-218B, , 224A- 224B, , 230A-230B, , 232A-232B, , 234A-234B, , 460A-460B, , 462A-462B, , 464A-464B, , 466A-466B, , 472A-472B, , 474A-474B, , 476A-476B, , 478A- 478B, Check the reasonableness of results of computations. 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, , 204A- 204B, , 474A-474B, , 494A-494B, , 672A-672B, Understand and use the various relationships among operations and properties of operations. 5: 36A-36B, 36-37, 66A-66B, 66-67, 84A-84B, 84-85, 108A-108B, , 132A- 132B, , 148A-148B, , 696A-696B, , 700A-700B, , 702A-702B, C. Estimation 1. Use a variety of estimation strategies for both number and computation. 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, , 204A- 204B, , 474A-474B, , 494A-494B, , 672A-672B, Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. 5: 624A-624B,

18 3. Determine the reasonableness of an answer by estimating the result of operations. 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, , 204A- 204B, , 474A-474B, , 494A-494B, , 672A-672B, Determine whether a given estimate is an overestimate or an underestimate. 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, , 204A- 204B, , 474A-474B, , 494A-494B, , 672A-672B, Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will: A. Number Sense 1. Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well). All integers All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers All decimals 6: 76A-76B, 76-77, 160A-160B, , 408A-408B, Recognize the decimal nature of United States currency and compute with money. 6: 86A-86B, 86-89, 90A-90B, 90-93, 94A-94B, Demonstrate a sense of the relative magnitudes of numbers. 6: 12A-12B, 12-13, 78A-78B, 78-79, 176A-176B, , 410A-410B, Explore the use of ratios and proportions in a variety of situations. 6: 300A-300B, , 302A-302B, , 316A-316B, , 318A-318B, , 322A-322B, Understand and use whole-number percents between 1 and 100 in a variety of situations. 6: 354A-354B, , 358A-358B, , 366A-366B, , 368A-368B, , 370A-370B, , 380A-380B, , 384A-384B, , 386A-386B,

19 6. Use whole numbers, fractions, and decimals to represent equivalent forms of the same number. 6: 164A-164B, , 168A-168B, , 172A-172B, Develop and apply number theory concepts in problem solving situations. Primes, factors, multiples Common multiples, common factors 6: 142A-142B, , 146A-146B, , 150A-150B, , 152A-152B, Compare and order numbers. 6: 12A-12B, 12-13, 78A-78B, 78-79, 176A-176B, , 410A-410B, B. Numerical Operations 1. Recognize the appropriate use of each arithmetic operation in problem situations. 6: 86A-86B, 86-89, 90A-90B, 90-93, 94A-94B, 94-97, 100A-100B, , 204A-204B, , 206A-206B, , 252A-252B, , 266A-266B, , 418A-418B, , 422A-422B, , 426A-426B, , 428A-428B, Construct, use, and explain procedures for performing calculations with fractions and decimals with: Pencil-and-paper Mental math Calculator 6: 86A-86B, 86-89, 90A-90B, 90-93, 94A-94B, 94-97, 100A-100B, , , 206A-206B, , 218A-218B, , 220A-220B, , 248A- 248B, , 252A-252B, , 258A-258B, , 266A-266B, , 270A-270B, Use an efficient and accurate pencil-and-paper procedure for division of a 3- digit number by a 2-digit number. 6: 18A-18B,

20 4. Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers. 6: 86A-86B, 86-89, 90A-90B, 90-93, 94A-94B, 94-97, 100A-100B, , , 206A-206B, , 218A-218B, , 220A-220B, , 248A- 248B, , 252A-252B, , 258A-258B, , 266A-266B, , 270A-270B, Find squares and cubes of whole numbers. 6: 8A-8B, 8-11, 110A-110B, Check the reasonableness of results of computations. 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, , 256A-256B, , 368A-368B, Understand and use the various relationships among operations and properties of operations. 6: 24A-24B, 24-27, 28A-28B, 28-29, 30A-30B, 30-31, 48A-48B, Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses. 6: 24A-24B, 24-27, 28A-28B, 28-29, 30A-30B, 30-31, 48A-48B, 48-51, 430A- 430B, C. Estimation 1. Use a variety of strategies for estimating both quantities and the results of computations. 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, , 256A-256B, , 368A-368B, Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer. 6: 226A-226B, Determine the reasonableness of an answer by estimating the result of operations. 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, , 256A-256B, , 368A-368B,

21 4. Determine whether a given estimate is an overestimate or an underestimate. 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, , 256A-256B, , 368A-368B,

22 STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA. Cumulative Progress Indicators By the end of Grade 2, students will: A. Geometric Properties 1. Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Inside/outside, left/right, above/below, between Smaller/larger/same size, wider/ narrower, longer/shorter Congruence (i.e., same size and shape) K: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8, 9A-9B, 9-10, 199A-199B, : 169A-169B, : 257A-257B, , 259A-259B, Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. Vertex, edge, face, side 3D figures cube, rectangular prism, sphere, cone, cylinder, and pyramid 2D figures square, rectangle, circle, triangle Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape) K: 197A-197B, , 199A-199B, , 201A-201B, , 203A-203B, , 205A-205B, : 157A-157B, , 159A-159B, , 161A-161B, , 165A-165B, , 167A-167B, : 247A-247B, , 249A-249B, , 255A-255B, Describe, identify and create instances of line symmetry. K: 211A-211B, : 171A-171B, : 261A-261B, Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors. K: 39A-39B, : 3A-3B, 3-4, 5A-5B, 5-6 2: 413B 19

23 B. Transforming Shapes 1. Use simple shapes to make designs, patterns, and pictures. K: 39A-39B, : 3A-3B, 3-4, 5A-5B, 5-6 2: 259A-259B, Combine and subdivide simple shapes to make other shapes. K: 209A-209B, : , , : 255A-255B, C. Coordinate Geometry 1. Give and follow directions for getting from one point to another on a map or grid. K: Related material: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8, 9A-9B, : 315A-315B, , 317A-317B, : Related material: 325a-325b, D. Units of Measurement 1. Directly compare and order objects according to measurable attributes. Attributes length, weight, capacity, time, temperature K: 133A-133B, , 135A-135B, , 137A-137B, , 145A-145B, , 149A-149B, : 383A-383B, , 389A-389B, : , , 304, 341A-341B, , , 345A-345B, 347A, 353A- 353B, , , Recognize the need for a uniform unit of measure. K: 133A-133B, , 135A-135B, : 365A-365B, , 383A-383B, : 341A-341B, , 353A-353B, , 359A-359B, , 363A-363B

24 3. Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Length inch, foot, yard, centimeter, meter Weight pound, gram, kilogram Capacity pint, quart, liter Time second, minute, hour, day, week, month, year Temperature degrees Celsius, degrees Fahrenheit K: 133A-133B, , 135A-135B, , 137A-137B, , 139A-139B, , 141A-141B, , 145A-145B, , 147A-147B, , 149A- 149B, , 151A-151B, , 153A-153B, , 171A-171B, , 173A-173B, , 175A-175B, : 365A-365B, , 369A-369B, , 371A-371B, , 373A-373B, , 375A-375B, , 383A-383B, , 385A-385B, , 387A- 387B, , 389A-389B, , 391A-391B, , 393A-393B, , 397A-397B, : 343A-343B, , 345A-345B, , 347A-347B, , 355A-355B, , 357A-357B , 365A-365B, , 367A-367B, , 369A- 369B, Estimate measures. K: 141A-141B, , 147A-147B, , 151A-151B, : 365A-365B, , 371A-371B, , 373A-373B, , 375A-375B, , 383A-383B, , 389A-389B, : 297A-279B, , 341A-341B, E. Measuring Geometric Objects 1. Directly measure the perimeter of simple two-dimensional shapes. K: Preparation: 139A-139B, , 141A-141B, , 203A-203B, : 377A-377B, : Directly measure the area of simple two-dimensional shapes by covering them with squares. K: Preparation: 203A-203B, , 205A-205B, : Preparation: 377A-377B, : Preparation: 343A-343B, , 345A-345B,

25 Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will: A. Geometric Properties 1. Identify and describe spatial relationships of two or more objects in space. Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?) Relative shapes and sizes 3: 432A-432B, , 456A-456B, Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. Vertex, edge, face, side, angle 3D figures cube, rectangular prism, sphere, cone, cylinder, and pyramid 2D figures square, rectangle, circle, triangle, pentagon, hexagon, octagon 3: 428A-428B, , 442A-442B, , 444A-444B, , 446A-446B, , 450A-450B, , 454A-454B, Identify and describe relationships among two-dimensional shapes. Same size, same shape Lines of symmetry 3: 456A-456B, , 460A-460B, Understand and apply concepts involving lines, angles, and circles. Line, line segment, endpoint 3: 442A-442B, Recognize, describe, extend, and create space-filling patterns. 3: Related material: , B. Transforming Shapes 1. Describe and use geometric transformations (slide, flip, turn). 3: 456A-456B, Investigate the occurrence of geometry in nature and art. 3:

26 C. Coordinate Geometry 1. Locate and name points in the first quadrant on a coordinate grid. 3: 218A-218B, D. Units of Measurement 1. Understand that everyday objects have a variety of attributes, each of which can be measured in many ways. 3: 464A-464B, , 468A-468B, , 472A-472B, , 532A-532B, Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Length fractions of an inch (1/4, 1/2), mile, decimeter, kilometer Area square inch, square centimeter Weight ounce Capacity fluid ounce, cup, gallon, milliliter 3: 468A-468B, , 532A-532B, , 680A-680B, , 690A-690B, Incorporate estimation in measurement activities (e.g., estimate before measuring). 3: 533, 535, , 628, 681, 682, 685, 691, 697 E. Measuring Geometric Objects 1. Determine the area of simple two-dimensional shapes on a square grid. 3: 468A-468B, Determine the perimeter of simple shapes by measuring all of the sides. 3: 464A-464B, Measure and compare the volume of three dimensional objects using materials such as rice or cubes. 3: 472A-472B,

27 Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will: A. Geometric Properties 1. Identify and describe spatial relationships of two or more objects in space. Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?) Relative shapes and sizes Shadows (projections) of everyday objects 4: 434A-434B, , 452A-452B, Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. Vertex, edge, face, side, angle 3D figures cube, rectangular prism, sphere, cone, cylinder, and pyramid 2D figures square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon Inclusive relationships squares are rectangles, cubes are rectangular prisms 4: 434A-434B, , 438A-438B, , 440A-440B, , 444A-444B, , 448A-448B, Identify and describe relationships among two-dimensional shapes. Congruence Lines of symmetry 4: 452A-452B, , 456A-456B, Understand and apply concepts involving lines, angles, and circles. Point, line, line segment, endpoint Parallel, perpendicular Angles acute, right, obtuse 4: 440A-440B, Circles diameter, radius, center 4: 448A-448B, Recognize, describe, extend, and create space-filling patterns. 4: Related material: 452A-452B,

28 B. Transforming Shapes 1. Use simple shapes to cover an area (tessellations). 4: Related material: 452A-452B, Describe and use geometric transformations (slide, flip, turn). 4: 452A-452B, Investigate the occurrence of geometry in nature and art. 4: 447 C. Coordinate Geometry 1. Locate and name points in the first quadrant on a coordinate grid. 4: 212A-212B, Use coordinates to give or follow directions from one point to another on a map or grid. 4: Related material: 212A-212B, D. Units of Measurement 1. Understand that everyday objects have a variety of attributes, each of which can be measured in many ways. 4: 464A-464B, , 468A-468B, , 588A-588B, , 652A-652B, Select and use appropriate standard units of measure and measurement tools to solve real-life problems Length fractions of an inch (1/8, 1/4, 1/2), mile, decimeter, kilometer Area square inch, square centimeter 4: 590A-590B, , 468A-468B, Volume cubic inch, cubic centimeter Weight ounce Capacity fluid ounce, cup, gallon, milliliter 4: 476A-476B, , 592A-592B, , 594A-594B, , 654A-654B, , 656A-656B,

29 3. Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long). 4: 600A-600B, Incorporate estimation in measurement activities (e.g., estimate before measuring). 4: Solve problems involving elapsed time. 4: 196A-196B, E. Measuring Geometric Objects 1. Determine the area of simple two-dimensional shapes on a square grid. 4: 468A-468B, Distinguish between perimeter and area and use each appropriately in problem-solving situations. 4: 464A-464B, , 468A-468B, Measure and compare the volume of three dimensional objects using materials such as rice or cubes. 4: 476A-476B, Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will: A. Geometric Properties 1. Understand and apply concepts involving lines and angles. Notation for line, ray, angle, line segment Properties of parallel, perpendicular, and intersecting lines Sum of the measures of the interior angles of a triangle is 180 5: 328A-328B, , 332A-332B, , 336A-336B, , 340A-340B,

30 2. Identify, describe, compare, and classify polygons. Triangles by angles and sides Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi Polygons by number of sides. Equilateral, equiangular, regular All points equidistant from a given point form a circle 5: 340A-340B, , 342A-342B, , 346A-346B, Identify similar figures. 5: 360A-360B, Understand and apply the concepts of congruence and symmetry (line and rotational). 5: 360A-360B, , 368A-368B, B. Transforming Shapes 1. Use a translation, a reflection, or a rotation to map one figure onto another congruent figure. 5: 364A-364B, Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings. 5: 345, 597 C. Coordinate Geometry 1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid. 5: 174A-174B, D. Units of Measurement 1. Select and use appropriate units to measure angles and area. 5: 332A-332B, , 548A-548B, , 550A-550B, , 552A-552B, , 554A-554B,

31 2. Convert measurement units within a system (e.g., 3 feet = inches). 5: 536A-536B, Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). 5: 528A-528B, , 534A-534B, Use measurements and estimates to describe and compare phenomena. 5: 332A-332B, , 532A-532B, , 540A-540B, , 548A-548B, , 550A-550B, , 552A-552B, , 554A-554B, E. Measuring Geometric Objects 1. Use a protractor to measure angles. 5: 332A-332B, Develop and apply strategies and formulas for finding perimeter and area. Square Rectangle 5: 540A-540B, , 548A-548B, , 550A-550B, , 552A-552B, Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa. 5: 540A-540B, , 548A-548B, , 550A-550B, Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one s foot). 5: 528A-528B, , 532A-532B,

32 Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will: A. Geometric Properties 1. Understand and apply concepts involving lines and angles. Notation for line, ray, angle, line segment Properties of parallel, perpendicular, and intersecting lines Sum of the measures of the interior angles of a triangle is 180 6: 472A-472B, , 476A-476B, , 480A-480B, , 484A-484B, Identify, describe, compare, and classify polygons and circles. Triangles by angles and sides Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi Polygons by number of sides. Equilateral, equiangular, regular All points equidistant from a given point form a circle 6: 494A-494B, , 496A-496B, , 500A-500B, , 502A-502B, Identify similar figures. 6: 506A-506B, Understand and apply the concepts of congruence and symmetry (line and rotational). 6: 506A-506B, , 514A-514B, Compare properties of cylinders, prisms, cones, pyramids, and spheres. 6: 586A-586B, Identify, describe, and draw the faces or shadows (projections) of threedimensional geometric objects from different perspectives. 6: 586A-586B, Identify a three-dimensional shape with given projections (top, front and side views). 6: 586A-586B,

33 8. Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape). 6: 586A-586B, B. Transforming Shapes 1. Use a translation, a reflection, or a rotation to map one figure onto another congruent figure. 6: 510A-510B, Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings. 6: 479, 557 C. Coordinate Geometry 1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid. 6: 510A-510B, D. Units of Measurement 1. Select and use appropriate units to measure angles, area, surface area, and volume. 6: 476A-476B, , 568A-568B, , 570A-570B, , 572A-572B, , 590A-590B, , 594A-594B, Use a scale to find a distance on a map or a length on a scale drawing. 6: 330A-330B, Convert measurement units within a system (e.g., 3 feet = inches). 6: 542A-542B, , 546A-546B,

34 4. Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). 6: 552A-552B, Use measurements and estimates to describe and compare phenomena. 6: 542A-542B, , 546A-546B, , 550A-550B, E. Measuring Geometric Objects 1. Use a protractor to measure angles. 6: 476A-476B, , 484A-484B, Develop and apply strategies and formulas for finding perimeter and area. Triangle, square, rectangle, parallelogram, and trapezoid Circumference and area of a circle 6: 564A-564B, , 568A-568B, , 570A-570B, , 572A-572B, , 576A-576B, , 580A-580B, Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders. 6: 590A-590B, , 594A-594B, Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa. 6: 570A-570B, Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one s foot). 6: 550A-550B,

35 STANDARD 4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES. Cumulative Progress Indicators By the end of Grade 2, students will: A. Patterns 1. Recognize, describe, extend, and create patterns. Using concrete materials (manipulatives), pictures, rhythms, & whole numbers Descriptions using words and symbols (e.g., "add two" or "+ 2") Repeating patterns Whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward) K: 35A-35B, 35-36, 37A-37B, 37-38, 39A-39B, 39-40, 41A-41B, 41-42, 43A-43B, 43-44, 45A-45B, 45-46, 95-96, 293A-293B, , 295A-295B, , : 3A-3B, 3-4, 5A-5B, 5-6, 255A-255B, , 257A-257B, , 261A-261B, : 99A-99B, , 413A-413B, , 467A-467B, B. Functions and Relationships 1. Use concrete and pictorial models of function machines to explore the basic concept of a function. K: Preparation: 293A-293B, , 295A-295B, : 261A-261B, : Preparation: 99A-99B, , 413A-413B, , 467A-467B, C. Modeling 1. Recognize and describe changes over time (e.g., temperature, height). K: Preparation: 141A-141B, , 153A-153B, : Preparation: 373A-373B, , 389A-389B, : 323A-323B,

36 2. Construct and solve simple open sentences involving addition or subtraction. Result unknown (e.g., 6 2 = or n = 3 + 5) Part unknown (e.g., 3 + = 8) K: 255A-255B, , 275A-275B, : 57A-57B, 57-58, 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 103A-103B, , 105A-105B, , 107A-107B, , 129A-129B, , 137A- 137B, , 139A-139B, , 141A-141B, : 5A-5B, 5-6, 9A-9B, 9-10, 17A-17B, 17-18, 23A-23B, 23-24, 25A-25B, 25-26, 27A- 27B, 27-28, 29A-29B, 29-30, 57A-57B, D. Procedures 1. Understand and apply (but don t name) the following properties of addition: Commutative (e.g., = 3 + 5) Zero as the identity element (e.g., = 7) Associative (e.g., can be found by first adding either or 3 + 2) K: 251A-251B, , 253A-253B, , 255A-255B, , 257A-257B, , 271A-271B, , 273A-273B, , 275A-275B, , 277A- 277B, : 103A-103B, , 105A-105B, , 107A-107B, , 129A-129B, , 137A-137B, , 139A-139B, , 141A-141B, : 5A-5B, 5-6, 9A-9B, 9-10, 17A-17B, 17-18, 23A-23B, 23-24, 25A-25B, 25-26, 27A- 27B, 27-28, 29A-29B, 29-30, 57A-57B, Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will: A. Patterns 1. Recognize, describe, extend, and create patterns. Descriptions using words and number sentences/expressions Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11,... or 800, 400, 200,...) 3: 24-27, 277, 282, 286, , 332A-332B, , ,