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A Correlation of

to the

Colorado

Model Content Standards Suggested Grade Level

Expectations

Grades K-6

M/M-104

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 Colorado Model Content Standards and Suggested Grade Level Expectations. 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.

Table of Contents

Standard One...……………………………...…………………………………….….……..…1

Standard Two………………………………………………………………….…….……..…17

Standard Three……………………………………………………………….…….……..… 24

Standard Four……………………………………………………………….…….……..…...36

Standard Five……………………………………………………………….…….……..……48

Standard Six…………………………………………………….…………….…….……..….61

Scott Foresman – Addison Wesley Mathematics to the

Colorado Model Content Standards Suggested Grade Level Expectations

Grades K - 6

Standard 1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

Grades K-4 In grades K-4, what students know and are able to do includes 1.1 DEMONSTRATING MEANINGS FOR WHOLE NUMBERS, COMMONLY USED FRACTIONS AND DECIMALS (FOR EXAMPLE, 1/3, 3/4, 0.5, 0.75), AND REPRESENTING EQUIVALENT FORMS OF THE SAME NUMBER THROUGH THE USE OF PHYSICAL MODELS, DRAWINGS, CALCULATORS, AND COMPUTERS. Kindergarten students will: using objects and pictures, represent whole numbers from 0 to 50 in a variety

of ways K: 53A-53B, 53-54, 57A-57B, 57-58, 77A-77B, 77-78, 79A-79B, 79-80, 83A-83B, 83-84, 103A-103B, 103-104

using two or more sets of objects, demonstrate which set is equal to, less than, or greater than the other set K: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32

using concrete materials, demonstrate the meaning of wholes and parts (for example, halves) K: 213A-213B, 213-214, 215A-215B, 215-216

name pennies, nickels, dimes, quarters, and dollars K: 179A-179B, 179-180, 181A-181B, 181-182, 183A-183B, 183-184, 187A-187B, 187-188

1

Scott Foresman – Addison Wesley Mathematics Colorado Model Content Standards Suggested Grade Level Expectations

First grade students will: using objects and pictures, represent whole numbers from 0 to 100 in a variety

of ways 1: 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18, 25A-25B, 25-26, 27A-27B, 27-28

using objects, demonstrate the meanings of equal, less than, and greater than with the whole numbers 0 to 100 1: 29A-29B, 29-30, 31A-31B, 31-32, 297A-297B, 297-298, 301A-301B, 301-302

apply equalities using the ‘=’ symbol 1: 133A-133B, 133-134, 137A-137B, 137-138, 139A-139B, 139-140, 141A-141B, 141-142

using concrete materials, demonstrate the meanings of halves, thirds, and fourths of sets and wholes 1: 183A-183B, 183-184, 185A-185B, 185-186, 187A-187B, 187-188

demonstrate the value of nickels, dimes, quarters, and dollars in terms of pennies (for example, 25 pennies = 1 quarter) 1: 331A-331B, 331-332, 333A-333B, 333-334, 335A-335B, 335-336, 337A-337B, 337-338, 343A-343B, 343-344, 345A-345B, 345-346

Second grade students will: using objects and pictures, represent whole numbers including odds and

evens from 0 to 1,000 2: 15A-15B, 15-16, 91A-91B, 91-92, 399A-399B, 399-400, 409A-409B, 409-410

apply equalities and inequalities with whole numbers from 0 to 1,000 using the symbols =, •, <, > 2: 5A-5B, 5-6, 15A-15B, 15-16, 17A-17B, 17-18, 91A-91B, 91-92, 399A-399B, 399-400, 409A-409B, 409-410

using concrete materials, demonstrate the meanings of fractions, including halves, thirds, fourths, eighths, and tenths of sets and wholes 2: 269A-269B, 296-270, 271A-271B, 271-272, 273A-273B, 273-274, 275A-275B, 275-276, 277A-277B, 277-278

demonstrate equivalencies of coins (for example, 5 nickels = 1 quarter) 2: 109A-109B, 109-110, 111A-111B, 111-112

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combine coins up to $1.00 (for example, 20¢ = 2 dimes = 1 dime + 2 nickels = 4 nickels)

2: 113A-113B, 113-114, 115A-115B, 115-116, 117A-117B, 117-118, 119A-119B, 119-120, 121A-121B, 121-122

Third grade students will: using objects and pictures, represent whole numbers including odds and

evens from 0 to 10,000 3: 18A-18B, 18-21, 22A-22B, 22-23

apply equalities and inequalities with whole numbers from 0 to 10,000 using the symbols =, •, <, > 3: 18A-18B, 18-21, 22A-22B, 22-23

using concrete materials (for example, fraction strips), compare and order fractions with like denominators, such as halves, thirds, fourths, eighths, and tenths 3: 506A-506B, 506-509

demonstrate different combinations of coins for change (for example, 52¢ = 2 quarters and 2 pennies) 3: 36A-36B, 36-39

using concrete materials, make change up to $1.00 3: 40A-40B, 40-41

Fourth grade students will: using objects and pictures, represent whole numbers including odds and

evens from 0 to 1,000,000 4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11

apply equalities and inequalities with whole numbers from 0 to 1,000,000 using the symbols =, •, <, > 4: 16A-16B, 16-19, 522A-522B, 522-523, 524A-524B, 524-527, 534A-534B, 534-536, 630A-630B, 630-631

using concrete materials (for example, fraction strips), compare and order fractions with like and unlike denominators, such as halves, thirds, fourths, eighths, and tenths 4: 522A-522B, 522-523, 524A-524B, 524-527, 534A-534B, 534-535

3


using concrete materials (for example, base ten blocks), represent the decimal

fractions of tenths and hundredths 4: 624A-624B, 624-627, 628A-628B, 628-629

using concrete materials, equate terminating decimals to their common fraction equivalents (for example, 0.25 = 1/4) 4: 624A-624B, 624-627

demonstrate different combinations of currency and coins for change (for example, $2.39 = 2 dollar bills, 1 quarter, 1 dime, and 4 pennies) 4: 30A-30B, 30-31

using concrete materials, count change from the cost of the item, where the item costs no more than $10.00, up to the amount of money received 4: 32A-32B, 32-33

1.2 READING AND WRITING WHOLE NUMBERS AND KNOWING PLACE-VALUE CONCEPTS AND NUMERATION THROUGH THEIR RELATIONSHIPS TO COUNTING, ORDERING, AND GROUPING. Kindergarten students will: read and write numerals from 0 to 10 in meaningful contexts

K: 55A-55B, 55-56, 59A-59B, 59-60, 81A-81B, 85A-85B, 85-86

group objects into sets of ten K: 287A-287B, 287-288

First grade students will: read and write numerals from 0 to 100 in meaningful contexts

1: 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18, 25A-25B, 25-26, 27A-27B, 27-28, 241A-241B, 241-242

read the number words for zero to ten 1: 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18, 25A-25B, 25-26, 27A-27B, 27-28

group objects by ones and tens 1: 281A-281B, 281-282, 283A-283B, 283-284, 285A-285B, 285-286, 287A-287B, 287-288

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order according to place value (for example, given 9 ones and 2 tens, the

student can write the number 29; given the number 29 the student can show 2 tens and 9 ones) 1: 29A-29B, 29-30, 31A-31B, 31-32, 297A-297B, 297-298, 301A-301B, 301-302

write one- and two-digit whole numbers in expanded form (for example, 29 = 20 + 9) 1: 247A-247B, 247-248

Second grade students will: read and write numerals from 0 to 1,000 in meaningful contexts

2: 15A-15B, 15-16, 91A-91B, 91-92, 399A-399B, 399-400, 409A-409B, 409-410

read and write the number words for zero to one hundred 2: 85A-85B, 85-86

group objects by ones, tens, and hundreds 2: 81A-81B, 81-82, 83A-83B, 83-84, 95A-95B, 95-96

order according to place value (for example, given 9 ones, 5 tens, and 4 hundreds, the student can write the number 459; given the number 459, the student can show 4 hundreds, 5 tens, and 9 ones) 2: 81A-81B, 81-82, 83A-83B, 83-84, 95A-95B, 95-96

write three-digit numbers in expanded form (for example, 459 = 400 + 50 + 9) 2: 395a-395b, 395-396

Third grade students will: read and write numerals from 0 to 10,000 in meaningful contexts

3: 6A-6B, 6-7, 8A-8B, 8-9, 10A-10B, 10-11, 12A-12B, 12-13

read and write the number words for selected numbers from zero to one thousand 3: 6A-6B, 6-7, 8A-8B, 8-9, 10A-10B, 10-11, 12A-12B, 12-13

order according to place value (for example, given 9 ones, 5 tens, 4 hundreds, and 7 thousands, the student can write the number 7,459; given the number 7,459, the student can show 7 thousands, 4 hundreds, 5 tens, and 9 ones) 3: 6A-6B, 6-7, 8A-8B, 8-9, 10A-10B, 10-11, 12A-12B, 12-13

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identify place value through ten thousands (for example, in 86,243, ‘6’ is in the thousands place)

3: 6A-6B, 6-7, 8A-8B, 8-9, 10A-10B, 10-11, 12A-12B, 12-13 write four-digit numbers in expanded form (for example, 7,459 = 7,000 + 400 +

50 + 9) 3: 10A-10B, 10-11, 12A-12B, 12-13

Fourth grade students will: read and write numerals from 0 to 1,000,000 in meaningful contexts

4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11, 16A-16B, 16-19

read the number words for selected numbers from zero to one million 4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11

write the number words for selected numbers from zero to one hundred thousand 4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11

order according to place value (for example, given 9 ones, 5 tens, 4 hundreds, 7 thousands, and 8 hundred thousands, the student can write the number 807,459; given the number 807,459, the student can show 8 hundred thousands, 7 thousands, 4 hundreds, 5 tens, and 9 ones) 4: 16A-16B, 16-19

identify place value through hundred thousands (for example, in 807,459, ‘8’ is

in the hundred thousands place) 4: 4A-4B, 4-7, 8A-8B, 8-9, 10A-10B, 10-11

write six-digit numbers in expanded form (for example, 807,459 = 800,000 + 7,000 + 400 + 50 + 9) 4: 4A-4B, 4-7, 8A-8B, 8-9

relate decimals and fractions (that is, tenths and hundredths) to one another using objects and pictures 4: 624A-624B, 624-627

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1.3 USING NUMBERS TO COUNT, TO MEASURE, TO LABEL, AND TO INDICATE LOCATION. Kindergarten students will: count from 1 to 50

K: 53A-53B, 53-54, 57A-57B, 57-58, 77A-77B, 77-78, 79A-79B, 79-80, 83A-83B, 83-84, 103A-103B, 103-104

use one-to-one correspondence to count and compare sets of objects containing 0 to 10 members K: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32

starting with any whole number less than 50, count forward to 50 K: 53A-53B, 53-54, 57A-57B, 57-58, 77A-77B, 77-78, 79A-79B, 79-80, 83A-83B, 83-84, 103A-103B, 103-104

use ordinal positions for first through tenth K: 69A-69B, 69-70, 93A-93B, 93-94

sequence whole numbers from 0 to 10 (for example, 5 is before 7; 5 is after 4) K: 69A-69B, 69-70, 91A-91B, 91-92

First grade students will: count from 1 to 20 by 2’s

1: 255A-255B, 255-256, 257A-257B, 257-258

count from 1 to 100 by 1’s, 5’s, and 10’s 1: 243A-243B, 243-244, 255A-255B, 255-256, 257A-257B, 257-258

starting with any whole number less than 100, count forward to 100 1: 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18, 25A-25B, 25-26, 27A-27B, 27-28

use ordinal positions for first through twentieth 1: 267A-267B, 267-268

sequence selected whole numbers from 0 to 100 1: 29A-29B, 29-30, 31A-31B, 31-32, 297A-297B, 297-298, 301A-301B, 301-302

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Second grade students will: count by 1’s, 2’s, 5’s, and 10’s

2: 99A-99B, 99-100, 467A-467B, 467-468

count from 1 to 1,000 by 100’s 2: 467A-467B, 467-468

starting with any whole number less than 1,000, count forward to 1,000 2: 43A-43B, 43-44

use ordinal positions for first through thirty-first 2: 103A-103B, 103-104

sequence selected whole numbers from 0 to 1,000 2: 15A-15B, 15-16, 91A-91B, 91-92, 399A-399B, 399-400, 409A-409B, 409-410

locate and label the halfway point between whole numbers on the number line 2: 95A-95B, 95-96, 419

locate and label a point in the first quadrant of the coordinate plane (for example, locates the point (4,1)) 2: 325A-325B, 325-326

Third grade students will: count forward from any even number by 2’s; and from any number by 10’s and

100’s (for example, 216, 316, 416, 516, ...) 3: 260A-260B, 260-261

use ordinal positions for selected whole numbers greater than thirty-first 3: 4A-4B, 4-5

sequence selected whole numbers form 0 to 10,000 3: 18A-18B, 18-21, 22A-22B, 22-23

locate and label 1/2’s and multiples of 1/4’s between whole numbers on the number line 3: 512A-512B, 512-513

locate and label a point in the first quadrant of the coordinate plane (for example, locates the point (11,15)) 3: 218A-218B, 218-221

8


Fourth grade students will: count forward from any number by 2’s, 3’s, 5’s, 10’s, and 100’s

4: 128A-128B, 128-131

sequence selected whole numbers from 0 to 100,000 4: 16A-16B, 16-19

locate and label 1/2’s and multiples of 1/4’s and 1/3’s between whole numbers on the number line 4: 504A-504B, 504-507

locate and label a point in the first quadrant of the coordinate plane (for example, locates the point (27,15)) and on a city map (for example, (E23, 11)) 4: 212A-212B, 212-215, 216A-216B, 216-221, 692A-692B, 692-695

1.4 DEVELOPING, TESTING AND EXPLAINING CONJECTURES ABOUT PROPERTIES OF WHOLE NUMBERS, AND COMMONLY USED FRACTIONS AND DECIMALS (FOR EXAMPLE, 1/3, 3/4, 0.5, 0.75). Kindergarten students will: describe the concept of zero

K: 61A-61B, 61-62

First grade students will: know the commutative property of addition of whole numbers

1: 93A-93B, 93-94

verify the addition and subtraction properties of zero with whole numbers 1: 97A-97B, 97-98

Second grade students will: verify the commutative and associative properties of addition of whole

numbers 2: 23A-23B, 23-24

verify that subtraction of whole numbers is not commutative 2: 17A-17B, 17-18

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Third grade students will: verify the commutative and associative properties of addition and

multiplication of whole numbers 3: 66A-66B, 66-69, 260A-260B, 260-261, 262A-262B, 262-265

verify the multiplication properties of zero and one with whole numbers 3: 286A-286B, 286-287

Fourth grade students will: verify division of whole numbers is not commutative

4: 146A-146B, 146-147, 148A-148B, 148-149

continue to verify number properties from previous grades 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 270A-270B, 270-273, 274A-274B, 274-277, 332A-332B, 332-335, 336A-336B, 336-337, 380A-380B, 380-383, 386A-386B, 386-389, 390A-390B, 390-391

1.5 USING NUMBER SENSE TO ESTIMATE AND JUSTIFY THE REASONABLENESS OF SOLUTIONS TO PROBLEMS INVOLVING WHOLE NUMBERS, AND COMMONLY USED FRACTIONS AND DECIMALS (FOR EXAMPLE, 1/3, 3/4, 0.5, 0.75). Kindergarten students will: estimate a reasonable quantity for a given number of objects less than 20

K: 119A-119B, 119-120

describe a relationship between two sets of quantities with more, less, or equal numbers of objects K: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32

First grade students will: estimate a reasonable quantity for a given number of objects from 0 to 100

1: 249A-249B, 249-250

10


Second grade students will: estimate sums and differences first by rounding to the nearest ten prior to

performing the operation, and then using the estimate to determine the reasonableness of the solution 2: 141A-141B, 141-142, 149A-149B, 149-150, 191A-191B, 191-192, 229A-229B, 229-230, 429A-429B, 429-430, 445A-445B, 445-446

Third grade students will: estimate sums and differences first by rounding to the nearest ten and

hundred prior to performing the operation and, then, using the estimate to determine the reasonableness of the solution 3: 160A-160B, 160-161

estimate products first by rounding to the nearest ten prior to performing the operation, and then using the estimate to determine the reasonableness of the solution 3: 612A-612B, 612-615, 616A-616B, 616-617

Fourth grade students will: estimate sums and differences first by rounding to the nearest ten, hundred,

and thousand prior to performing the operation, and then using the estimate to determine the reasonableness of the solution 4: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71

estimate products first by rounding to the nearest ten and hundred prior to performing the operation and, then, using the estimate to determine the reasonableness of the solution 4: 258A-258B, 258-261, 316A-316B, 316-319

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GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 1.1 DEMONSTRATING MEANINGS FOR INTEGERS, RATIONAL NUMBERS, PERCENTS, EXPONENTS, SQUARE ROOTS, AND PI (•) USING PHYSICAL MATERIALS AND TECHNOLOGY IN PROBLEM-SOLVING SITUATIONS. Fifth grade students will: locate commonly-used positive rational numbers, including fractions, mixed

numbers, terminating decimals through thousandths, and percents, on the number line 5: 8A-8B, 8-11, 404A-404B, 404-405, 430A-430B, 430-431

using concrete materials, demonstrate the meaning of integers 5: 712A-712B, 712-715

using concrete materials, demonstrate the equivalence of commonly-used fractions, terminating decimals, and percents (for example, 7/10 = 0.7 = 70%) 5: 426A-426B, 426-429, 430A-430B, 430-433, 668A-668B, 668-669

pictorially, demonstrate the meaning of square numbers 5: 167

Sixth grade students will: continue to locate commonly-used positive rational numbers, including

fractions, mixed numbers, terminating decimals through thousandths, and percents, on the number line 6: 78A-78B, 78-79, 176A-176B, 176-179

locate integers on the number line 6: 408A-408B, 408-409, 410A-410B, 410-411

identify subsets of integers, including counting and whole numbers 6: 408A-408B, 408-409, 410A-410B, 410-411

demonstrate the equivalence of commonly-used fractions, decimals, and percents 6: 172A-172B, 172-175, 176A-176B, 176-179, 358A-358B, 358-361

12


pictorially, demonstrate the meaning of square roots of perfect square numbers through 100 6: 8A-8B, 8-11

1.2 Reading, writing, and ordering integers, rational numbers, and common irrational numbers such as •2 and •5 and •. Fifth grade students will: read, write, and order positive rational numbers, including commonly-used

fractions and terminating decimals through thousandths 5: 6A-6B, 6-7, 12A-12B, 12-13, 418A-418B, 418-419, 420A-420B, 420-423, 430A-430B, 430-433

compare commonly-used proper fractions and terminating decimals using the symbols =, •, <, > 5: 12A-12B, 12-13, 418A-418B, 418-419, 420A-420B, 420-423, 430A-430B, 430-433

Sixth grade students will: read, write, and order positive rational numbers, including commonly-used

fractions and terminating decimals through thousandths 6: 168A-168B, 168-169, 172A-172B, 172-175, 176A-176B, 176-179, 358A-358B, 358-361, 412A-412B, 412-413

compare positive fractions and decimals using the symbols =, •, <, > 6: 168A-168B, 168-169, 172A-172B, 172-175, 176A-176B, 176-179, 358A-358B, 358-361

1.3 APPLYING NUMBER THEORY CONCEPTS (FOR EXAMPLE, PRIMES, FACTORS, MULTIPLES) TO REPRESENT NUMBERS IN VARIOUS WAYS. Fifth grade students will: identify factors, multiples, and prime composite numbers

5: 162A-162B, 162-163, 164A-164B, 164-167, 202A-202B, 202-203, 414A-414B, 414-415

write the prime factorization of whole numbers up to 50 (for example, 36 = 2 • 2 • 3 • 3) 5: 164A-164B, 164-167

13


relate exponential notation to repeated multiplication (for example, 81 = 3 • 3 • 3 • 3 = 81) 5: 167

write whole numbers in expanded form without powers of ten (for example, 579 = 500 + 70 + 9 = (5 x 100) + ( 7 x 10) + (9 x 1)) 5: 4A-4B, 4-5

demonstrate the divisibility rules for 2, 5, and 10 5: 162A-162B, 162-163

demonstrate an = a • a • ... • a, where ‘a’ and ‘n’ are counting numbers 5: 14A-14B, 14-17, 66A-66B, 66-67, 84A-84B, 84-85, 106A-106B, 106-107, 136A-136B, 136-137, 728A-728B, 728-729

Sixth grade students will: write the prime factorization of whole numbers in exponential form (for

example, 36 = 22 • 32) 6: 146A-146B, 146-149

write whole numbers in expanded form with powers of ten (for example, 579 = 500 + 70 + 9 = 5 x 100+ 7 x 10 + 9 x 1) 6: 106A-106B, 106-109

write large whole numbers using scientific notation (for example, 246,000,000 = 2.46 x 10 8 ; 2.46 x 10 8 = 246,000,000) 6: 110A-110B, 110-111

demonstrate the divisibility rules for 2, 3, 5, 6, 9, and 10 6: 142A-142B, 142-145

determine the greatest common factor and least common multiple of a pair of whole numbers 6: 150A-150B, 150-151, 152A-152B, 152-155

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1.4 USING THE RELATIONSHIPS AMONG FRACTIONS, DECIMALS, AND PERCENTS, INCLUDING THE CONCEPTS OF RATIO AND PROPORTION, IN PROBLEM-SOLVING SITUATIONS. Fifth grade students will: demonstrate the meaning of ratio in different contexts

5: 646A-646B, 646-647, 648A-648B, 648-651, 652A-652B, 652-653, 660A-660B, 660-661, 662A-662B, 662-663

use appropriate notation to express ratios, including a/b, a to b, and a: b 5: 646A-646B, 646-647, 648A-648B, 648-651, 652A-652B, 652-653, 660A-660B, 660-661, 662A-662B, 662-663

Sixth grade students will: represent fractions, decimals, and percents as ratios

6: 300A-300B, 300-301, 302A-302B, 302-305

demonstrate the similarities and differences between ratios and fractions 6: 300A-300B, 300-301, 302A-302B, 302-305

interpret and use ratios in different contexts (e.g. batting averages, miles per hour) to show the relative sizes of two quantities using appropriate notations, including a/b, a to b, a : b 6: 300A-300B, 300-301, 302A-302B, 302-305

1.5 DEVELOPING, TESTING, AND EXPLAINING CONJECTURES ABOUT PROPERTIES OF INTEGERS AND RATIONAL NUMBERS. Fifth grade students will: demonstrate the commutative, associative, and identity properties for addition

and multiplication, and the multiplication property of zero for fractions 5: 36A-36B, 36-37, 72A-72B, 72-72, 152A-152B, 152-155, 496A-496B, 496-499

Sixth grade students will: demonstrate multiplication inverses of positive rational numbers (for example,

1/9 • 9 = 1) 6: 248A-248B, 248-251

demonstrate that division by zero is undefined

6: 94A-94B, 94-97

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1.6 USING NUMBER SENSE TO ESTIMATE AND JUSTIFY THE REASONABLENESS OF SOLUTIONS TO PROBLEMS INVOLVING INTEGERS, RATIONAL NUMBERS, AND COMMON IRRATIONAL NUMBERS SUCH AS •2, •5, AND •.

Fifth grade students will: estimate sums and differences of fractions and decimals using benchmarks

(for example, 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1) 5: 28A-28B, 28-31

estimate, using appropriate techniques, determine, and, then, justify the reasonableness of solutions to problems involving whole numbers 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, 138-143, 204A-204B, 204-209

Sixth grade students will: estimate, using appropriate techniques, determine, and, then, justify the

reasonableness of solutions to problems involving whole numbers and sums and differences of commonly-used fractions and decimals 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, 216-217, 256A-256B, 256-257, 368A-368B, 368-369

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Standard 2: Students use algebraic methods to explore, model and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems. GRADES K-4 In grades K-4, what students know and are able to do includes 2.1 REPRODUCING, EXTENDING, CREATING, AND DESCRIBING PATTERNS AND SEQUENCES USING A VARIETY OF MATERIALS (FOR EXAMPLE, BEANS, TOOTHPICKS, PATTERN BLOCKS, CALCULATORS, UNIFIX CUBES, COLORED TILES). Kindergarten students will: recognize, construct, and extend patterns in a variety of motions, colors,

designs, sounds, rhythms, music, positions, sizes, or quantities 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

First grade students will: create and extend patterns using concrete materials (for example, uses

pattern blocks to create a pattern and has another student extend the pattern) 1: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8

Second grade students will: verbally describe patterns

2: 99A-99B, 99-100, 413A-413B, 413-414, 467A-467B, 467-468

create and extend patterns using symbols, such as words and numbers 2: 99A-99B, 99-100, 413A-413B, 413-414, 467A-467B, 467-468

find missing elements of a repeating pattern (for example, 1,3, __,7) 2: 99A-99B, 99-100, 413A-413B, 413-414, 467A-467B, 467-468

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Third grade students will: reproduce, extend, create, and describe patterns, such as in common

fractions, geometric shapes, money, measurement, addition, subtraction, and multiplication facts 3: 24-27, 277, 282, 286, 288-289, 332A-332B, 332-335, 340-341, 344-345

find missing elements of patterns of multiples 3: 332A-332B, 332-335

Fourth grade students will: reproduce, extend, create, and describe patterns, such as in common

fractions, geometric shapes, measurement, addition, subtraction, multiplication, and division facts 4: 10A-10B, 10-11, 90A-90B, 90-91, 366A-366B, 366-367, 641

find missing elements of a complex repeating pattern (for example, 1,1,2,3,5,__,13,…) 4: 10A-10B, 10-11, 90A-90B, 90-91, 366A-366B, 366-367, 641

2.2 DESCRIBING PATTERNS AND OTHER RELATIONSHIPS USING TABLES, GRAPHS, AND OPEN SENTENCES. Kindergarten students will: sort, classify, describe, and order collections of objects in a variety of ways

(for example, sorts buttons into two groups and explains why he/she sorted them this way) K: 11A-11B, 11-12, 13A-13B, 13-14, 15A-15B, 15-16, 17A-17B, 17-18

First grade students will: continue the pattern given in a table of data using numbers and/or concrete

materials 1: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8

Second grade students will: match tables and graphs of points on a coordinate plane

2: 325A-325B, 325-326

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Third grade students will: given data, extend a table and plot points on a coordinate plane

3: 218A-218B, 218-221, 222A-222B, 222-223

Fourth grade students will: match tables, graphs, and open sentences that represent the same numerical

pattern 4: 76A-76B, 76-79, 98A-98B, 98-99, 100A-100B, 100-101

2.3 RECOGNIZING WHEN A PATTERN EXISTS AND USING THAT INFORMATION TO SOLVE A PROBLEM. Kindergarten students will: recognize when a pattern exists, describe the pattern verbally, reproduce that

pattern, and create a new pattern (for example, describes red, blue, red, blue as an AB, AB pattern) K: 41A-41B, 41-42, 43A-43B, 43-44, 45A-45B, 45-46

First grade students will: continue a pattern from a table and verbally describe the pattern

1: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8

Second grade students will: verbally describe the relationship between a graph and a table

2: 325A-325B, 325-326

Third grade students will: identify a rule using addition or subtraction and solve a problem using the rule

3: 72A-72B, 72-75

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Fourth grade students will: identify a rule using addition, subtraction, or multiplication, and solve a

problem using the rule 4: 164A-164B, 164-165

2.4 OBSERVING AND EXPLAINING HOW A CHANGE IN ONE QUANTITY CAN PRODUCE A CHANGE IN ANOTHER (FOR EXAMPLE, THE RELATIONSHIP BETWEEN THE NUMBER OF BICYCLES AND THE NUMBERS OF WHEELS). First grade students will: using concrete or pictorial patterns, determine how the change in one variable

affects the change in another (for example, how changing the number of bicycles changes the number of wheels) 1: preparation: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8

Second grade students will: using concrete or pictorial patterns, determine how the change in one variable

affects the change in another (for example, how changing the number of hands changes the number of fingers) 2: preparation: 99A-99B, 99-100, 413A-413B, 413-414, 467A-467B, 467-468

Third grade students will: determine how the change in one variable affects the change in the other by

addition or subtraction 3: 72A-72B, 72-75

Fourth grade students will: determine how the change in one variable affects the change in the other by

addition, subtraction, or multiplication 4: 164A-164B, 164-165

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GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 2.1 REPRESENTING, DESCRIBING, AND ANALYZING PATTERNS AND RELATIONSHIPS USING TABLES GRAPHS, VERBAL RULES, AND STANDARD ALGEBRAIC NOTATION. Fifth grade students will: represent, describe, and analyze patterns for relationships involving whole

numbers and common proper fractions 5: 14A-14B, 14-17, 66A-66B, 66-67, 84A-84B, 84-85, 106A-106B, 106-107, 136A-136B, 136-137, 728A-728B, 728-729

recognize that a variable is used to represent an unknown quantity 5: 100A-100B, 100-103, 104A-104B, 104-105, 108A-108B, 108-109, 176A-176B, 176-179, 660A-660B, 660-661, 706A-706B, 706-709

Sixth grade students will: represent, describe, and analyze patterns for relationships involving positive

rational numbers 6: 620A-620B, 620-623, 624A-624B, 624-627, 628A-628B, 628-631, 632A-632B, 632-633

use variables such as boxes, letters, or other symbols to describe a general rule and to solve problems 6: 620A-620B, 620-623, 624A-624B, 624-627, 628A-628B, 628-631, 632A-632B, 632-633

2.2 DESCRIBING PATTERNS USING VARIABLES, EXPRESSIONS, EQUATIONS, AND INEQUALITIES IN PROBLEM-SOLVING SITUATIONS. Fifth grade students will: solve problems from patterns involving whole numbers and common proper

fractions using tables, graphs, and rules 5: 106A-106B, 106-107, 728A-728B, 728-729

21


Sixth grade students will: solve problems from patterns involving positive rational numbers using

tables, graphs, and rules 6: 620A-620B, 620-623, 624A-624B, 624-627, 628A-628B, 628-631, 632A-632B, 632-633

2.3 ANALYZING FUNCTIONAL RELATIONSHIPS TO EXPLAIN HOW A CHANGE IN ONE QUANTITY RESULTS IN A CHANGE IN ANOTHER (FOR EXAMPLE, HOW THE AREA OF A CIRCLE CHANGES AS THE RADIUS INCREASES, OR HOW A PERSON’S HEIGHT CHANGES OVER TIME). Fifth grade students will: in any functional relationship involving whole numbers and common proper

fractions, describe how a change in one quantity affects the other 5: 106A-106B, 106-107, 728A-728B, 728-729

Sixth grade students will: in any functional relationship involving positive rational numbers, describe

how a change in one quantity affects the other 6: 620A-620B, 620-623, 624A-624B, 624-627, 628A-628B, 628-631, 632A-632B, 632-633

2.4 DISTINGUISHING BETWEEN LINEAR AND NONLINEAR FUNCTIONS THROUGH INFORMAL INVESTIGATIONS. Fifth grade students will: graph discrete linear and nonlinear functions

5: 728A-728B, 728-729

match a description of a situation with its continuous graph 5: 728A-728B, 728-729

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Sixth grade students will: graph discrete linear and nonlinear functions

6: 444A-444B, 444-447, 448A-448B, 448-449

graph a continuous linear function for a given situation 6: 448A-448B, 448-449

2.5 SOLVING SIMPLE LINEAR EQUATIONS IN PROBLEM-SOLVING SITUATIONS USING A VARIETY OF METHODS (INFORMAL, FORMAL AND GRAPHICAL) AND A VARIETY OF TOOLS (PHYSICAL MATERIALS, CALCULATORS AND COMPUTERS). Fifth grade students will: solve problems involving linear relationships in whole numbers

5: 700A-700B, 700-701, 702A-702B, 702-705, 728A-728B, 728-729

solve simple linear equations with coefficients of 1 by informal methods using manipulatives, tables, graphs, or technology

5: 700A-700B, 700-701, 702A-702B, 702-705, 728A-728B, 728-729 Sixth grade students will: solve problems involving linear relationships in positive rational numbers

6: 444A-444B, 444-447, 448A-448B, 448-449

solve simple linear equations with whole number coefficients by informal methods using manipulatives, tables, graphs, or technology 6: 444A-444B, 444-447, 448A-448B, 448-449

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Standard 3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning and processes used in solving these problems. GRADES K-4 In grades K-4, what students know and are able to do includes 3.1 CONSTRUCTING, READING, AND INTERPRETING DISPLAYS OF DATA INCLUDING TABLES, CHARTS, PICTOGRAPHS, AND BAR GRAPHS. Kindergarten students will: read and display simple picture and real object graphs

K: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32, 33A-33B, 33-34

gather data relating to familiar experiences by counting and tallying K: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32, 33A-33B, 33-34

First grade students will: gather data about recurring and quantifiable events (for example, daily

temperature or attendance) 1: 313A-313B, 313-314

display and explain data from a bar graph or tallies 1: 309A-039B, 309-310, 311A-311B, 311-312, 313A-313B, 313-314, 315A-315B, 315-316

Second grade students will: design a survey and collect data

2: 311A-311B, 311-312, 313A-313B, 313-314, 315A-315B, 315-316

display data using tallies, bar graphs, pictographs, or tables 2: 319A-319B, 319-320, 321A-321B, 321-322, 323A-323B, 323-324, 325A-325B, 325-326, 327A-327B, 327-328

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transfer the same set of data to different displays (for example, from a table to a bar graph) 2: 319A-319B, 319-320, 321A-321B, 321-322, 323A-323B, 323-324, 325A-325B, 325-326, 327A-327B, 327-328

Third grade students will: select the appropriate type of graph to use in various problem-solving

situations 3: 212A-212B, 212-215, 226A-226B, 226-227, 228A-228B, 228-231, 232A-232B, 232-235

collect and display data using surveys, tallies, bar graphs, dot plots, pictographs, or tables 3: 212A-212B, 212-215, 226A-226B, 226-227, 228A-228B, 228-231, 232A-232B, 232-235

use a computer to create bar and circle graphs 3: 207, 231

use a timeline to display a sequence of events 3: related material: 200A-200B, 200-201

Fourth grade students will: select the appropriate type of graph to use in various problem-solving

situations 4: 204A-204B, 204-205, 206A-206B, 206-207, 208A-208B, 208-211, 216A-216B, 216-221, 226A-226B, 226-229

collect and display data using line, dot plots, circle, or bar graphs 4: 204A-204B, 204-205, 206A-206B, 206-207, 208A-208B, 208-211, 216A-216B, 216-221, 226A-226B, 226-229

use graph paper using the horizontal and vertical axes appropriately 4: 222A-222B, 222-223

explain the basic concepts of sample bias and sample size when designing a survey 4: 230A-230B, 230-231, 232A-232B, 232-233

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3.2 INTERPRETING DATA USING THE CONCEPTS OF LARGEST, SMALLEST, MOST OFTEN, AND MIDDLE. Kindergarten students will: use "more" and "fewer" or "most," "same," and "fewest" to describe sets of manipulatives, pictures, or object graphs

K: 27A-27B, 27-28 First grade students will: using a bar graph, interpret data for "more" and "fewer" or "most," "same,"

and "fewest" 1: 311A-311B, 311-312

Second grade students will: interpret and compare data from displays, using the terms "least often," "most

often", and "how much more" or "how much less" 2: 321A-321B, 321-322, 323A-323B, 323-324

Third grade students will: determine the median and mode from a data set

3: 211

using various displays of data, interpret and draw conclusions 3: 212A-212B, 212-215, 226A-226B, 226-227, 228A-228B, 228-231, 232A-232B, 232-235

Fourth grade students will: choose between median and mode to best describe the "middle" of a data set

4: 226A-226B, 226-229

transfer the use of median and mode to other curricular areas 4: 226A-226B, 226-229

using various displays of data, formulate questions, interpret, and draws conclusions 4: 204A-204B, 204-205, 206A-206B, 206-207, 208A-208B, 208-211, 216A-216B, 216-221, 226A-226B, 226-229

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3.3 GENERATING, ANALYZING, AND MAKING PREDICTIONS BASED ON DATA OBTAINED FROM SURVEYS AND CHANCE DEVICES. Kindergarten students will: flip a two-colored counter or coin to generate and tally results

K: preparation: 27A-27B, 27-28, 29A-29B, 29-30, 31A-31B, 31-32, 33A-33B, 33-34

First grade students will: use survey data to make a prediction displayed on a bar graph

1: 311A-311B, 311-312 spin a spinner such as to generate and record results

1: 401A-401B, 401-402, 403A-403B, 403-404

analyze the results from flipping a two-colored counter or coin 1: 401A-401B, 401-402, 403A-403B, 403-404

Second grade students will: use survey data to make predictions about a larger similar population (for

example, from a class survey make a prediction about all second graders in the school) 2: 313A-313B, 313-314

roll a number cube to generate and record results 2: 373A-373B, 373-374, 375A-375B, 375-376

analyze the results (including likely, more likely, less likely, and unlikely outcomes) of spinning a spinner 2: 373A-373B, 373-374, 375A-375B, 375-376

recognize if different spinners are fair or unfair 2: 373A-373B, 373-374

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Third grade students will: use survey data to make a prediction from various displays of data

3: 204A-204B, 204-207

analyze the results of rolling a number cube 3: 700A-700B, 700-701, 702A-702B, 702-703, 704A-704B, 704-707

predict the most likely outcome from spinners 3: 700A-700B, 700-701, 702A-702B, 702-703

analyze the fairness of different spinners 3: 700A-700B, 700-701, 702A-702B, 702-703

Fourth grade students will: uses survey data to make and justify a real-world decision

4: 230A-230B, 230-231 compare the outcomes of flipping a coin, spinning a spinner with four

congruent sectors, and rolling a number cube 4: 700A-700B, 700-703, 706A-706B, 706-709, 710A-710B, 710-713

analyze and predict which outcome is more likely from several events such as obtaining “heads” when flipping a coin, the spinner landing in one of the sectors, or rolling a “1” on a number cube 4: 700A-700B, 700-703, 706A-706B, 706-709, 710A-710B, 710-713

analyze the fairness of various chance devices 4: 700A-700B, 700-703, 706A-706B, 706-709, 710A-710B, 710-713

3.4 SOLVING PROBLEMS USING VARIOUS STRATEGIES FOR MAKING COMBINATIONS (FOR EXAMPLE, DETERMINING THE NUMBER OF DIFFERENT OUTFITS THAT CAN BE MADE USING TWO BLOUSES AND THREE SKIRTS). First grade students will: determine the number of outcomes when flipping a coin

1: preparation: 401A-401B, 401-402, 403A-403B, 403-404

28


using manipulatives or pictures, determine the possible combinations of matching a set containing one element with a set containing two elements 1: preparation: 401A-401B, 401-402, 403A-403B, 403-404

Second grade students will: determine the number of outcomes when spinning a spinner

2: 373A-373B, 373-374, 375A-375B, 375-376

using manipulatives or pictures, determine the possible combinations of matching a set containing two elements with a different set containing two elements 2: related material: 373A-373B, 373-374, 375A-375B, 375-376

Third grade students will: determine the number of outcomes when rolling a number cube

3: 700A-700B, 700-701, 702A-702B, 702-703

using manipulatives or pictures, determine the possible combinations of matching a set containing two elements with a set containing three elements 3: related material: 700A-700B, 700-701, 702A-702B, 702-703, 704A-704B, 704-707

Fourth grade students will: determine the number of outcomes obtained from a variety of chance devices

4: 700A-700B, 700-703, 706A-706B, 706-709, 710A-710B, 710-713

using paper-and-pencil techniques (for example, tree diagrams), display the possible combinations of matching two sets of elements 4: 704A-704B, 704-705

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GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 3.1 READING AND CONSTRUCTING DISPLAYS OF DATA USING APPROPRIATE TECHNIQUES (FOR EXAMPLE, LINE GRAPHS, CIRCLE GRAPHS, SCATTER PLOTS, BOX PLOTS, STEM-AND-LEAF PLOTS) AND APPROPRIATE TECHNOLOGY. Fifth grade students will: differentiate between categorical and numerical data

5: 262A-262B, 262-265, 266A-266B, 266-269, 286A-286B, 286-287

organize and display data using appropriate graphs, such as line, bar, circle, dot plots, frequency tables, and stem-and-leaf 5: 262A-262B, 262-265, 266A-266B, 266-269, 286A-286B, 286-287

read, interpret, and draw conclusions from various displays of data 5: 262A-262B, 262-265, 266A-266B, 266-269, 286A-286B, 286-287

Sixth grade students will: organize and display data using appropriate graphs, such as line, bar, circle,

dot plots, frequency tables, stem-and-leaf, and histograms 6: 624A-624B, 624-627, 628A-628B, 628-631, 636A-636B, 636-637, 638A-638B, 638-641, 642A-642B, 642-647

read, interpret, and draw conclusions from various displays of data

6: 624A-624B, 624-627, 628A-628B, 628-631, 636A-636B, 636-637, 638A-638B, 638-641, 642A-642B, 642-647

3.2 DISPLAYING AND USING MEASURES OF CENTRAL TENDENCY, SUCH AS MEAN, MEDIAN, AND MODE, AND MEASURES OF VARIABILITY, SUCH AS RANGE AND QUARTILES. Fifth grade students will: determine the mean of a set of data using manipulatives

5: 282A-282B, 282-285

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informally distinguish between mean, median, and mode 5: 282A-282B, 282-285

determine the range of a set of data 5: 282A-282B, 282-285

given various displays of the same set of data (line, bar, circle, and stem-and-leaf), determine which measure of central tendency is most evident 5: 282A-282B, 282-285

Sixth grade students will: determine the mean of a set of data by using an algorithm

6: 624A-624B, 624-627

formally distinguish between mean, median, and mode 6: 624A-624B, 624-627

given various displays of the same set of data (line, bar, circle, stem-and-leaf, and histograms), determine which measure of central tendency is most evident 6: 624A-624B, 624-627

3.3 EVALUATING ARGUMENTS THAT ARE BASED ON STATISTICAL CLAIMS. Fifth grade students will: critically evaluate line graphs, bar graphs, pictographs, or dot plots which do

not begin at zero 5: 262A-262B, 262-265, 266A-266B, 266-269, 286A-286B, 286-287

Sixth grade students will: recognize a misleading display of data due to scaling

6: 650A-650B, 650-651

critically evaluate biased sampling of a survey 6: 620A-620B, 620-623

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3.3 EVALUATING ARGUMENTS THAT ARE BASED ON STATISTICAL CLAIMS. Fifth grade students will: critically evaluate line graphs, bar graphs, pictographs, or dot plots which do

not begin at zero 5: 262A-262B, 262-265, 266A-266B, 266-269, 286A-286B, 286-287

Sixth grade students will: recognize a misleading display of data due to scaling

6: 650A-650B, 650-651

critically evaluate biased sampling of a survey 6: 620A-620B, 620-623

3.4 FORMULATING HYPOTHESES, DRAWING CONCLUSIONS, AND MAKING CONVINCING ARGUMENTS BASED ON DATA ANALYSIS. Fifth grade students will: distinguish between a census and a survey

5: 260A-260B, 260-261 explain why there may be differences in the data of two or more samples

5: 260A-260B, 260-261

Sixth grade students will: demonstrate the meaning of random sampling and biased versus unbiased

samples 6: 620A-620B, 620-623

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3.5 DETERMINING PROBABILITIES THROUGH EXPERIMENTS OR SIMULATIONS. Fifth grade students will: apply probability terms such as event, outcome, trials, and sample space

5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

assign a number between 0 and 1, inclusive, to the probability of an event 5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

perform experiments of independent compound events to estimate probability 5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

Sixth grade students will: pictorially demonstrate the equivalence of probabilities as either a common

fraction, decimal, or percent 6: 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

assigns 0% to an impossible event and 100% to a certain event 6: 662A-662B, 662-663, 664A-664B, 664-665

performs experiments of independent compound events to estimate probability 6: 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

3.6 MAKING PREDICTIONS AND COMPARING RESULTS USING BOTH EXPERIMENTAL AND THEORETICAL PROBABILITY DRAWN FROM REAL-WORLD PROBLEMS. Fifth grade students will: predict the probability of independent compound events, such as tossing two

coins or determining the gender of two children in a family, and conduct an experiment or simulation to determine the probability 5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

33


demonstrates that the sum of the probabilities equals one (as applied to the sample space) 5: 302A-032B, 302-305

using one chance device, such as a number cube or a spinner, design a fair game and an unfair game, and write the directions for each game 5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

Sixth grade students will: predict the probability of independent compound events, such as the sum of

two number cubes, conduct an experiment or simulation to determine the probability, and assign the probability to all possible sums of two number cubes 6: 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

demonstrate that the sum of all probabilities of two number cubes equals one 6: 668A-668B, 668-671

using two chance devices, such as two number cubes or two spinners, design a fair game, and an unfair game, and write the directions for each game 6: 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

3.7 USING COUNTING STRATEGIES TO DETERMINE ALL THE POSSIBLE OUTCOMES FROM AN EXPERIMENT (FOR EXAMPLE, THE NUMBER OF WAYS STUDENTS CAN LINE UP TO HAVE THEIR PICTURE TAKEN). Fifth grade students will: determine the number of outcomes of independent compound events, such as

tossing two coins or determining the gender of two children in a family by making a list or tree diagram 5: 296A-296B, 296-299, 300A-300B, 300-301, 302A-032B, 302-305

34


Sixth grade students will: determine the number of outcomes of independent compound events, such as

the sum of tossing two number cubes by making a list or tree diagram 6: 658A-658B, 658-661

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Standard 4: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems. GRADES K-4 In grades K-4, what students know and are able to do includes 4.1 RECOGNIZING SHAPES AND THEIR RELATIONSHIPS (FOR EXAMPLE, SYMMETRY AND CONGRUENCE) USING A VARIETY OF MATERIALS (FOR EXAMPLE, PASTA, BOXES, PATTERN BLOCKS). Kindergarten students will: place manipulatives on pictures of shapes congruent to the manipulatives

K: preparation: 203-204, 205-206, 207-208

First grade students will: recognize two-dimensional congruent figures in different positions

1: 169A-169B, 169-170

create simple designs using concrete materials such as tangrams and pattern blocks 1: 193A-193B, 193-194

Second grade students will: identify congruent figures from a selection of similar figures

2: 257A-257B, 257-258

slide, flip, and turn concrete materials such as tangrams and pattern blocks to create and reproduce simple designs 2: 259A-259B, 259-260

describe symmetry 2: 261A-261B, 261-262

identify lines of symmetry of squares and rectangles 2: 261A-261B, 261-262

36


Third grade students will: compare similarities and differences between the concepts of similarity and

congruence 3: 456A-456B, 456-459

make a pattern by rotating, flipping, and sliding a two-dimensional figure 3: 456A-456B, 456-459

identify lines of symmetry of regular hexagons, pentagons, and octagons 3: 460A-460B, 460-461

Fourth grade students will: define similarity and congruence

4: 452A-452B, 452-455, 458A-458B, 458-459

identify the transformation that occurs when a figure is translated, reflected, or rotated 4: 452A-452B, 452-455

identify the lines of symmetry of an equilateral triangle, parallelogram, and rhombus 4: 456A-456B, 456-457

4.2 IDENTIFYING, DESCRIBING, DRAWING, COMPARING, CLASSIFYING, AND BUILDING PHYSICAL MODELS OF GEOMETRIC FIGURES. Kindergarten students will: recognize and identify circles, triangles, squares, rectangles, ovals (ellipses),

and diamonds (rhombuses) K: 203A-203B, 203-204, 205A-205B, 205-206

using manipulatives (for example, straws or string loops), build circles, triangles, squares, rectangles, ovals (ellipses), and diamonds (rhombuses) K: 203A-203B, 203-204, 205A-205B, 205-206

37


First grade students will: describe the number of sides in triangles and in quadrilaterals such as

squares and rectangles 1: 165A-165B, 165-166, 167A-167B, 167-168

draw triangles, squares, rectangles, and circles 1: 165A-165B, 165-166, 167A-167B, 167-168

Second grade students will: describe the attributes of circles, triangles, and quadrilaterals such as squares

and rectangles 2: 255A-255B, 255-256

identifies right angles and not-right angles 2: 255A-255B, 255-256

recognize the three-dimensional figures: cubes, spheres, cylinders, cones, and pyramids 2: 247A-247B, 247-248, 249A-249B, 249-250

draw right angles and not-right angles 2: 255A-255B, 255-256

Third grade students will: identify points, lines, line segments, and rays

3: 442A-442B, 442-443

recognize and identify hexagons, pentagons, and octagons 3: 446A-446B, 446-449

classify angles as obtuse, acute, or right 3: 444A-444B, 444-445

draw obtuse, acute, and right angles 3: 444A-444B, 444-445

compare what is the same and what is different between two-dimensional figures and three-dimensional figures 3: 456A-456B, 456-459

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draw rectangles and squares on a coordinate plane and identify the vertices with coordinates 3: 456A-456B, 456-459

identify cubes, spheres, cylinders, cones, and pyramids 3: 428A-428B, 428-431

build cubes (for example, with marshmallows and toothpicks) and spheres (for example, soap bubbles)

3: 428A-428B, 428-431 Fourth grade students will: identify parallel, perpendicular, and intersecting lines

4: 440A-440B, 440-443

identify attributes of closed curves 4: 448A-448B, 448-449

recognize and identify polygons including quadrilaterals such as trapezoids, parallelograms, and rhombuses 4: 438A-438B, 438-439, 444A-444B, 444-447, 448A-448B, 448-449

draw geometric polygons including quadrilaterals such as trapezoids, parallelograms, and rhombuses 4: 438A-438B, 438-439, 444A-444B, 444-447, 448A-448B, 448-449

describe squares as rectangles 4: 444A-444B, 444-447

describe a right angle as having a measure of 90° 4: 440A-440B, 440-443

classify triangles by their angles (obtuse, acute, right) 4: 444A-444B, 444-447

draw obtuse, acute, and right triangles on a coordinate plane and identify the vertices with coordinates 4: 440A-440B, 440-443

compare what is the same and what is different between two-dimensional figures and three-dimensional figures 4: 434A-434B, 434-437

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identify rectangular prisms 4: 434A-434B, 434-437

recognize and identify in three-dimensional figures the vertices, edges, and faces 4: 434A-434B, 434-437

build cubes, prisms, and pyramids (for example, using straws and string) 4: 434A-434B, 434-437

4.3 RELATING GEOMETRIC IDEAS TO MEASUREMENT AND NUMBER SENSE. Kindergarten students will: measure the lengths of the sides of triangles, squares, and rectangles using

non-standard units (for example, cubes or paper clips) K: preparation: 135A-135B, 135-136, 139A-139B, 139-140

First grade students will: measure the lengths of the sides of triangles, squares, rectangles to the

nearest inch and centimeter 1: 377A-377B, 377-378

Second grade students will: measure the lengths of the sides of triangles, squares, and rectangles to the

nearest half inch and centimeter 2: 343A-343B, 343-344, 345A-345B, 345-346, 347A-347B, 347-348, 384

measures the perimeter of triangles, squares, and rectangles using non-standard and standard units 2: 384

Third grade students will: measure the sides and perimeters of geometric shapes to the nearest half inch

and centimeter 3: 464A-464B, 464-467

measure the area of geometric figures using nonstandard units 3: 468A-468B, 468-471

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Fourth grade students will: measure the sides and perimeters of geometric shapes to the nearest fourth

inch and centimeter 4: 464A-464B, 464-467

measure the area of geometric figures using standard units 4: 468A-468B, 468-472

4.4 SOLVING PROBLEMS USING GEOMETRIC RELATIONSHIPS AND SPATIAL REASONING (FOR EXAMPLE, USING RECTANGULAR COORDINATES TO LOCATE OBJECTS, CONSTRUCTING MODELS OF THREE-DIMENSIONAL OBJECTS). Kindergarten students will: use geometric shapes to solve a problem (for example, use geometric shapes

to create a house) K: 217A-217B, 217-218

indicate positions of three or more objects or pictures (for example, left to right, top to bottom, next, last) K: 3A-3B, 3-4, 5A-5B, 5-6, 7A-7B, 7-8, 9A-9B, 9-10

combine triangular manipulatives to make a square, and square manipulatives to make a rectangle K: 209A-209B, 209-210

First grade students will: draw a picture or diagram to solve a problem (for example, use a circle to

create a clock face; fold a rectangle to show one half) 1: 111A-111B, 111-112

manipulate pattern blocks to form a variety of geometric shapes 1: related material: 173A-173B, 173-174, 193-194

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Second grade students will: draw a picture or diagram to solve a problem (for example, draw a map of the

room to show how to get from a desk to the reading area; draw a map of the neighborhood) 2: 479A-479B, 479-480

investigate and predict which pattern block shapes can be formed from the pattern block triangles 2: 255A-255B, 255-256

investigate and predict the geometric shapes that result from cutting along a line of symmetry 2: 261A-261B, 261-262

Third grade students will: draw a picture or diagram to solve a problem (for example, use a number line

to locate one half) 3: 140A-140B, 140-143

investigate and predict geometric shapes by combining and subdividing groups of pattern blocks 3: related material: 456A-456B, 456-459

investigate and predict the result of changing the lengths of sides of polygons 3: related material: 456A-456B, 456-459

investigate and predict the geometric figures that result from cutting along a line of symmetry 3: 460A-460B, 460-461

Fourth grade students will: draw a picture or diagram to solve a problem (for example, uses triangular

pattern blocks to create a star; uses pattern blocks to tile a plane) 4: 512A-512B, 512-513

investigate and predict the changing of angles (for example, those made from the hands of a clock over time) 4: 440A-440B, 440-443

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investigate and predict what must occur for similar figures to become congruent figures 4: 452A-452B, 452-455, 458A-458B, 458-459

investigate and predict the geometric figures that result from cutting along a line of symmetry 4: 456A-456B, 456-457

GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 4.1 CONSTRUCTING TWO- AND THREE-DIMENSIONAL MODELS USING A VARIETY OF MATERIALS AND TOOLS. Fifth grade students will: using a straight edge and a compass, paper folding, or computer software

application, demonstrate the geometric constructions of copying a segment and copying an angle 5: 328A-328B, 328-331, 332A-332B, 332-335

build models of rectangular prisms including their nets 5: 598A-598B, 598-601

given a three-dimensional model built with cubes, draw the two-dimensional orthogonal drawings (that is, the front view, right side view, and top view) and, conversely, given orthogonal drawings, build the model

5: 598A-598B, 598-601, 602A-602B, 602-605 Sixth grade students will: using a straight edge and a compass, paper folding, or computer software

application, demonstrate the geometric construction of an angle bisector 6: 484A-484B, 484-489

build models of triangular prisms including their nets 6: 586A-586B, 586-589

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given a three-dimensional model built with cubes, draw the orthogonal drawings (that is, the front view, right side view, and top view) and the foundation drawing (that is, the shape of the foundation, placement and the number of cubes that are built on this foundation) and, conversely, given the orthogonal and foundation drawing, build the model 6: 586A-586B, 586-589

4.2 DESCRIBING, ANALYZING, AND REASONING INFORMALLY ABOUT THE PROPERTIES (FOR EXAMPLE, PARALLELISM, PERPENDICULARITY, CONGRUENCE) OF TWO- AND THREE-DIMENSIONAL FIGURES; AND 4.3 APPLYING THE CONCEPTS OF RATIO, PROPORTION, AND SIMILARITY IN PROBLEM-SOLVING SITUATIONS. Fifth grade students will: know that the measurement of an acute angle is less than 90°, a right angle is

90°, and an obtuse angle is greater than 90° 5: 332A-332B, 332-335

uses correct geometric symbols for lines, segments, rays, and angles 5: 332A-332B, 332-335, 336A-336B, 336-337

reason informally about properties of parallel lines, perpendicular lines, intersecting lines, line segments, and rays 5: 336A-336B, 336-337

reason informally about properties (including lines of symmetry) of rectangles, squares, triangles (named by both lengths of sides and angles), and rectangular prisms 5: 340A-340B, 340-341, 342A-342B, 342-345, 346A-346B, 346-351

reason informally about congruence involving rectangles, squares, triangles, and rectangular prisms 5: 360A-360B, 360-363

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Sixth grade students will: describe complementary and supplementary angles

6: 480A-480B, 480-483

use correct geometric symbols for parallelism, perpendicularity, and triangles 6: 472A-472B, 472-475, 496A-496B, 496-499

reason informally about the properties (including lines of symmetry) of parallelograms, rhombuses, and triangular prisms 6: 500A-500B, 500-501, 514A-514B, 514-515

reason informally about congruence involving parallelograms, rhombuses, and triangular prisms 6: 506A-506B, 506-509

4.4 SOLVING PROBLEMS USING COORDINATE GEOMETRY. Fifth grade students will: set up a coordinate graph (include axes, origin, and scale) and use it to mark

and read coordinate pairs in the first quadrant 5: 724A-724B, 72-4727

from a scenario, choose the correct graph from given possible graph representations 5: 724A-724B, 72-4727

given a distance, find pairs of points on the coordinate plane in the first quadrant separated by that horizontal or vertical distance 5: 724A-724B, 72-4727

Sixth grade students will: identify the four quadrants of the coordinate plane

6: 440A-440B, 440-443

set up a coordinate graph (include axes, origin, and scale) and use it to mark and read coordinate pairs in all four quadrants 6: 440A-440B, 440-443

draw a graph from a given scenario 6: 440A-440B, 440-443, 448A-448B, 448-449

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given a distance, find pairs of points on the coordinate plane separated by that horizontal or vertical distance

6: 440A-440B, 440-443 4.5 SOLVING PROBLEMS INVOLVING PERIMETER AND AREA IN TWO DIMENSIONS, AND INVOLVING SURFACE AREA AND VOLUME IN THREE DIMENSIONS. Fifth grade students will: solve problems involving perimeter and area of rectangles, squares, and

triangles 5: 540A-540B, 540-541, 548A-548B, 548-549, 550A-550B, 550-551, 552A-552B, 552-553, 554A-554B, 554-557

solve problems involving volume of rectangular prisms 5: 610A-610B, 610-613

Sixth grade students will: solve problems involving perimeter and area of parallelograms and

rhombuses 6: 564A-564B, 564-567, 572A-572B, 572-575

solve problems involving volume of triangular prisms 6: 594A-594B, 594-597

solve problems involving surface area of rectangular prisms 6: 590A-590B, 590-593

4.6 Transforming geometric figures using reflections, translations, and rotations to explore congruence. Fifth grade students will: use pattern blocks to tile a plane

5: 606A-606B, 606-607

show lines of symmetry of geometric shapes 5: 368A-368B, 368-371

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Sixth grade students will: tile a plane with polygons

6: related material: 590A-590B, 590-593

demonstrate clockwise and counterclockwise rotation with 90°, 180°, and 270° turns 6: 510A-510B, 510-511

using models, demonstrate the multiple transformations which occur to get from one congruent figure to the other, and give a written explanation of the transformations 6: 510A-510B, 510-511

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Standard 5: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems. GRADES K-4 In grades K-4, what students know and are able to do includes 5.1 KNOWING, USING, DESCRIBING, AND ESTIMATING MEASURES OF LENGTH, PERIMETER, CAPACITY, WEIGHT, TIME, AND TEMPERATURE; AND 5.3 DEMONSTRATING THE PROCESS OF MEASURING AND EXPLAINING THE CONCEPTS RELATED TO UNITS OF MEASUREMENT. Kindergarten students will: tell time to the nearest hour, using an analog and digital clock

K: 173A-173B, 173-174, 175A-175B, 175-176

describe the units for measuring time K: 171A-171B, 171-172

estimate and measure length in non-standard units (for example, use cubes to measure the length of a hand) K: 139A-139B, 139-140, 141A-141B, 141-142

estimate the measurement of weight by “heavier” and “lighter” K: 149A-149B, 149-150, 151A-151B, 151-152

First grade students will: tell time to the nearest hour and half-hour, using an analog and digital clock

1: 209A-209B, 209-210, 211A-211B, 211-212

name the days of the week in order 1: 225A-225B, 225-226

estimate and measures the length of objects to the nearest inch, foot and centimeter 1: 365A-365B, 365-366, 371A-371B, 371-372, 373A-373B, 373-374, 375A-375B, 375-376

estimate and measure the capacity of a container in cups 1: 383A-383B, 383-384, 385A-385B, 385-386, 387A-387B, 387-388

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estimate and weigh an object on a balance with a non-standard unit

1: 389A-389B, 389-390

measure temperature to the nearest 10° F 1: 395A-395B, 395-396

describe the units for measuring time, length, capacity, and temperature 1: 209A-209B, 209-210, 211A-211B, 211-212, 365A-365B, 365-366, 371A-371B, 371-372, 373A-373B, 373-374, 375A-375B, 375-376, 383A-383B, 383-384, 385A-385B, 385-386, 387A-387B, 387-388, 395A-395B, 395-396

tell the number of minutes in an hour, days in a week, pennies in a nickel, dime, quarter, and dollar 1: 207A-207B, 207-208, 2225A-225B, 225-226, 227A-227B, 227-228, 337A-337B, 337-338, 343A-343B, 343-344

Second grade students will: tell time to the nearest fifteen minutes, using an analog and digital clock

2: 293A-293B, 293-294, 295A-295B, 295-296

use AM and PM 2: 301A-301B, 301-302

estimate and measure the length of objects to the nearest half inch, foot, yard, centimeter, and meter

2: 343A-343B, 343-344, 345A-345B, 345-346, 347A-347B, 347-348 estimate and measure the perimeter of a figure using non-standard and

standard units 2: 384

estimate and measure the capacity of a container in cups, pints, quarts and gallons 2: 355A-355B, 355-356, 357A-357B, 357-358

estimate and weigh an object on a balance with a non-standard unit and use a scale to measure an object to the nearest pound 2: 363A-363B, 363-364, 365A-365B, 365-366

measures temperature to the nearest 2° and 10° F 2: 369A-369B, 369-370

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describe the units for measuring time, length, capacity, weight, and

temperature 2: 343A-343B, 343-344, 345A-345B, 345-346, 347A-347B, 347-348, 355A-355B, 355-356, 357A-357B, 357-358, 363A-363B, 363-364, 365A-365B, 365-366, 369A-369B, 369-370

know the number of hours in a day, months in a year, inches in a foot, feet in a yard, and cups in a pint 2: 303A-303B, 303-304, 345A-345B, 345-346

Third grade students will: tell time to the nearest five minutes, using an analog and digital clock

3: 196A-196B, 196-197

estimate how long a minute is 3: 192A-192B, 192-195

estimate and measure the length of objects 3: 532A-532B, 532-533, 534A-534B, 534-535, 536A-536B, 536-537

estimate and measure the perimeter of an object with a string measured in U.S. customary and metric units 3: 464A-464B,464-467

estimate and measure areas using non-standard units 3: 468A-468B, 468-471

estimate and measure the capacity of a container in cups, pints, quarts, gallons, and liters 3: 680A-680B, 680-683, 684A-684B, 684-687

estimate and weigh an object on a balance or scale to the nearest ounce 3: 690A-690B, 690-693

measure temperatures in both Fahrenheit and Celsius 3: 696A-696B, 696-697

describe the units for measuring time, length, area, capacity, and temperature 3: 532A-532B, 532-533, 534A-534B, 534-535, 536A-536B, 536-537, 680A-680B, 680-683, 684A-684B, 684-687, 690A-690B, 690-693, 696A-696B, 696-697

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know the number of seconds in a minute, hours in a day, days in a month, days in a year, pints in a quart, quarts in a gallon, and centimeters in a meter 3: 200A-200B, 200-201, 582A-582B, 582-583, 584A-584B, 584-587, 538A-538B, 538-539, 684A-684B, 684-687

Fourth grade students will: tell time to the nearest minute, using an analog and digital clock

4: 190A-190B, 190-191

tell the number of minutes in a day, days in a year and when a leap year occurs 4: 200A-200B, 200-201

describes the units for measuring time 4: 192A-192B, 192-195

estimate the perimeters of similarly-sized figures (for example, trapezoids, parallelograms and rectangles), measure the sides, and determine the perimeters

4: 464A-464B, 464-467 measure the lengths of the sides of squares and rectangles and determine the

areas 4: 468A-468B, 468-473

measure the lengths of the sides of cubes and determine the volumes 4: 476A-476B, 476-477

estimate and measure the capacity of containers 4: 592A-592B, 592-593, 654A-653B, 654-655

estimate and weigh objects on a balance to the nearest ounce and gram 4: 594A-594B, 594-595, 656A-656B, 656-657

compare the relationship between the temperature in Fahrenheit and Celsius 4: 664A-664B, 664-665

determine the distance between points on vertical and horizontal line segments on a coordinate plane 4: 212A-212B, 212-213

51


given a distance, find pairs of points on the coordinate plane separated by that distance 4: 212A-212B, 212-213

describe the units for measuring length, area, volume, capacity, and temperature in U.S. customary and metric units 4: 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665

know the number of years in a decade and a century, feet in a mile, millimeters and centimeters in a meter, ounces in a pound, and pounds in a ton 4: 192A-192B, 192-195, 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665

5.2 Comparing and ordering objects according to measurable attributes (for example, longest to shortest, lightest to heaviest). Kindergarten students will: compare objects according to the measurable attributes of length and weight

K: 133A-133B, 133-134, 135A-135B, 135-136, 149A-149B, 149-150

order objects according to the measurable attributes of length and weight K: 133A-133B, 133-134, 137A-137B, 137-138, 149A-149B, 149-150

compares and order various times (for example, morning comes before lunch) K: 171A-171B, 171-172

First grade students will: compare objects according to the measurable attributes of length, capacity,

weight, and temperature 1: 365A-365B, 365-366, 383A-383B, 383-384, 389A-389B, 389-390

order objects according to the measurable attributes of length, capacity, weight, and temperature 1: 365A-365B, 365-366, 383A-383B, 383-384, 389A-389B, 389-390

compare and order various times 1: 221A-221B, 221-222

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Second grade students will: compare objects according to the measurable attributes of length, capacity,

weight, and temperature 2: 341A-341B, 341-342, 353A-353B, 353-354, 363A-363B, 363-364

order objects according to the measurable attributes of length, capacity, weight and temperature 2: 341A-341B, 341-342, 353A-353B, 353-354, 363A-363B, 363-364

compare and order various times 2: 297A-297B, 297-298, 299A-299B, 299-300

Third grade students will: compare objects according to the measurable attributes of length, area,

capacity, weight, and temperature 3: 534A-534B, 534-535

order objects according to the measurable attributes of length, area, capacity, weight and temperature 3: 534A-534B, 534-535


Fourth grade students will: compare objects according to the measurable attributes of length, area,

volume, capacity, weight, and temperature in U.S. customary and metric units 4: 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665

order objects according to the measurable attributes of length, area, volume, capacity, weight and temperature in U.S. customary and metric units 4: 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665


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5.4 USING THE APPROXIMATE MEASURES OF FAMILIAR OBJECTS (FOR EXAMPLE, THE WIDTH OF YOUR FINGER, THE TEMPERATURE OF A ROOM, THE WEIGHT OF A GALLON OF MILK) TO DEVELOP A SENSE OF MEASUREMENT. First grade students will: use familiar objects as referents for measurement (for example, the length of

the student’s index finger is about two paper clips) 1: 365A-365B, 365-366, 383A-383B, 383-384, 389A-389B, 389-390

Second grade students will: use familiar objects as referents for measurement (for example, a second

grader is a little taller than a meter) 2: 341A-341B, 341-342, 353A-353B, 353-354, 363A-363B, 363-364

Third grade students will: use familiar objects as referents for measurement (for example, the width of

the index fingernail equals approximately one centimeter; ten pennies weigh approximately an ounce) 3: 532A-532B, 532-533, 534A-534B, 534-535

Fourth grade students will: use familiar objects as referents for measurement (for example, one paper clip

equals one gram; the length of the arm span equals approximately one meter) 4: 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665

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5.5 SELECTING AND USING APPROPRIATE STANDARD AND NON-STANDARD UNITS OF MEASUREMENT IN PROBLEM-SOLVING SITUATIONS. Kindergarten students will: select the appropriate units of measurement of time and length

K: 173A-173B, 173-174, 175A-175B, 175-176, 139A-139B, 139-140, 141A-141B, 141-142

First grade students will: select the appropriate units of measurement of time, length, capacity, and

temperature 1: 365A-365B, 365-366, 371A-371B, 371-372, 373A-373B, 373-374, 375A-375B, 375-376, 385A-385B, 385-386, 387A-387B, 387-388, 389A-389B, 389-390

Second grade students will: select the appropriate units of measurement of time, length, capacity, weight,

and temperature 2: 343A-343B, 343-344, 345A-345B, 345-346, 347A-347B, 347-348, 355A-355B, 355-356, 357A-357B, 357-358, 363A-363B, 363-364, 365A-365B, 365-366, 369A-369B, 369-370

Third grade students will: select the appropriate units of measurement of time, length, area, capacity,

weight, and temperature 3: 532A-532B, 532-533, 534A-534B, 534-535, 536A-536B, 536-537, 680A-680B, 680-683, 684A-684B, 684-687, 690A-690B, 690-693, 696A-696B, 696-697

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Fourth grade students will: select the appropriate units of measurement of time

4: 192A-192B, 192-195

select the appropriate units of measurement of length, area, volume, capacity,

weight, and temperature in U.S. customary and metric units 4: 588A-588B, 588-589, 652A-652B, 652-653, 592A-592B, 592-593, 594A-594B, 594-595, 654A-653B, 654-655, 656A-656B, 656-657, 664A-664B, 664-665

GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 5.1 ESTIMATING, USING, AND DESCRIBING MEASURES OF DISTANCE, PERIMETER, AREA, VOLUME, CAPACITY, WEIGHT, MASS, AND ANGLE COMPARISON. Fifth grade students will: estimate the length of the sides and height of rectangles, squares, triangles,

and rectangular prisms 5: 532A-532B, 532-533

estimate the perimeter and area of rectangles, squares, and triangles 5: 540A-540B, 540-541

estimate the volume of rectangular prisms 5: 610A-610B, 610-613

continue to estimate and use the capacity, weight, and mass measurements from previous grades 5: 614A-614B, 614-615, 616A-616B, 616-617, 620A-620B, 620-621, 622A-622B, 622-623

estimate measures of angles (for example, 30°, 45°, 60°, 90°, 120°, 150°, 180°) 5: 332A-332B, 332-335

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Sixth grade students will: estimate the length of the sides and height of parallelograms and rhombuses

6: 572A-572B, 572-575

estimate the perimeter and area of parallelograms and rhombuses 6: 564A-564B, 564-567, 572A-572B, 572-575

estimate the volume of triangular prisms 6: 594A-594B, 594-597

estimate the surface area of rectangular prisms 6: 590A-590B, 590-593

continue to estimate and use the capacity, weight, and mass measurements from previous grades 6: 542A-542B, 542-545, 546A-546B, 546-549

estimate measures of angles 6: 476A-476B, 476-479

5.2 ESTIMATING, MAKING, AND USING DIRECT AND INDIRECT MEASUREMENTS TO DESCRIBE AND MAKE COMPARISONS. Fifth grade students will: compares the estimates and direct measurements obtained in benchmarks

5.1, 5.4, and 5.6 5: 532A-532B, 532-533, 540A-540B, 540-541, 548A-548B, 548-549, 550A-550B, 550-551, 552A-552B, 552-553, 554A-554B, 554-557

Sixth grade students will: compare the estimates and direct measurements obtained in benchmarks 5.1,

5.4, and 5.6 6: 542A-542B, 542-545, 546A-546B, 546-549

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5.3 READING AND INTERPRETING VARIOUS SCALES INCLUDING THOSE BASED ON NUMBER LINES, GRAPHS, AND MAPS.

Fifth grade students will:

read and interpret scales on number lines, graphs, and maps 5: 662A-662B, 662-663

select the appropriate scale for a given problem 5: 662A-662B, 662-663

Sixth grade students will: read and interpret scales on number lines, graphs, and maps

6: 330A-330B, 330-333, 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

selects the appropriate scale for a given problem 6: 662A-662B, 662-663, 664A-664B, 664-665, 668A-668B, 668-671, 672A-672B, 672-673

5.4 DEVELOPING AND USING FORMULAS AND PROCEDURES TO SOLVE PROBLEMS INVOLVING MEASUREMENT.

Fifth grade students will:

develop and use formulas for perimeter and area of rectangles, squares, and triangles using appropriate units 5: 540A-540B, 540-541, 548A-548B, 548-549, 550A-550B, 550-551, 552A-552B, 552-553, 554A-554B, 554-557

develop and use the formula for volume of rectangular prisms using appropriate units 5: 610A-610B, 610-613

Sixth grade students will:

develop and use formulas for perimeter and area of parallelograms and rhombuses using appropriate unit 6: 564A-564B, 564-567, 572A-572B, 572-575

develop and use the formula for volume of triangular prisms using appropriate units 6: 594A-594B, 594-597

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5.5 DESCRIBING HOW A CHANGE IN AN OBJECT’S LINEAR DIMENSIONS AFFECTS ITS PERIMETER, AREA, AND VOLUME. Fifth grade students will: describe how changes in one of the dimensions of a rectangle affects its

perimeter and area 5: 540A-540B, 540-541, 548A-548B, 548-549, 550A-550B, 550-551, 552A-552B, 552-553, 554A-554B, 554-557

using graph paper, demonstrate the changes in area of a rectangle having a constant perimeter and variable side lengths 5: 540A-540B, 540-541, 548A-548B, 548-549, 550A-550B, 550-551, 552A-552B, 552-553, 554A-554B, 554-557

Sixth grade students will: describe how changes in the base of a triangle affect its area when its height

is constant 6: 572A-572B, 572-575

describe how changes in one of the dimensions of a rectangular prism affects its volume 6: 594A-594B, 594-597

5.6 SELECTING AND USING APPROPRIATE UNITS AND TOOLS TO MEASURE TO THE DEGREE OF ACCURACY REQUIRED IN A PARTICULAR PROBLEM-SOLVING SITUATION. Fifth grade students will: select and use the appropriate units and tools to measure to the degree of

accuracy required in a particular problem 5: 532A-532B, 532-533

measure the length of the sides and heights of rectangles, squares, triangles, and rectangular prisms to the nearest inch and nearest centimeter 5: 532A-532B, 532-533, 534A-534B, 534-535

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measure and draw angles using a protractor (for example, 30° , 45° , 60°, 90°, 120°, 150°, 180°)

5: 332A-332B, 332-335 Sixth grade students will: select and use the appropriate units and tools to measure to the degree of

accuracy required in a particular problem 6: 550A-550B, 550-551

measure the length of the sides and heights of parallelograms and rhombuses to the nearest inch and nearest centimeter 6: 564A-564B, 564-567

measure angles and draw complements and supplements, where possible, using a protractor 6: 476A-467B, 476-479, 480A-480B, 480-483, 484A-484B, 484-489

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Standard 6: Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems. GRADES K-4 In grades K-4, what students know and are able to do includes 6.1 DEMONSTRATING CONCEPTUAL MEANINGS FOR THE FOUR BASIC ARITHMETIC OPERATIONS OF ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION. Kindergarten students will: add and subtract whole numbers by combining and separating objects

K: 245A-245B, 245-246, 247A-247B, 247-248, 265A-265B, 265-266, 267A-267B, 267-268

draw pictures to form sets of up to ten items K: 245A-245B, 245-246, 247A-247B, 247-248

First grade students will: demonstrate the operations of addition and subtraction of whole numbers with

concrete materials 1: 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 97A-97B, 97-98, 103A-103B, 103-104, 105A-105B, 105-106, 107A-107B, 107-108, 125A-125B, 125-126, 127A-127B, 127-128, 129A-129B, 129-130, 133A-133B, 133-134

link the operations of addition and subtraction, and equality with mathematical terms (for example, add, subtract and equal) and mathematical symbols (for example, +, –, =) 1: 417A-417B, 417-418, 419A-419B, 419-420, 425A-425B, 425-426, 435A-435B, 435-436, 437A-437B, 437-438, 439A-439B, 439-440; 459A-459B, 459-460, 461A-461B, 461-462, 463A-463B, 463-464, 465A-465B, 465-466, 471A-471B, 471-472, 473A-473B, 473-474, 475A-475B, 475-476, 477A-477B, 477-478

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Second grade students will: using concrete materials, demonstrate and verbally explain addition of whole

numbers with regrouping for two-digit numbers 2: 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

using concrete materials, demonstrate and verbally explain subtraction of whole numbers without regrouping for two-digit numbers 2: 61-62, 63A-63B, 63-64, 65A-65B, 65-66

using concrete materials or pictures, demonstrate multiplication without regrouping of whole numbers (for example, using arrays or grouping sets of objects) 2: 467A-467B, 467-468, 469A-469B, 469-470, 471A-471B, 471-742, 473A-473B, 473-474

using concrete materials or pictures, demonstrate division of whole numbers without remainders as partitioning of sets 2: 483A-483B, 483-484, 485A-485B, 485-486

using concrete materials or pictures, demonstrate the inverse relationship of addition and subtraction of whole numbers 2: 27A-27B, 27-28, 65A-65B, 65-66

using concrete materials or pictures, demonstrate multiplication of whole numbers as repeated addition 2: 469A-469B, 469-470

Third grade students will: using concrete materials, demonstrate and verbally explain addition and

subtraction of whole numbers with regrouping for up to four-digit numbers 3: 126A-126B, 126-127, 128A-128B, 128-131, 132A-132B, 132-135, 146A-146B, 146-147, 148A-148B, 148-149, 150A-150B, 150-151, 152A-152B, 152-155, 156A-156B, 156-157

using concrete materials or pictures, demonstrate multiplication with regrouping of whole numbers 3: 626A-626B, 626-629, 630A-630B, 630-631, 632A-632B, 632-635, 636A-636B, 636-637

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using concrete materials, demonstrate division of whole numbers with remainders as partitioning of sets 3: 652A-652B, 652-655, 656A-656B, 656-657

using paper-and-pencil, demonstrate the inverse relationship of addition and subtraction of whole numbers 3: 70A-70B, 70-71

using paper-and-pencil, demonstrate multiplication of whole numbers as repeated addition 3: 260A-260B, 260-261

Fourth grade students will: explain in writing what addition, subtraction, multiplication, and division of

whole numbers means 4: 203, 301, 302-303, 421, 422-423, 603, 635, 651, 662A-662B, 662-663, 669, 675, 676-677, 715, 717, 719, 725, 726-727

demonstrate the inverse relationship of multiplication and division of whole numbers 4: 148A-148B, 148-149

demonstrate division of whole numbers as repeated subtraction 4: 146A-146B, 146-147

6.2 ADDING AND SUBTRACTING COMMONLY USED FRACTIONS AND DECIMALS USING PHYSICAL MODELS (FOR EXAMPLE, 1/3, 3/4, 0.5, 0.75). First grade students will: using concrete materials or pictures, add and subtract halves and fourths

1: preparation: 181A-181B, 181-182, 183A-183B, 183-184

Second grade students will: using concrete materials or pictures, add and subtract halves, thirds, and

fourths 2: preparation: 269A-269B, 269-270, 271A-271B, 271-272

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find the total value of coins not to exceed $1.00 2: 109A-109B, 109-110, 111A-111B, 111-112, 113A-113B, 113-114

Third grade students will: using concrete materials, demonstrate addition and subtraction of proper

fractions with common denominators of ten or less 3: 520A-520B, 520-521

using coins as models, add and subtract decimals in which sums and differences may exceed $1.00 3: 572A-572B, 572-577

Fourth grade students will: using concrete materials, demonstrate addition and subtraction of proper

fractions with common denominators of twelve or less without regrouping 4: 564A-564B, 564-467, 574A-574B, 574-577

using concrete materials, demonstrate addition and subtraction of mixed numerals with common denominators of twelve or less 4: preparation: 564A-564B, 564-467, 574A-574B, 574-577

add and subtract decimals to the one-hundredths 4: 638A-638B, 638-641, 642A-642B, 642-647

compute the total cost of items to $10.00 4: 638A-638B, 638-641, 642A-642B, 642-647

determine change received for $10.00 or less 4: 638A-638B, 638-641, 642A-642B, 642-647

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6.3 DEMONSTRATING UNDERSTANDING OF AND PROFICIENCY WITH BASIC ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION FACTS WITHOUT THE USE OF A CALCULATOR. First grade students will: demonstrate understanding of basic addition sums to 20 and subtraction

differences of 10 1: 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 97A-97B, 97-98, 103A-103B, 103-104, 105A-105B, 105-106, 107A-107B, 107-108, 125A-125B, 125-126, 127A-127B, 127-128, 129A-129B, 129-130, 133A-133B, 133-134

Second grade students will: demonstrate understanding of basic addition and subtraction facts

2: 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, 65-66

demonstrate automatic recall of basic addition and subtraction facts 2: 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, 65-66

use sums on an addition facts table to locate all addends for a particular sum (for example, 7 = 0 + 7, 7 = 1 + 6, . . . ) 2: 43A-43B, 43-44, 45A-45B, 45-46, 47A-47B, 47-48, 49A-49B, 49-50, 51A-51B, 51-52, 53A-53B, 53-54

Third grade students will: demonstrate understanding of basic multiplication and division facts of 1’s,

2’s, 3’s, 5’s, and 10’s 3: 276A-276B, 276-279, 280A-280B, 280-281, 282A-282B, 282-283, 286A-286B, 286-287, 288A-288B, 288-291, 292A-292B, 292-293, 316A-316B, 316-317, 318A-318B, 318-319, 320A-320B, 320-323, 324A-324B, 324-327, 328A-328B, 328-331, 386A-386B, 386-387, 388A-388B, 388-389, 390A-390B, 390-391, 392A-392B, 392-393, 396A-396B, 396-397, 402A-402B, 402-403

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demonstrate automatic recall of basic multiplication facts of 1’s, 2’s, 3’s, 5’s, and 10’s 3: 276A-276B, 276-279, 280A-280B, 280-281, 282A-282B, 282-283, 286A-286B, 286-287, 288A-288B, 288-291, 292A-292B, 292-293, 316A-316B, 316-317, 318A-318B, 318-319, 320A-320B, 320-323, 324A-324B, 324-327, 328A-328B, 328-331

continue automatic recall of basic addition and subtraction facts 3: 66A-66B, 66-69, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 94A-94B, 94-95, 96A-96B, 96-97

use a multiplication facts table to locate all factors for a particular product (for example, 6 = 1 x 6, 6 = 2 x 3, . . . ) 3: 276A-276B, 276-279, 280A-280B, 280-281, 282A-282B, 282-283, 286A-286B, 286-287, 288A-288B, 288-291, 292A-292B, 292-293

Fourth grade students will: demonstrate understanding of basic multiplication and division facts through

100 4: 124A-124B, 124-127, 128A-128B, 128-131, 132A-132B, 132-135, 136A-136B, 136-139, 146A-146B, 146-147, 148A-148B, 148-149, 150A-150B, 150-151, 152A-152B, 152-153

demonstrate automatic recall of basic multiplication and division facts through 100 4: 124A-124B, 124-127, 128A-128B, 128-131, 132A-132B, 132-135, 136A-136B, 136-139, 146A-146B, 146-147, 148A-148B, 148-149, 150A-150B, 150-151, 152A-152B, 152-153

continue automatic recall of basic addition and subtraction facts 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89

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6.4 CONSTRUCTING, USING, AND EXPLAINING PROCEDURES TO COMPUTE AND ESTIMATE WITH WHOLE NUMBERS. Kindergarten students will: add and subtract whole numbers by combining and separating objects

K: 251A-251B, 251-252, 253A-253B, 253-254, 255A-255B, 255-256, 271A-271B, 271-272, 273A-273B, 273-274, 275A-275B, 275-276

draw pictures to form sets of up to ten items K: 245A-245B, 245-246, 247A-247B, 247-248

First grade students will: demonstrate the operations of addition and subtraction of whole numbers with

concrete materials 1: 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 97A-97B, 97-98, 103A-103B, 103-104, 105A-105B, 105-106, 107A-107B, 107-108, 125A-125B, 125-126, 127A-127B, 127-128, 129A-129B, 129-130, 133A-133B, 133-134

link the operations of addition and subtraction, and equality with mathematical terms (for example, add, subtract and equal) and mathematical symbols (for example, +, –, =) 1: 417A-417B, 417-418, 419A-419B, 419-420, 425A-425B, 425-426, 435A-435B, 435-436, 437A-437B, 437-438, 439A-439B, 439-440; 459A-459B, 459-460, 461A-461B, 461-462, 463A-463B, 463-464, 465A-465B, 465-466, 471A-471B, 471-472, 473A-473B, 473-474, 475A-475B, 475-476, 477A-477B, 477-478

using paper-and-pencil, demonstrate simple single-digit addition and subtraction 1: 91A-91B, 91-92, 93A-93B, 93-94, 95A-95B, 95-96, 97A-97B, 97-98, 103A-103B, 103-104, 105A-105B, 105-106, 107A-107B, 107-108, 125A-125B, 125-126, 127A-127B, 127-128, 129A-129B, 129-130, 133A-133B, 133-134, 417A-417B, 417-418, 419A-419B, 419-420, 425A-425B, 425-426, 435A-435B, 435-436, 437A-437B, 437-438, 439A-439B, 439-440

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Second grade students will: use estimation techniques such as rounding and compatible numbers

(numbers whose sum is 10) before performing operations 2: 175A-175B, 175-176, 177A-177B, 177-178, 179A-179B, 179-180, 181A-181B, 181-182, 185A-185B, 185-186, 187A-187B, 187-188, 189A-189B, 189-190, 191A-191B, 191-192, 193A-193B, 193-194, 227A-227B, 227-228

using paper-and-pencil, demonstrate addition of two-digit whole numbers with and without regrouping 2: 175A-175B, 175-176, 177A-177B, 177-178, 179A-179B, 179-180, 181A-181B, 181-182, 185A-185B, 185-186, 187A-187B, 187-188, 189A-189B, 189-190, 191A-191B, 191-192, 193A-193B, 193-194

using paper-and-pencil, demonstrate subtraction of two-digit whole numbers without regrouping 2: 211A-211B, 211-212, 215A-215B, 215-216

Third grade students will: use estimation techniques such as front-end rounding, rounding, and

compatible numbers (numbers whose sum is 10, 100, 1,000..) before performing operations 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, 98-101, 160A-160B, 160-161

using paper-and-pencil, demonstrate the four basic operations of whole numbers including a) addition and subtraction of four digits

3: 132A-132B, 132-135

b) multiplication of two digits by one digit, regrouping included 3: 632A-632B, 632-633, 636A-636B, 636-637 c) division of two digits by a one-digit divisor obtaining one-digit quotients

3: 652A-652B, 652-655

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Fourth grade students will: use estimation techniques such as front-end rounding, rounding, compatible

numbers (numbers whose sum is 10, 100, 1,000...) and clustering (for example, 27 + 28 + 30 + 31 equals approximately 4 x 30 = 120) before performing operations 4: 62A-62B, 62-63, 64A-64B, 64-67, 68A-68B, 68-71, 72A-72B, 72-73, 258A-258B, 258-261, 316A-316B, 316-319, 368A-368B, 368-371, 636A-636B, 636-637

using paper-and-pencil, demonstrate the four basic operations of whole numbers including

a) multiplication of two digits by two digits and three digits by one digit with regrouping

4: 270A-270B, 270-273, 274A-274B, 274-277, 332A-332B, 332-335, 336A-336B, 336-337, 340A-340B, 340-341

b) division of two digits by a one-digit divisor 4: 380B, 380-383, 386A-386B, 386-389, 390A-390B, 390-391

6.5 SELECTING AND USING APPROPRIATE METHODS FOR COMPUTING WITH WHOLE NUMBERS IN PROBLEM-SOLVING SITUATIONS FROM AMONG MENTAL ARITHMETIC, ESTIMATION, PAPER-AND-PENCIL, CALCULATOR AND COMPUTER METHODS. First grade students will: given a real-world problem-solving situation, use the correct operation

(addition or subtraction with concrete materials) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem 1: 143A-143B, 143-144, 445A-445B, 445-446

Second grade students will: given a real-world problem-solving situation, use the correct operation

(addition or subtraction) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem 2: 175A-175B, 175-176, 177A-177B, 177-178, 179A-179B, 179-180, 181A-181B, 181-182, 185A-185B, 185-186, 187A-187B, 187-188, 189A-189B, 189-190, 191A-191B, 191-192, 193A-193B, 193-194, 227A-227B, 227-228

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determine from real-world problems whether an estimated or exact sum or

difference is acceptable 2: 453A-453B, 453-454

Third grade students will: given a real-world problem-solving situation, use the correct operation

(addition, subtraction, or multiplication) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem 3: 66A-66B, 66-69, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 94A-94B, 94-95, 96A-96B, 96-97, 276A-276B, 276-279, 280A-280B, 280-281, 282A-282B, 282-283, 286A-286B, 286-287, 288A-288B, 288-291, 292A-292B, 292-293, 316A-316B, 316-317, 318A-318B, 318-319, 320A-320B, 320-323, 324A-324B, 324-327, 328A-328B, 328-331, 386A-386B, 386-387, 388A-388B, 388-389, 390A-390B, 390-391, 392A-392B, 392-393, 396A-396B, 396-397, 402A-402B, 402-403, 632A-632B, 632-633, 636A-636B, 636-637, 652A-652B, 652-655

determine from real-world problems whether an estimated or exact sum, difference, or product is acceptable 3: 160A-160B, 160-161

Fourth grade students will: given a real-world problem-solving situation, use the correct operation

(addition, subtraction, multiplication, or division) and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem 4: 76A-76B, 76-79, 80A-80B, 80-81, 82A-82B, 82-85, 86A-86B, 86-89, 270A-270B, 270-273, 274A-274B, 274-277, 332A-332B, 332-335, 336A-336B, 336-337, 380A-380B, 380-383, 386A-386B, 386-389, 390A-390B, 390-391

determine from real-world problems whether an estimated or exact sum, difference, product, or quotient is acceptable 4: 600A-600B, 600-601

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GRADES 5-8 As students in grades 5-8 extend their knowledge, what they know and are able to do includes 6.1 USING MODELS TO EXPLAIN HOW RATIOS, PROPORTIONS, AND PERCENTS CAN BE USED TO SOLVE REAL-WORLD PROBLEMS. Fifth grade students will: use appropriate notations of ratio such as a/b, a to b, and a:b

5: 646A-646B, 646-647, 648A-648B, 648-651, 652A-652B, 652-653, 660A-660B, 660-661, 662A-662B, 662-663

using concrete materials, determine commonly-used percentages (e.g., 25% and 50%) in real-world problems 5: 668A-668B, 668-669, 670A-670B, 670-671, 672A-672B, 672-675

Sixth grade students will: demonstrate the equivalence of fractions, decimals, and percents

6: 172A-172B, 172-175, 358A-358B, 358-361

using concrete materials, determine commonly-used percentages in real-world problems

6: 380A-380B, 380-383, 384A-384B, 384-385, 386A-386B, 386-387 6.2 CONSTRUCTING, USING, AND EXPLAINING PROCEDURES TO COMPUTE AND ESTIMATE WITH WHOLE NUMBERS, FRACTIONS, DECIMALS, AND INTEGERS. Fifth grade students will: demonstrate order of operations with whole numbers

5: 172A-172B, 172-173

demonstrate with proficiency multiplication of whole numbers of three digits by two digits and three digits by three digits 5: 84A-84B, 84-85, 86A-86B, 86-87, 88A-88B, 88-91, 92A-92B, 92-93, 94A-94B, 94-97

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demonstrate with proficiency division of whole numbers with a two-digit divisor 5: 202-203, 214A-214B, 214-217, 218A-218B, 218-221, 224A-224B, 224-225, 230A-230B, 230-231, 232A-232B, 232-233, 234A-234B, 234-237

demonstrate equivalencies and simplification of proper fractions 5: 410A-410B, 410-411, 412A-412B, 412-413, 416A-416B, 416-417

using paper-and-pencil, demonstrate with proficiency addition and subtraction of proper fractions and mixed numerals with common denominators and without regrouping 5: 460A-460B, 460-461

using concrete materials, demonstrate addition and subtraction of mixed numerals with common denominators with regrouping 5: 472A-472B, 472-473, 476A-476B, 476-477, 478A-478B, 478-483

using concrete materials, demonstrate addition and subtraction of proper fractions with unlike denominators 5: 462A-462B, 462-463, 464A-464B, 464-465, 466A-466B, 466-469

demonstrate the inverse relationship of addition and subtraction of proper fractions and mixed numerals with common denominators 5: 460A-460B, 460-461, 472A-472B, 472-473

demonstrate how the value of a fraction changes as the denominator increases 5: 418A-418B, 418-419, 420A-420B, 420-423

demonstrate with proficiency addition and subtraction of decimals 5: 38A-38B, 38-39, 40A-40B, 40-41

demonstrate the inverse relationship of addition and subtraction of decimals 5: 38A-38B, 38-39, 40A-40B, 40-41

make change from any dollar denomination 5: 40A-40B, 40-41

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Sixth grade students will: demonstrate order of operations including exponents with whole numbers

6: 24A-24B, 24-27

choose the appropriate representation of the remainder in a division problem 6: 98A-98B, 98-99

demonstrate equivalencies of mixed numerals and improper fractions 6: 168A-168B, 168-169

simplify fractions 6: 164A-164B, 164-167

using paper-and-pencil, demonstrate with proficiency addition and subtraction of fractions including mixed numerals 6: 204A-204B, 204-205, 206A-206B, 206-211, 218A-218B, 218-219, 220A-220B, 220-223, 224A-224B, 224-225

using concrete materials, demonstrate multiplication and division of a common proper fraction and a whole number 6: 248A-248B, 248-251

using concrete materials, demonstrate multiplication and division of proper fractions 6: 252A-252B, 252-255, 256A-256B, 256-257, 258A-258B, 258-259, 266A-266B, 266-269, 270A-270B, 270-271

using concrete materials, demonstrate the meaning of multiplication and division of decimals by whole numbers 6: 90A-90B, 90-93

demonstrate, by modeling, the inverse relationship of multiplication and division of common proper fractions 6: 266A-266B, 266-269

count change up to the amount given 6: 86A-86B, 86-89

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6.3 DEVELOPING, APPLYING AND EXPLAINING A VARIETY OF DIFFERENT ESTIMATION STRATEGIES IN PROBLEM-SOLVING SITUATIONS, AND EXPLAINING WHY AN ESTIMATE MAY BE ACCEPTABLE IN PLACE OF AN EXACT ANSWER. Fifth grade students will: determine from real-world problems whether an estimated or exact answer is

acceptable 5: 624A-624B, 624-625

use estimation techniques before performing operations 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, 138-143, 204A-204B, 204-209

Sixth grade students will: determine from real-world problems whether an estimated or exact answer is

acceptable 6: 226A-226B, 226-227

use estimation techniques before performing operations 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, 216-217, 256A-256B, 256-257, 368A-368B, 368-369

6.4 SELECTING AND USING APPROPRIATE METHODS FOR COMPUTING WITH COMMONLY-USED FRACTIONS AND DECIMALS, PERCENTS, AND INTEGERS IN PROBLEM-SOLVING SITUATIONS FROM AMONG MENTAL ARITHMETIC, ESTIMATION, PAPER-AND-PENCIL, CALCULATOR, AND COMPUTER METHODS, AND DETERMINING WHETHER THE RESULTS ARE REASONABLE. Fifth grade students will: determine whether information given in a problem-solving situation is

sufficient, insufficient, or extraneous 5: 406A-406B, 406-407

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given a real-world problem-solving situation, use the correct operation and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator, or computer) to solve the problem 5: 36A-36B, 36-37, 38A-38B, 38-39, 40A-40B, 40-41, 88A-88B, 88-91, 94A-94B, 94-97, 152A-152B, 152-155, 156A-156B, 156-157, 158A-158B, 158-159, 160A-160B, 160-161202A-202B, 202-203, 214A-214B, 214-217, 218A-218B, 218-221, 224A-224B, 224-225, 230A-230B, 230-231, 232A-232B, 232-233, 234A-234B, 234-237, 460A-460B, 460-461, 462A-462B, 462-463, 464A-464B, 464-465, 466A-466B, 466-469, 472A-472B, 472-473, 474A-474B, 474-475, 476A-476B, 476-477, 478A-478B, 478-483

given a math sentence using the four operations with whole numbers, create and illustrate a real-world problem 5: 36A-36B, 36-37, 38A-38B, 38-39, 40A-40B, 40-41, 88A-88B, 88-91, 94A-94B, 94-97, 152A-152B, 152-155, 156A-156B, 156-157, 158A-158B, 158-159, 160A-160B, 160-161202A-202B, 202-203, 214A-214B, 214-217, 218A-218B, 218-221, 224A-224B, 224-225, 230A-230B, 230-231, 232A-232B, 232-233, 234A-234B, 234-237, 460A-460B, 460-461, 462A-462B, 462-463, 464A-464B, 464-465, 466A-466B, 466-469, 472A-472B, 472-473, 474A-474B, 474-475, 476A-476B, 476-477, 478A-478B, 478-483

in a problem-solving situation, determine whether the results are reasonable and justify those results with correct computations 5: 28A-28B, 28-31, 68A-68B, 68-70, 86A-86B, 86-87, 138A-138B, 138-143, 204A-204B, 204-209, 474A-474B, 474-475, 494A-494B, 494-495, 672A-672B, 672-675

Sixth grade students will: determine whether information given in a problem-solving situation is

sufficient, insufficient, or extraneous 6: 582A-582B, 582-583

given a real-world problem-solving situation, use the correct operation and appropriate method (mental arithmetic, estimation, paper-and-pencil,

calculator, or computer) to solve the problem 6: 86A-86B, 86-89, 90A-90B, 90-93, 94A-94B, 94-97, 100A-100B, 100-103, 204-205, 206A-206B, 206-211, 218A-218B, 218-219, 220A-220B, 220-223, 248A-248B, 248-251, 252A-252B, 252-255, 258A-258B, 258-259, 266A-266B, 266-267, 270A-270B, 270-271

given a math sentence with sums and differences of common fractions and

decimals, create and illustrate a real-world problem 6: 90A-90B, 90-93, 204A-204B, 204-205, 206A-206B, 206-211, 218A-218B, 218-219, 220A-220B, 220-223, 224A-224B, 224-225, 252A-252B, 252-255, 256A-256B, 256-257, 258A-258B, 258-259, 266A-266B, 266-269, 270A-270B, 270-271

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in a problem-solving situation, determine whether the results are reasonable and justify those results with correct computations 6: 16A-16B, 16-17, 18A-18B, 18-19, 216A-216B, 216-217, 256A-256B, 256-257, 368A-368B, 368-369

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