District of Columbia State Standards Alignment Grades One through Twelve Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries. P.O. Box 8036 Wisconsin Rapids, WI 54495-8036 Phone: (800) 338-4204 Fax: (715) 424-4242 www.renlearn.com
District of Columbia State Standards Alignment The Report is a standardsoriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product. Note to Educator...iii Grade 1... 1 Grade 2... 8 Grade 3...16 Grade 4...25 Grade 5...37 Grade 6...50 Grade 7...62 Grade 8...74 Algebra 1...82 Geometry...89 Algebra 2...98 Precalculus and Trigonometry...107 Probability and Statistics...113 2009 by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the express written consent of Renaissance Learning, Inc. ii
P.O. Box 8036 Wisconsin Rapids, WI 54495-8036 Phone: (800) 338-4204 Fax: (715) 424-4242 www.renlearn.com Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) 338-4204. Sincerely, Renaissance Sales and Funding Staff iii
Accelerated Math Grade 1 Grade 1, Learning Standards, State DC 1.NSO - Number Sense and DC 1.NSO-N.1 - Count, read, and write whole numbers to 110 and relate them to the quantities they represent (e.g., knows that 60 is bigger than 20). DC 1.NSO-N.2 - Compare and order whole numbers to 110 by using symbols for less than, equal to, or greater than (<, =, >). DC 1.NSO-N.3 - Identify the place value of the digits to 110. DC 1.NSO-N.4 - Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (e.g., 9 may be represented as 4 + 5, 3 + 6, 3 + 3 + 3, 10-1, 12-3). Accelerated Math Second Edition Grade 1 Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Obj. 1 - Read a whole number to 30 Obj. 2 - Read a whole number from 31 to 100 Obj. 3 - Determine the word form of a whole number to 30 Obj. 4 - Determine the word form of a whole number from 31 to 100 Obj. 5 - Count objects to 20 Obj. 19 - Count objects grouped in tens and ones Obj. 26 - Compare sets of objects using words Obj. 27 - Compare whole numbers to 100 using words Obj. 28 - Order whole numbers to 100 in ascending order Obj. 29 - Order whole numbers to 100 in descending order Obj. 22 - Represent a 2-digit number as tens and ones Obj. 23 - Determine the 2-digit number represented as tens and ones Obj. 24 - Determine the value of a digit in a 2-digit number Obj. 20 - Model a number to 100 using tens and ones Obj. 21 - Recognize a number from a model of tens and ones to 100 DC 1.NSO-N.5 - Identify numbers to 20 as odd or even. DC 1.NSO-N.6 - Make combinations of different coins up to 50 cents. Topic 1 - Numbers and Obj. 30 - Determine equivalent forms of a number, up to 10 Obj. 18 - Determine the value of a collection of mixed coins Page 1 of 114
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State DC 1.NSO-F.7 - Model, identify, and represent fractions such as 1/2, 1/3, and 1/4 as parts of wholes (e.g., 1/4 of a pie) and parts of groups. DC 1.NSO-C.8 - Demonstrate the ability to use conventional algorithms for addition and subtraction (two twodigit whole numbers). Topic 1 - Numbers and DC 1.NSO-C.9 - Demonstrate an Topic 1 - Numbers and understanding of various meanings of addition and subtraction, such as addition as combination (i.e., plus, combined with, more), subtraction as comparison (i.e., how much less, how much more), equalizing (i.e., how many more are needed to make these equal), and separation (i.e., how much remaining). Page 2 of 114 Obj. 49 - Add multiples of 10, sums to 90 Obj. 50 - Subtract multiples of 10 up to 90 Obj. 51 - Add zero to any number less than 100 Obj. 52 - Subtract zero from any number less than 100 Obj. 53 - Add a 2-digit and a 1-digit number without regrouping Obj. 54 - Add two 2-digit numbers without regrouping Obj. 55 - Subtract a 1-digit number from a 2-digit number without regrouping Obj. 56 - Subtract a 2-digit number from a 2-digit number without regrouping Obj. 57 - WP: Add or subtract a 1- and 2-digit number without regrouping Obj. 58 - WP: Add or subtract two 2- digit numbers without regrouping Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects Obj. 32 - Relate a picture model to a basic addition fact Obj. 33 - Determine the basic addition fact shown by a picture model Obj. 34 - Relate a number-line model to a basic addition fact Obj. 35 - Determine the basic addition fact shown by a number-line model
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State Obj. 36 - Relate a picture model to a basic subtraction fact Obj. 37 - Determine the basic subtraction fact shown by a picture model Obj. 38 - Determine the basic subtraction fact shown by a numberline model Obj. 39 - Relate a number-line model to a basic subtraction fact Obj. 40 - Apply the relationship between addition and counting on Obj. 41 - Apply the relationship between subtraction and counting back Obj. 45 - Determine equivalent addition or subtraction expressions involving words or symbols Topic 2 - Algebraic Thinking Obj. 65 - WP: Determine a basic addition- or subtraction-fact number sentence for a given situation DC 1.NSO-C.10 - Know addition and subtraction facts (addends to 10), commit to memory, and use them to solve problems. Topic 1 - Numbers and Topic 2 - Algebraic Thinking Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects Obj. 33 - Determine the basic addition fact shown by a picture model Obj. 37 - Determine the basic subtraction fact shown by a picture model Obj. 42 - Know basic addition facts to 10 plus 10 Obj. 43 - Know basic subtraction facts to 20 minus 10 Obj. 46 - WP: Use basic addition or subtraction facts to solve problems Obj. 65 - WP: Determine a basic addition- or subtraction-fact number sentence for a given situation DC 1.NSO-C.11 - Demonstrate the Topic 1 - Numbers and ability to fluently add and subtract one-operationand two-digit whole numbers that do not require regrouping. Page 3 of 114 Obj. 51 - Add zero to any number less than 100 Obj. 52 - Subtract zero from any number less than 100 Obj. 53 - Add a 2-digit and a 1-digit number without regrouping
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State Obj. 55 - Subtract a 1-digit number from a 2-digit number without regrouping Obj. 57 - WP: Add or subtract a 1- and 2-digit number without DC 1.NSO-C.12 - Use mental arithmetic to find the sum or difference of two one-digit whole numbers. Topic 1 - Numbers and regrouping Obj. 42 - Know basic addition facts to 10 plus 10 Obj. 43 - Know basic subtraction facts to 20 minus 10 Obj. 46 - WP: Use basic addition or subtraction facts to solve problems DC 1.NSO-C.13 - Find the sum of three one-digit whole numbers (e.g., 3 + 4 + 2 =). DC 1.NSO-C.14 - Identify one more than, one less than, 10 more than, and 10 less than for any number up to 100. DC 1.NSO-C.15 - Understand and use the inverse relationship between addition and subtraction (e.g., 8 + 6 = 14 is equivalent to 14-6 = 8 and is also equivalent to 14-8 = 6) to solve problems and check solutions. DC 1.NSO-C.16 - Know the meaning of "two times something" or "three times something" as an addition (e.g., two times seven means 7 + 7). Page 4 of 114 Topic 1 - Numbers and Topic 1 - Numbers and Topic 1 - Numbers and Topic 2 - Algebraic Thinking Obj. 44 - Add three 1-digit numbers Obj. 11 - Determine one more than or one less than a given number Obj. 12 - Determine ten more than or ten less than a given number Obj. 47 - Complete an addition and subtraction fact family Obj. 48 - Apply the inverse relationship between addition facts and subtraction facts Obj. 60 - Determine a missing addend in a basic addition-fact number sentence Obj. 61 - Determine a missing subtrahend in a basic subtraction-fact number sentence Obj. 63 - Determine a missing addend in an addition sentence with three 1-digit numbers Obj. 64 - WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State DC 1.PRA - Patterns, Relations, and Algebra DC 1.PRA.1 - Identify, reproduce, describe, extend, and create simple rhythmic, shape, size, number, color, and letter repeating patterns. Topic 2 - Algebraic Thinking Obj. 66 - Extend a repeating picture pattern DC 1.PRA.2 - Describe and create arithmetic progressions (e.g., 1, 4, 7, 10... or 25, 23, 21...). DC 1.PRA.3 - Identify arithmetic progressions on the hundreds chart. Topic 2 - Algebraic Thinking Obj. 68 - Determine a pattern on a 1 to 100 chart Topic 2 - Algebraic Thinking Obj. 68 - Determine a pattern on a 1 to 100 chart DC 1.PRA.4 - Skip count forward and backward by twos, fives, and tens up to at least 50, starting at any number and using appropriate aids (e.g., hundreds chart, number line). Topic 1 - Numbers and Obj. 69 - Complete a pattern on a 1 to 100 chart Obj. 13 - Count by 2s to 50 starting from a multiple of 2 DC 1.PRA.5 - Write and solve number sentences from problem situations that express relationships involving addition and subtraction, including +, -, <, >, =. DC 1.PRA.6 - Apply knowledge of fact families to solve simple open sentences for addition and subtraction that have variables (e.g., + 2 = 7 and 10 - = 6). Page 5 of 114 Topic 1 - Numbers and Topic 2 - Algebraic Thinking Topic 2 - Algebraic Thinking Obj. 14 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively Obj. 32 - Relate a picture model to a basic addition fact Obj. 33 - Determine the basic addition fact shown by a picture model Obj. 35 - Determine the basic addition fact shown by a number-line model Obj. 36 - Relate a picture model to a basic subtraction fact Obj. 37 - Determine the basic subtraction fact shown by a picture model Obj. 38 - Determine the basic subtraction fact shown by a numberline model Obj. 65 - WP: Determine a basic addition- or subtraction-fact number sentence for a given situation Obj. 60 - Determine a missing addend in a basic addition-fact number sentence
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State DC 1.G - Geometry DC 1.G.1 - Describe attributes and parts of two- and three-dimensional shapes (e.g., length of sides and number of corners, edges, faces, and sides). DC 1.G.2 - Identify congruent shapes. DC 1.G.3 - Identify symmetry in twodimensional shapes. DC 1.G.4 - Combine shapes and take them apart to make other shapes (e.g., two congruent right triangles can be arranged to form a rectangle). Topic 3 - Geometry and Measurement Obj. 61 - Determine a missing subtrahend in a basic subtraction-fact number sentence Obj. 64 - WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence Obj. 82 - Determine the common attributes in a set of geometric shapes DC 1.G.5 - Arrange and describe objects in space by proximity, position, and direction (e.g., near, far, below, above, up, down, behind, in front of, next to, left or right of). Topic 3 - Geometry and Measurement Obj. 72 - Apply the vocabulary of position or direction DC 1.M - Measurement DC 1.M.1 - Compare the length, weight, and volume of two or more objects by using direct comparison. Topic 3 - Geometry and Measurement Obj. 70 - Compare objects using the vocabulary of measurement Obj. 71 - Compare and order objects by attributes of height or length DC 1.M.2 - Make and use estimates of measurement, including time and weight. DC 1.M.3 - Measure the length of objects by repeating a nonstandard or standard unit. DC 1.M.4 - Tell time at half-hour intervals on analog and digital clocks using a.m. and p.m., and relate time to events (e.g., before/after, shorter/longer). DC 1.M.5 - Make combinations of coins up to 50 cents. Page 6 of 114 Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 1 - Numbers and Obj. 74 - Estimate length in nonstandard units Obj. 76 - Tell time to the hour Obj. 77 - Tell time to the half hour Obj. 78 - Order events by time Obj. 17 - Determine the value of a collection of like coins
Accelerated Math Grade 1 Accelerated Math Second Edition Grade 1 Grade 1, Learning Standards, State DC 1.DASP - Data Analysis, Statistics, and Probability DC 1.DASP.1 - Use surveys and observations to gather data about themselves and their surroundings (e.g., What is your favorite dessert?). Obj. 18 - Determine the value of a collection of mixed coins DC 1.DASP.2 - Represent and compare data (e.g., largest, smallest, most often, least often) using tally charts, pictures, and bar graphs. Topic 4 - Data Analysis and Statistics Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object) DC 1.DASP.3 - Ask and answer simple questions related to data representations (e.g., Who is the tallest student in the class? What is the favorite fruit of the class?). Topic 4 - Data Analysis and Statistics Obj. 92 - Use a picture graph to represent groups of objects (1 symbol = 1 object) Obj. 98 - Use a bar graph to represent groups of objects Obj. 88 - Read a 2-category tally chart Obj. 90 - Answer a question using information from a 2-category tally chart Obj. 91 - Read a picture graph Obj. 93 - Answer a question using information from a picture graph Obj. 97 - Read a bar graph Obj. 99 - Answer a question using information from a bar graph Page 7 of 114
Accelerated Math Grade 2 Grade 2, Learning Standards, State DC 2.NSO - Number Sense and DC 2.NSO-N.1 - Count, read, and write whole numbers to 1,000 and relate them to the quantities they represent. Accelerated Math Second Edition Grade 2 DC 2.NSO-N.2 - Compare and order numbers to 1,000; use the symbols >, <, =. Obj. 1 - Read a whole number to 1,000 Obj. 2 - Determine the word form of a whole number to 1,000 Obj. 20 - Compare whole numbers to 1,000 using words Obj. 21 - Compare whole numbers to 1,000 using the symbols <, >, and = DC 2.NSO-N.3 - Identify the place value of the digits to 1,000. DC 2.NSO-N.4 - Use words, models, and expanded forms (e.g., 35 = 3 tens + 5 ones) to represent numbers to 1,000. Obj. 22 - Order whole numbers to 1,000 in ascending order Obj. 23 - Order whole numbers to 1,000 in descending order Obj. 9 - Determine the value of a digit in a 3-digit number Obj. 10 - Determine which digit is in a specified place in a 3-digit whole number Obj. 12 - Model a number using hundreds, tens, and ones to 1,000 Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000 Obj. 14 - Represent a 3-digit number as hundreds, tens, and ones DC 2.NSO-N.5 - Know that even numbers end in 0, 2, 4, 6, or 8; recognize even numbers as multiples of two; know that odd numbers end in 1, 3, 5, 7, or 9. DC 2.NSO-N.6 - Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $5. Page 8 of 114 Obj. 15 - Determine the 3-digit number represented as hundreds, tens, and ones Obj. 16 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones Obj. 6 - Identify odd and even numbers between 100 and 1,000 Obj. 17 - Determine the value of a collection of bills and coins Obj. 18 - Translate between a dollar sign and a cent sign
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State Obj. 19 - Convert money amounts in words to amounts in symbols Obj. 26 - Determine cent amounts DC 2.NSO-F.7 - Know that fractions may represent a portion of a whole that has been partitioned into parts of equal area or length; use the terms "numerator" and "denominator." that total a dollar Obj. 58 - Identify a unit fraction as part of a whole DC 2.NSO-F.8 - Recognize the inverse relationship between the size of a unit fraction and the size of the denominator (e.g., 1/4 < 1/3). DC 2.NSO-F.9 - Recognize, name, and write commonly used fractions such as 1/2, 2/3, and 3/4. DC 2.NSO-F.10 - Recognize that fractions such as 2/2, 3/3, 4/4, 10/10, and 100/100 are equal to the whole and to one. DC 2.NSO-C.11 - Demonstrate the ability to use conventional algorithms for addition (two three-digit whole numbers and three two-digit whole numbers) and subtraction (two threedigit whole numbers). Obj. 61 - Identify a fraction as part of a whole Obj. 62 - Relate a fraction equal to a whole to a pictorial model Obj. 63 - Compare unit fractions using pictorial models Obj. 58 - Identify a unit fraction as part of a whole Obj. 59 - Identify a unit fraction as part of a set of objects Obj. 60 - Identify a fraction as part of a set of objects Obj. 61 - Identify a fraction as part of a whole Obj. 62 - Relate a fraction equal to a whole to a pictorial model Obj. 28 - Add two 3-digit numbers without regrouping Obj. 29 - Add two 2-digit numbers with regrouping, given a model Obj. 31 - Add a 2-digit number to a 1- digit number with regrouping Obj. 32 - Add two 2-digit numbers with regrouping Obj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100 Obj. 34 - Add 2- and 3-digit numbers with no more than one regrouping Page 9 of 114
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State Obj. 35 - Add two 3-digit numbers with one regrouping Obj. 36 - Subtract a 3-digit number from a 3-digit number without regrouping Obj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regrouping Obj. 39 - Subtract a 1- or 2-digit number from a 3-digit number with one regrouping Obj. 40 - Subtract a 3-digit number from a 3-digit number with one regrouping Obj. 41 - WP: Add or subtract numbers without regrouping Obj. 42 - WP: Add or subtract up to 2- digit numbers with one regrouping DC 2.NSO-C.12 - Find the distance between numbers on the number line (e.g., how far is 76 from 24). DC 2.NSO-C.13 - Know addition and subtraction facts (addends to 12), commit to memory, and use them to solve problems. Select and use appropriate operations (addition and subtraction) to solve problems, including those involving money. DC 2.NSO-C.14 - Demonstrate the ability to add and subtract three-digit whole numbers accurately and efficiently. Page 10 of 114 Obj. 26 - Determine cent amounts that total a dollar Obj. 27 - WP: Add or subtract a collection of bills or coins Obj. 30 - Add money values using cents or dollars with regrouping Obj. 37 - Subtract money values using cents or dollars with one regrouping Obj. 28 - Add two 3-digit numbers without regrouping Obj. 29 - Add two 2-digit numbers with regrouping, given a model Obj. 31 - Add a 2-digit number to a 1- digit number with regrouping Obj. 32 - Add two 2-digit numbers with regrouping Obj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State Obj. 34 - Add 2- and 3-digit numbers with no more than one regrouping Obj. 35 - Add two 3-digit numbers with one regrouping Obj. 36 - Subtract a 3-digit number from a 3-digit number without regrouping Obj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regrouping Obj. 39 - Subtract a 1- or 2-digit number from a 3-digit number with one regrouping Obj. 40 - Subtract a 3-digit number from a 3-digit number with one regrouping Obj. 41 - WP: Add or subtract numbers without regrouping Obj. 42 - WP: Add or subtract up to 2- digit numbers with one regrouping DC 2.NSO-C.15 - Use mental arithmetic to find the sum or difference of two two-digit numbers. DC 2.NSO-C.16 - Represent multiplication as repeated addition. DC 2.NSO-C.17 - Demonstrate proficiency with multiplication facts for the ones, twos, and fives. DC 2.NSO-C.18 - Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and check solutions. Topic 2 - Algebraic Thinking Obj. 24 - Determine a number pair that totals 100 Obj. 46 - Determine the sum of equal groups using pictures Obj. 47 - Use a repeated addition sentence to represent the sum of equal groups Obj. 49 - Represent repeated addition as multiplication Obj. 51 - Know multiplication tables for 2, 5, and 10 Obj. 52 - WP: Multiply a 1-digit number by 2, 5, or 10 Obj. 43 - Apply the inverse relationship between addition and subtraction with 2- and 3-digit numbers Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbers Obj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbers Page 11 of 114
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State Obj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers DC 2.NSO-C.19 - Know and identify various meanings of addition and subtraction, such as addition as combination (i.e., plus, combined with, more), subtraction as comparison (i.e., how much less, how much more), equalizing (i.e., how many more are needed to make these equal), and separation (i.e., how much remaining). DC 2.NSO-E.20 - Estimate, calculate, and solve problems involving addition and subtraction of two-digit numbers. Describe differences between estimates and actual calculations. Obj. 24 - Determine a number pair that totals 100 Obj. 25 - Determine a number pair that totals 1,000 Obj. 44 - Estimate the sum of two 2- digit numbers DC 2.PRA - Patterns, Relations, and Algebra DC 2.PRA.1 - Recognize and describe simple repeating and growing patterns using numbers, shapes, sizes, colors, and letters. DC 2.PRA.2 - Describe functions related to coin trades and measurement trades (e.g., 5 pennies make 1 nickel; 4 cups make 1 quart). Topic 2 - Algebraic Thinking Obj. 45 - Estimate the difference of two 2-digit numbers Obj. 70 - Determine an addition or subtraction number pattern given a rule Obj. 71 - Determine the rule for an addition or subtraction number pattern Obj. 72 - Extend a number pattern involving addition Obj. 73 - Extend a number pattern involving subtraction Obj. 74 - Extend a pattern given a table of related number pairs Obj. 75 - Determine a repeating pattern corresponding to the same pattern expressed using different elements Page 12 of 114
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State DC 2.PRA.3 - Skip count forward and backward by twos, fives, and tens up to at least 100, starting at any number. Obj. 3 - Complete a skip pattern starting from a multiple of 2, 5, or 10 Obj. 4 - Complete a skip pattern of 2, 5, or 10 starting from any number DC 2.PRA.4 - Construct and solve open sentences with variables for addition and subtraction of up to two three-digit numbers (e.g., 42 + = 292). Topic 2 - Algebraic Thinking Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbers Obj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbers Obj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers Obj. 69 - WP: Use an open sentence to represent a given situation DC 2.PRA.5 - Use the commutative and associative rules for addition to simplify mental calculations and to check results. DC 2.G - Geometry DC 2.G.1 - Identify, describe, draw, and compare two-dimensional shapes, including both polygonal (up to six sides) and curved figures such as circles. DC 2.G.2 - Classify familiar two- and three-dimensional shapes by common attributes such as shape of curved and straight lines, number and shape of faces, edges, and vertices. DC 2.G.3 - Match and construct congruent (e.g., two triangles that are the same shape and size) and symmetric shapes (e.g., two halves of a heart divided down the center line). DC 2.G.4 - Identify shapes under rotation (turns), reflections (flips), translation (slides), and enlargement. Describe direction of translations (e.g., left, right, up, down). Page 13 of 114 Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj. 85 - Identify a parallelogram, a trapezoid, a pentagon, a hexagon, or an octagon Obj. 84 - Identify figures that are the same size and shape Obj. 88 - Identify symmetry in a 2- dimensional shape
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State DC 2.G.5 - Predict and explain the results of putting two-dimensional shapes together and taking them apart (e.g., two congruent right triangular shapes form a rectangle). Topic 3 - Geometry and Measurement Obj. 86 - Decompose a plane shape composed of three or more simpler shapes DC 2.G.6 - Relate geometric ideas to numbers (e.g., seeing rows in an array as a model of repeated addition). DC 2.M - Measurement DC 2.M.1 - Measure and compare the length of common objects using metric and U.S. customary units to the nearest centimeter or inch. DC 2.M.2 - Make and use estimates of measurement including time, volume, weight, area, and perimeter. DC 2.M.3 - Select and correctly use the appropriate measurement tool (ruler, balance scale, thermometer). Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj. 50 - Relate a multiplication sentence to an array model Obj. 76 - Measure length in inches Obj. 77 - Measure length in centimeters Obj. 76 - Measure length in inches DC 2.M.4 - Tell time at quarter-hour intervals. DC 2.M.5 - Identify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar. Topic 3 - Geometry and Measurement Obj. 77 - Measure length in centimeters Obj. 81 - Read a thermometer in degrees Celsius Obj. 82 - Read a thermometer in degrees Fahrenheit Obj. 78 - Tell time to the quarter hour DC 2.M.6 - Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and bills and different ways to represent an amount of money up to $5 using appropriate notation. Page 14 of 114 Obj. 17 - Determine the value of a collection of bills and coins Obj. 18 - Translate between a dollar sign and a cent sign Obj. 19 - Convert money amounts in words to amounts in symbols Obj. 26 - Determine cent amounts that total a dollar
Accelerated Math Grade 2 Accelerated Math Second Edition Grade 2 Grade 2, Learning Standards, State DC 2.DASP - Data Analysis, Statistics, and Probability DC 2.DASP.1 - Use interviews, surveys, and observations to gather data about themselves and their surroundings. DC 2.DASP.2 - Organize, classify, and represent data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations. DC 2.DASP.3 - Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data. Topic 4 - Data Analysis and Statistics Obj. 90 - Read a multi-category tally chart Obj. 91 - Use a tally chart to represent data Obj. 92 - Answer a question using information from a tally chart Obj. 93 - Read a pictograph (1 symbol = more than 1 object) Obj. 94 - Use a pictograph to represent data (1 symbol = more than 1 object) Obj. 95 - Answer a question using information from a pictograph (1 symbol = more than 1 object) Obj. 96 - Read a bar graph with a y- axis scale by 2s Obj. 97 - Use a bar graph with a y- axis scale by 2s to represent data Obj. 98 - Answer a question using information from a bar graph with a y- axis scale by 2s Page 15 of 114
Accelerated Math Grade 3 Grade 3, Learning Standards, State Accelerated Math Second Edition Grade 3 DC 3.NSO - Number Sense and DC 3.NSO-N.1 - Exhibit an understanding of the base 10 number system by reading, modeling, and writing whole numbers to at least 10,000; demonstrate an understanding of the values of the digits. Obj. 1 - Read a 4- or 5-digit whole number Obj. 2 - Determine the word form of a 4- or 5-digit whole number Obj. 3 - Determine the value of a digit in a 4- or 5-digit whole number Obj. 4 - Determine which digit is in a specified place in a 4- or 5-digit whole number Obj. 5 - Represent a 4-digit whole number as thousands, hundreds, tens, and ones Obj. 6 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones Obj. 7 - Represent a 4- or 5-digit whole number in expanded form Obj. 8 - Determine the 4- or 5-digit whole number represented in expanded form Obj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones DC 3.NSO-N.2 - Represent, compare, and order numbers to 10,000 using various forms, including expanded notation (e.g., 3,206 = 3 x 1,000 + 2 x 100 + 6) and written out in words (e.g., three thousand twohundred six). Obj. 10 - Determine the result of changing a digit in a 4- or 5-digit whole number Obj. 1 - Read a 4- or 5-digit whole number Obj. 2 - Determine the word form of a 4- or 5-digit whole number Obj. 5 - Represent a 4-digit whole number as thousands, hundreds, tens, and ones Obj. 6 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones Page 16 of 114
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State Obj. 7 - Represent a 4- or 5-digit whole number in expanded form Obj. 8 - Determine the 4- or 5-digit whole number represented in expanded form Obj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones DC 3.NSO-N.3 - Round whole numbers through 10,000 to the nearest 10, 100, and 1,000. DC 3.NSO-N.4 - Recognize sets to which a number may belong (odd numbers, even numbers, and multiples of numbers through 10). Identify the numbers in those classes (e.g., the class of multiples of 7 between 1 and 29 consists of 7, 14, 21, 28). DC 3.NSO-F.5 - Identify and represent fractions (between 0 and 1 with denominators through 10) as parts of unit wholes and parts of a collection. Obj. 11 - Compare 4- or 5-digit whole numbers using the symbols <, >, and = Obj. 12 - Order 4- or 5-digit whole numbers in ascending or descending order Obj. 27 - Round a 2- to 4-digit whole number to its greatest place Obj. 44 - Determine a pictorial model of a fraction of a whole Obj. 45 - Determine a pictorial model of a fraction of a set of objects DC 3.NSO-F.6 - Recognize, name, and use equivalent fractions with denominators 2, 3, 4, and 8; place these fractions on the number line; compare and order them and relate the number line to a ruler (e.g., 1/2 = 2/4 = 4/8). Obj. 55 - Estimate fractions of a whole Obj. 46 - Identify a fraction represented by a point on a number line Obj. 47 - Locate a fraction on a number line Obj. 50 - Identify equivalent fractions using models Page 17 of 114
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State DC 3.NSO-F.7 - Know the meaning of 0.75, 0.50, and 0.25 as they relate to money; know that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar). DC 3.NSO-F.8 - Know that any fraction can be written as a sum of unit fractions (e.g., 3/4 = 1/4 + 1/4 + 1/4). DC 3.NSO-F.9 - Model and represent a mixed number (with denominator 2, 3, or 4) as a whole number and a fraction (e.g., 1 2/3, 3 1/2). DC 3.NSO-C.10 - Demonstrate an understanding of and the ability to use conventional algorithms for the addition and subtraction of up to fivedigit whole numbers. DC 3.NSO-C.11 - Add and subtract up to four-digit whole numbers accurately and efficiently. DC 3.NSO-C.12 - Use concrete objects and visual models to add and subtract common fractions (halves, thirds, fourths, sixths, and eighths) with like denominators. DC 3.NSO-C.13 - Solve problems involving addition and subtraction of money amounts in decimal notation. Obj. 13 - Add 3- and 4-digit whole numbers with regrouping Obj. 14 - Add three 2- to 3-digit whole numbers Obj. 15 - Subtract 3- and 4-digit whole numbers with regrouping Obj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping Obj. 13 - Add 3- and 4-digit whole numbers with regrouping Obj. 14 - Add three 2- to 3-digit whole numbers Obj. 15 - Subtract 3- and 4-digit whole numbers with regrouping Obj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping Obj. 17 - Add two money amounts less than $1 in decimal notation Obj. 18 - Subtract two money amounts less than $1 in decimal notation Page 18 of 114
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State Obj. 19 - Add or subtract cent amounts to or from whole dollar amounts Obj. 20 - Add dollars and cents to cents Obj. 21 - Add dollars and cents to dollars Obj. 22 - Subtract cents from dollars and cents Obj. 23 - Subtract dollars from dollars and cents Obj. 24 - Determine money amounts that total $10 Obj. 25 - WP: Determine the amount of change from whole dollar amounts DC 3.NSO-C.14 - Know multiplication is the result of counting the total number of objects in a set of equal groups (e.g., 3 x 5 gives the number of objects in 3 groups of 5 objects). DC 3.NSO-C.15 - Know division ( ) as another way of expressing multiplication, i.e., that division is the inverse of multiplication (e.g., 2 x 3 = 6 can be rewritten as 6 2 = 3 or 6 3 = 2). DC 3.NSO-C.16 - Know multiplication facts through 10 x 10 and related division facts (e.g., 9 x 8 = 72 and 72 9 = 8). Use these facts to solve related problems (e.g., 3 x 5 is related to 3 x 50). DC 3.NSO-C.17 - Solve simple problems involving multiplication of multidigit whole numbers by one-digit numbers (2,431 x 2). DC 3.NSO-C.18 - Solve division problems in which a multidigit whole number is evenly divided by a onedigit number (e.g., 125 5). Page 19 of 114 Obj. 26 - WP: Add or subtract money amounts less than $1 Obj. 33 - Use a multiplication sentence to represent an area or an array model Obj. 41 - Complete a multiplication and division fact family Obj. 35 - Know basic multiplication facts to 10 x 10 Obj. 37 - Know basic division facts to 100 10 Obj. 39 - WP: Multiply using basic facts to 10 x 10 Obj. 40 - WP: Divide using basic facts to 100 10 Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100 Obj. 43 - Multiply a 2-digit whole number by a 1-digit number Obj. 34 - Use a division sentence to represent objects divided into equal groups
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State DC 3.NSO-C.19 - Multiply up to twodigit whole numbers by a one-digit whole number accurately and efficiently. DC 3.NSO-C.20 - Use the commutative (order) and identity properties of addition and multiplication on whole numbers in computations and problem situations (e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4). Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100 Obj. 43 - Multiply a 2-digit whole number by a 1-digit number DC 3.NSO-C.21 - Know and apply the special properties of 0 and 1 in multiplication. DC 3.NSO-C.22 - Use multiplication and division fact families to understand the inverse relationship of these two operations and to compare and check results (e.g., because 3 x 8 = 24, we know that 24 8 = 3 or 24 3 = 8). Obj. 41 - Complete a multiplication and division fact family DC 3.NSO-E.23 - Estimate the sum and difference of two numbers with three digits (sums up to 1,000) and judge reasonableness of estimates. DC 3.NSO-E.24 - Understand and use the strategies of rounding and regrouping to estimate quantities, measures, and the results of wholenumber computations (addition, subtraction, and multiplication) up to two-digit whole numbers and amounts of money to $100 and to judge the reasonableness of answers. Page 20 of 114 Obj. 28 - Estimate a sum or difference of whole numbers to 10,000 by rounding Obj. 29 - Estimate a sum or difference of two 3- or 4-digit whole numbers using front-end estimation Obj. 30 - Estimate a sum or difference of 2- to 4-digit whole numbers using any method Obj. 31 - Estimate a sum of three 2- to 4-digit numbers using any method Obj. 32 - WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method Obj. 30 - Estimate a sum or difference of 2- to 4-digit whole numbers using any method
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State Obj. 31 - Estimate a sum of three 2- to 4-digit numbers using any method DC 3.PRA - Patterns, Relations, and Algebra DC 3.PRA.1 - Create, describe, and Topic 2 - Algebraic Thinking extend symbolic (geometric) patterns and addition and subtraction patterns. DC 3.PRA.2 - Select appropriate operational and relational symbols to make an expression true (e.g., if 4 _ 3 = 12, what operational symbol goes in the blank?). DC 3.PRA.3 - Determine values of variables in simple equations involving addition, subtraction, or multiplication (e.g., 4106 - "triangle" = 37, 5 = "circle" + 3, and "square" - "circle" = 3). DC 3.PRA.4 - Know and express the relationships among linear units of measure, i.e., unit conversions (e.g., 3 feet = 1 yard; 12 inches = 1 foot). Topic 2 - Algebraic Thinking Topic 2 - Algebraic Thinking DC 3.PRA.5 - Extend and recognize Topic 2 - Algebraic Thinking a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by fours or by multiplying the number of horses by 4). Obj. 64 - Extend a number pattern Obj. 65 - Determine a rule for a table of related number pairs Obj. 66 - WP: Find the missing number in a table of paired values Obj. 11 - Compare 4- or 5-digit whole numbers using the symbols <, >, and = Obj. 61 - Determine the operation needed to make a number sentence true Obj. 62 - WP: Determine the operation needed for a given situation Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbers Obj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbers Obj. 58 - Determine the missing multiplicand in a number sentence involving basic facts Obj. 64 - Extend a number pattern DC 3.G - Geometry Page 21 of 114
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State DC 3.G.1 - Compare and analyze attributes and other features (e.g., number and shape of sides, faces, corners, right angles) of twodimensional geometric shapes, especially the attributes of triangles (isosceles, equilateral, right) and quadrilaterals (rectangle, square). Topic 3 - Geometry and Measurement Obj. 95 - Determine attributes of a triangle or a quadrilateral from a model Obj. 96 - Relate a model of a triangle or a quadrilateral to a list of attributes DC 3.G.2 - Describe, model, draw, compare, and classify threedimensional and two-dimensional shapes, especially circles and polygons (e.g., triangles and quadrilaterals). DC 3.G.3 - Identify angles as right, acute (less than a right angle), or obtuse (greater than a right angle). DC 3.G.4 - Identify and draw lines that are parallel, perpendicular, and intersecting. DC 3.G.5 - Identify and draw lines of symmetry in two-dimensional shapes. DC 3.G.6 - Apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent. DC 3.G.7 - Using ordered pairs of whole numbers and/or letters, locate and identify points on a grid. DC 3.M - Measurement DC 3.M.1 - Demonstrate an understanding of such attributes as length, area, and weight; select the appropriate type of unit for measuring each attribute using both the U.S. customary and metric systems. Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Topic 3 - Geometry and Measurement Obj. 97 - Identify a picture of a 3- dimensional shape Obj. 98 - Name a 3-dimensional shape from a picture Obj. 92 - Identify parallel, perpendicular, and intersecting lines Obj. 101 - Identify mirror images Obj. 103 - Determine a location using map coordinates Obj. 104 - Determine the map coordinates for a location Obj. 67 - Measure length to the nearest half inch or quarter inch DC 3.M.2 - Carry out simple unit conversions within a system of measurement such as hours to minutes and cents to dollars (e.g., 1 hour = 60 minutes). Page 22 of 114 Topic 3 - Geometry and Measurement Obj. 68 - Convert between inches, feet, and yards
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State Obj. 69 - Convert between centimeters and meters Obj. 75 - Convert hours to minutes or DC 3.M.3 - Identify time to the nearest 5 minutes on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since...) and using a calendar (e.g., days since...). Topic 3 - Geometry and Measurement minutes to seconds Obj. 76 - Calculate elapsed time within an hour, given two clocks, without regrouping Obj. 77 - Calculate elapsed time within an hour, given two clocks, with regrouping Obj. 78 - WP: Calculate elapsed time within an hour given two clocks DC 3.M.4 - Estimate and find area and perimeter of a rectangle and triangle using diagrams, models, and grids or by measuring. Topic 3 - Geometry and Measurement DC 3.DASP - Data Analysis, Statistics, and Probability DC 3.DASP.1 - Collect and organize data using observations, measurements, surveys, or experiments. DC 3.DASP.2 - Construct, identify the Topic 4 - Data Analysis, main idea, and make predictions Statistics, and Probability from various representations of data sets in the forms of tables, bar graphs (horizontal and vertical forms), pictographs, and tallies. Page 23 of 114 Obj. 79 - WP: Calculate elapsed time within an hour Obj. 83 - Determine a date using a calendar Obj. 86 - Determine a method for finding the perimeter of a shape given the side lengths Obj. 87 - WP: Determine the perimeter of a rectangular shape given a grid with a reference unit Obj. 88 - WP: Determine the perimeter of a shape given a model showing all side lengths Obj. 90 - WP: Determine the area of a rectangular shape given a picture on a grid Obj. 91 - Estimate the area of a shape composed of rectangles given a reference square Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data Obj. 110 - Use a frequency table to represent data
Accelerated Math Grade 3 Accelerated Math Second Edition Grade 3 Grade 3, Learning Standards, State DC 3.DASP.3 - Record all possible outcomes for a simple event using concrete objects (e.g., tossing a coin). DC 3.DASP.4. - Classify outcomes as certain, likely, unlikely, or impossible. DC 3.DASP.5 - List and count the number of possible combinations of objects from 2 sets (e.g., How many different outfits can one make from a set of 2 sweaters and a set of 3 skirts?). Topic 4 - Data Analysis, Statistics, and Probability Obj. 113 - Determine if a situation is certain or impossible Obj. 114 - Determine which event is least likely or most likely to occur Page 24 of 114
Accelerated Math Grade 4 Grade 4, Learning Standards, State Accelerated Math Second Edition Grade 4 DC 4.NSO - Number Sense and DC 4.NSO-N.1 - Exhibit an understanding of the base 10 number system by reading, modeling, and writing whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers. Obj. 3 - Determine the value of a digit in a 6-digit whole number DC 4.NSO-N.2 - Represent, compare, and order numbers to 100,000 using various forms, including expanded notation. DC 4.NSO-N.3 - Round whole numbers to 100,000 to the nearest 10, 100, 1,000, 10,000, and 100,000. Obj. 4 - Determine which digit is in a specified place in a 6-digit whole number Obj. 5 - Determine the whole number represented in expanded form written in powers of ten Obj. 7 - Convert between proper expanded form and improper expanded form up to a 5-digit whole number Obj. 8 - Convert between standard form and improper expanded form up to a 5-digit whole number Obj. 17 - Round a 4- to 6-digit whole number to a specified place DC 4.NSO-N.4 - Recognize sets to which a number may belong (odds, evens, multiples and factors of given numbers, and squares), and use these in the solution of problems. DC 4.NSO-N.5 - Read and interpret whole numbers and decimals up to two decimal places; relate to money and place-value decomposition. DC 4.NSO-N.6 - Determine if a whole number is a multiple of a given onedigit whole number and if a one-digit number is a factor of a given whole number. Obj. 62 - Read a decimal number through the hundredths place Obj. 63 - Determine the word form of a decimal number through the hundredths place Page 25 of 114
Accelerated Math Grade 4 Accelerated Math Second Edition Grade 4 Grade 4, Learning Standards, State DC 4.NSO-N.7 - Find all factors of a whole number up to 50; know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except one and itself and that such numbers are called prime numbers. DC 4.NSO-N.8 - Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in owing money). DC 4.NSO-F.9 - Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on a number line. DC 4.NSO-F.10 - Know the relationships among halves, fourths, and eighths and among thirds, sixths, and twelfths; compare and order such fractions. DC 4.NSO-F.11 - Recognize, name, and generate equivalent forms of common decimals (0.5, 0.25, 0.2, 0.1) and fractions (halves, quarters, fifths, and tenths) and explain why they are equivalent. DC 4.NSO-F.12 - Select, use, and explain models to relate common fractions and mixed numbers (e.g., 1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/12, and 1 1/2); find equivalent fractions, mixed numbers, and decimals. Obj. 52 - Compare fractions on a number line Obj. 53 - Order fractions on a number line Obj. 68 - Determine the decimal number equivalent to a fraction with a denominator of 10 or 100 Obj. 69 - Determine a fraction equivalent to a decimal, using a denominator of 10 or 100 Obj. 70 - Determine the decimal number equivalent to a fraction model Obj. 71 - Determine the fraction equivalent to a decimal number model Obj. 43 - Identify a mixed number represented by a model Obj. 51 - Determine a set of equivalent fractions Obj. 68 - Determine the decimal number equivalent to a fraction with a denominator of 10 or 100 Page 26 of 114
Accelerated Math Grade 4 Accelerated Math Second Edition Grade 4 Grade 4, Learning Standards, State Obj. 69 - Determine a fraction equivalent to a decimal, using a denominator of 10 or 100 Obj. 70 - Determine the decimal number equivalent to a fraction model Obj. 71 - Determine the fraction equivalent to a decimal number DC 4.NSO-F.13 - Represent positive decimals to the hundredths. model Obj. 62 - Read a decimal number through the hundredths place DC 4.NSO-C.14 - Demonstrate an understanding of and the ability to use conventional algorithms for the addition and subtraction of multidigit whole numbers. Obj. 63 - Determine the word form of a decimal number through the hundredths place Obj. 64 - Determine the decimal number from a pictorial model of tenths or hundredths Obj. 65 - Identify a pictorial model of tenths or hundredths of a decimal number Obj. 66 - Identify a decimal number to tenths represented by a point on a number line Obj. 67 - Locate a decimal number to tenths on a number line Obj. 9 - Add up to 4-digit whole numbers in expanded form Obj. 10 - Add a 5-digit or greater whole number and a 3-digit or greater whole number Obj. 11 - Add three multi-digit whole numbers Obj. 12 - Subtract a smaller number from a 3- or 4-digit whole number in expanded form Obj. 13 - Subtract a 3-digit or greater whole number from a 5-digit or greater whole number Obj. 14 - WP: Add a 5-digit or greater whole number and a 3-digit or greater whole number Obj. 15 - WP: Add three multi-digit whole numbers Obj. 16 - WP: Subtract a 3-digit or greater whole number from a 5-digit or greater whole number Page 27 of 114
Accelerated Math Grade 4 Accelerated Math Second Edition Grade 4 Grade 4, Learning Standards, State Obj. 19 - WP: Solve a 2-step problem involving addition and/or subtraction of multi-digit whole numbers DC 4.NSO-C.15 - Add and subtract up to five-digit numbers accurately and efficiently. Obj. 9 - Add up to 4-digit whole numbers in expanded form Obj. 10 - Add a 5-digit or greater whole number and a 3-digit or greater whole number Obj. 11 - Add three multi-digit whole numbers Obj. 12 - Subtract a smaller number from a 3- or 4-digit whole number in expanded form Obj. 13 - Subtract a 3-digit or greater whole number from a 5-digit or greater whole number Obj. 14 - WP: Add a 5-digit or greater whole number and a 3-digit or greater whole number Obj. 15 - WP: Add three multi-digit whole numbers Obj. 16 - WP: Subtract a 3-digit or greater whole number from a 5-digit or greater whole number Obj. 19 - WP: Solve a 2-step problem involving addition and/or subtraction of multi-digit whole numbers DC 4.NSO-C.16 - Use concrete objects and visual models to add and subtract fractions where the denominators are equal or when one denominator is a multiple of the other (denominators 2 through 12, and 100). DC 4.NSO-C.17 - Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations. Obj. 54 - Add fractions with like denominators no greater than 10 using models Obj. 58 - Subtract fractions with like denominators no greater than 10 using models Page 28 of 114