Classworks Common Core Transition Guide. South Carolina 4th Grade Mathematics

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1 Classworks Common Core Transition Guide South Carolina 4th Mathematics OFFICIALLY ENDORSED

2 Classworks Common Core Transition Guide - BETA Making The Transition With the increased rigor, the transition to the Common Core State Standards requires teachers to not only change their teaching methodologies, but to teach new standards/skills. To support this transition, Classworks has developed this Common Core Transition Guide to help with the two primary aspects that are changing: College and Career Ready Standards for Mathematical Practice Movement of skills across the grades Together, these require teachers to revisit the skills being taught and the method in which they are evaluating student knowledge and understanding of the standards. Part One - Projects To enable more performance- based assessment, Classworks includes student projects. This guide includes up to ten Classworks projects that align to the Common Core State Standards and provide meaningful real- world application. These projects also include recommendations for using ipad and Android Tablet apps, so teachers can better integrate newer technology. Each project can be graded using the College and Career Readiness Rubric, which includes the Common Core s eight Mathematical Practices. Rubrics are graded within Classworks, so teachers can track student performance throughout the school year. Part Two - Crosswalks This document indicates the key changes taking place in the transition from state standards to the Common Core. The Classworks Crosswalks help teachers easily identify which grade level the standards were previously taught or if the standard is new, and then provide Classworks units that help with concept introduction, practice, and review. Send Us Feedback! This guide is available for use in all Classworks classrooms. We appreciate all you are doing to help students in your classroom, and we hope this guide eases your transition. We welcome your input as we finalize this Beta release. Please send feedback to For additional information, please view the Common Core Resources user guide located in the Classworks Help Center. Curriculum Advantage 2012 As of July 2012

3 Applying Mathematical Practices with Classworks Projects

4 CC Standard Unit # Project OA Recycling Estimates Applying Mathematical Practices with Classworks Projects 4th Project Description Students develop a spreadsheet that records the refunds generated by recyclables. MD Local Customs Students create a table showing the conversions for customary units of length then explain how to use the table. MD A Walk In the Park MD Babysitting Record MD Is the Price Right? Students track expenses during a trip to an amusement park to practice adding and subtracting decimals. Students track the time spent babysitting and the money earned during that time. Students cut and paste pictures of money along with various toys to represent how much money is needed to buy the toys. MD Savings Account Students determine how much money they will need to save in order to buy something. NBT Sizing Up the Students demonstrate an understanding of States whole number place value while working with a table listing the areas of some states. NBT Translation Students translate expanded forms of numbers Vacation into standard forms. NF Pizza Part y Students manipulate and compare pizza models to demonstrate equivalent fractions and simplest terms. G Holiday Symmetry College and Career Ready Practices Students select things associated with holidays that have more than one line of symmetry. Make sense of problems, persevere Reason abstractly & quant. Construct viable arguments Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Express regularity in repeated reasoning Curriculum Advantage 2012

5 Student: Teacher: 4 Math CCR PRACTICES Score Makes sense of problems and perseveres in solving them Reasons abstractly and quantitatively Constructs viable arguments and critiques the reasoning of others Models with mathematics Uses appropriate tools strategically Attends to precision Looks for and makes use of structure Looks for and expresses regularity in repeated reasoning Requires teacher or partner assistance in representing and solving all problems. Is unable to represent or manipulate any of the quantities. Requires assistance in generating an argument. Does not listen to the reasoning of others. Is unable to use illustrations, charts, or numbers to solve the problem. Is unable to choose the correct tools. Does not use the tools appropriately. Is unable to give clear explanations about work. Has little success identifying or using patterns or structures. Requires assistance when looking for general methods, shortcuts, or repetition. Masters skills Masters 25% of the skills from the activity but cannot apply them to other situations. Uses manipulatives, illustrations, and/or numbers to represent problems. Requires assistance when solving most problems. With assistance, represents and manipulates the quantities. Has difficulty understanding the meaning of the quantities. Makes a flawed argument because the problem was not read or reviewed carefully. Is able to listen to the reasoning of others. With assistance uses illustrations, charts, and/or numbers to solve the problem. Determines which tools to use to best complete the task. Requires assistance in order to use the tools. Is able to give explanations orally. Requires assistance when putting explanation into written form. Requires assistance when identifying or using the pattern or structure. For some of the activity is able to find general methods, shortcuts, and repeating calculations. Masters 50% of the skills from the activity but struggles to apply them to other situations. Uses manipulatives, illustrations, and/or numbers to represent and solve problems. Requires assistance when solving some problems. With assistance, represents and manipulates the quantities and explains their relationships. Does not always use the correct quantities and symbols. Makes an argument but does not use enough evidence to justify conclusion. Is able to listen to the reasoning of others. For most of the activity is able to use illustrations, charts, and/or numbers to solve the problem. Determines which tools to use to best complete the task. Uses the tools to gain a deeper understanding of the concept. Does not show work. For most of the activity is able to give explanations orally and in written form. Requires some assistance writing about work. Is able to identify a pattern or structure. Requires assistance using the pattern or structure. Finds general methods and shortcuts. Sometimes notices repeating calculations. Masters 75% of the skills from the activity and can apply them to other situations 50% of the time. Uses manipulatives, illustrations, and/or numbers to represent and solve problems. Is able to create and solve original word problems. Does not ask questions when a new skill is not understood. Represents and manipulates the quantities and explains their relationships. Uses the correct quantities and symbols but makes mistakes during computation. Justifies conclusion by referring to objects, pictures, or diagrams but has difficulty acting it out. Is sometimes able to defend, refute, or improve the arguments of others. Uses illustrations, charts, and/or numbers to solve the problem. Not all work is accurate. Determines which tools to use to best complete the task. Uses the tools to gain a deeper understanding of the concept. Shows but does not check answers. Is able to give explanations orally and in written form. Can sometimes state the reason for a list, answer, or operation chosen. Is able to identify a pattern or structure. Uses the pattern or structure correctly in most instances. Finds general methods and shortcuts. Notices repeating calculations. Masters 100% of the skills from the activity and can apply them to other situations 75% of the time. Uses manipulatives, illustrations, and/or numbers to represent and solve problems. Is able to create and solve original word problems. Perseveres and asks questions when learning a new skill. Represents and manipulates the quantities and explains their relationships. Attends to details during computation, using the correct quantities and symbols. Justifies conclusion by acting it out or referring to objects, pictures, or diagrams. Is able to defend, refute, or improve the arguments of others. Uses illustrations, charts, and/or numbers to solve the problem. Work is complete and accurate. Determines which tools to use to best complete the task. Uses the tools to gain a deeper understanding of the concept. Shows and checks all answers. Is able to give explanations orally and in written form. Can state the reason for a list, answer, or operation chosen. Is able to identify a pattern or structure. Uses the pattern or structure to complete the activity. Finds general methods and shortcuts. Is able to use repeating calculations to make conclusions. Masters 100% of the skills from the activity and can demonstrate them 100% of the time in other situations. Copyright 2011 Classworks by Curriculum Advantage, Inc.

6 Common Core Crosswalks

7 Common Core Crosswalks: South Carolina 4th Math OA.4 OA.4.A OA.4.1 OA.4.2 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., : Skill Builder Multiplication interpret 35 = 5 x 7 as a statement that 35 is 5 times as Patterns many as 7 and 7 times as many as 5. Represent verbal 1380: Multiplication and Division Fact statements of multiplicative comparisons as Families multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison : Solving Problems by Choosing Multiplication or Division Concept Intro Practice OA.4.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 20 (with 0 representing a count of no objects). OA.4.B Gain familiarity with factors and multiples. OA.4.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one digit number. Determine whether a given whole number in the range is prime or composite : Skill Builder Finding Reasonable Estimated Answers 1347: Guessing and Checking 1350: Solving Multistep Addition and Subtraction Problems 1400: Solving Problems by Choosing Multiplication or Division 1433: Understanding Choosing Addition or Subtraction NEW 1370: Skill Builder Factors and Multiples to : Skill Builder Prime and Composite Numbers Curriculum Advantage

8 Common Core Crosswalks: South Carolina 4th Math OA.4.C OA.4.5 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way : Understanding Finding a Pattern 1346: Skill Builder Recognizing Number Patterns 1348: More Function Tables 1389: Skill Builder Introducing Tesselations Concept Intro Practice NBT.4 NBT.4.A NBT.4.1 Number and Operations in Base Ten Generalize place value understanding for multi digit whole numbers. Recognize that in a multi digit whole number, a digit in NEW one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. 1332: Place Value to Hundred Thousands 1331: Place Value to Thousands NBT.4.2 NBT.4.3 Read and write multi digit whole numbers using base ten numerals, number names, and expanded form. Compare two multi digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi digit whole numbers to any place : Using Number Forms to Hundred Thousands 1330: Comparing and Ordering Numbers to 100, : Place Value to Thousands NEW 1363: Skill Builder More Rounding 1338: Rounding Rules Curriculum Advantage

9 Common Core Crosswalks: South Carolina 4th Math NBT.4.B NBT.4.4 NBT.4.5 Use place value understanding and properties of operations to perform multi digit arithmetic. NEW Fluently add and subtract multi digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two two digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 1351: Subtracting 4 Digit Numbers 1342: Adding 2 and 3 Digit Numbers with Regrouping 1349: Subtracting 2 and 3 Digit Numbers with Regrouping 1343: Adding 4 Digit Numbers 1353: Skill Builder Add/Subtract 6 Digit Whole Numbers : Using 1 Digit Multipliers 1423: Skill Builder More 1 Digit Multiplication 1446: Using 2 Digit Multipliers Concept Intro Practice NBT.4.6 NF.4 NF.4.A NF.4.1 Find whole number quotients and remainders with up to four digit dividends and one digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Number and Operations Fractions Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n x a) (n x b) by using visual frac on models, with a en on to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions : 2 Digit Divisors and Dividends Up to 4 Digits 1442: Skill Builder Divide 2 or 3 Digits/1 Digit 1397: 1 Digit Divisors and Dividends up to 4 Digits : Finding Equivalent Fractions Using Models 1443: Skill Builder Working with Fractions 1404: Introducing Equivalent Fractions and Simplest Form Curriculum Advantage

10 Common Core Crosswalks: South Carolina 4th Math NF.4.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Concept Intro Practice : Comparing and Ordering Fractions NF.4.B NF.4.3 NF.4.3.a NF.4.3.b Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 4 1/b. Understand addition and subtraction of fractions as : Subtracting Fractions with Unlike joining and separating parts referring to the same whole. Denominators 1409: Adding Fractions with Unlike Denominators 1408: Adding and Subtracting Fractions with Models Decompose a fraction into a sum of fractions with the : Finding Fractions as Part of a Whole same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8. Curriculum Advantage

11 Common Core Crosswalks: South Carolina 4th Math NF.4.3.c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction : Introducing Adding and Subtracting Mixed Numbers Concept Practice Intro 1 2 NF.4.3.d NF.4.4 NF.4.4.a NF.4.4.b NF.4.4.c Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? : Fraction Word Problems NEW NEW NEW 1557: Introducing Multiplying Fractions NEW 1413: Fraction Word Problems Curriculum Advantage

12 Common Core Crosswalks: South Carolina 4th Math NF.4.C Understand decimal notation for fractions, and compare decimal fractions. NF.4.5 Express a fraction with denominator 10 as an equivalent 4 fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. NF.4.6 Use decimal notation for fractions with denominators : Skill Builder Decimals and or 100. For example, rewrite 0.62 as 62/100; describe a Fractions length as 0.62 meters; locate 0.62 on a number line 1407: Understanding Equivalent Decimals diagram. and Fractions NF.4.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model : Comparing and Ordering Decimals to Hundredths Concept Intro Practice MD.4 MD.4.A MD.4.1 Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), : Converting Metric Units of Measure 1416: Converting Customary Units of Length Curriculum Advantage

13 Common Core Crosswalks: South Carolina 4th Math MD.4.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale : Using Maps: Distance Between Locations 1372: Skill Builder Problem Solving With Money 1421: Skill Builder Measurement Word Problems 1429: Elapsed Time Concept Practice Intro MD.4.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. NEW 1431: Skill Builder Word Problems (Perimeter, Area, and Volume) 1436: Skill Builder Concepts of Area and Perimeter 4 MD.4.B MD.4.4 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. NEW Curriculum Advantage

14 Common Core Crosswalks: South Carolina 4th Math MD.4.C MD.4.5 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed 4 wherever two rays share a common endpoint, and understand concepts of angle measurement: Concept Intro Practice MD.4.5.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "onedegree angle," and can be used to measure angles. 4 MD.4.5.b MD.4.6 MD.4.7 An angle that turns through n one degree angles is said to have an angle measure of n degrees. Measure angles in whole number degrees using a protractor. Sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. 4 NEW 1386: Introducing Angles 1 2 NEW Curriculum Advantage

15 Common Core Crosswalks: South Carolina 4th Math G.4 G.4.A G.4.1 G.4.2 Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, : Introducing Points, Lines, acute, obtuse), and perpendicular and parallel lines. Segments, and Rays Identify these in two dimensional figures. 1385: Skill Builder Parallel and Perpendicular Lines 1386: Introducing Angles Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles : Skill Builder Parallel and Perpendicular Lines Concept Intro Practice G.4.3 Recognize a line of symmetry for a two dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. NEW 1414: Skill Builder Shape Symmetry 3 3 Curriculum Advantage

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