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# CCGPS Math

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### CCGPS Math

1. 1. Common Core  Georgia Performance  Standards  CCGPS      Mathematics Curriculum Maps Grade K ‐ 12
2. 2. Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics Kindergarten – At a Glance Common Core Georgia Performance Standards: Curriculum Map Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Sophisticated Counting With Comparing Measuring and Investigating Further Show What We Shapes Friends Numbers Analyzing Data Addition and Investigation of Know Subtraction Addition and Subtraction MCCK.G.1 MCCK.CC.1 MCCK.NBT.1 MCCK.MD.1 MCCK.OA.1 MCCK.OA.2 ALL MCCK.G.2 MCCK.CC.2 MCCK.CC.3 MCCK.MD.2 MCCK.OA.2 MCCK.OA.3 MCCK.G.3 MCCK.CC.3 MCCK.CC.4a MCCK.MD.3 MCCK.OA.3 MCCK.OA.4 MCCK.G.4 MCCK.CC.4 MCCK.CC.5 MCCK.OA.4 MCCK.OA.5 MCCK.G.5 MCCK.MD.3 MCCK.CC.6 MCCK.OA.5 MCCK.G.6 MCCK.CC.7 MCCK.MD.3 MCCK.MD.3 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts and standards addressed in earlier units. All units include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades K-2 Key: CC = Counting and Cardinality, G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, OA = Operations and Algebraic Thinking. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
3. 3. Georgia Department of Education Common Core Georgia Performance Standards Kindergarten Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice (the context in which mathematics is learned) 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 1 Unit 2 Unit 3 Unit 4 Sophisticated Shapes Counting with Friends Comparing Numbers Investigating Addition and Subtraction Identify and describe shapes (squares, circles, Know number names and the count Work with numbers 11–19 to gain Understand addition as putting together triangles, rectangles, hexagons, cubes, cones, sequence foundations for place value. and adding to, and understand subtraction cylinders, and spheres). MCCK.CC.1 Count to 100 by ones and MCCK.NBT.1 Compose and decompose as taking apart and taking from. MCCK.G.1 Describe objects in the environment by tens. numbers from 11 to 19 into ten ones and some MCCK.OA.1 Represent addition and using names of shapes, and describe the relative MCCK.CC.2 Count forward beginning further ones, e.g., by using objects or subtraction with objects, fingers, mental positions of these objects using terms such as from a given number within the known drawings, and record each composition or images, drawings5, sounds (e.g., claps), acting above, below, beside, in front of, behind, and next sequence (instead of having to begin at 1). decomposition by a drawing or equation (e.g., out situations, verbal explanations, to. MCCK.CC.3 Write numbers from 0 to 18 = 10 + 8); understand that these numbers expressions, or equations. MCCK.G.2 Correctly name shapes regardless of 20. Represent a number of objects with a are composed of ten ones and one, two, three, MCCK.OA.2 Solve addition and subtraction their orientations or overall size. written numeral 0-20 (with 0 representing a four, five, six, seven, eight, or nine ones. word problems, and add and subtract within MCCK.G.3 Identify shapes as two-dimensional count of no objects). Know number names and the count 10, e.g., by using objects or drawings to (lying in a plane, “flat”) or three-dimensional Count to tell the number of objects. sequence. represent the problem. (“solid”). MCCK.CC.4 Understand the relationship MCCK.CC.3 Write numbers from 0 to 20. MCCK.OA.3 Decompose numbers less than Analyze, compare, create, and compose shapes. between numbers and quantities; connect Represent a number of objects with a written or equal to 10 into pairs in more than one way, MCCK.G.4 Analyze and compare two- and counting to cardinality. numeral 0-20 (with 0 representing a count of e.g., by using objects or drawings, and record three-dimensional shapes, in different sizes and a. When counting objects, say the no objects). each decomposition by a drawing or equation orientations, using informal language to describe number names in the standard order, Count to tell the number of objects. (e.g., 5 = 2 + 3 and 5 = 4 + 1). their similarities, differences, parts (e.g., number pairing each object with one and MCCK.CC.4 Understand the relationship MCCK.OA.4 For any number from 1 to 9, of sides and vertices/“corners”) and other only one number name and each between numbers and quantities; connect find the number that makes 10 when added to attributes (e.g., having sides of equal length). number name with one and only one counting to cardinality. the given number, e.g., by using objects or MCCK.G.5 Model shapes in the world by object. a. When counting objects, say the number drawings, and record the answer with a building shapes from components (e.g., sticks and b. Understand that the last number names in the standard order, pairing drawing or equation. clay balls) and drawing shapes. name said tells the number of each object with one and only one MCCK.OA.5 Fluently add and subtract MCCK.G.6 Compose simple shapes to form objects counted. The number of number name and each number name within 5. larger shapes. For example, “Can you join these objects is the same regardless of with one and only one object. two triangles with full sides touching to make a their arrangement or the order in MCCK.CC.5 Count to answer “how many?” rectangle?” which they were counted. questions about as many as 20 things arranged c. Understand that each successive in a line, a rectangular array, or a circle, or as number name refers to a quantity many as 10 things in a scattered configuration;5  Drawings need not show details, but should show the mathematics in the problem.  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
4. 4. Georgia Department of Education Classify objects and count the number of that is one larger. given a number from 1–20, count out that objects in each category. Classify objects and count the number of many objects. MCCK.MD.3 Classify objects into given objects in each category. Compare numbers. categories; count the numbers of objects in each MCCK.MD.3 Classify objects into given MCCK.CC.6 Identify whether the number of category and sort the categories by count.1  categories; count the numbers of objects in objects in one group is greater than, less than, each category and sort the categories by or equal to the number of objects in another count.2 group, e.g., by using matching and counting strategies.3 MCCK.CC.7 Compare two numbers between 1 and 10 presented as written numerals. Classify objects and count the number of objects in each category. MCCK.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.4 1 Limit category counts to be less than or equal to 10.2 Limit category counts to be less than or equal to 10.3 Include groups with up to ten objects.4 Limit category counts to be less than or equal to 10.  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
5. 5. Georgia Department of Education Common Core Georgia Performance Standards Kindergarten Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 5 Unit 6 Unit 7 Further Investigation of Addition and Measuring and Analyzing Data Show What We Know Subtraction Understand addition as putting together and adding to, and Describe and compare measurable attributes. ALL understand subtraction as taking apart and taking from. MCCK.MD.1 Describe measurable attributes of objects, such MCCK.OA.1 Represent addition and subtraction with objects, as length or weight. Describe several measurable attributes of a fingers, mental images, drawings6, sounds (e.g., claps), acting single object. out situations, verbal explanations, expressions, or equations. MCCK.MD.2 Directly compare two objects with a MCCK.OA.2 Solve addition and subtraction word problems, measurable attribute in common, to see which object has “more and add and subtract within 10, e.g., by using objects or of”/“less of” the attribute, and describe the difference. For drawings to represent the problem. example, directly compare the heights of two children and MCCK.OA.3 Decompose numbers less than or equal to 10 describe one child as taller/shorter. into pairs in more than one way, e.g., by using objects or Classify objects and count the number of objects in each drawings, and record each decomposition by a drawing or category. equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). MCCK.MD.3 Classify objects into given categories; count MCCK.OA.4 For any number from 1 to 9, find the number the numbers of objects in each category and sort the categories that makes 10 when added to the given number, e.g., by using by count.7  objects or drawings, and record the answer with a drawing or equation. MCCK.OA.5 Fluently add and subtract within 5.6  Drawings need not show details, but should show the mathematics in the problem. 7 Limit category counts to be less than or equal to 10.  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
6. 6. Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics First Grade – At a Glance Common Core Georgia Performance Standards: Curriculum Map Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Creating Developing Base Understanding Sorting, Understanding Operations and Show What We Know Routines Using Ten Number Shapes and Comparing Place Value Algebraic Thinking Data Sense Fractions and Ordering MCC1.NBT.1 MCC1.NBT.1 MCC1.G.1 MCC1.MD.1 MCC1.NBT.2 MCC1.OA.1 ALL MCC1.MD.4 MCC1.MD.4 MCC1.G.2 MCC1.MD.2 MCC1.NBT.3 MCC1.OA.2 MCC1.G.3 MCC1.MD.3 MCC1.NBT.4 MCC1.OA.3 MCC1.MD.4 MCC1.MD.4 MCC1.NBT.5 MCC1.OA.4 MCC1.NBT.6 MCC1.OA.5 MCC1.MD.4 MCC1.OA.6 MCC1.OA.7 MCC1.OA.8 MCC1.MD.4 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades K-2 Key: CC = Counting and Cardinality, G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, OA = Operations and Algebraic Thinking. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
7. 7. Georgia Department of Education Common Core Georgia Performance Standards First Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 1 Unit 2 Unit 3 Unit 4 Creating Routines Using Data Developing Base Ten Number Understanding Shapes and Sorting, Comparing and Ordering Sense Fractions Extend the counting sequence Extend the counting sequence Reason with shapes and their attributes. Measure lengths indirectly and by iterating MCC1.NBT.1 Count to 120, starting at any MCC1.NBT.1 Count to 120, starting at any MCC1.G.1 Distinguish between defining length units number less than 120. In this range, read and number less than 120. In this range, read and attributes (e.g., triangles are closed and three- MCC1.MD.1 Order three objects by length; write numerals and represent a number of write numerals and represent a number of sided) versus non-defining attributes (e.g., compare the lengths of two objects indirectly objects with a written numeral. objects with a written numeral. color, orientation, overall size); build and by using a third object. Represent and interpret data. Represent and interpret data. draw shapes to possess defining attributes. MCC1.MD.2 Express the length of an object MCC1.MD.4 Organize, represent, and MCC1.MD.4 Organize, represent, and MCC1.G.2 Compose two-dimensional as a whole number of length units, by laying interpret data with up to three categories; ask interpret data with up to three categories; ask shapes (rectangles, squares, trapezoids, multiple copies of a shorter object (the length and answer questions about the total number and answer questions about the total number triangles, half-circles, and quarter-circles) or unit) end to end; understand that the length of data points, how many in each category, of data points, how many in each category, three-dimensional shapes (cubes, right measurement of an object is the number of and how many more or less are in one and how many more or less are in one rectangular prisms, right circular cones, and same-size length units that span it with no category than in another. category than in another. right circular cylinders) to create a composite gaps or overlaps. Limit to contexts where the shape, and compose new shapes from the object being measured is spanned by a whole composite shape.1 number of length units with no gaps or MCC1.G.3 Partition circles and rectangles overlaps.  into two and four equal shares, describe the Tell and write time. shares using the words halves, fourths, and MCC1.MD.3 Tell and write time in hours quarters, and use the phrases half of, fourth of, and half-hours using analog and digital clocks. and quarter of. Describe the whole as two of, Represent and interpret data. or four of the shares. Understand for these MCC1.MD.4 Organize, represent, and examples that decomposing into more equal interpret data with up to three categories; ask shares creates smaller shares. and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.1  Students do not need to learn formal names such as “right rectangular prism.”  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
8. 8. Georgia Department of Education Common Core Georgia Performance Standards First Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 5 Unit 6 Unit 7 Understanding Place Value Operations and Algebraic Thinking Show What We Know Understand place value Represent and solve problems involving addition and ALL MCC1.NBT.2 Understand that the two digits of a two-digit subtraction. number represent amounts of tens and ones. Understand the MCC1.OA.1 Use addition and subtraction within 20 to solve following as special cases: word problems involving situations of adding to, taking from, a. 10 can be thought of as a bundle of ten ones — putting together, taking apart, and comparing, with unknowns called a “ten.” in all positions, e.g., by using objects, drawings, and equations b. The numbers from 11 to 19 are composed of a ten with a symbol for the unknown number to represent the and one, two, three, four, five, six, seven, eight, or problem.2 nine ones. MCC1.OA.2 Solve word problems that call for addition of c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer three whole numbers whose sum is less than or equal to 20, to one, two, three, four, five, six, seven, eight, or e.g., by using objects, drawings, and equations with a symbol nine tens (and 0 ones). for the unknown number to represent the problem. MCC1.NBT.3 Compare two two-digit numbers based on Understand and apply properties of operations and the meanings of the tens and ones digits, recording the results of relationship between addition and subtraction. comparisons with the symbols >, =, and <. MCC1.OA.3 Apply properties of operations as strategies to Use place value understanding and properties of operations add and subtract.3 to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also MCC1.NBT.4 Add within 100, including adding a two-digit known. (Commutative property of addition.) To add 2 + 6 + 4, number and a one-digit number, and adding a two-digit the second two numbers can be added to make a ten, so 2 + 6 + number and a multiple of 10, using concrete models or 4 = 2 + 10 = 12. (Associative property of addition.) drawings and strategies based on place value, properties of MCC1.OA.4 Understand subtraction as an unknown-addend operations, and/or the relationship between addition and problem. For example, subtract 10 – 8 by finding the number subtraction; relate the strategy to a written method and explain that makes 10 when added to 8. the reasoning used. Understand that in adding two-digit Add and subtract within 20 numbers, one adds tens and tens, ones and ones; and MCC1.OA.5 Relate counting to addition and subtraction sometimes it is necessary to compose a ten. (e.g., by counting on 2 to add 2). MCC1.NBT.5 Given a two-digit number, mentally find 10 MCC1.OA.6 Add and subtract within 20, demonstrating2  See Glossary, Table 1 3 Students need not use formal terms for these properties. Problems should be within 20.   Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
9. 9. Georgia Department of Educationmore or 10 less than the number, without having to count; fluency for addition and subtraction within 10. Use strategiesexplain the reasoning used. such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 +MCC1.NBT.6 Subtract multiples of 10 in the range 10-90 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 =from multiples of 10 in the range 10-90 (positive or zero 13 – 3 – 1 = 10 – 1 = 9); using the relationship betweendifferences), using concrete models or drawings and strategies addition and subtraction (e.g., knowing that 8 + 4 = 12, onebased on place value, properties of operations, and/or the knows 12 – 8 = 4); and creating equivalent but easier or knownrelationship between addition and subtraction; relate the sums (e.g., adding 6 + 7 by creating the known equivalent 6 +strategy to a written method and explain the reasoning used.  6 + 1 = 12 + 1 = 13).Represent and interpret data. Work with addition and subtraction equationsMCC1.MD.4 Organize, represent, and interpret data with up MCC1.OA.7 Understand the meaning of the equal sign, andto three categories; ask and answer questions about the total determine if equations involving addition and subtraction arenumber of data points, how many in each category, and how true or false. For example, which of the following equationsmany more or less are in one category than in another. are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. MCC1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = □ – 3, 6 + 6 = ∆.  Represent and interpret data. MCC1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
10. 10. Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics Second Grade – At a Glance Common Core Georgia Performance Standards: Curriculum Map Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Extending Becoming Fluent Understanding Applying Base Understanding Plane Developing Show What We Know Base Ten with Addition Measurement, Ten and Solid Figures Multiplication Understanding and Subtraction Length, and Time Understanding MCC2.NBT.1 MCC2.OA.1 MCC2.MD.1 MCC2.NBT.6 MCC2.G.1 MCC2.OA.3 ALL MCC2.NBT.2 MCC2.OA.2 MCC2.MD.2 MCC2.NBT.7 MCC2.G.2 MCC2.OA.4 MCC2.NBT.3 MCC2.NBT.5 MCC2.MD.3 MCC2.NBT.8 MCC2.G.3 MCC2.MD.10 MCC2.NBT.4 MCC2.MD.10 MCC2.MD.4 MCC2.NBT.9 MCC2.MD.10 MCC2.MD.4 MCC2.MD.5 MCC2.MD.8 MCC2.MD.10 MCC2.MD.6 MCC2.MD.10 MCC2.MD.7 MCC2.MD.9 MCC2.MD.10 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades K-2 Key: CC = Counting and Cardinality, G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, OA = Operations and Algebraic Thinking. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
11. 11. Georgia Department of Education Common Core Georgia Performance Standards Second Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically.2 Reason abstractly and quantitatively. 6 Attend to precision.3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure.4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 1 Unit 2 Unit 3 Unit 4Extending Base Ten Understanding Becoming Fluent with Addition and Understanding Measurement, Applying Base Ten Understanding Subtraction Length, and TimeUnderstand place value. Represent and solve problems involving Measure and estimate lengths in standard Use place value understanding andMCC2.NBT.1 Understand that the three addition and subtraction. units. properties of operations to add anddigits of a three-digit number represent MCC2.OA.1 Use addition and subtraction MCC2.MD.1 Measure the length of an object subtract.amounts of hundreds, tens, and ones; e.g., 706 within 100 to solve one- and two-step word by selecting and using appropriate tools such MCC2.NBT.6 Add up to four two-digitequals 7 hundreds, 0 tens, and 6 ones. problems involving situations of adding to, as rulers, yardsticks, meter sticks, and numbers using strategies based on place valueUnderstand the following as special cases: taking from, putting together, taking apart, and measuring tapes. and properties of operations. a. 100 can be thought of as a bundle of comparing, with unknowns in all positions, MCC2.MD.2 Measure the length of an object MCC2.NBT.7 Add and subtract within 1000, ten tens — called a “hundred.” e.g., by using drawings and equations with a twice, using length units of different lengths using concrete models or drawings and b. The numbers 100, 200, 300, 400, symbol for the unknown number to represent for the two measurements; strategies based on place value, properties of 500, 600, 700, 800, 900 refer to one, the problem.2 MCC2.MD.3 Estimate lengths using units of operations, and/or the relationship between two, three, four, five, six, seven, Add and subtract within 20. inches, feet, centimeters, and meters. addition and subtraction; relate the strategy to eight, or nine hundreds (and 0 tens MCC2.OA.2 Fluently add and subtract MCC2.MD.4 Measure to determine how a written method. Understand that in adding or and 0 ones). within 20 using mental strategies.3 By end of much longer one object is than another, subtracting three-digit numbers, one adds orMCC2.NBT.2 Count within 1000; skip-count Grade 2, know from memory all sums of two expressing the length difference in terms of a subtracts hundreds and hundreds, tens andby 5s, 10s, and 100s. one-digit numbers. standard length unit. tens, ones and ones; and sometimes it isMCC2.NBT.3 Read and write numbers to Use place value understanding and properties Relate addition and subtraction to length. necessary to compose or decompose tens or1000 using base-ten numerals, number names, of operations to add and subtract. MCC2.MD.5 Use addition and subtraction hundreds.and expanded form. MCC2.NBT.5 Fluently add and subtract within 100 to solve word problems involving MCC2.NBT.8 Mentally add 10 or 100 to aMCC2.NBT.4 Compare two three-digit within 100 using strategies based on place lengths that are given in the same units, e.g., given number 100–900, and mentally subtractnumbers based on meanings of the hundreds, value, properties of operations, and/or the by using drawings (such as drawings of rulers) 10 or 100 from a given number 100–900.tens, and ones digits, using >, =, and < relationship between addition and subtraction. and equations with a symbol for the unknown MCC2.NBT.9 Explain why addition andsymbols to record the results of comparisons. Represent and interpret data number to represent the problem. subtraction strategies work, using place valueRepresent and interpret data MCC2.MD.10 Draw a picture graph and a MCC2.MD.6 Represent whole numbers as and the properties of operations.6MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent lengths from 0 on a number line diagram with Represent and interpret databar graph (with single-unit scale) to represent a data set with up to four categories. Solve equally spaced points corresponding to the MCC2.MD.8 Solve word problems involvinga data set with up to four categories. Solve simple put-together, take-apart, and compare numbers 0, 1, 2, ..., and represent whole- dollar bills, quarters, dimes, nickels, and Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
12. 12. Georgia Department of Education simple put-together, take-apart, and compare problems4 using information presented in a bar number sums and differences within 100 on a pennies, using \$ and ¢ symbols appropriately. problems1 using information presented in a bar graph. number line diagram. Example: If you have 2 dimes and 3 pennies, graph. MCC2.MD.7 Tell and write time from analog how many cents do you have? and digital clocks to the nearest five minutes, MCC2.MD.10 Draw a picture graph and a using a.m. and p.m. bar graph (with single-unit scale) to represent MCC2.MD.8 Solve word problems involving a data set with up to four categories. Solve dollar bills, quarters, dimes, nickels, and simple put-together, take-apart, and compare pennies, using \$ and ¢ symbols appropriately. problems7 using information presented in a bar Example: If you have 2 dimes and 3 pennies, graph. how many cents do you have? Represent and interpret data MCC2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole- number units. Represent and interpret data MCC2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems5 using information presented in a bar graph.2 See Glossary, Table 1.3  See standard 1.OA.6 for a list of mental strategies. 6 Explanations may be supported by drawings or objects. 1  See Glossary, Table 1. 4  See Glossary, Table 1. 5  See Glossary, Table 1. 7  See Glossary, Table 1.  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
13. 13. Georgia Department of Education Common Core Georgia Performance Standards Second Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically.2 Reason abstractly and quantitatively. 6 Attend to precision.3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure.4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 5 Unit 6 Unit 7 Understanding Plane and Solid Figures Developing Multiplication Show What We KnowReason with shapes and their attributes. Work with equal groups of objects to gain foundations for ALLMCC2.G.1 Recognize and draw shapes having specified multiplication.attributes, such as a given number of angles or a given number of MCC2.OA.3 Determine whether a group of objects (up to 20)equal faces.8 Identify triangles, quadrilaterals, pentagons, has an odd or even number of members, e.g., by pairing objects orhexagons, and cubes. counting them by 2s; write an equation to express an even numberMCC2.G.2 Partition a rectangle into rows and columns of same- as a sum of two equal addends.size squares and count to find the total number of them. MCC2.OA.4 Use addition to find the total number of objectsMCC2.G.3 Partition circles and rectangles into two, three, or arranged in rectangular arrays with up to 5 rows and up to 5four equal shares, describe the shares using the words halves, columns; write an equation to express the total as a sum of equalthirds, half of, a third of, etc., and describe the whole as two addends.halves, three thirds, four fourths. Recognize that equal shares of Represent and interpret dataidentical wholes need not have the same shape  MCC2.MD.10 Draw a picture graph and a bar graph (with Represent and interpret data single-unit scale) to represent a data set with up to four categories.MCC2.MD.10 Draw a picture graph and a bar graph (with Solve simple put-together, take-apart, and compare problems10single-unit scale) to represent a data set with up to four categories. using information presented in a bar graph.Solve simple put-together, take-apart, and compare problems9using information presented in a bar graph.8 Sizes are compared directly or visually, not compared by measuring. 9  See Glossary, Table 1. 10  See Glossary, Table 1.  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
14. 14. Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics Third Grade – At a Glance Common Core Georgia Performance Standards: Curriculum Map Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Numbers and Operations and Operations and Operations Geometry Representing Measurement Show What Operations in Algebraic Algebraic and Algebraic and We Know Base Ten Thinking: the Thinking: the Thinking: Comparing Relationship Properties of Patterns in Fractions Between Multiplication and Addition and Multiplication and Division Multiplication Division MCC3.NBT.1 MCC3.OA.1 MCC3.OA.5 MCC3.OA.8 MCC3.G.1 MCC3.NF.1 MCC3.MD.1 ALL MCC3.NBT.2 MCC3.OA.2 MCC3.OA.6 MCC3.OA.9 MCC3.G.2 MCC3.NF.2 MCC3.MD.2 MCC3.NBT.3 MCC3.OA.3 MCC3.OA.7 MCC3.MD.3 MCC3.MD.3 MCC3.NF.3 MCC3.MD.3 MCC3.MD.3 MCC3.OA.4 MCC3.MD.3 MCC3.MD.4 MCC3.MD.4 MCC3.MD.3 MCC3.MD.4 MCC3.MD.4 MCC3.MD.3 MCC3.MD.4 MCC3.MD.5 MCC3.MD.4 MCC3.MD.7 MCC3.MD.4 MCC3.MD.6 MCC3.MD.8 MCC3.MD.7 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades 3-5 Key: G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, NF = Number and Operations, Fractions, OA = Operations and Algebraic Thinking. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
15. 15. Georgia Department of Education Common Core Georgia Performance Standards Third Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 1 Unit 2 Unit 3 Unit 4 Numbers and Operations in Base Operations and Algebraic Operations and Algebraic Operations and Algebraic Ten Thinking: the Relationship Between Thinking: the Properties of Thinking: Patterns in Addition and Multiplication and Division Multiplication and Division Multiplication Use place value understanding and Represent and solve problems involving Understand properties of multiplication Solve problems involving the four properties of operations to perform multi- multiplication and division. and the relationship between multiplication operations, and identify and explain digit arithmetic. MCC3.OA.1 Interpret products of whole and division. patterns in arithmetic. MCC3.NBT.1 Use place value understanding numbers, e.g., interpret 5 × 7 as the total MCC3.OA.5 Apply properties of operations MCC3.OA.8 Solve two-step word problems to round whole numbers to the nearest 10 or number of objects in 5 groups of 7 objects as strategies to multiply and divide.2 using the four operations. Represent these 100. each. For example, describe a context in which Examples: If 6 × 4 = 24 is known, then 4 × 6 = problems using equations with a letter MCC3.1.NBT.2 Fluently add and subtract a total number of objects can be expressed as 5 24 is also known. (Commutative property of standing for the unknown quantity. Assess the within 1000 using strategies and algorithms × 7. multiplication.) 3 × 5 × 2 can be found by 3 × reasonableness of answers using mental based on place value, properties of operations, MCC3.OA.2 Interpret whole-number 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, computation and estimation strategies and/or the relationship between addition and quotients of whole numbers, e.g., interpret 56 then 3 × 10 = 30. (Associative property of including rounding.3 subtraction. ÷ 8 as the number of objects in each share multiplication.) Knowing that 8 × 5 = 40 and 8 MCC3.OA.9 Identify arithmetic patterns MCC3.NBT.3 Multiply one-digit whole when 56 objects are partitioned equally into 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 (including patterns in the addition table or numbers by multiples of 10 in the range 10–90 shares, or as a number of shares when 56 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive multiplication table), and explain them using (e.g., 9 × 80, 5 × 60) using strategies based on objects are partitioned into equal shares of 8 property.) properties of operations. For example, observe place value and properties of operations. objects each. For example, describe a context MCC3.OA.6 Understand division as an that 4 times a number is always even, and Represent and interpret data. in which a number of shares or a number of unknown-factor problem. For example, find explain why 4 times a number can be MCC3.MD.3 Draw a scaled picture graph groups can be expressed as 56 ÷ 8. 32 ÷ 8 by finding the number that makes 32 decomposed into two equal addends. and a scaled bar graph to represent a data set MCC3.OA.3 Use multiplication and division when multiplied by 8. Represent and interpret data. with several categories. Solve one- and two- within 100 to solve word problems in Multiply and divide within 100 MCC3.MD.3 Draw a scaled picture graph step “how many more” and “how many less” situations involving equal groups, arrays, and MCC3.OA.7 Fluently multiply and divide and a scaled bar graph to represent a data set problems using information presented in measurement quantities, e.g., by using within 100, using strategies such as the with several categories. Solve one- and two- scaled bar graphs. For example, draw a bar drawings and equations with a symbol for the relationship between multiplication and step “how many more” and “how many less” graph in which each square in the bar graph unknown number to represent the problem.1 division (e.g., knowing that 8 × 5 = 40, one problems using information presented in1  See Glossary, Table 2. 2  Students need not use formal terms for these properties. 3  This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order where there are no parentheses to specify a particular order (Order of Operations).  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
16. 16. Georgia Department of Educationmight represent 5 pets. MCC3.OA.4 Determine the unknown whole knows 40 ÷ 5 = 8) or properties of operations. scaled bar graphs. For example, draw a barMCC3.MD.4 Generate measurement data by number in a multiplication or division By the end of Grade 3, know from memory all graph in which each square in the bar graphmeasuring lengths using rulers marked with equation relating three whole numbers. For products of two one-digit numbers. might represent 5 pets.halves and fourths of an inch. Show the data example, determine the unknown number that Represent and interpret data. MCC3.MD.4 Generate measurement data byby making a line plot, where the horizontal makes the equation true in each of the MCC3.MD.3 Draw a scaled picture graph measuring lengths using rulers marked withscale is marked off in appropriate units— equations 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?. × ? and a scaled bar graph to represent a data set halves and fourths of an inch. Show the datawhole numbers, halves, or quarters. = 48, 5 = □ ÷ 3, 6 × 6 = ?. with several categories. Solve one- and two- by making a line plot, where the horizontal Represent and interpret data. step “how many more” and “how many less” scale is marked off in appropriate units— MCC3.MD.3 Draw a scaled picture graph problems using information presented in whole numbers, halves, or quarters. and a scaled bar graph to represent a data set scaled bar graphs. For example, draw a bar Geometric Measurement: understand concepts with several categories. Solve one- and two- graph in which each square in the bar graph of area and relate area to multiplication and to step “how many more” and “how many less” might represent 5 pets. addition. problems using information presented in MCC3.MD.4 Generate measurement data by MCC3.MD.5 Recognize area as an attribute scaled bar graphs. For example, draw a bar measuring lengths using rulers marked with of plane figures and understand concepts of graph in which each square in the bar graph halves and fourths of an inch. Show the data area measurement. might represent 5 pets. by making a line plot, where the horizontal a. A square with side length 1 unit, MCC3.MD.4 Generate measurement data by scale is marked off in appropriate units— called “a unit square,” is said to measuring lengths using rulers marked with whole numbers, halves, or quarters. have “one square unit” of area, and halves and fourths of an inch. Show the data can be used to measure area. by making a line plot, where the horizontal b. A plane figure which can be covered scale is marked off in appropriate units— without gaps or overlaps by n unit whole numbers, halves, or quarters. squares is said to have an area of n square units. MCC3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). MCC3.MD.7 Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
17. 17. Georgia Department of Education mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Georgia Department of EducationDr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
18. 18. Georgia Department of Education Common Core Georgia Performance Standards Third Grade Common Core Georgia Performance Standards: Curriculum Map Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. 2 Reason abstractly and quantitatively. 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. 7 Look for and make use of structure. 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. Unit 5 Unit 6 Unit 7 Unit 8 Geometry Representing and Comparing Measurement Show What We Know Fractions Reason with shapes and their attributes. Develop understanding of fractions as Solve problems involving measurement and ALL MCC3.G.1 Understand that shapes in numbers. estimation of intervals of time, liquid different categories (e.g., rhombuses, MCC3.NF.1 Understand a fraction 1/b as the volumes, and masses of objects. rectangles, and others) may share attributes quantity formed by 1 part when a whole is MCC3.MD.1 Tell and write time to the (e.g., having four sides), and that the shared partitioned into b equal parts; understand a nearest minute and measure time intervals in attributes can define a larger category (e.g., fraction a/b as the quantity formed by a parts minutes. Solve word problems involving quadrilaterals). Recognize rhombuses, of size 1/b. addition and subtraction of time intervals in rectangles, and squares as examples of MCC3.NF.2 Understand a fraction as a minutes, e.g., by representing the problem on quadrilaterals, and draw examples of number on the number line; represent fractions a number line diagram. quadrilaterals that do not belong to any of on a number line diagram. MCC3.MD.2 Measure and estimate liquid these subcategories. a. Represent a fraction 1/b on a volumes and masses of objects using standard MCC3.G.2 Partition shapes into parts with number line diagram by defining the units of grams (g), kilograms (kg), and liters equal areas. Express the area of each part as a interval from 0 to 1 as the whole and (l).4 Add, subtract, multiply, or divide to solve unit fraction of the whole. For example, partitioning it into b equal parts. one-step word problems involving masses or partition a shape into 4 parts with equal area, Recognize that each part has size 1/b volumes that are given in the same units, e.g., and describe the area of each part as 1/4 of and that the endpoint of the part by using drawings (such as a beaker with a the area of the shape. based at 0 locates the number 1/b on measurement scale) to represent the problem.5  Represent and interpret data. the number line. Represent and interpret data. MCC3.MD.3 Draw a scaled picture graph b. Represent a fraction a/b on a MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set number line diagram by marking off and a scaled bar graph to represent a data set with several categories. Solve one- and two- a lengths 1/b from 0. Recognize that with several categories. Solve one- and two- step “how many more” and “how many less” the resulting interval has size a/b step “how many more” and “how many less” problems using information presented in and that its endpoint locates the problems using information presented in scaled bar graphs. For example, draw a bar number a/b on the number line. scaled bar graphs. For example, draw a bar graph in which each square in the bar graph MCC3.NF.3 Explain equivalence of fractions graph in which each square in the bar graph might represent 5 pets. in special cases, and compare fractions by might represent 5 pets. MCC3.MD.4 Generate measurement data by reasoning about their size. MCC3.MD.4 Generate measurement data by4  Excludes compound units such as cm3 and finding the geometric volume of a container. 5  Excludes multiplicative comparison problems (problems involving notions of “times as much”; see Glossary, Table 2).  Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
19. 19. Georgia Department of Educationmeasuring lengths using rulers marked with a. Understand two fractions as measuring lengths using rulers marked withhalves and fourths of an inch. Show the data equivalent (equal) if they are the halves and fourths of an inch. Show the databy making a line plot, where the horizontal same size, or the same point on a by making a line plot, where the horizontalscale is marked off in appropriate units— number line. scale is marked off in appropriate units—whole numbers, halves, or quarters. b. Recognize and generate simple whole numbers, halves, or quarters. equivalent fractions, e.g., 1/2 = 2/4, MCC3.MD.7 Relate area to the operations of 4/6 = 2/3). Explain why the fractions multiplication and addition. are equivalent, e.g., by using a a. Find the area of a rectangle with visual fraction model. whole-number side lengths by tiling c. Express whole numbers as fractions, it, and show that the area is the same and recognize fractions that are as would be found by multiplying equivalent to whole numbers. the side lengths. Examples: Express 3 in the form 3 = b. Multiply side lengths to find areas of 3/1; recognize that 6/1 = 6; locate rectangles with whole number side 4/4 and 1 at the same point of a lengths in the context of solving real number line diagram. world and mathematical problems, d. Compare two fractions with the and represent whole-number same numerator or the same products as rectangular areas in denominator by reasoning about mathematical reasoning. their size. Recognize that c. Use tiling to show in a concrete case comparisons are valid only when the that the area of a rectangle with two fractions refer to the same whole-number side lengths a and b whole. Record the results of + c is the sum of a × b and a × c. comparisons with the symbols >, =, Use area models to represent the or <, and justify the conclusions, distributive property in e.g., by using a visual fraction mathematical reasoning. model.  d. Recognize area as additive. Find Represent and interpret data. areas of rectilinear figures by MCC3.MD.3 Draw a scaled picture graph decomposing them into non- and a scaled bar graph to represent a data set overlapping rectangles and adding with several categories. Solve one- and two- the areas of the non-overlapping step “how many more” and “how many less” parts, applying this technique to problems using information presented in solve real world problems. scaled bar graphs. For example, draw a bar Geometric measurement: recognize graph in which each square in the bar graph perimeter as an attribute of plane figures might represent 5 pets. and distinguish between linear and area MCC3.MD.4 Generate measurement data by measures. measuring lengths using rulers marked with MCC3.MD.8 Solve real world and halves and fourths of an inch. Show the data mathematical problems involving perimeters by making a line plot, where the horizontal of polygons, including finding the perimeter scale is marked off in appropriate units— given the side lengths, finding an unknown whole numbers, halves, or quarters. side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved
20. 20. Georgia Department of Education Common Core Georgia Performance Standards Elementary School Mathematics Fourth Grade – At a Glance Common Core Georgia Performance Standards: Curriculum Map Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Whole Fraction Adding and Multiplying Fractions and Geometry Measurement Show What WeNumbers, Place Equivalents Subtracting and Dividing Decimals Know Value and Fractions Fractions Rounding in Computation MCC4.NBT.1 MCC4.NF.1 MCC4.NF.3 MCC4.NF.4 MCC4.NF.5 MCC4.G.1 MCC4.MD.1 ALL MCC4.NBT.2 MCC4.NF.2 MCC4.NF.6 MCC4.G.2 MCC4.MD.2 MCC4.NBT.3 MCC4.OA.1 MCC4.NF.7 MCC4.G.3 MCC4.MD.3 MCC4.NBT.4 MCC4.OA.4 MCC4.MD.4 MCC4.NBT.5 MCC4.MD.5 MCC4.NBT.6 MCC4.MD.6 MCC4.OA.1 MCC4.MD.7 MCC4.OA.2 MCC4.OA.3 MCC4.OA.4 MCC4.OA.5 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain.NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.Grades 3-5 Key: G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, NF = Number and Operations, Fractions, OA = Operations and Algebraic Thinking. Georgia Department of Education Dr. John D. Barge, State School Superintendent September 9, 2011 All Rights Reserved