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K.CC.1 
K 
Counting & Cardinality 
Know number names and the count sequence. Count to 100 by ones and by tens. 


K.CC.2 
K 
Counting & Cardinality 
Know number names and the count sequence. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 


K.CC.3 
K 
Counting & Cardinality 
Know number names and the count sequence. Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). 


K.CC.4 
K 
Counting & Cardinality 
Count to tell the number of objects. Understand the relationship between numbers and quantities; connect counting to cardinality. 


K.CC.4a 
K 
Counting & Cardinality 
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. 


K.CC.4b 
K 
Counting & Cardinality 
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. 


K.CC.4c 
K 
Counting & Cardinality 
Understand that each successive number name refers to a quantity that is one larger. 


K.CC.5 
K 
Counting & Cardinality 
Count to tell the number of objects. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. 


K.CC.6 
K 
Counting & Cardinality 
Compare numbers. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.). 


K.CC.7 
K 
Counting & Cardinality 
Compare numbers. Compare two numbers between 1 and 10 presented as written numerals. 


K.OA.1 
K 
Operations & Algebraic Thinking 
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. 


K.OA.2 
K 
Operations & Algebraic Thinking 
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. 


K.OA.3 
K 
Operations & Algebraic Thinking 
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). 


K.OA.4 
K 
Operations & Algebraic Thinking 
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. 


K.OA.5 
K 
Operations & Algebraic Thinking 
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Fluently add and subtract within 5. 


K.NBT.1 
K 
Number & Operations in Base Ten 
Work with numbers 1119 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. 


K.MD.1 
K 
Measurement & Data 
Describe and compare measurable attributes. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 


K.MD.2 
K 
Measurement & Data 
Describe and compare measurable attributes. Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. 


K.MD.3 
K 
Measurement & Data 
Classify objects and count the number of objects in each category. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.). 


K.G.1 
K 
Geometry 
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. 


K.G.2 
K 
Geometry 
Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Correctly name shapes regardless of their orientations or overall size. 


K.G.3 
K 
Geometry 
Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Identify shapes as twodimensional (lying in a plane, flat) or threedimensional (solid). 


K.G.4 
K 
Geometry 
Analyze, compare, create, and compose shapes. Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners) and other attributes (e.g., having sides of equal length). 


K.G.5 
K 
Geometry 
Analyze, compare, create, and compose shapes. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. 


K.G.6 
K 
Geometry 
Analyze, compare, create, and compose shapes. Compose simple shapes to form larger shapes. For example, can you join these two triangles with full sides touching to make a rectangle?. 


1.OA.1 
1 
Operations & Algebraic Thinking 
Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 


1.OA.2 
1 
Operations & Algebraic Thinking 
Represent and solve problems involving addition and subtraction. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 


1.OA.3 
1 
Operations & Algebraic Thinking 
Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.). 


1.OA.4 
1 
Operations & Algebraic Thinking 
Understand and apply properties of operations and the relationship between addition and subtraction. Understand subtraction as an unknownaddend problem. For example, subtract 10  8 by finding the number that makes 10 when added to 8. 


1.OA.5 
1 
Operations & Algebraic Thinking 
Add and subtract within 20. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 


1.OA.6 
1 
Operations & Algebraic Thinking 
Add and subtract within 20. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13  4 = 13  3  1 = 10  1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12  8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 


1.OA.7 
1 
Operations & Algebraic Thinking 
Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8  1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 


1.OA.8 
1 
Operations & Algebraic Thinking 
Work with addition and subtraction equations. Determine the unknown whole number in an addition or subtraction equation relating 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 = _. 


1.NBT.1 
1 
Number & Operations in Base Ten 
Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 


1.NBT.2 
1 
Number & Operations in Base Ten 
Understand place value. Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases:. 


1.NBT.3 
1 
Number & Operations in Base Ten 
Understand place value. Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 


1.NBT.4 
1 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 


1.NBT.5 
1 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 


1.NBT.6 
1 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 


1.MD.1 
1 
Measurement & Data 
Measure lengths indirectly and by iterating length units. Order three objects by length; compare the lengths of two objects indirectly by using a third object. 


1.MD.2 
1 
Measurement & Data 
Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 


1.MD.3 
1 
Measurement & Data 
Tell and write time. Tell and write time in hours and halfhours using analog and digital clocks. 


1.MD.4 
1 
Measurement & Data 
Represent and interpret data. 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. 


1.G.1 
1 
Geometry 
Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes. 


1.G.2 
1 
Geometry 
Reason with shapes and their attributes. Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as right rectangular prism.). 


1.G.3 
1 
Geometry 
Reason with shapes and their attributes. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 


2.OA.1 
2 
Operations & Algebraic Thinking 
Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 


2.OA.2 
2 
Operations & Algebraic Thinking 
Add and subtract within 20. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. 


2.OA.3 
2 
Operations & Algebraic Thinking 
Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 


2.OA.4 
2 
Operations & Algebraic Thinking 
Work with equal groups of objects to gain foundations for multiplication. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 


2.NBT.1 
2 
Number & Operations in Base Ten 
Understand place value. Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:. 


2.NBT.2 
2 
Number & Operations in Base Ten 
Understand place value. Count within 1000; skipcount by 5s, 10s, and 100s. 


2.NBT.3 
2 
Number & Operations in Base Ten 
Understand place value. Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 


2.NBT.4 
2 
Number & Operations in Base Ten 
Understand place value. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 


2.NBT.5 
2 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 


2.NBT.6 
2 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Add up to four twodigit numbers using strategies based on place value and properties of operations. 


2.NBT.7 
2 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 


2.NBT.8 
2 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100900. 


2.NBT.9 
2 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to add and subtract. Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.). 


2.MD.1 
2 
Measurement & Data 
Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 


2.MD.2 
2 
Measurement & Data 
Measure and estimate lengths in standard units. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 


2.MD.3 
2 
Measurement & Data 
Measure and estimate lengths in standard units. Estimate lengths using units of inches, feet, centimeters, and meters. 


2.MD.4 
2 
Measurement & Data 
Measure and estimate lengths in standard units. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 


2.MD.5 
2 
Measurement & Data 
Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 


2.MD.6 
2 
Measurement & Data 
Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, â€¦ , and represent wholenumber sums and differences within 100 on a number line diagram. 


2.MD.7 
2 
Measurement & Data 
Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 


2.MD.8 
2 
Measurement & Data 
Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and Â¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?. 


2.MD.9 
2 
Measurement & Data 
Represent and interpret data. 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 wholenumber units. 


2.MD.10 
2 
Measurement & Data 
Represent and interpret data. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. 


2.G.1 
2 
Geometry 
Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.). 


2.G.2 
2 
Geometry 
Reason with shapes and their attributes. Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 


2.G.3 
2 
Geometry 
Reason with shapes and their attributes. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 


3.OA.1 
3 
Operations & Algebraic Thinking 
Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 


3.OA.2 
3 
Operations & Algebraic Thinking 
Represent and solve problems involving multiplication and division. Interpret wholenumber quotients of whole numbers, e.g., interpret 56 Ã· 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 Ã· 8. 


3.OA.3 
3 
Operations & Algebraic Thinking 
Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 


3.OA.4 
3 
Operations & Algebraic Thinking 
Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __Ã· 3, 6 × 6 = ?. 


3.OA.5 
3 
Operations & Algebraic Thinking 
Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.). 


3.OA.6 
3 
Operations & Algebraic Thinking 
Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknownfactor problem. For example, divide 32 Ã· 8 by finding the number that makes 32 when multiplied by 8. 


3.OA.7 
3 
Operations & Algebraic Thinking 
Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 Ã· 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of onedigit numbers. 


3.OA.8 
3 
Operations & Algebraic Thinking 
Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).). 


3.OA.9 
3 
Operations & Algebraic Thinking 
Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 


3.NBT.1 
3 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to perform multidigit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100. 


3.NBT.2 
3 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to perform multidigit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.). 


3.NBT.3 
3 
Number & Operations in Base Ten 
Use place value understanding and properties of operations to perform multidigit arithmetic. Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.). 


3.NF.1 
3 
Number & Operations  Fractions 
Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.2 
3 
Number & Operations  Fractions 
Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.2a 
3 
Number & Operations  Fractions 
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.2b 
3 
Number & Operations  Fractions 
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.3 
3 
Number & Operations  Fractions 
Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.3a 
3 
Number & Operations  Fractions 
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.3b 
3 
Number & Operations  Fractions 
Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.3c 
3 
Number & Operations  Fractions 
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.NF.3d 
3 
Number & Operations  Fractions 
Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.). 


3.MD.1 
3 
Measurement & Data 
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 


3.MD.2 
3 
Measurement & Data 
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of times as much.). 


3.MD.3 
3 
Measurement & Data 
Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 


3.MD.4 
3 
Measurement & Data 
Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. 


3.MD.5 
3 
Measurement & Data 
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. 


3.MD.6 
3 
Measurement & Data 
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 


3.MD.7 
3 
Measurement & Data 
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition. 

