Standards in this Framework
Standard  Lessons 

K.CC.A.1a
Count to 100 by ones and by tens. 

K.CC.A.1b
Count backwards by ones from 20. 

K.CC.A.2
Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 

K.CC.A.3
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.B.4
Understand the relationship between numbers and quantities; connect counting to cardinality. 

K.CC.B.4a
Use onetoone correspondence when counting objects. 

K.CC.B.4b
Understand that the last number name said, tells the number of objects counted regardless of their arrangement. 

K.CC.B.4c
Understand that each successive number name refers to a quantity that is one more, and each previous number name refers to a quantity that is one less. 

K.CC.B.5
When counting: 

K.CC.B.5a
Answer the question "how many?" by counting up to 20 objects arranged in a line, a rectangular array, a circle, or as many as 10 objects in a scattered configuration. 

K.CC.B.5b
Given a number from 120, count out that many objects. 

K.CC.C.6
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.C.7
Compare two numbers between 1 and 10 presented as written numerals. 

K.OA.D1
Model situations that involve representing addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. 

K.OA.D2
Solve word problems using objects and drawings to find sums up to 10 and differences within 10. 

K.OA.D3
Decompose numbers less than or equal to 10 in more than one way. 

K.OA.D4
For any number from 1 to 9, find the number that makes 10 when added to the given number. 

K.OA.D5
Fluently add and subtract within 5. 

K.NBT.E.1
Describe, explore, and explain how the counting numbers 11 to 19 is: 

K.NBT.E.1a
Composed of ten ones and more ones. 

K.NBT.E.1b
Decomposed into ten ones and more ones. 

K.MD.F.1
Describe several measurable attributes of one or more objects. 

K.MD.F.2
Make direct comparisons of the length, capacity, weight, and temperature of objects, and recognize which object is shorter/longer, taller, lighter/heavier, warmer/cooler, and which holds more/less. 

K.MD.G.3
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.MD.G.4
Identify U.S. coins by name (pennies, nickels, dimes, and quarters). 

K.G.H.1
Describe objects in the environment using the 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.H.2
Correctly name shapes regardless of their orientations or overall size. 

K.G.H.3
Identify shapes as twodimensional or threedimensional. 

K.G.I.4
Analyze and compare two and threedimensional shapes, using informal language to describe their similarities, differences, and attributes. 

K.G.I.5
Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. 

K.G.I.6
Use simple shapes to compose squares, rectangles, and hexagons. 

1.OA.A.1
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, by using objects, drawings, or equations with a symbol for the unknown number to represent the problem. 

1.OA.A.2
Solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, by using objects, drawings, or equations. 

1.OA.B.3
Apply commutative and associative properties of addition as strategies to add and subtract. 

1.OA.B.4
Understand subtraction as an unknownaddend problem. 

1.OA.C.5
Relate counting to addition and subtraction using strategies, such as, by counting on and back. 

1.OA.C.6
Add and subtract within 20, demonstrating fluency in addition and subtraction within 10. Use strategies such as counting on; making ten using the relationship between addition and subtraction. 

1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. 

1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. 

1.NBT.E.1
Extend the number sequences to 120. In this range: 

1.NBT.E.1a
Count forward and backward, starting at any number less than 120. 

1.NBT.E.1b
Read numerals. 

1.NBT.E.1c
Write numerals. 

1.NBT.E.1d
Represent a number of objects with a written numeral. 

1.NBT.F.2
Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: 

1.NBT.F.2a
10 can be thought of as a bundle of ten ones — called a “ten”. 

1.NBT.F.2b
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 

1.NBT.F.2c
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 

1.NBT.F.3
Compare pairs of twodigit numbers based on the values of the tens digit and the ones digits, recording the results of comparisons with the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and <. 

1.NBT.G.4
Add within 100, using concrete models or drawings and strategies based on place value: 

1.NBT.G.4a
Including adding a twodigit number and a onedigit number. 

1.NBT.G.4b
Adding a twodigit number and a multiple of 10. 

1.NBT.G.4c
Understand that in adding twodigit numbers, adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 

1.NBT.G.4d
Relate the strategy to a written method and explain the reasoning used. 

1.NBT.G.5
Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 

1.NBT.G.6
Subtract multiples of 10 from an equal or larger multiple of 10 both in the range 1090, using concrete models, drawings, and strategies based on place value. 

1.MD.H.1
Order three objects by length; compare the lengths of two objects indirectly by using a third object. 

1.MD.H.2
Use nonstandard units to show the length of an object as the number of same size units of length with no gaps or overlaps. 

1.MD.I.3a
Tell and write time in hours and halfhours using analog and digital clocks. 

1.MD.I.3b
Identify U.S. coins by value (pennies, nickels, dimes, quarters). 

1.MD.J.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. 

1.G.K.1
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.K.2
Use twodimensional shapes (rectangles, squares, trapezoids, rhombuses, and triangles) or threedimensional shapes (cubes, rectangular prisms, cones, and cylinders) to create a composite figure, and create new figures from the composite figure. 

1.G.K.3
Partition circles and rectangles into two and four equal shares and: 

1.G.K.3a
Describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. 

1.G.K.3b
Describe the whole as two of, or four of the shares. 

1.G.K.3c
Recognize that decomposing into more equal shares creates smaller shares. 

2.OA.A.1
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, by using drawings and equations with a symbol for the unknown number to represent the problem. 

2.OA.B.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know automatically all sums of two onedigit numbers based on strategies. 

2.OA.C.3
Determine whether a group (up to 20) has an odd or even number of objects (i.e. by pairing objects or counting them by 2s). 

2.OA.C.3a
If the number of objects is even, then write an equation to express this as the sum of two equal addends. 

2.OA.C.3b
If the number of objects group is odd, then write an equation to express this as a sum of a near double (double plus 1). 

2.OA.C.4
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.D.1
Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; and demonstrate that cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 

2.NBT.D.1a
100 can be thought of as a bundle of ten tens — called a “hundred.” 

2.NBT.D.1b
The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 

2.NBT.D.1c
Threedigit numbers can be decomposed in multiple ways (e.g. 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.) 

2.NBT.D.2
Skipcount by 10s and 100s within 1000 starting at any given number. 

2.NBT.D.3
Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 

2.NBT.D.4
Compare pairs of threedigit numbers based on meanings of the hundreds, tens, and ones digits, using the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and < to record the results of comparisons. 

2.NBT.E.5
Add and subtract within 100 using strategies based on place value, properties of addition, and/or the relationship between addition and subtraction. 

2.NBT.E.6
Add up to four twodigit numbers using strategies based on place value and/or properties of addition. 

2.NBT.E.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of addition, and/or the relationship between addition and subtraction: 

2.NBT.E.7a
Relate the strategy to a written method and explain the reasoning used. 

2.NBT.E.7b
Understand that in adding or subtracting threedigit numbers, add or subtract hundreds and hundreds, tens and tens, ones and ones. 

2.NBT.E.7c
Understand that sometimes it is necessary to compose or decompose tens or hundreds. 

2.NBT.E.8
Mentally: 

2.NBT.E.8a
Add 10 or 100 to a given number 100900. 

2.NBT.E.8b
Subtract 10 or 100 from a given number 100900. 

2.NBT.E.9
Explain why addition and subtraction strategies work, using place value and the properties of addition. (Explanations may be supported by drawings, objects, or written form.) 

2.MD.F.1
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 

2.MD.F.2
Measure the same object or distance using a standard unit of one length and then a standard unit of a different length. Explain how the two measurements relate to the size of the unit chosen. 

2.MD.F.3
Estimate lengths using units of inches, feet, centimeters, and meters. 

2.MD.F.4
Measure in standard length units to determine how much longer one object is than another. 

2.MD.G.5
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units. 

2.MD.G.6
Use a number line diagram with equally spaced points to: 

2.MD.G.6a
Represent wholenumber sums and differences within 100 on a number line diagram. 

2.MD.G.6b
Locate the multiple of 10 before and after a given number within 100. 

2.MD.H.7
Tell and write time from analog and digital clocks in five minute increments using a.m. and p.m. 

2.MD.H.8
Solve word problems up to $10 involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. 

2.MD.I.9
Generate measurement data based on whole units and show data by making a line plot. 

2.MD.I.10
Use data to: 

2.MD.I.10a
Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. 

2.MD.I.10b
Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. 

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

2.G.J.2
Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 

2.G.J.3
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. 

2.G.J.3a
Describing the shares using the words halves, thirds, half of, a third of, etc. 

2.G.J.3b
Describing the whole as two halves, three thirds, four fourths. 

2.G.J.3c
Recognizing that equal shares of identical wholes need not have the same shape. 

3.OA.A.1
Represent the concept of multiplication of whole numbers using models including, but not limited to, equalsized groups ("groups of"), arrays, area models, repeated addition, and equal "jumps" on a number line. 

3.OA.A.2
Represent the concept of division of whole numbers (resulting in whole number quotients) using models including, but not limited to, partitioning, repeated subtraction, sharing, and inverse of multiplication. 

3.OA.A.3
Solve multiplication and division word problems within 100 using appropriate modeling strategies and equations. 

3.OA.A.4
Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. (Students need not know formal terms.) 

3.OA.B.5
Apply properties of multiplication as strategies to multiply and divide. (Students need not use formal terms for these properties.) 

3.OA.B.6
Understand division as an unknownfactor problem. 

3.OA.C.7
Fluently multiply and divide with factors 1  10 using mental strategies. By the end of Grade 3, know automatically all products of onedigit factors based on strategies. 

3.OA.D.8
Solve twostep word problems (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order. 

3.OA.D.8a
Represent these problems using equations with a symbol standing for the unknown quantity. 

3.OA.D.8b
Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 

3.OA.D.9
Identify arithmetic patterns and explain the relationships using properties of operations. 

3.NBT.E.1
Use place value understanding to round whole numbers to the nearest 10 or 100. 

3.NBT.E.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of addition, and/or the relationship between addition and subtraction. 

3.NBT.E.3
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 multiplication. 

3.NF.F.1
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. 

3.NF.F.2
Understand and represent fractions on a number line diagram. 

3.NF.F.2a
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. 

3.NF.F.2b
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. 

3.NF.F.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 

3.NF.F.3a
Understand two fractions as equivalent if they are the same size, or the same point on a number line. 

3.NF.F.3b
Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. 

3.NF.F.3c
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 

3.NF.F.3d
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. 

3.MD.G.1
Use analog clocks to 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. 

3.MD.G.2
Measure and estimate liquid volumes and masses of objects using 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. (Excludes multiplicative comparison problems involving notions of “times as much.”) 

3.MD.H.3
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 graphs. 

3.MD.H.4
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Use the data to create a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. 

3.MD.I.5
Understand area as an attribute of plane figures and understand concepts of area measurement, such as square units without gaps or overlaps. 

3.MD.I.6
Measure areas by counting unit squares (square cm, square m, square in., square ft, and improvised units). 

3.MD.I.7
Relate area to the operations of multiplication and addition. 

3.MD.I.7a
Find the area of a rectangle with wholenumber side lengths (dimensions) by multiplying them. Show that this area is the same as when counting unit squares. 

3.MD.I.7b
Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. 

3.MD.I.7c
Use area models to represent the distributive property in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. 

3.MD.J.8
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. 

3.G.K.1
Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 

3.G.K.2
Partition rectangles, regular polygons, and circles into parts with equal areas. Express the area of each part as a unit fraction of the whole. 

4.OA.A.1
Intentionally removed 

4.OA.A.2
Multiply or divide to solve word problems involving multiplicative comparison, by using strategies including, but not limited to, drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 

4.OA.A.3
Solve multistep word problems posed with whole numbers, including problems in which remainders must be interpreted. 

4.OA.A.3a
Represent these problems using equations with a letter standing for the unknown quantity. 

4.OA.A.3b
Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 

4.OA.B.4
Demonstrate an understanding of factors and multiples. 

4.OA.B.4a
Find all factor pairs for a whole number in the range 1100. 

4.OA.B.4b
Recognize that a whole number is a multiple of each of its factors. 

4.OA.B.4c
Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. 

4.OA.B.4d
Determine whether a given whole number in the range 1100 is prime or composite. 

4.OA.C.5
Given a pattern, explain a rule that the pattern follows and extend the pattern. 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. 

4.NBT.D.1
Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. 

4.NBT.D.2
Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols. 

4.NBT.D.3
Use place value understanding to round multidigit whole numbers to any place. 

4.NBT.E.4
Add and subtract multidigit whole numbers using place value strategies including the standard algorithm. 

4.NBT.E.5
Use strategies based on place value and the properties of multiplication to: 

4.NBT.E.5a
Multiply a whole number of up to four digits by a onedigit whole number. 

4.NBT.E.5b
Multiply a pair of twodigit numbers. 

4.NBT.E.5c
Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models. 

4.NBT.E.6
Use strategies based on place value, the properties of multiplication, and/or the relationship between multiplication and division to find quotients and remainders with up to fourdigit dividends and onedigit divisors. Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models. 

4.NF.F.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention 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. 

4.NF.F.2
Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. 

4.NF.F.2a
Recognize that comparisons are valid only when the two fractions refer to the same whole. 

4.NF.F.2b
Record the results of comparisons with symbols >, =, or <. 

4.NF.F.2c
Justify the conclusions by using a visual fraction model. 

4.NF.G.3
Understand a fraction a/b with a > 1 as a sum of unit fractions (1/b). 

4.NF.G.3a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 

4.NF.G.3b
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions by using a visual fraction model. 

4.NF.G.3c
Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction, and/or by using properties of addition and the relationship between addition and subtraction. 

4.NF.G.3d
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. 

4.NF.G.4
Apply and extend an understanding of multiplication by multiplying a whole number and a fraction. 

4.NF.G.4a
Understand a fraction a/b as a multiple of 1/b. 

4.NF.G.4b
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. 

4.NF.G.4c
Solve realworld problems involving multiplication of a fraction by a whole number, using visual fraction models and equations to represent the problem. 

4.NF.H.5
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 

4.NF.H.6
Use decimal notation for fractions with denominators 10 or 100. 

4.NF.H.7
Compare and order decimal numbers to hundredths and justify by using concrete and visual models. Record the results of comparisons with the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and <. 

4.MD.I.1
Know relative sizes of measurement units within one system of units including, but not limited to, km, m, cm; kg, g; lb., oz.; l L, ml; hr., min, sec; ft, in., gal., qt. pt., c., . Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. 

4.MD.I.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. Assessment Boundary: Use denominators of 2, 4, 8 and decimals up to hundredths. 

4.MD.I.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 

4.MD.J.4
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. 

4.MD.K.5
Regarding angles: 

4.MD.K.5a
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 

4.MD.K.5b
Understand concepts of angle measurement. An angle is measured with reference to a circle with its center at the common endpoint of the rays. 

4.MD.K.6
Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 

4.MD.K.7
Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. 

4.G.L.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 

4.G.L.2
Classify twodimensional 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. 

4.G.L.3
Identify linesymmetric figures. Recognize and draw lines of symmetry for twodimensional figures. 

5.OA.A.1
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 

5.OA.A.2
Write simple expressions requiring parentheses that record calculations with numbers, and interpret numerical expressions without evaluating them. 

5.OA.B.3
Generate two numerical patterns with each pattern having its own rule. Explain informally the relationship(s) between corresponding terms in the two patterns. 

5.OA.B.3a
Form ordered pairs consisting of corresponding terms from the two patterns. 

5.OA.B.3b
Graph the ordered pairs on a coordinate plane. 

5.NBT.C.1
Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 

5.NBT.C.2
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. 

5.NBT.C.3
Read, write, and compare decimals to thousandths. 

5.NBT.C.3a
Read and write decimals to thousandths using baseten numerals, number names, and expanded form. 

5.NBT.C.3b
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols. 

5.NBT.C.4
Use place value understanding to round decimals to any place to a given place. Assessment Boundary: Limit place value to the thousandths. 

5.NBT.D.5
Multiply multidigit whole numbers using place value strategies including the standard algorithm. 

5.NBT.D.6
Find wholenumber quotients with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of multiplication, and/or the relationship between multiplication and division, including the standard algorithm. Use appropriate models to Illustrate and explain the calculation, such as equations, rectangular arrays, and/or area models. Assessment Boundary: The standard algorithm for division will not be assessed. 

5.NBT.D.7
Add, subtract, multiply, and divide decimals to hundredths 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. 

5.NF.E.1
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 

5.NF.E.2
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. 

5.NF.F.3
Extend the concept of multiplication to multiply a fraction or whole number by a fraction. 

5.NF.F.4
Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths. 

5.NF.F.4a
Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product. 

5.NF.F.4b
Interpret multiplication in which both factors are fractions less than one and compute the product. 

5.NF.F.4c
Justify the reasonableness of a product when multiplying with fractions. 

5.NF.F.5
Estimate the size of the product based on the size of the two factors. 

5.NF.F.5a
Explain why multiplying a given number by a number greater than 1 (improper fractions, mixed numbers, whole numbers) results in a product larger than the given number. 

5.NF.F.5b
Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. 

5.NF.F.5c
Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1. 

5.NF.F.5d
Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. 

5.NF.F.6
Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. 

5.NF.F.7
Interpret division of a unit fraction by a nonzero whole number and compute the quotient. 

5.NF.F.7a
Interpret division of a whole number by a unit fraction and compute the quotient. 

5.NF.F.7b
Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. 

5.NF.F.7c
Solve multistep real world problems by converting among differentsized standard measurement units within a given measurement system. 

5.MD.G.1
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions to solve problems involving information presented in line plots. 

5.MD.H.2
Recognize volume as an attribute of threedimensional figures and understand concepts of volume measurement such as "unit cube" and a volume of n cubic units. 

5.MD.I.3
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 

5.MD.I.4
Relate volume to the operations of multiplication and solve real world and mathematical problems involving volume. 

5.MD.I.5
Find the volume of a right rectangular prism with whole number dimensions by multiplying them. Show that this volume is the same as when counting unit cubes. 

5.MD.I.5a
Find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems given the formulas V =(l)(w)(h) and V = (B)(h) for rectangular prisms. 

5.MD.I.5b
Find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems given the formulas V =(l)(w)(h) and V = (B)(h) for rectangular prisms. 

5.G.J.1
Understand a coordinate system. 

5.G.J.1a
The x and y axes are perpendicular number lines that intersect at 0 (the origin). 

5.G.J.1b
Any point on the coordinate plane can be represented by its coordinates. 

5.G.J.1c
The first number in an ordered pair is the xcoordinate and represents the horizontal distance from the origin. 

5.G.J.1d
The second number in an ordered pair is the ycoordinate and represents the vertical distance from the origin. 

5.G.J.2
Plot and interpret points in the first quadrant of the coordinate plane to represent realworld and mathematical situations. 

5.G.K.3
Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. Assessment Boundary: Use polygons only. 

5.G.K.4
Classify polygons in a hierarchy based on properties. 
