Fifth Grade Math
Standards
Book 
MAT05 "I can ... statements" 

(OA)  (NBT)  (NF)  (MD)  (G)  
Operations Algebraic Thinking 
Number Operations Base Ten 
Number Operations Fraction 
Measurement Data 
Geometry 

Prioritized Standards  
Kindergarten Math  First Grade Math  Second Grade Math 
Prioritized 
MAT05.G.02
5^{th} Grade (MAT) Targeted Standard
MAT05.G.02 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. Interpret coordinate values of points in the context of the situation.  
MAT05.G.04  
MAT05.MD
Narrative for the (MD) Measurement and DataIn Grade 5, students extend their measurement abilities from Grade 4 to express measurements in larger or smaller units within a measurement system. The major emphasis for measurement in Grade 5 is volume. Volume not only introduces a third dimension and thus a significant challenge to students’ spatial structuring, but also complexity in the nature of the materials measured. As students work with data in Grades K–5, they build foundations for their study of statistics and probability in Grades 6 and beyond, and they strengthen and apply what they are learning in arithmetic. Kindergarten work with data uses counting and order relations. In Grades 3–5, work with data is closely related to the number line, fraction concepts, fraction arithmetic, and solving problems that involve the four operations. By the end of Grade 5, students should be comfortable making line plots for measurement data and analyzing data shown in the form of a line plot. As in earlier grades, students should work with data in science and other subjects. Grade 5 students working in these contexts should be able to give deeper interpretations of data than in earlier grades. Calculation Method for DomainsDomains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.  
MAT05.MD.05
5^{th} Grade (MAT) Targeted Standard
MAT05.MD.05 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes. Show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
b. Represent threefold wholenumber products as volumes to represent the associative property of multiplication. c. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. d. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problem.  
MAT05.NBT
Narrative for the (NBT) Number and Operation in Base TenIn Grade 5, students extend their understanding of the baseten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. New at Grade 5 is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left. For example, multiplying by 104 is multiplying by 10 four times. Students students fluently compute products of whole numbers using the standard algorithm for multiplication. In division, they reason about dividing whole numbers with twodigit divisors, and reason about adding, subtracting, multiplying, and dividing decimals to hundredths. Division strategies in Grade 5 involve breaking the dividend apart into like baseten units and applying the distributive property to find the quotient place by place, starting from the highest place. Place value understandings and general methods for computing are used to add, subtract, multiply, and divide decimals to hundredths. Students use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to solve decimal problems. They also relate the strategy to a written method and explain the reasoning used. Calculation Method for DomainsDomains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.  
MAT05.NBT.03
5^{th} Grade (MAT) Targeted Standard
MAT05.NBT.03 Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using baseten numerals, word form, and expanded form.
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.  
MAT05.NBT.05  
MAT05.NBT.06
5^{th} Grade (MAT) Targeted Standard
MAT05.NBT.06 Using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.  
MAT05.NBT.07
5^{th} Grade (MAT) Targeted Standard
MAT05.NBT.07 Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, add, subtract, multiply, and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used.  
MAT05.NF
Narrative for (NF) Number and Operations  FractionsIn Grade 4, students have some experience calculating sums of fractions with different denominators. They understand the process as expressing both quantities in terms of the same unit fraction so that they can be added. Grade 5 students extend this reasoning to situations where it is necessary to reexpress both fractions in terms of a new denominator. Students make sense of fractional quantities when solving word problems, estimating answers mentally to see if they make sense. Grade 4 students connected fractions with addition and multiplication. In Grade 5, students connect fractions with division, understanding a fraction as division of the numerator by the denominator. Using the relationship between division and multiplication, students start working with simple fraction division problems. They solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Grade 5 work with multiplying by unit fractions, and interpreting fractions in terms of division, enables students to see that multiplying a quantity by a number smaller than 1 produces a smaller quantity. This work  interpreting multiplication as scaling (resizing), prepares students for Grade 6 work in ratios and proportional reasoning. Calculation Method for DomainsDomains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.  
MAT05.NF.01
5^{th} Grade (MAT) Targeted Standard
MAT05.NF.01 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.  
MAT05.NF.02
5^{th} Grade (MAT) Targeted Standard
MAT05.NF.02 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models and equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.  
MAT05.NF.06
5^{th} Grade (MAT) Targeted Standard
MAT05.NF.06 Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models and equations to represent the problem.  
MAT05.NF.07
5^{th} Grade (MAT) Targeted Standard
MAT05.NF.07 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a nonzero whole number, and compute such quotients.
b. Interpret division of a whole number by a unit fraction, and compute such quotients. c. Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions using visual fraction models and equations to represent the problem.  
MAT05.OA
Narrative for the (OA) Operations and Algebraic ThinkingAlgebraic thinking is about generalizing arithmetic operations and operating on unknown quantities. It involves recognizing and analyzing patterns and developing generalizations about these patterns. In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations  addition, subtraction, multiplication, and division  the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships. As preparation for the Expressions and Equations domain in the middle grades, students in Grade 5 begin working more formally with expressions. They write expressions to express a calculation, e.g., writing 2 x (8+7) to express the calculation “add 8 and 7, then multiply by 2.” They also evaluate and interpret expressions, e.g., using their conceptual understanding of multiplication to interpret 3 x (18932+921) as being three times as large as 18932+921, without having to calculate the indicated sum or product. Students in Grade 5 begin to think about numerical expressions in ways that prepare their later work with variable expressions (e.g., three times an unknown length is 3 x L). Students extend their Grade 4 pattern work by working briefly with two numerical patterns that can be related and examining these relationships within sequences of ordered pairs and in graphs. This work prepares students for studying proportional relationships and functions in middle school. Calculation Method for DomainsDomains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.  
MAT05.OA.03
5^{th} Grade (MAT) Targeted Standard
MAT05.OA.03 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns. Graph the ordered pairs on a coordinate plane. Use the graph to verify relationships.  
MAT05.OA.04
5^{th} Grade (MAT) Targeted Standard
MAT05.OA.04 Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite.  