Grade 3 Mathematics CCRS Standards and Alabama COS
CCRS Standard / Standard ID / Evidence of Student Attainment / Teacher Vocabulary / Knowledge / Skills / Understanding / Resources1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
Example: Describe a context in which a total number of objects can be expressed as 5 × 7. / Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
3.OA.1 / Students:
Given any multiplication problem in the form a x b = c,
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (i.e., given 3 x 5 = 15, students make 3 piles of buttons with 5 buttons in each pile. They explain that 15 represents the total number of buttons, 3 is the number of piles and 5 is the number of buttons in each pile) ,
Write a corresponding word problems containing a multiplication context. / Students know:
Characteristics of multiplication contexts. / Students are able to:
Represent quantities and operations (multiplication) physically, pictorially, or symbolically,
Use mathematical language to communicate the connections between multiplication equations and related representations,
Write word problems containing multiplication contexts. / Students understand that:
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication. / Click below to access all ALEX resources aligned to this standard.
ALEX Resources
2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 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.
Example: Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. / Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
3.OA.2 / Students:
Given any division problem in the form a ÷ b = c,
Represent the problem physically or pictorially and describe the relationship between the dividend, divisor, and quotient in the equation and the attributes of the representation (e.g., given 15 ÷ 3 = 5, students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons, 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile),
Write a corresponding word problem containing a division context. / Students know:
Characteristics of division contexts. / Students are able to:
Represent quantities and operations (division) physically, pictorially, or symbolically,
Use mathematical language to communicate the connections between division equations and related representations,
Write word problems containing division contexts. / Students understand that:
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
3. 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.1
(1See Appendix A, Table 2.) / Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
3.OA.3 / Students:
Given a variety of multiplication and division word problems within 100,
Explain and justify solutions and solution paths using connections among a variety of representations (e.g., place value blocks, drawings, open arrays, and equations with a symbol for the unknown). / See glossary for problem types (Table 2). / Students know:
Characteristics of multiplication and division contexts,
Multiplication and division strategies. / Students are able to:
Represent quantities and operations (multiplication and division) physically, pictorially, or symbolically,
Strategically use a variety of representations to solve multiplication and division word problems,
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical, pictorial, or symbolic representations,
Accurately compute products and quotients,
Use symbols to represent unknown quantities in equations. / Students understand that:
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups,
Mathematical problems can be solved using a variety of strategies, models, representations,
Variables represent unknown quantities when representing mathematical situations algebraically. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
Example: Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?. / Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
3.OA.4 / Students:
Solve single operation multiplication/division equations containing a single unknown (e.g. 8x? = 48, 5= __ ÷3, 6x6 = ___). / Students know:
Strategies for solving simple equations with one unknown. / Students are able to:
Efficiently apply strategies for solving simple equations with one unknown,
Justify solutions for single unknown equations. / Students understand that:
Equalities contain phrases that name the same amount on each side of the equal sign. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
5. Apply properties of operations as strategies to multiply and divide.2
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)
(2Students need not use formal terms for these properties.) / Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5 / Students:
Given multiplication and division problems within 100,
Use the properties of operations and descriptive language for the property to justify their products and quotients (e.g., If I know that 8 x 5 is 40, and two more groups of 8 would be 16, then 8 x 7 must be 40 + 16 or 56). / Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property / Students know:
Commutative, Associative, Identity and Zero Properties of Multiplication and the Distributive Property,
Strategies for finding products and quotients. / Students are able to:
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients. / Students understand that:
The order in which factors are multiplied does not change the product. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
6. Understand division as an unknown-factor problem.
Example: Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. / Operations and Algebraic Thinking
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.6 / Students:
Given a division problem with an unknown quotient,
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation. / Factor / Students know:
Strategies for finding quotients and products. / Students are able to:
Use symbols to represent unknown quantities in equations,
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem,
Use the inverse relationship between multiplication and division to find quotients. / Students understand that:
The relationship between multiplication and division (that one "undoes" the other) can be used to solve problems,
Efficient application of computation strategies are based on the numbers in the problems. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
7. 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 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. / Operations and Algebraic Thinking
Multiply and divide within 100.
3.OA.7 / Students:
Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient,
Use an efficient strategy (e.g., recall, inverse operations, arrays, derived facts, properties of operations, etc.) to name the product or quotient. / Students know:
Strategies for finding products and quotients. / Students are able to:
Use multiplication and division strategies efficiently based on the numbers in the problems. / Students understand that:
Efficient application of computation strategies are based on the numbers in the problems. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
8. Solve two-step 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.3
(3This 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 when there are no parentheses to specify a particular order (Order of Operations).) / Operations and Algebraic Thinking
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8 / Students:
Given a variety of two-step word problems involving all four operations,
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities,
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus 50 is 125."). / Students know:
Characteristics of addition, subtraction, multiplication, and division situations,
Addition, subtraction, multiplication, and division strategies,
Strategies for mentally computing and estimating sums, differences, products, and quotients. / Students are able to:
Strategically use a variety of representations to solve two-step word problems involving all four operations,
Use symbols to represent unknown quanities in equations that relate to word problem contexts,
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical, pictorial, or symbolic representations and justify solutions/solution paths,
Accurately compute sums, differences, products and quotients,
Use logical reasoning, mental computation strategies, and estimation strategies to justify the reasonableness of solutions. / Students understand that:
Multiplication is putting together equal sized groups,
Division is sharing into equal-sized shares or as sharing equally among a given number of groups,
Mathematical problems can be solved using a variety of strategies, models, and representations,
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
Example: Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. / Operations and Algebraic Thinking
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.9 / Students:
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends). / Students know:
Characteristics of numbers and properties of operations (e.g., odd, even),
Properties from Table 3, etc. / Students are able to:
Identify arithmetic patterns in number sequences, in the addition table or multiplication table,
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns. / Students understand that:
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations, form conjectures, and solve problems. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
10. Use place value understanding to round whole numbers to the nearest 10 or 100. / Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic. 4
(4 A range of algorithms may be used.)
3.NBT.1 / Students:
Given any number less than 1,000,
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary, (e.g., "Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150). / Students know:
Place value (ones, tens, hundreds),
Rounding. / Students are able to:
Count by 10s and 100s,
Determine what is halfway between two multiples of 10 or 100,
Round to the nearest 10 or 100,
Use place value vocabulary and logical reasoning to justify solutions to rounding problems. / Students understand that:
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
11. 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. / Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic. 4
(4 A range of algorithms may be used.)
3.NBT.2 / Students:
Fluently add and subtract within 1000, using strategies based on place values, properties of operations, and/or the relationship between addition and subtraction,
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning. / Students know:
Tools for modeling addition and subtraction,
Strategies for solving addition and subtraction problems,
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems. / Students are able to:
Model addition and subtraction problems using appropriate tools,
Record strategies for solving addition and subtraction problems,
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems. / Students understand that:
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
12. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. / Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic. 4
(4 A range of algorithms may be used.)
3.NBT.3 / Students:
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers. / Students know:
Place value models for multiplying numbers (e.g., open arrays, place value blocks),
Strategies for multiplying one-digit numbers,
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10. / Students are able to:
Use mental strategies based on an understanding of place value, properties of operations, and knowledge of one-digit multiplication to find products,
Use a variety of place value models of multiplication problems to justify strategies and solutions. / Students understand that:
Patterns in the place value system and properties of operations can be used to efficiently compute products. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
13. 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. / Number & Operations—Fractions
Develop understanding of fractions as numbers.5
(5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)
3.NF.1 / Students:
Given any fraction in the form a/b,
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1). (e.g., 3/5 = 1/5 + 1/5 + 1/5).
Given a model of a fraction,
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model. / Students know:
Fractions,
Strategies for creating models of fractional quantities (e.g., folding, repeatedly dividing the whole in half, etc.). / Students are able to:
Write fractions that correspond to pictorial or physical models,
Create models of fractions that correspond to fractions written in the form a/b,
Communicate the relationship between models of fractions and the corresponding written fraction. / Students understand that:
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole),
The unit fraction (1/b) names the size of the unit with respect to the referenced whole,
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned. / Click below to access all ALEX resources aligned to this standard.
- ALEX Resources
14. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. 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.
b. 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. / Number & Operations—Fractions
Develop understanding of fractions as numbers.5
(5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.)
3.NF.2 / Students:
Given any common fraction a/b between 0 and 1 (denominators of 2, 3, 4, 6, 8),
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction. / Students know: