The Product is Right

Part of

• Learn to Multiply

Standards alignment

Common Core State Standards

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Alabama

• MA19.3.7 — Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.
• MA19.3.7a — Fluently determine all products obtained by multiplying two one-digit numbers.
• MA19.3.5 — Develop and apply properties of operations as strategies to multiply and divide.
• MA19.3.7b — State automatically all products of two one-digit numbers by the end of third grade.

Alaska

• 3.OA.5 — Make, test, support, draw conclusions and justify conjectures about properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) • Commutative property of multiplication: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. • Associative 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. • Distributive property: 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. • Inverse property (relationship) of multiplication and division.
• 3.OA.7 — Fluently multiply and divide numbers up to 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.
• 3.OA.9 — 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.

Arizona

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Properties include commutative and associative properties of multiplication and the distributive property. (Students do not need to use the formal terms for these properties.)
• 3.OA.C.7 * — Fluently multiply and divide within 100. By the end of Grade 3, know from memory all multiplication products through 10 x 10 and division quotients when both the quotient and divisor are less than or equal to 10.
• 3.OA.D.9 — 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.

Arkansas

• 3.CAR.2 — Use basic fact fluency to multiply and divide whole numbers with mastery by the end of third grade. • Knowing all products with factors up to and including 12 and the corresponding division facts from the products with factors up to and including 12. • 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.
• 3.CAR.3 — Apply properties of operations as strategies to multiply and divide. • Properties include: Distributive, Commutative, and Associative Properties of Multiplication

California

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.
• 3.OA.D.9 — 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.

Colorado

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) 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.)
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Connecticut

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.

Delaware

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.

Florida

• MA.3.NSO.2.2 — Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
• MA.3.NSO.2.4 — Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.
• MA.3.AR.1.1 — Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.

Georgia

• 3.PAR.3.1 — Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

Hawaii

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.

Idaho

• 3.OA.C.7 — Demonstrate fluency for multiplication within 100.
• 3.OA.C.7.b — Know from memory all products of two single-digit numbers and related division facts.
• 3.MP.8 — Look for and express regularity in repeated reasoning.
• 3.OA.B.5 — Apply the properties of operations to multiply and divide.

Illinois

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Indiana

• 3.CA.6 — Demonstrate fluency with mastery of multiplication facts and corresponding division facts of 0 to 10.
• 3.CA.8 — Create, extend, and give an appropriate rule for number patterns within 100 (including patterns in the addition table or multiplication table).

Iowa

• 3.OA.B.5 — Use properties of operations as strategies to multiply and divide. For example, 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.)
• 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. For example, knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8. By the end of Grade 3, flexibly, efficiently, and accurately find all products of two one-digit numbers. Note: Fluency of this standard is critical by the end of grade level.
• SMP8 — Look for and express regularity in repeated reasoning.
• 3.OA.D.9 — 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.

Kansas

• 3.OA.5 — 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.7 — Fluently (efficiently, accurately, and flexibly) multiply and divide with single digit multiplications and related divisions using strategies (e.g. relationship between multiplication and division, doubles, double and double again, half and then double, etc.) or properties of operations.
• MP.8 — Look for and express regularity in repeated reasoning.

Kentucky

• KY.3.OA.5 — Apply properties of operations as strategies to multiply and divide.
• KY.3.OA.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
• KY.3.OA.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Louisiana

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.

Maine

• 3.OA.B.5 — Apply properties of operations as strategies to multiply. 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.)
• 3.OA.C.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.

Maryland

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.

Massachusetts

• 3.OA.C.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 single-digit numbers and related division facts. For example, the product 4 x 7 = 28 has related division facts 28 ÷ 7 = 4 and 28 ÷ 4 = 7.
• 3.OA.B.5 — Apply properties of operations to multiply. For example: When multiplying numbers order does not matter. If 6  4 = 24 is known, then 4  6 = 24 is also known (Commutative property of multiplication); The product 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); When multiplying two numbers either number can be decomposed and multiplied; one can find 8 x 7 by knowing that 7 = 5 + 2 and that 8  5 = 40 and 8  2 = 16, resulting in 8  (5 + 2) = (8  5) + (8  2) = 40 + 16 = 56 (Distributive property); When a number is multiplied by 1 the result is the same number (Identity property of 1 for multiplication).
• 4.OA.A.3.a — Know multiplication facts and related division facts through 12 × 12.

Michigan

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Minnesota

• 3.1.2.3 — Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
• 4.1.1.1 — Demonstrate fluency with multiplication and division facts.

Mississippi

• 3.OA.5 — 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.)
• 3.OA.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. Know from memory all products of two one-digit numbers; and fully understand the concept when a remainder does not exist under division.

Missouri

• 3.RA.C.7 — Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers.
• 3.RA.C.8 — Demonstrate fluency with products within 100.
• 3.RA.B.6 — Apply properties of operations as strategies to multiply and divide.

Montana

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Nebraska

• 3.A.1.g — Fluently multiply and divide within 100 using strategies based on understanding and properties of operations.
• 3.A.1 — Operations and Algebraic Thinking: Students will extend understanding of multiplication and apply operational properties to solve problems.

Nevada

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.
• 3.OA.D.9 — 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.

New Hampshire

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

New Jersey

• 3.OA.B.5 — 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.)
• 3.OA.C.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.
• 8 — Look for and express regularity in repeated reasoning.

New Mexico

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.

New York

• NY-3.OA.5 — Apply properties of operations as strategies to multiply and divide.
• NY-3.OA.7.a — Fluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations.
• MP.8 — Look for and express regularity in repeated reasoning.
• NY-3.OA.7.b — Know from memory all products of two one-digit numbers.

North Carolina

• NC.3.OA.7 — Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. • Know from memory all products with factors up to and including 10. • Illustrate and explain using the relationship between multiplication and division. • Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
• NC.3.OA.1 — For products of whole numbers with two factors up to and including 10: • Interpret the factors as representing the number of equal groups and the number of objects in each group. • Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties.

North Dakota

• 3.AR.OA.1 — Using mental strategies, multiply and divide basic facts within 100. Automatically multiply and divide up to 5x5 and 10s facts.
• 4.AR.OA.1 — Automatically multiply and divide through 10x10.

Ohio

• 3.OA.5 — Apply properties of operations as strategies to multiply and divide. For example, 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 = 4 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.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. Limit to division without remainders. By the end of Grade 3, know from memory all products of two one-digit numbers.
• 3.OA.9 — 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.

Oklahoma

• 3.N.2.2 — Demonstrate fluency with multiplication facts using factors up to 10.
• 3.N.2.1 — Represent multiplication facts by modeling a variety of approaches (e.g., manipulatives, repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, skip counting).

Oregon

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.7 — Fluently multiply and divide within 100 using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
• 3.OA.A.1 — Represent and interpret multiplication of two factors as repeated addition of equal groups.

Pennsylvania

• CC.2.2.3.A.3 — Demonstrate multiplication and division fluency.
• Look for and express regularity in repeated reasoning.
• CC.2.2.3.A.2 — Understand properties of multiplication and the relationship between multiplication and division.
• CC.2.2.3.A.4 — Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Rhode Island

• 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two single- digit numbers and related division facts. For example, the product 4 x 7 = 28 has related division facts 28 ÷ 7 = 4 and 28 ÷ 4 = 7.
• 3.OA.B.5 — Apply properties of operations to multiply. For example, when multiplying numbers order does not matter. If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication); The product 3 x 5 x 2 can be found by 3 x 5 = 15 then 15 x 2 = 30, or by 5 x 2 = 10 then 3 x 10 = 30 (Associative property of multiplication); When multiplying two numbers either number can be decomposed and multiplied; one can find 8 x 7 by knowing that 7 = 5 + 2 and that 8 x 5 = 40 and 8 x 2 = 16, resulting in 8 (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive property); When a number is multiplied by 1 the result is the same number (Identity property of 1 for multiplication).
• MP8 — Look for and express regularity in repeated reasoning.

South Carolina

• 3.ATO.7 — Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.
• 3.ATO.5 — Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning.
• 3.ATO.1 — Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0 - 10) and the product.

South Dakota

• 3.OA.C.7.a — 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.
• 3.OA.C.7.b — Demonstrate fluency (skill in carrying out procedures flexibly, appropriately, efficiently, and accurately) for all products of two one-digit numbers.
• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.7 — Multiply and divide within 100.

Tennessee

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (distributive property of multiplication over addition).
• 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the properties of operations or the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8). By the end of 3rd grade, know all products of two one-digit numbers and related division facts.
• 3.OA.D.9 — Identify patterns in a multiplication chart and explain them using properties of operations. For example, in the multiplication chart, observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6 = 2 x (2 x 6), which uses the associative property of multiplication) or, for example, observe that 6 times 7 is one more group of 7 than 5 times 7 (because 6 x 7 = (5 + 1) x 7 = (5 x 7) + (1 x 7), which uses the distributive property of multiplication over addition).

Texas

• 3.4E — represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting;
• 3.4F — recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts;

Utah

• 3.OA.5 — Apply properties of operations as strategies to multiply and divide. For example: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (commutative property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30 (associative property of multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (distributive property). (Third grade students may, but need not, use formal terms for these properties.)
• 3.OA.7.a — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. (For example, knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
• 3.OA.7.b — By the end of Grade 3, know from memory all products of two one-digit numbers.

Vermont

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• 3.OA.D.9 — 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.

Virginia

• 3.CE.2d — Demonstrate fluency with multiplication facts through 10 × 10 by applying reasoning strategies (e.g., doubling, add-a-group, subtract-a-group, near squares, and inverse relationships).
• 3.CE.2 — The student will recall with automaticity multiplication and division facts through 10 × 10; and represent, solve, and justify solutions to single-step contextual problems using multiplication and division with whole numbers. Students will demonstrate the following Knowledge and Skills:
• 3.CE.2c — Apply strategies (e.g., place value, the properties of multiplication and/or addition) when multiplying and dividing whole numbers.
• 3.CE.2f — Recall with automaticity the multiplication facts through 10 × 10 and the corresponding division facts.
• 3.CE.2a — Represent multiplication and division of whole numbers through 10 × 10, including in a contextual situation, using a variety of approaches and models (e.g., repeated addition/subtraction, equal-sized groups/sharing, arrays, equal jumps on a number line, using multiples to skip count).

Washington

• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.C.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.
• MP8 — Look for and express regularity in repeated reasoning.
• 3.OA.D.9 — 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.

Washington, D.C.

• 3.OA.C.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.
• 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide.
• 3.OA.D.9 — 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.

West Virginia

• M.3.5 — Apply properties of operations as strategies to multiply and divide (e.g., if 6 x 4 = 24 is known, then 4 x 6 = 24 is also known: Commutative Property of Multiplication; 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30: Associative Property of Multiplication; knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56: Distributive Property). Instructional Note: Students should focus on conceptual understanding not use formal terms for these properties.
• M.3.7 — Fluently (efficiently, flexibly, and accurately) multiply and divide within 100 using strategies such as the relationship between multiplication and division and the properties of operations. By the end of Grade 3, know the multiplication table (facts) within 100 (Os10s) efficiently.

Wisconsin

• M.3.OA.B.4 — Apply properties of operations as strategies to multiply and divide. Student use of the formal terms for these properties is not necessary.
• M.3.OA.C.6 — Use multiplicative thinking to multiply and divide within 100. a. Use the meanings of multiplication and division, the relationship between the operations (e.g., knowing that 8 x 5 = 40, one could reason that 40 ÷ 5 = 8), and properties of operations (e.g., the distributive property) to develop and understand strategies to multiply and divide within 100. b. Flexibly and efficiently use strategies, the relationship between the operations, and properties of operations to find products and quotients with multiples of 0, 1, 2, 5, & 10 within 100.
• M.4.OA.D.6 — Flexibly and efficiently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations [e.g., knowing that 7 x 6 can be thought of as 7 groups of 6 so one could think 5 groups of 6 is 30 and 2 more groups of 6 is 12 and 30 + 12 = 42 (informal use of the distributive property)].

Wyoming

• 3.OA.C — Multiply and divide within 100.
• 3.OA.C.7 — Fluently multiply and divide with factors 1 - 10 using mental strategies. By end of Grade 3, know automatically all products of one-digit factors based on strategies.
• 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 — Understand properties of multiplication and the relationship between multiplication and division.