Magnificent Multipliers

Magnificent Multipliers

Ages 7–10 · 9 minutes · Math

Lightning Liza and Tenacious Troy battle multiplication up to 6!

In this multiplication lesson, students will review and practice:

- Multiplying a number by itself (ex: 4x4, 5x5)
- Special tricks for multiplying by zero and one
- Making equal groups of up to 5
- Repeated addition (ex: 3 + 3 + 3 = 12)
- Skip counting to solve larger multiplication problems more efficiently

Part of

Standards alignment

Common Core State Standards

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 ÷ 7.
  • 3.OA.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.

Alabama

  • MA19.3.1 — Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.
  • MA19.3.7 — Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.
  • MA19.3.5 — Develop and apply properties of operations as strategies to multiply and divide.
  • MA19.3.7a — Fluently determine all products obtained by multiplying two one-digit numbers.

Alaska

  • 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.1 — Interpret products of whole numbers (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each). For example, show objects in rectangular arrays or describe a context in which a total number of objects can be expressed as 5 × 7.
  • 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.

Arizona

  • 3.OA.A.1 — Interpret products of whole numbers as the total number of objects in equal groups (e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each).
  • 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.5 — Identify arithmetic patterns including, but not limited to, patterns in an addition or multiplication table, explaining use of properties of operations appropriate to the pattern.
  • 2.CAR.5 — 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.

California

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • MP8 — Look for and express regularity in repeated reasoning.

Colorado

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7
  • 3.OA.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. (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.)

Connecticut

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • MP8 — Look for and express regularity in repeated reasoning.

Delaware

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Florida

  • MA.2.AR.3.2 — Use repeated addition to find the total number of objects in a collection of equal groups. Represent the total number of objects using rectangular arrays and equations.
  • MA.3.NSO.2.2 — Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
  • 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.
  • MA.3.AR.3.2 — Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number.
  • MA.3.NSO.2.4 — Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.

Georgia

  • 3.PAR.3.2 — Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.
  • 2.NR.3 — Work with equal groups to gain foundations for multiplication through real-life, mathematical problems.
  • 3.PAR.3.1 — Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

Hawaii

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
  • 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.

Idaho

  • 3.OA.A.1 — Interpret a product of whole numbers as a grouping of sets, e.g., 5 × 7 as five groups of seven objects each.
  • 3.OA.C.7 — Demonstrate fluency for multiplication within 100.
  • 3.OA.B.5 — Apply the properties of operations to multiply and divide.
  • 3.OA.C.7.b — Know from memory all products of two single-digit numbers and related division facts.
  • 3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Illinois

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Indiana

  • 3.CA.3 — Model the concept of multiplication of whole numbers using equal-sized groups, arrays, area models, and equal intervals on a number line. Model the properties of 0 and 1 in multiplication using objects or drawings. (E)
  • 3.CA.5 — 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)
  • 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.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.
  • 2.OA.C.4 — Use repeated addition to find the total number of objects arranged in equal groups and rectangular arrays; write an equation to express the total as a sum of equal addends.
  • 3.OA.A.1 — Interpret products of whole numbers. For example, interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each; describe a context in which a total number of objects can be expressed as 5 × 7.
  • 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.1 — Interpret products of whole numbers, (e.g. interpret 5 ⋅ 7 as the total number of objects in 5 groups of 7 objects each.)
  • 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.
  • 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.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.

Kentucky

  • KY.3.OA.1 — Interpret and demonstrate products of whole numbers.
  • 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.5 — Apply properties of operations as strategies to multiply and divide.
  • 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.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Maine

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • 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.
  • 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.)

Maryland

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Massachusetts

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in five groups of seven objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 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).
  • 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.
  • 2.OA.C.4 — Use addition to find the total number of objects arranged in rectangular arrays with up to five rows and up to five columns; write an equation to express the total as a sum of equal addends.

Michigan

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • 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.

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.
  • 2.2.1.1 — Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. For example: Skip count by 5s beginning at 3 to create the pattern 3, 8, 13, 18, … . Another example: Collecting 7 empty milk cartons each day for 5 days will generate the pattern 7, 14, 21, 28, 35, resulting in a total of 35 milk cartons.

Mississippi

  • 3.OA.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • 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.)

Missouri

  • 3.RA.A.1 — Interpret products of whole numbers.
  • 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.B.6 — Apply properties of operations as strategies to multiply and divide.
  • 3.RA.C.8 — Demonstrate fluency with products within 100.

Montana

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • MP8 — Look for and express regularity in repeated reasoning.

Nebraska

  • 3.A.1.f — Use drawings, words, arrays, symbols, repeated addition, equal groups, and number lines to interpret and explain the meaning of multiplication and division and their relationship.
  • 3.A.1 — Operations and Algebraic Thinking: Students will extend understanding of multiplication and apply operational properties to solve problems.
  • 3.A.1.e — Apply commutative, associative, distributive, identity, and zero properties as strategies to multiply and divide.
  • 3.A.1.g — Fluently multiply and divide within 100 using strategies based on understanding and properties of operations.

Nevada

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • MP8 — Look for and express regularity in repeated reasoning.

New Hampshire

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

New Jersey

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe and/or represent a context in which a total number of objects can be expressed as 5 × 7.
  • 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. 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.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 Mexico

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

New York

  • NY-3.OA.1 — Interpret products of whole numbers.
  • 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.
  • NY-3.OA.5 — Apply properties of operations as strategies to multiply and divide.
  • NY-3.OA.7.b — Know from memory all products of two one-digit numbers.
  • NY-3.OA.9 — Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).

North Carolina

  • 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.
  • 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.
  • MP.8 — Look for and express regularity in repeated reasoning.

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.
  • 2.AR.OA.5 — Use repeated addition to find the total number of objects arranged in a rectangular array.
  • 3.AR.OA.6 — Identify arithmetic patterns and explain them using the properties of operations.

Ohio

  • 3.OA.1 — Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. (Note: These standards are written with the convention that a x b means a groups of b objects each; however, because of the commutative property, students may also interpret 5 x 7 as the total number of objects in 7 groups of 5 objects each).
  • 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.
  • 2.OA.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.

Oklahoma

  • 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).
  • 2.N.2.6 — Use concrete models and structured arrangements, such as repeated addition, arrays, and ten frames to develop an understanding of multiplication.
  • 3.N.2.2 — Demonstrate fluency with multiplication facts using factors up to 10.

Oregon

  • 3.OA.A.1 — Represent and interpret multiplication of two factors as repeated addition of equal groups.
  • 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.D.9 — Identify and explain arithmetic patterns using properties of operations, including patterns in the addition table or multiplication table.

Pennsylvania

  • CC.2.2.3.A.1 — Represent and solve problems involving multiplication and division.
  • CC.2.2.2.A.3 — Work with equal groups of objects to gain foundations for multiplication.
  • CC.2.2.3.A.2 — Understand properties of multiplication and the relationship between multiplication and division.
  • CC.2.2.3.A.3 — Demonstrate multiplication and division fluency.

Rhode Island

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 x7 as the total number of objects in five groups of seven objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 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).
  • 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.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.

South Carolina

  • 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.
  • 3.ATO.3 — Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown.
  • 3.ATO.7 — Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.
  • 2.ATO.4 — Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

South Dakota

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.A.1 — Interpret the factors and products in whole number multiplication equations (e.g., 4 x 7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total length of 28 inches).
  • 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.
  • 2.OA.C.4 — Use repeated 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. For example, a 3 by 4 array can be expressed as 3 + 3 + 3 + 3 = 12 or 4 + 4 + 4 = 12.
  • 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).

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;
  • 3.4D — determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10;
  • 3.4F — recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts;

Utah

  • 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 — Fluently multiply and divide.
  • 3.OA.7.b — By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 2.OA.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.
  • 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 four times a number is always even, and explain why four times a number can be decomposed into two equal addends.

Vermont

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Virginia

  • 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).
  • 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.2f — Recall with automaticity the multiplication facts through 10 × 10 and the corresponding division facts.
  • 3.CE.2c — Apply strategies (e.g., place value, the properties of multiplication and/or addition) when multiplying and dividing whole numbers.

Washington

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.

Washington, D.C.

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.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.
  • MP8 — Look for and express regularity in repeated reasoning.

West Virginia

  • M.3.1 — Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 x 7).
  • 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.
  • M.3.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those 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).
  • 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.

Wisconsin

  • M.3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.
  • 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.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.D.8 — Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Wyoming

  • 3.OA.A.1 — Represent the concept of multiplication of whole numbers using models including, but not limited to, equal-sized groups ("groups of"), arrays, area models, repeated addition, and equal "jumps" on a number line.
  • 3.OA.C — Multiply and divide within 100.