Skyscraper Square

Ages 7–10 · 8 minutes · Math

Join Troy on a tour of Skyscraper Square and learn how to use perfect squares to multiply

In this advanced multiplication lesson, students will:

- Learn how to use perfect squares as an aid in multiplying near squares, like 6×7, 7×8, 6×8 and more.

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.A.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.
3.MP8 — Look for and express regularity in repeated reasoning.

Alabama

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.
MA19.2.10 — Fluently add and subtract within 100, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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.3 — Use multiplication and division numbers up to 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).
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.

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.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.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.
MP7 — Look for and make use of structure.

Arkansas

3.CAR.3 — Apply properties of operations as strategies to multiply and divide. • Properties include: Distributive, Commutative, and Associative Properties of Multiplication
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.6 — Solve real-world problems using multiplication and division within 100 involving equal groups, arrays, partitive and measurement division.

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

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.A.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. (see Appendix, Table 2)

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

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

Florida

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.NSO.2.4 — Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.
MA.3.NSO.2.2 — Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.K12.MTR.3.1 — Complete tasks with mathematical fluency. Mathematicians who complete tasks with mathematical fluency: • Select efficient and appropriate methods for solving problems within the given context. • Maintain flexibility and accuracy while performing procedures and mental calculations. • Complete tasks accurately and with confidence. • Adapt procedures to apply them to a new context. • Use feedback to improve efficiency when performing calculations.

Georgia

3.PAR.3 — Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100.

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

Idaho

3.MP.8 — Look for and express regularity in repeated reasoning.
3.OA.C.7 — Demonstrate fluency for multiplication within 100.
3.MD.C.7.d — Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths 𝑎 and 𝑏 + 𝑐 is the sum of 𝑎 × 𝑏 and 𝑎 × 𝑐. Use area models to represent the distributive property in mathematical reasoning

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.A.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.
MP.7 — Look for and make use of structure.
3.MD.C.7.c — Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Indiana

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.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.6 — Demonstrate fluency with mastery of multiplication facts and corresponding division facts of 0 to 10.
4.CA.3 — Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can be multiplied in any order. Investigate and apply the distributive property. (E)
3.CA.7 — Solve real-world problems involving whole number multiplication and division within 100 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). (E)

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.
SMP7 — Look for and make use of structure.
SMP8 — Look for and express regularity in repeated reasoning.
3.OA.A.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, with unknowns in all positions. For example, by using drawings and equations with a symbol for the unknown number to represent the problem. (See Problem Types Table 2 in Appendix A)

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.
3.OA.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.)
MP.7 — Look for and make use of structure.

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.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities, by using drawings and equations with a symbol for the unknown number to represent the problem.
MP8 — Look for and express regularity in repeated reasoning.

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

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

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

Massachusetts

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.
3.OA.A.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.
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.A.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.
MP7 — Look for and make use of structure.

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.
3.1.2.4 — Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. For example: You have 27 people and 9 tables. If each table seats the same number of people, how many people will you put at each table? Another example: If you have 27 people and tables that will hold 9 people, how many tables will you need?

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.
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.
MP7 — Look for and make use of structure.

Missouri

3.RA.B.6 — Apply properties of operations as strategies to multiply and divide.
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.A.4 — Use multiplication and division within 100 to solve problems.

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.A.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.
MP7 — Look for and make use of structure.

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.
3.A.1.e — Apply commutative, associative, distributive, identity, and zero properties as strategies to multiply and divide.
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.

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

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.A.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.
MP7 — Look for and make use of structure.

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.
3.OA.A.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.
7 — Look for and make use of structure.

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

New York

NY-3.OA.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
NY-3.OA.5 — Apply properties of operations as strategies to multiply and divide.
MP.7 — Look for and make use of structure.
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.7.b — Know from memory all products of two one-digit numbers.

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.
NC.3.OA.3 — Represent, interpret, and solve one-step problems involving multiplication and division. • Solve multiplication word problems with factors up to and including 10. Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem. • Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem.

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.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. Drawings need not show details, but should show the mathematics in the problem.

Oklahoma

3.N.2.2 — Demonstrate fluency with multiplication facts using factors up to 10.
4.N.2.1 — Demonstrate fluency with multiplication and division facts with factors up to 12.

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.3 — Use multiplication and division within 100 to solve problems in authentic contexts involving equal groups, arrays, and/or measurement quantities.
MP7 — Look for and make use of structure.
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.2 — Understand properties of multiplication and the relationship between multiplication and division.
CC.2.2.3.A.3 — Demonstrate multiplication and division fluency.
CC.2.2.3.A.1 — Represent and solve problems involving multiplication and division.
CC.2.4.3.A.5 — Determine the area of a rectangle and apply the concept to multiplication and to addition.

Rhode Island

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.A.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.
MP7 — Look for and make use of structure.

South Carolina

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.7 — Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.
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.

South Dakota

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

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).
3.OA.A.3 — Multiply and divide within 100 to solve contextual problems, with the unknown in any positions, in situations involving equal groups, arrays/area, and measurement quantities using strategies based on place value, the properties of operations, and the relationship between multiplication and division (e.g., contexts including computations such as 3 x ? = 24, 6 x 16 = ?, ? ÷ 8 = 3, or 96 ÷ 6 = ?).

Texas

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;
3.4E — 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;
3.4K — solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of 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.MD.7.c — Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.

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.A.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.
MP7 — Look for and make use of structure.

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.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.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.

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.
3.OA.A.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.
MP7 — Look for and make use of structure.

Washington, D.C.

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.A.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.
MP7 — Look for and make use of structure.
3.MD.C.7.c — Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

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.
M.3.3 — 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).

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.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.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)].
M.3.MD.C.7 — Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Wyoming

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