Key Concept: Using facts you know can help you find the product of facts you have not yet mastered.

Topic Overview | Standards Alignment | #### Common Core

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.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.#### Georgia

MGSE3.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.

MGSE3.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.)

MGSE3.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. By the end of Grade 3, know from memory all products of one-digit numbers. IEP Goals

This topic focuses on building the conceptual understanding of the distributive property, specifically adding and removing 1 group from a known fact to determine the product of an unknown fact. Students work with arrays and number lines to model a given fact by decomposing the new unknown fact into 2 known facts. Models are faded so that the last lesson is numbers only.

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.

MGSE3.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.)

MGSE3.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. By the end of Grade 3, know from memory all products of one-digit numbers.

1. Given multiplication equations for facts containing 3, 6 and 9 along with visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy within the first quarter.

2. Given a multiplication story problem involving factors 3, 6 or 9 and vocabulary reinforcement, the student will paraphrase the problem, create a model and correctly find the product or quotient for 5 out of 6 examples by the end of the first marking period.

3. Given a set of 10 multiplication problem for factors 6, 7, 9 and visual models, the student will apply the commutative or associative property to correctly solve the problems with 90% accuracy.

2. Given a multiplication story problem involving factors 3, 6 or 9 and vocabulary reinforcement, the student will paraphrase the problem, create a model and correctly find the product or quotient for 5 out of 6 examples by the end of the first marking period.

3. Given a set of 10 multiplication problem for factors 6, 7, 9 and visual models, the student will apply the commutative or associative property to correctly solve the problems with 90% accuracy.

Unit Launcher

View Cornerstone School's Cafeteria: Discussion Guide and KWL Chart

3.2-1-1 Modeling the Distributive Property |

View Guided Lesson Make models to show how you can multiply in parts to match the value of a given model. (12-18 min)

3.2-1-2 Using Groups of 1, 2 and 5 to Solve for Groups of 3 and 6 |

View Guided Lesson Make 2-part models using facts you know to solve harder facts. Complete equations with parentheses and partial products. (12-18 min)

3.2-1-3 Writing Equations with the Distributive Property: Groups of 3 and 6 |

View Guided Lesson Make 2-part models and write equations using the distributive property. (12-18 min)

3.2-1-4 Multiplying by Groups of 3 and 6: Numbers Only |

View Guided Lesson Write and solve equations using the distributive property without models. (12-18 min)

Real World Investigation Part 1

View Cornerstone School's Cafeteria: Cornerstone School's Data

Key Concept: Division can be used to find how many equal-sized groups are contained in a starting amount.

Topic Overview | Standards Alignment | #### Common Core

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.

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.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.#### Georgia

MGSE3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.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.

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

MGSE3.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.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. IEP Goals

This topic builds the conceptual understanding that division like multiplication is about solving problems involving equal sized groups. While multiplication is a procedure used to determine a total value when equal-sized groups are combined, division is a procedure that can be used to determine the number of equal-sized groups that are contained in a starting amount.

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.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MGSE3.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.

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

MGSE3.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.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

1. Given division equations with divisors of 3, 6, 9 and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy.

2. Given a set of division problems or prompts with divisors of 4, 6, and 9, the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.

3. Given a division story problem containing divisors 3, 6, or 9 and visual models, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for unknowns for 5 out of 6 examples by the end of the first marking period.

2. Given a set of division problems or prompts with divisors of 4, 6, and 9, the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.

3. Given a division story problem containing divisors 3, 6, or 9 and visual models, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for unknowns for 5 out of 6 examples by the end of the first marking period.

3.2-2-1 Modeling with Divisors of 3, 6, and 9: Find the Number of Groups |

Lesson Plan

View Guided Lesson Make models and count the number of groups of 3, 6 and 9 in a starting amount, then complete a "groups of" sentence. (12-18 min)

3.2-2-2 Dividing with Divisors of 3, 6, and 9: Writing Equations |

Lesson Plan

View Guided Lesson Write a “groups of__ are in__” sentence and use models to find the quotient of a word problem involving for the divisors 3, 6 and 9. (12-18 min)

3.2-2-3 Modeling Inverse Relationships with Factors of 3, 6, and 9 |

Lesson Plan

View Guided Lesson Use division models and equations to solve multiplication problems with unknowns, and use multiplication models and equations to solve division problems with unknowns to see the inverse relationship. (12-18 min)

3.2-2-4 Dividing with Divisors of 3, 6, and 9: Numbers Only |

Lesson Plan

View Guided Lesson Write equations and solve word problems for divisors of 3, 6, or 9 without models. (12-18 min)

Real World Investigation Part 2

View Cornerstone School's Cafeteria: Create Some Data

Key Concept: Using facts you know can help you find the product of facts you have not yet mastered.

Topic Overview | Standards Alignment | #### Common Core

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.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.#### Georgia

MGSE3.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.

MGSE3.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.)

MGSE3.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. By the end of Grade 3, know from memory all products of one-digit numbers. IEP Goals

This topic focuses on building the conceptual understanding of the distributive property. Students work with arrays and number lines to model a given fact by decomposing the new unknown fact into 2 known facts. Students are introduced to the strategy of breaking apart an unknown so that one of the factors is a 5. Models are faded so that the last lesson is numbers only.

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.

MGSE3.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.)

MGSE3.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. By the end of Grade 3, know from memory all products of one-digit numbers.

1. Given multiplication equations for facts containing 6, 7, and 9 and previous guided practice using visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy upon completion of the IEP.

2. Given a multiplication story problem involving factors 3, 6 or 9 and a paraphrasing strategy, the student will paraphrase the problem and correctly find the product or quotient for 5 out of 6 examples without the use of models by the end of the first marking period.

2. Given a multiplication story problem involving factors 3, 6 or 9 and a paraphrasing strategy, the student will paraphrase the problem and correctly find the product or quotient for 5 out of 6 examples without the use of models by the end of the first marking period.

3.2-3-1 Modeling the Distributive Property: Groups of 7, 8 and 9 |

Lesson Plan

View Guided Lesson Make models to show how you can multiply in parts to match the value of a given model using the 5 + n strategy. (12-18 min)

3.2-3-2 Using Smaller Group Sizes to Solve for Groups of 7, 8 and 9 |

Lesson Plan

View Guided Lesson Make models and complete equations that contain parenthesis and partial products using the 5 + n strategy. (12-18 min)

3.2-3-3 Writing Equations with the Distributive Property: Groups of 7, 8 and 9 |

Lesson Plan

View Guided Lesson Make models and write equations including products using the distributive property. (12-18 min)

3.2-3-4 Multiplying by 7, 8 and 9: Numbers Only |

Lesson Plan

View Guided Lesson Write and solve equations using the distributive property without models. (12-18 min)

Real World Investigation Part 3

View Your School's Cafeteria: Your Data

Key Concept: Division can be used to find how many equal-sized groups are contained in a starting amount.

Topic Overview | Standards Alignment | #### Common Core

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.

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.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.#### Georgia

MGSE3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.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.

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

MGSE3.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.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. IEP Goals

This topic builds the conceptual understanding that division like multipliction is about solving problems involving equal sized groups. While multiplication is a procedure used to determine a total value when equal-sized groups are combined, division is a procedure that can be used to determine the number of equal-sized groups that are contained in a starting amount.

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.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MGSE3.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.

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

MGSE3.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.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

1. Given division equations with divisors of 6, 7, 8 and 9 and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy.

2. Given a set of division problems or prompts with divisors of 6, 7, 8 and 9, the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.

3. Given a division story problem containing divisors 6, 7, 8 9 and visual models, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for unknowns for 5 out of 6 examples by the end of the first marking period.

2. Given a set of division problems or prompts with divisors of 6, 7, 8 and 9, the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.

3. Given a division story problem containing divisors 6, 7, 8 9 and visual models, the student will apply an understanding of the inverse relationship of multiplication and division to accurately solve for unknowns for 5 out of 6 examples by the end of the first marking period.

3.2-4-1 Modeling with Divisors of 6, 7, 8, and 9: Find the Number of Groups |

Lesson Plan

View Guided Lesson Make models and count the number of groups of 6, 7, 8, and 9 in a starting amount, then complete a "groups of" sentence. (12-18 min)

3.2-4-2 Dividing with Divisors of 6, 7, 8, and 9: Writing Equations |

Lesson Plan

View Guided Lesson Write a “groups of__ are in__” sentence and use models to find the quotient of a word problem involving for the divisors 6, 7, 8, and 9. (12-18 min)

3.2-4-3 Modeling Inverse Relationships with Factors of 6, 7, 8 and 9 |

Lesson Plan

View Guided Lesson Use division models and equations to solve multiplication problems with unknowns, and use multiplcations models and equations to solve division problems with unknowns to see the inverse relationship. (12-18 min)

Multiplication and division are about working with groups of items and are related. There are many patterns and strategies using known facts that can be used to find the results for unknown facts.

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.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

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.

MGSE3.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.

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

MGSE3.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.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MGSE3.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. By the end of Grade 3, know from memory all products of one-digit numbers.