Key Concept: Multiplication is used to find the product of groups of items and is more efficient than repeated addition.

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

3.OA.A.1--Interpret products of whole numbers, e.g., interpret 5x7 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.#### Georgia

MGSE3.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.

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.) IEP Goals

This topic focuses on building the conceptual understanding that multiplication is a procedure used to determine a total value when equal groups are combined. Through the use of multiple models and the “groups of” paraphrase, students link multiplication to repeated addition for groups of 5 and 10. They apply skip counting and the commutative property to solve problems with and without context.

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

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.)

- Given multiplication equations using the foundation facts of 5 and 10 and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy within the first quarter.
- Given a multiplication story problem involving the foundation facts of 5 and 10 and a paraphrasing strategy, 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.
- Given a set of 2 factors containing at least a 5 or a 10, the student will write a multiplication equation and use either skip counting or the commutative property to correctly solve for the product without the use of models for 5 out of 6 examples in 3 consecutive sessions.

Unit Launcher

View Midtown Movie Schedule: Discussion Guide and KWL Chart

3.1-1-1 Multiplying with Groups of 5 and 10: Modeling and Skip Counting |

View Guided Lesson Make models and use skip counting or repeated addition to find the total for groups of 5 and 10, then complete a "groups of" sentence. (12-18 min)

3.1-1-2 Multiplying with Groups of 5 and 10: Modeling with Arrays |

View Guided Lesson Make arrays to find the total for groups of 5 and 10, then complete a "groups of" sentence. (12-18 min)

3.1-1-3 Multiplying with Groups of 5 and 10: Writing Equations |

View Guided Lesson Write a “groups of” sentence and use models to find the product of a word problem for the factors 5 and 10. (12-18 min)

3.1-1-4 Multiplying by 5 and 10: Commutative Property |

View Guided Lesson Make models, complete "groups of" sentences, and write equations that demonstrate the commutative property for the factors 5 and 10. (12-18 min)

3.1-1-5 Multiplying with Groups of 5 and 10: Numbers Only |

View Guided Lesson Write equations and solve word problems for products when one factor is 5 or 10. (12-18 min)

Real World Investigation Part 1

View Midtown Movie Schedule: Midtown'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 into equal shares of 8 objects each.#### 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. IEP Goals

This topic focuses on building the conceptual understanding that division is related to multiplication. While multiplication is a procedure used to determine a total value when equal groups are combined, division is a procedure in which equal groups are removed from a starting amount. Through the use of multiple models and the “How many groups of ___ in ___” sentence students link division to repeated subtraction for groups of 5 and 10.

- Given division equations using the foundation facts of 5 and 10 and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy.
- Given a set of division problems or prompts using the foundation facts of 5 and 10, the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.
- Given a division story problem involving foundation facts and a paraphrasing strategy, 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.
- Given a multiplication equation containing foundation facts and the skip counting strategy, the student will solve the problem.

3.1-2-1 Dividing with Divisors of 5 and 10: Modeling |

Lesson Plan

View Guided Lesson Make models and count the number of "skips" or groups of 5 and 10 in a starting amount, then complete a "groups of" sentence. (12-18 min)

3.1-2-2 Dividing with Divisors of 5 and 10: 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 for the divisors 5 and 10. (12-18 min)

3.1-2-3 Modeling Inverse Relationships with Factors of 5 and 10 |

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)

3.1-2-4 Dividing with Divisors of 5 and 10: Numbers Only |

Lesson Plan

View Guided Lesson Write equations and solve word problems for divisors of 5 or 10 without models. (12-18 min)

Real World Investigation Part 2

View Midtown Movie Schedule: Create Some Data

Key Concept: Multiplication is used to find the product of groups of items and is more efficient than repeated addition.

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

3.OA.A.1--Interpret products of whole numbers, e.g., interpret 5x7 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.#### Georgia

MGSE3.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.

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.) IEP Goals

This topic focuses on building the conceptual understanding that multiplication is a procedure used to determine a total value when equal groups are combined. Through the use of multiple models and the “groups of” paraphrase, students link multiplication to repeated addition for groups of 0, 1, 2 & 4. They apply skip counting and the commutative property to solve problems with and without context.

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

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.)

- Given multiplication equations using the foundation facts of 0, 1, 2 & 4 and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy within the first quarter.
- Given a multiplication story problem involving the foundation facts of 0, 1, 2 & 4 and a paraphrasing strategy, 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.
- Given a set of 2 factors containing at least a 0, 1, 2 & 4, the student will write a multiplication equation and use either skip counting or the commutative property to correctly solve for the product without the use of models for 5 out of 6 examples in 3 consecutive sessions.

3.1-3-1 Multiplying with Groups of 0, 1, 2, and 4: Modeling |

Lesson Plan

View Guided Lesson Make models and use skip counting or repeated addition to find the total for groups of 0, 1, 2, and 4, then complete a "groups of" sentence. (12-18 min)

3.1-3-2 Multiplying with Groups of 0, 1, 2, and 4: Writing Equations |

Lesson Plan

View Guided Lesson Write a “groups of” sentence and use models to find the product of a word problem for the factors 0, 1, 2 and 4. (12-18 min)

3.1-3-3 Multiplying by 1, 2, and 4: Commutative Property |

Lesson Plan

View Guided Lesson Make models, complete "groups of" sentences and write equations that

demonstrate the commutative property for the factors 1, 2 and 4. (12-18 min)

demonstrate the commutative property for the factors 1, 2 and 4. (12-18 min)

3.1-3-4 Multiplying with Groups of 0, 1, 2, and 4: Numbers Only |

Lesson Plan

View Guided Lesson Write equations and solve word problems for products when one factor is a 0, 1, 2 or 4 without models. (12-18 min)

Real World Investigation Part 3

View Your Movie Schedule: 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 into equal shares of 8 objects each.#### 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. IEP Goals

This topic focuses on building the conceptual understanding that division is related to multiplication. While multiplication is a procedure used to determine a total value when equal groups are combined, division is a procedure in which equal groups are removed from a starting amount. Through the use of multiple models and the “How many groups of ___ in ___” sentence students link division to repeated subtraction for groups of 1, 2 & 4.

- Given division equations using the foundation facts of 1, 2 & 4. and visual models, the student will gain fluency by passing automaticity tests with at least 90% accuracy.
- Given a set of division problems or prompts using the foundation facts of 1, 2 & 4. , the student will write equations and apply previously learned strategies to find the quotient with 90% accuracy for 3 out of 5 trials.
- Given a division story problem involving foundation facts and a paraphrasing strategy, 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.
- Given a multiplication equation containing foundation facts and the skip counting strategy, the student will solve the problem.

3.1-4-1 Modeling with Divisors of 0, 1, 2, and 4: Find the Number of Groups |

Lesson Plan

View Guided Lesson Make models to find how many groups of 1, 2 and 4 are contained in a starting amount, then complete a "groups of" sentence. (12-18 min)

3.1-4-2 Dividing with Divisors of 0, 1, 2, and 4: Writing Equations |

Lesson Plan

View Guided Lesson Make models and write equations to find the quotient of word problems using factors of 0, 1, 2, and 4. (12-18 min)

3.1-4-3 Modeling Inverse Relationships with Factors of 1, 2 and 4 |

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)

Big Idea:

Multiplication and division are related operations. Multiplication is about combining equal groups of items to find the total. In division equal groups of items are removed from a starting amount.

Description

This Big Idea develops both the conceptual understanding and procedural skills of multiplying and dividing with whole numbers, specifically foundation facts of 1,2,4,5 and 10. These facts can be used to find the product or quotients of other facts.

Students link the multiplication to skip counting and learn that the use of multiplication is more efficient than repeated addition operation. They learn that in division the answer represents the number of same sized groups found in a starting amount and is more efficient than repeated subtraction. Students learn the commutative property of multiplication and the distributive property. Lessons require students to use models and strategies to represent foundation in isolation, in context and to solve story problems.

Multiplication and division are related operations. Multiplication is about combining equal groups of items to find the total. In division equal groups of items are removed from a starting amount.

Description

This Big Idea develops both the conceptual understanding and procedural skills of multiplying and dividing with whole numbers, specifically foundation facts of 1,2,4,5 and 10. These facts can be used to find the product or quotients of other facts.

Students link the multiplication to skip counting and learn that the use of multiplication is more efficient than repeated addition operation. They learn that in division the answer represents the number of same sized groups found in a starting amount and is more efficient than repeated subtraction. Students learn the commutative property of multiplication and the distributive property. Lessons require students to use models and strategies to represent foundation in isolation, in context and to solve story problems.

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 into equal shares of 8 objects each.

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

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.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.)