In this unit, students begin to integrate their understanding of the inverse relationship between multiplication and division and their knowledge of the properties of multiplication to solve problems related to area. They begin using the formula \(l \times w\) as a more efficient tool for solving area problems than using a concrete model. Students may struggle as they move from using visual models to the area formula and will need a strong foundational understanding of the concept of area in order to move to an abstract representation. Students must also understand how to use the properties of multiplication (commutative and associative), as well as the distributive property, to help them solve problems.
Key Concepts:
 We can use the relationship between the three whole numbers in a multiplication or division equation to identify a missing number that makes the equation true.
 We can use the properties of multiplication and the relationship between multiplication and division to solve equations with an unknown.
 Area relates to multiplication and addition and that knowledge can be used to solve real world problems involving area.
Prior Knowledge Needed:
 Compare two twodigit numbers; (Grade 1, Unit 13, 1.NBT.B.3)
 Exploring equal groups as a foundation for multiplication and division; (Grade 3, Unit 1, 3.OA.1, 3.OA.2)
 Developing conceptual understanding of area (Grade 3, Unit 2, 3.OA.B.5, 3.MD.C.5,6,7)
 Understanding the relationship between multiplication and division (Grade 3, Unit 7, 3.OA.A.2,3, 3.OA.B.6, 3.OA.C.7)
 Developing strategies for multiplication and division (Grade 3, Unit 9, 3OA.B.5d, 3.MD.C.7c,d)
Units on the Horizon:
 Demonstrating conceptual fluency in problem solving; (Grade 3, Unit 15, 3.OA.7, 3.OA.8)
 Using multiplication and division strategies with larger numbers; (Grade 4, Unit 2, 4.MD.3 4.NBT.5,6)
 Using multiplication and division to solve measurement problems; (Grade 3, Unit 14)
Lessons

Lesson objective: Understand that a relationship exists between the three whole numbers in a multiplication and division equation that helps to identify a missing number to make an equation true. Students bring prior knowledge of multiplication and divi...

Lesson objective: Write related multiplication and division equations with unknowns. This lesson helps to build fluency with writing related multiplication and division equations with variables. The area model is used here because it illustrates what th...

Lesson objective: Apply understanding of the relationship between the three whole numbers in a multiplication and division equation to solve real world problems. This lesson provides an opportunity for students to apply their knowledge and understanding...

Lesson objective: Use the properties of multiplication and the relationship between multiplication and division to solve equations with an unknown. Students bring prior knowledge of the properties of multiplication from 3.OA.B.5. This prior knowledge is...

Lesson objective: Use the associative property to solve multiplication problems. This lesson helps to build procedural skill with using the associative property as a strategy to solve problems. The area model is used here because it can illustrate the e...

Lesson objective: Apply properties of multiplication to solve problems. This lesson provides an opportunity for students to apply their knowledge and understanding of the associative and distributive properties of multiplication to a reallife situation...

Lesson objective: Use the relationship between multiplication and addition to solve real world problems involving area. Students bring prior knowledge of the concept of area from 3.MD.C.7a. This prior knowledge is extended to using addition and multipli...

Lesson objective: Use multiplication and addition to solve area problems. This lesson helps to build fluency with calculating area. The area model is used here because it highlights the relationship between area and multiplication and addition. This wor...

Lesson objective: Solve real world area problems using multiplication and addition. This lesson helps to build procedural skill with solving real world area problems. The area model is used here because it supports the connection between real world area...

Lesson objective: Apply knowledge of the relationship between multiplication and addition to solve a real world area problem. This lesson provides an opportunity for students to apply their knowledge and understanding of area to a reallife situation. S...