In this unit, students develop strategies to extend their understanding of multiplication and division using larger numbers. They begin exploring multiplication with multidigit factors by creating arrays using base ten blocks, and later solve problems using an area model. Students use area models and partial quotients to solve division problems, discovering how the context of the problem determines the interpretation of the remainder. By the end of the unit, students will explore the relationship between multiplication and division to solve realworld problems including perimeter and area.
Key Concepts:
 Place value understanding allows us to multiply multidigit numbers in different ways. (Lesson 1)
 Place value understanding allows us to divide multidigit numbers in different ways. (Lesson 6)
 The remainder can be interpreted as the whole number amount left over when a quantity is divided by its greatest wholenumber factor (Lesson 8)
 We can use the relationship between multiplication and division to solve mathematical and realworld problems. (Lesson 11)
Prior Knowledge Needed:
 Multiplication and division can be represented as arrays; (Grade 3, Unit 1, 3.OA.A.1 )
 We can use square units and using side lengths to find the area of a square; (Grade 3, Unit 2, 3.MD.C.5a )
 We can use the relationship of multiplication and division to solve equations with an unknown; (Grade 3, Unit 12, 3.OA.A.4)
Units on the Horizon:
 Solving measurement problems using the four operations (Grade 4, Unit 8)
 Problem solving with whole numbers (Grade 4, Unit 14)
 Developing multiplication and division strategies (Grade 5, Unit 2)
Lessons

Lesson objective: Understanding place value allows us to multiply more efficiently using base ten blocks and arrays. Students bring prior knowledge of multiplication arrays from 3.OA.A.1. This prior knowledge is extended to place value in arrays as stud...

Lesson objective: Multiply using place value representations. This lesson helps to build fluency with one by threedigit multiplication. Arrays and area models are used here because they support place value decomposition for efficiency. This work devel...

Lesson objective: Using place value and array models can make it easier for us to multiply two multidigit numbers. Students bring prior knowledge of multiplication arrays from 3.OA.A.1. This prior knowledge is extended to multidigit arrays as students...

Lesson objective: Multiply multidigit numbers using arrays and area models. This lesson helps to build fluency with multiplying multidigit numbers. Arrays and area models are used here because they allow for place value decomposition and clearly repre...

Lesson objective: Apply various place value representations to solve multidigit multiplication problems. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplication and place value to a reallife situat...

Lesson objective: Extend understanding of place values and arrays to answer multidigit division problems. Students bring prior knowledge of arrays from 3.OA.A.3. This prior knowledge is extended to multidigit division problems as students use arrays a...

Lesson objective: Divide multidigit numbers using arrays and partial quotients. This lesson helps to build fluency with multidigit division. Arrays and partial quotients are used here because they clearly display the division taking place in the probl...

Lesson objective: Understand the context of the problem will determine the appropriate way to handle a remainder. Students bring prior knowledge of division from 3.OA.A.2 . This prior knowledge is extended to remainders as students determine what to do ...

Lesson objective: Find quotients and determine how to interpret a remainder. This lesson helps to build fluency with interpeting remainders. Partial quotients is used here because its allows students to clearly follow the division and better understand ...

Lesson objective: Apply knowledge of place value decomposition to divide multidigit numbers and interpret remainders based on question context. This lesson provides an opportunity for students to apply their knowledge and understanding of dividing mult...

Lesson objective: Understand that we can use the area formula to determine the length of a missing side. Students bring prior knowledge of determining the area of a rectangle by tiling it with unit squares or by multiplying the side lengths (3.MD.C.7.a)...

Lesson objective: Divide to find the measure of an unknown side of a rectangle. This lesson helps to build fluency with whole number division. Partial quotients is used here because it further develops a strategy for solving division problems when the e...

Lesson objective: Apply area and perimeter formulas to realworld problems. This lesson helps to build procedural skill of finding the area and perimeter. The four operations are used throughout the lesson, as students are asked to select a strategy bas...

Lesson objective: Find the area of an irregular figure. This lesson helps to build procedural skills with finding the area of an irregular figure. Multiplication, addition, and subtraction are used as students integrate different operations to extend th...

Lesson objective: Apply formulas to find area, perimeter, and the measure of a missing side. This lesson provides an opportunity for students to apply their knowledge and understanding of area and perimeter to a reallife situation. Students are asked t...