Students will discover that we can break rectangles and rectangular shapes apart in order to find their areas. This discovery builds on studentsâ€™ understanding of area and gives them a strategy for moving past counting individual squares. They also solidify the idea that the order of factors does not change the product. Students may struggle with how to decompose the numbers in a way that makes it easier to solve.
Key Concepts:
 A given set of factors has the same product, regardless of the order in which the factors are written.
 The area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and a x c.
 We can decompose rectilinear figures because area is additive.
Prior Knowledge Needed:
 Commutative property; Grade 3, Unit 2, 3.OA.B.5
 Area; Grade 3, Unit 2; 3.MD.C.5 a & b, 3.MD.C.6, 3.MD.C.7a
 Multiplication; Grade 3, Unit 1, 3.OA.7
 Arrays; Grade 3, Unit 7; 3.OA.A.3
Units on the Horizon:
 Solving problems using area; (Grade 3, Unit 12)
 Understanding fractions equivalence and comparison; (Grade 4, Unit 5)
Lessons

Lesson objective: Extend understanding that the order of two factors can be switched while still having the same product. Students bring prior knowledge of multiplication from 3.OA.7. and 3.OA.A.3. This prior knowledge is extended to the commutative pro...

Lesson objective: Multiply factors in a different order while keeping the same product. This lesson helps to build procedural skill with the commutative property. Arrays are used here because they highlight the idea that the total stays the same when th...

Lesson objective: Solve problems using the commutative property. This lesson provides an opportunity for students to apply their knowledge and understanding of the commutative property to a reallife situation. Students are asked to determine how many c...

Lesson objective: Understand that a rectangle can be decomposed into two smaller rectangles, and the area of those smaller rectangles can be added together to find the total area of the original rectangle. Students bring prior knowledge of area from 3.M...

Lesson objective: Add the area of two smaller rectangles to compute the area of a larger rectangle. This lesson helps to build procedural skill with using the distributive property to solve area problems. The area model is used here because it supports ...

Lesson objective: Find the area of a rectangle by decomposing one of the side lengths. This lesson helps to build procedural skill with the distributive property. The area model is used here because it supports decomposing rectangles. This work develops...

Lesson objective: Apply the distributive property to realworld area problems. This lesson provides an opportunity for students to apply their knowledge and understanding of the distributive property to a reallife situation. Students are asked to desig...

Lesson objective: Understand that the area of a rectilinear shape is additive. Students bring prior knowledge of area of rectangles from 3.MD.C.5 a & b, 3.MD.C.6, 3.MD.C.7a. This prior knowledge is extended to shapes that are not quadrilaterals as s...

Lesson objective: Add the areas of rectangles within a rectilinear figure to solve for the area of the whole rectilinear figure. This lesson helps to build procedural skill with finding the area of rectilinear figures. The area model is used here becaus...

Lesson objective: Solve area problems in which the figure is rectilinear. This lesson provides an opportunity for students to apply their knowledge and understanding of area of a rectilinear figure to a reallife situation. Students are asked to draw a ...