## Grade 3 Eureka Math Module 4 Lessons 9 - 11 Topic C

Foundations for Understanding Area

Standards: 3.MD.C.7.a | 3.MD.C.7.b | 3.MD.C.7.c

These standard cover:

Arithmetic Properties Using Area Models

Builds on: Grade 2 Module 2, Grade 3 Module 1, Grade 3 Module 3

Continued on: Grade 4 Module 3, Grade 4 Module 7

Eureka Math Grade 3 Module 4 Topic C Lesson 9: Arithmetic Properties Using Area Models

Analyze different rectangles and reason about their area.

Standards: 3.MD.C.7.a | 3.MD.C.7.b | 3.MD.C.7.C

In Lesson 9 Students learn to break apart rectangular arrays and reorder the pieces to make new rectangles that have the same area.

Eureka Math Grade 3 Module 4 Topic C Lesson 10: Arithmetic Properties Using Area Models

Apply the distributive property as a strategy to find the total area of a large rectangle by adding two products.

Standards: 3.MD.C.7.a | 3.MD.C.7.b | 3.MD.C.7.C

In earlier modules, students learned how to divide a set of different items into two parts, figure out how many items were in each part, and afterwards find the sum of both parts. Now, students see a link between this interaction and using the distributive property to figure out the unknown size of a side of an array whose area, for example, is 36 square units. They might divide the area into two rectangles: one 5 by 4 and one 4 by 4. The length of the unknown side can be found by adding 5 and 4.

Eureka Math Grade 3 Module 4 Topic C Lesson 9: Arithmetic Properties Using Area Models

Demonstrate the possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property.

Standards: 3.MD.C.7.a | 3.MD.C.7.b | 3.MD.C.7.C

In Lesson 11, students determine all possible whole number side lengths of rectangles with that area using a given number of square units. Students use the associative property to demonstrate that they have found all possible solutions for each given area. Areas of 24, 36, 48, and 72 are chosen to reinforce more difficult multiplication facts. Students understand that different factors produce the same result. For example, they discover that arrays of 4 by 12, 6 by 8, 1 by 48, and 2 by 24 all have an area of 48 square units. They use their understanding of the commutative property to recognize that area models, like arrays in Modules 1 and 3, can be rotated.