NC.3.MD.7
Relate area to the operations of multiplication and addition.
Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths.
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems and represent whole-number products as rectangular areas in mathematical reasoning.
Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles.
Step 1: Lesson Standards & Learning Goals
Students extend their understanding of area by transitioning from covering rectangles and counting tiles to repeated addition and then to multiplying the length and the width of a rectangle in order to find the area.
Students are expected to explain why multiplying the side lengths of a rectangle yields the same measurement of area as counting the number of tiles (with the same unit length) that fill the rectangle’s interior. Students who multiply the dimensions to find the area without providing a clear reason why multiplying works have not met the expectation for this standard.
Students also are expected to decompose a rectangle into two smaller rectangles in order to find the area of the smaller rectangles and the larger rectangle. This work overlaps the idea of decomposing a factor (NC.3.OA.1, NC.3.OA.2). The dimensions of the smaller rectangles should be 10 or less. This standard also addresses using multiplication to determine area while solving word problems (NC.3.OA.3). Students are expected to determine the possible dimensions of a rectangle when the area is given.
Sample Essential Questions
What are some strategies to find the area of a rectangle?
Using the same unit of measure, explain why multiplying the side lengths of a rectangle is the same as the number of tiles that fill the rectangle.
How is area related to the operations of multiplication and addition?
Vocabulary
area
decompose
dimensions
length
multiplication
side lengths
repeated addition
unit squares
width
Students will be able to...
Find the area of a rectangle using tiles or arrays and show that the area is the same as when using repeated addition or multiplying side lengths.
Multiply side lengths to find area of rectangles with whole-number side lengths in the context of problem solving.
Explain why multiplying the side lengths of a rectangle yields the same measurement of area as counting the number of tiles (with the same unit length) that fill the rectangle’s interior
Determine the possible dimensions of a rectangle when the area is given.
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.
Relate area to multiplication and addition.
Students will know...
The amount of space inside a shape is its area, and area can be estimated or found using square units.
The area of a rectangle can be found using tiles or arrays, repeated addition, or multiplying side lengths.
The area of irregular shapes can be found by breaking apart the original shape into other shapes for which areas can be found.
Step 2: Assessment
Mastery Connect
NC.3.MD.7 - CO - Howell - Jan.17, 2023
NC.3 - Cluster 6 Review - CO - Howell - Feb. 24, 2023
NC.3.EOG Review B - Howell - CO - May 12, 2023
Step 3: Lesson Instructions
Possible Activating Strategies
Exploration or Experience
Give students the area of a rectangle and have them try to determine possible side lengths.
Ex. Area is 20 square units. Side lengths could be 2 and 10 or 4 and 5.
Image: https://www.eaieducation.com/Product/503472/Color_Tiles_Plastic_-_Set_of_40.aspx
Anchor Chart
Image: https://ccwes.wilkescountyschools.org/apps/pages/index.jsp?uREC_ID=429151&type=d&pREC_ID=1854572
Graphic Organizer
Teacher Resources
Tools 4 NC Teachers
Cluster 6 Lessons
Math Expressions - (Barnes and Hearne) - Standards Alignment
Motivation Math
Think Up! Math
Khan Academy - 3rd Grade Math
Eureka Math/Engage NY Free Resources
Embarc Online (Eureka Math)
Zearn Math - Online Support Practice for Eureka Math (Requires free account)
North Carolina Collaborative for Mathematics Learning - Grade 3 Instructional Framework
NCDPI Resources
Thinking Blocks - Word Problem Practice with Bar Diagrams
You Tube Videos
Fact Practice