Curriculum / Math / 3rd Grade / Unit 4: Area / Lesson 10
Math
Unit 4
3rd Grade
Lesson 10 of 14
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Compose and decompose a rectangle, seeing and making use of the idea that the sum of the areas of the decomposed rectangle is equal to the area of the composed rectangle.
The core standards covered in this lesson
3.MD.C.7.C — Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students might naturally connect work of this lesson to the distributive property. You can discuss that connection and use the notation for the distributive property if students seem ready for it, but this lesson has been designed so that students are not expected to use it and thus is not on the Problem Set. The next lesson will make the connection to the distributive property more explicit.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
The area model below shows the floor plan for a storage closet. The storage closet will have a tiled floor with grey tiles on the left and white tiles on the right. Each tile is 1 square foot.
a. What is the area of the whole floor?
b. What is the area of the floor covered with gray tiles? What is the area of the floor covered with white tiles?
c. What do you notice about your answers to Parts (a) and (b) above? What do you wonder?
Adapted from Illustrative Mathematics task, “Introducing the Distributive Property,”, accessed on Sept. 23, 2022, 4:56 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Use the following area model to answer Parts (a) and (b).
a. Decompose the area model into smaller rectangles whose products you know from memory to be able to find the total product represented by the area model.
b. Find a second way to decompose the area model, then use that decomposition to find its area.
Problem Set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the two rectangles below to answer the questions.
a. Write an equation to represent the area of Rectangle A.
b. Write an equation to represent the area of Rectangle B.
c. Rectangles A and B are pushed together to make a larger rectangle. What is the area of that larger rectangle? Explain.
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
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Lesson 9
Lesson 11
Topic A: Understanding Concepts of Area
Understand that area is an attribute of plane figures that is a measure of how much flat space an object takes up. Find the area of a figure using pattern blocks, which can be used as concrete non-standard units.
3.MD.C.5 3.MD.C.6
Understand that area is measured using square units. Find the area of a figure using square tiles.
Find the area of a rectangle by counting unit squares on grids.
Find the area of a rectangle with incomplete information about its rows and columns of square units.
3.MD.C.6 3.MD.C.7.A
Find the area of a rectangle that has been superimposed over a grid.
Find the area of a rectangle through multiplication of the side lengths.
3.MD.C.7.A 3.MD.C.7.B
Understand standard units for measuring area, including square inches, square centimeters, square feet, and square meters, and choose an appropriate unit to measure the area of various rectangles.
3.MD.C.6
Measure the side lengths of a rectangle to find its area.
3.MD.C.7.B
Solve word problems involving area.
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Topic B: The Distributive Property and Composite Area
3.MD.C.7.C
Apply the distributive property as a strategy to find the total area of a large rectangle.
Recognize area as additive. Find the area of a composite figure as shown on a grid or with all side lengths labeled.
3.MD.C.7.D
Recognize area as additive. Find the area of a composite figure when not all dimensions are given.
Recognize area as additive. Find the area of a complex composite figure.
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