Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 5
Math
Unit 7
6th Grade
Lesson 5 of 17
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Lesson Notes
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Find the area of polygons using composition and decomposition.
The core standards covered in this lesson
6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
The foundational standards covered in this lesson
3.MD.C.7.D — 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, applying this technique to solve real world problems.
4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students will have further opportunities to find the area of irregular polygons using composition and decomposition in Lessons 7–9; in these lessons, the polygons will be located in the coordinate plane.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Jung's teacher drew a shape on the board (shown below), and asked the students to find the area of the shape. Describe a method Jung could use to find the area and then determine the area.
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Find the area of the trapezoid below in three different ways by:
a. Drawing a rectangle around the trapezoid and subtracting the additional area around it
b. Dividing the trapezoid into two triangles using a diagonal line across the trapezoid
c. Dividing the trapezoid into two right triangles and a rectangle
Find the area of the triangle in the grid below.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find the area that is shaded in each figure.
a.
b.
c.
d.
Finding Areas of Polygons, accessed on July 1, 2016, 9:08 a.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.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Solve real-world and mathematical problems involving area of polygons.
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
Standards
6.G.A.1
Find the area of right triangles.
Find the area of acute triangles using height and base.
Find the area of any triangle using height and base.
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Topic B: Polygons in the Coordinate Plane
Draw polygons in the coordinate plane and find area and perimeter (Part 1).
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 2).
Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.
6.G.A.16.G.A.3
Topic C: Volume of Rectangular Prisms
Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
6.G.A.2
Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.
Topic D: Nets and Surface Area
Describe features of and identify nets that match prisms and pyramids.
6.G.A.4
Create nets and use them to find surface area of three-dimensional figures.
Find the surface area of three-dimensional figures with and without nets.
Find surface area and volume in real-world problems.
6.G.A.26.G.A.4
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