Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 6
Math
Unit 7
6th Grade
Lesson 6 of 17
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Solve real-world and mathematical problems involving area of polygons.
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
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A carpenter is building a new wall for a house that he is renovating. He knows that there will be a door and a window in the wall. Around the door and window, he uses wooden board to create the wall. A blueprint of the wall is shown below.
How much wooden board, in square feet, does the carpenter need to build the wall?
Jamie is planning to cover a wall with red wallpaper. The dimensions of the wall are shown below.
a. How many square feet of wallpaper are required to cover the wall?
b. Wallpaper comes in long rectangular strips that are 24 inches wide. If Jamie lays the strips of wallpaper vertically, how many strips will she use and how long will each strip be? Explain.
c. If Jamie lays the strips of wallpaper horizontally, can she cover the wall without wasting any wallpaper? Explain.
Wallpaper Descomposition, accessed on March 20, 2018, 9:38 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.
Find the area of the shaded region in square units. Show your reasoning.
Grade 6 Unit 1 Lesson 11 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 20, 2018, 9:42 a.m..
A set of suggested resources or problem types that teachers can turn into a problem set
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
The diagram below shows one wall in an attic. The shape of the wall is a trapezoid, and there is a rectangular window in the wall.
Not including the window, what is the area of the wall’s surface?
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 5
Lesson 7
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
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.
Find the area of polygons using composition and decomposition.
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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.1 6.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.2 6.G.A.4
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