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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] (6) 26 :
26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 5, Topic A: Area of Triangles, Quadrilaterals, and Polygons
URL: https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-overview
Description:

In Module 5, Topic A, students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. They determine that area is additive. Students learn through exploration that the area of a triangle is exactly half of the area of its corresponding rectangle. In Lesson 1, students discover through a composition that the area of a parallelogram is the same as a rectangle. In Lesson 2, students compose rectangles using two copies of a right triangle. They extend their previous knowledge about the area formula for rectangles (4.MD.A.3) to evaluate the area of the rectangle using A = bh and discover through manipulation that the area of a right triangle is exactly half that of its corresponding rectangle. In Lesson 3, students discover that any triangle may be decomposed into right triangles, and in Lesson 4, students further explore all triangles and discover through manipulation that the area of all triangles is exactly half the area of its corresponding rectangle.  During this discovery process, students become aware that triangles have altitude, which is the length of the height of the triangle. The altitude is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. The opposite side is called the base. Students understand that any side of the triangle can be a base, but the altitude always determines the base. They move from recognizing right triangles as categories (4.G.A.2) to determining that right triangles are constructed when altitudes are perpendicular and meet the base at one side. Acute triangles are constructed when the altitude is perpendicular and meets within the length of the base, and obtuse triangles are constructed when the altitude is perpendicular and lies outside the length of the base. Students use this information to cut triangular pieces and rearrange them to fit exactly within one half of the corresponding rectangle to determine that the area formula for any triangle can be determined using A = 1/2(bh).

In Lesson 5, students apply their knowledge of the area of a triangular region, where they deconstruct parallelograms, trapezoids, and other quadrilaterals and polygons into triangles or rectangles in order to determine the area. They intuitively decompose rectangles to determine the area of polygons. Topic A closes with Lesson 6 where students apply their learning from the topic to find areas of composite figures in real-life contexts, as well as determine the area of missing regions (6.G.A.1).



   View Standards     Standard(s): [MA2019] (6) 26 :
26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.
Subject: Mathematics (6)
Title: Area of Irregular Figures StudyJam
URL: https://studyjams.scholastic.com/studyjams/jams/math/measurement/area-irregular-figures.htm
Description:

In this interactive activity, students will be led through steps to calculate the area of irregular figures. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.



   View Standards     Standard(s): [MA2019] (6) 26 :
26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.
[MA2019] REG-7 (7) 22 :
22. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.
Subject: Mathematics (6 - 7)
Title: Area of a Triangle StudyJam
URL: https://studyjams.scholastic.com/studyjams/jams/math/measurement/area-triangle.htm
Description:

In this interactive activity, students will be led through steps to calculate the area of a triangle. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.



ALEX Classroom Resources: 3

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