Covering & Surrounding
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File Size: | 327 kb |
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Goals for Covering & Surrounding
Students should...
- Understand that perimeter is a measure of linear units needed to surround a two-dimensional shape and that area is a measure of square units needed to cover a two-dimensional shape
- Understand that the linear measurements of the base, height, and slanted height of parallelograms and triangles are essential to finding the area and perimeter of these shapes
- Understand that the surface area of a three-dimensional shape is the sum of the areas of each two-dimensional surface of the shape and that the volume of a rectangular prism is a measure in cubic units of the capacity of the prism
Investigation 1
Vocabulary | |
File Size: | 238 kb |
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In the last two Problems, students explore fixed area and fixed perimeter. These Problems are sometimes referred to as maximum and minimum problems. One variable stays constant while another variable changes, which is a fundamental mathematical tool used to analyze a wide variety of problems. These experiences strengthen students’ understanding of area and perimeter, how they are related, and which measurement to use in solving a problem.
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Investigation 2
Vocabulary | |
File Size: | 284 kb |
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In this Investigation, students find areas and perimeters of triangles. Through these experiences students deepen their understanding of area and perimeter and of what it means to measure area and perimeter. The primary goal is for students to develop, understand, and use the formula for finding the area of a triangle. This is accomplished by first enclosing an acute or right triangle in a rectangle whose height and base match those of the triangle. This produces a figure that shows the area of the triangle is half of the area of the enclosing rectangle. Obtuse triangles are then dealt with by means of some auxiliary line segments. Students also develop understanding that there are many triangles that can be drawn with the same base and height.
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Investigation 3
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File Size: | 164 kb |
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In this Investigation, students deepen their understanding of area and perimeter. The primary goal is for students to develop, understand, and use procedures for finding areas and perimeters of parallelograms. Students decompose parallelograms into two congruent triangles to find that the area of a parallelogram is twice the area of a triangle with the same base and height. As with triangles, students come to understand that there are many parallelograms that can be drawn with the same base and height. In the last problem, polygons are located on a coordinate grid, and students determine the lengths of sides of the vertical and horizontal sides using the coordinates of the vertices. Finally, students find the area and perimeter of polygons by composing polygons into rectangles or decomposing them into triangles.
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Investigation 4
Vocabulary | |
File Size: | 306 kb |
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The main goal of this Investigation is to introduce students to surface area of three-dimensional figures made from triangles and rectangles. This builds on students’ understanding of finding the areas of these polygons. The first Problem introduces surface area by providing nets for rectangular prisms. Students find the number of unit cubes that will fill these prisms to provide a context for revisiting volume of rectangular prisms. Formulas for finding the volume of rectangular prisms were developed in Grades 4 and 5. However, the Grade 6 CCSS revisit volume of prisms with fractional-length sides. The second Problem addresses this topic. The third Problem extends surface area to prisms and pyramids made from rectangles and triangles.
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