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Big Idea 2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes.

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Benchmarks MA.7.G.2.1: Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2: Use formulas to find surface areas and volume of three-dimensional composite shapes.

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Vocabulary The vocabulary can easily be generated from the reference sheet and the Key. This will help you not only to review key vocabulary but the symbols for each word.

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Vocabulary Take out the vocabulary sheet provided for you and fill in the second column with the definition for each word. – Vocabulary Activity Sheet Vocabulary Activity Sheet Next label the part image in the third column with the letter representing the corresponding vocabulary word. If there is no image draw one.

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Review Perimeter Use the worksheets to review circumference and Pi – Rolling a circle Rolling a circle – Archemedes estimation of Pi Archemedes estimation of Pi Use the following PowerPoint to review Perimeter – Perimeter PowerPoint Perimeter PowerPoint

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Review Topics GeoGebra activities for Area of Polygons and Circles Rectangles: – Area of a Rectangle Area of a Rectangle Parallelograms: – Area of a Parallelogram Area of a Parallelogram Triangles: – Area of a Triangle Area of a Triangle

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Review Topics GeoGebra activities for Area of Polygons and Circles Trapezoids: – Area of a Trapezoid Area of a Trapezoid Circles: – Area of a Circles Area of a Circles

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Review Composite Shapes PowerPoint for discussing area and perimeter of composite figures. – Composite Shapes PowerPoint Composite Shapes PowerPoint

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Side 2 Bottom Back Top Side 1 Front Side 2 Bottom Back Top Side 1 Front Length (L) Breadth (B) Height (H) Rectangular Solid GeoGebra for a Cube

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Bases Do the words Bottom and Base mean the same thing?

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Base of a 3D Figure Prism: a prism has 2 Bases and the bases, in all but a rectangular prism, are the pair of non- rectangular sides. These sides are congruent, Parallel. Bases Triangular Prism

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Base of a 3D Figure Bases Cylinder GeoGebra Net for Cylinder

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Base of a 3D Figure Base Pyramid: There is 1 Base and the Base is the surface that is not a triangle.

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Base of a 3D Figure Pyramid: In the case of a triangular pyramid all sides are triangles. So the base is typically the side it is resting on, but any surface could be considered the base. Base

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Net Activity Directions sheet Net Sheets Scissors Tape/glue

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Building Polyhedra

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GeoGebra Nets Net of a Cube Net of a Square Pyramid Net of a Cylinder Net of a Cone Net of an Octahedron

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The net w w w w b h h h h w b b b bb h h h h ? ? ?

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Total surface Area = Total surface Area w w h b b b h h b x h w x h w x b + + +++ = 2(b x h) + 2(w x h) + 2(w x b) = 2(b x h + w x h + w x b)

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Total surface Area

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Nets of a Cube GeoGebra Net of a Cube

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Activity: Nets of a Cube Given graph paper draw all possible nets for a cube. Cube Activity Webpage

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Nets of a Cube

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Lateral Area is the surface area excluding the base(s). Lateral Area Net of a Cube

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Lateral Area Bases Lateral Sides

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Lateral Area Bases Lateral Surface Net of a cylinder

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Stations Activity At each station is the image of a 3D object. Find the following information: – Fill in the boxes with the appropriate labels – Write a formula for your surface area – Write a formula for the area of the base(s) – Write a formula for the lateral area

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Net handouts and visuals Printable nets – http://www.senteacher.org/wk/3dshape.php http://www.senteacher.org/wk/3dshape.php – http://www.korthalsaltes.com/index.html http://www.korthalsaltes.com/index.html – http://www.aspexsoftware.com/model_maker_nets_ of_shapes.htm http://www.aspexsoftware.com/model_maker_nets_ of_shapes.htm – http://www.mathsisfun.com/platonic_solids.html http://www.mathsisfun.com/platonic_solids.html GeoGebra Nets – http://www.geogebra.org/en/wiki/index.php/User:K note http://www.geogebra.org/en/wiki/index.php/User:K note

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Volume The amount of space occupied by any 3- dimensional object. The number of cubic units needed to fill the space occupied by a solid

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Volume Activity Grid paper Scissors 1 set of cubes Tape

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Solid 1

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Solid 2

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Solid 3

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Solids 4 & 5 Circular Base Pentagon Base

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Volume The number of cubic units needed to fill the space occupied by a solid. 1cm Volume = Base area x height = 1cm 2 x 1cm = 1cm 3

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Rectangular Prism Volume = Base area x height = (b x w) x h = B x h L L L Total surface area = 2(b x w + w x h + bxh)

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Comparing Volume h b w When comparing the volume of a Prism and a Pyramid we focus on the ones with the same height and congruent bases. b w h

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Comparing Volume h b w w b w b h

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h l

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h l

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b w h h b w Volume = B x h = b x w x hVolume = 1/3 (B x h) = 1/3 (b x w x h) Prism Pyramid

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2(LxB + BxH + LxH) b x w x h Rectangular Solid 6S 2 S3S3 Cube Sample net Total surface area VolumeFigureName

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Volume formulas Prism and Cylinder – V=B x h Pyramid and Cone – V=1/3 (B x h)

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Composite figure 8 12

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