UNIT 5 - AREA & VOLUME
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OVERVIEW
In this unit students will:
- Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals.
- Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes.
- Solve real-world and mathematical problems involving area.
- Decipher and draw views of rectangular and triangular prisms from a variety of perspectives.
- Recognize and construct nets for rectangular and triangular prisms.
- Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets.
- Solve real-world problems that require determining the surface area of rectangular and triangular prisms.
- Measure and compute volume with fractional edge lengths (like ½ of a unit) using cubic units of measure.
- Find the volumes of right rectangular prisms by substituting given values for their dimensions into the correct formulas.
- Make the connection that finding the volume given the length (l ) x width (w) is the same as the base (B).
- Solve real-world problems that require determining the volume of right rectangular prisms.
VOCABULARY
- Area: The number of square units it takes to completely fill a space or surface.
- Bases of a Prism: The two faces formed by congruent polygons that lie in parallel planes, all of the other faces being parallelograms.
- Composing: Composing is putting two or more geometric figures.
- Dimension: a measure of spatial length; a linear measurement
- Decomposing: subdividing a polygon
- Equilateral Triangle: A triangle which has all three of its sides equal in length.
- Kite: A quadrilateral with two distinct pairs of equal adjacent sides.
A kite-shaped figure. - Isosceles Triangle: A triangle which has two of its sides equal in length.
- Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
- Polygon: A number of coplanar line segments, each connected end to end to form a closed shape. A regular polygon has all sides equal and all interior angles equal. An irregular polygon sides are not all the same length nor does the interior angles have the same measure.
- Quadrilaterals: Four coplanar line segments linked end to end to create a closed figure.
A 4-sided polygon. - Rectangle: A 4-sided polygon where all interior angles are 90°.
- Rhombus: A quadrilateral with all four sides equal in length.
- Right Triangle: A triangle where one of its interior angles is a right angle (90 degrees).
- Scalene Triangle: A triangle where all three sides are different in length.
- Square: A quadrilateral that has four right angles and four equal sides.
- Trapezoid: A quadrilateral which has at least one pair of parallel sides.
- Bases of a Prism: The two faces formed by congruent polygons that lie in parallel planes, all of the other faces being parallelograms.
- Edge: The intersection of a pair of faces in a three-dimensional figure.
- Face: One of the polygons that makes up a polyhedron.
- Lateral Faces: In a prism, a face that is not a base of the figure.
- Net: A two-dimensional figure that, when folded, forms the surfaces of a three-dimensional object.
- Polyhedron: A 3-dimensional figure that has polygons as faces.
- Prism: A polyhedron with two parallel and congruent faces, called bases, and all other faces that are parallelograms.
- Rectangular prism: A solid (3-dimensional) object which has six faces that are rectangles.
- Surface area: The total area of the 2-dimensional surfaces that make up a 3-dimensional object.
- Triangular prism: A prism whose bases are triangles. A solid (3-dimensional object what has five faces: three rectangles and two bases.
- Vertices: The common endpoint of two or more rays or line segments