Grade 5 GT Mathematics
Geometry (6.G/7.G)
Students build on their work with area
in elementary school by reasoning about relationships among shapes to
determine area, surface area, and volume. They find areas of right
triangles, other triangles, and special quadrilaterals by decomposing
these shapes, rearranging or removing pieces, and relating the shapes
to rectangles. Using these methods, student discuss, develop, and
justify formulas for areas of triangles and parallelograms. Students
find areas of polygons and surface area they can determine. They reason
about right rectangular prisms with fractional side lengths to extend
formulas for the volume of a right rectangular prism to fractional side
lengths. They prepare for work on scale drawings and constructions in by drawing polygons in the coordinate plane.
Students also continue their work with area, solving problems involving the area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in later grades, they reason about relationships among informal geometric constructions. Students work with threedimensional figures, relating them to twodimensional figures by examining crosssections. They solve realworld and mathematical problems involving area, surface area, and volume of twoand threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
Students also continue their work with area, solving problems involving the area and circumference of a circle and surface area of threedimensional objects. In preparation for work on congruence and similarity in later grades, they reason about relationships among informal geometric constructions. Students work with threedimensional figures, relating them to twodimensional figures by examining crosssections. They solve realworld and mathematical problems involving area, surface area, and volume of twoand threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
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What will my child learn?
Students will:
Solve realworld and mathematical problems involving area, surface area, and volume.
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 realworld and mathematical problems.
6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems.
6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.
6.G.A.4
Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.
Draw construct, and describe geometrical figures and describe the relationships between them.
7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
7.G.A.3
Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.6
Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step problem to write and solve simple equations for an unknown angle in a figure.
Students will:
Solve realworld and mathematical problems involving area, surface area, and volume.
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 realworld and mathematical problems.
 Background Info. & Guided Practice
 Check for Understanding: Area of Triangles  Area of Triangles 2  Area of Quadrilaterals and Polygons  Area of Parallelograms  Areas of Trapezoids, Rhombi, and Kites  Finding Area by Composing and Decomposing Shapes
 Enrichment Tasks: Finding Areas of Polygons  Same Base and Height, Variation 1
6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems.
 Check for Understanding: Volume with Unit Cubes 2  Volume with Fractions  Volume Word Problems with Fractions
 Enrichment Tasks: Banana Bread  Computing Volume Progression 1
6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems.
 Background Info. & Guided Practice
 Check for Understanding: Drawing Polygons  Drawing Polygons 2  Rectangles on the Coordinate Plane
 Enrichment Tasks: Polygons in a Coordinate Plane
6.G.A.4
Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.
 Check for Understanding: Nets of 3D Figures  Surface Area Using Nets  Surface Area
 Enrichment Tasks: Christo's Building  Painting Barn
Draw construct, and describe geometrical figures and describe the relationships between them.
7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
 Background Info. & Guided Practice
 Check for Understanding: Constructing 2D Figures  Constructing Triangles
7.G.A.3
Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
 Background Info. & Guided Practice
 Check for Understanding: Slicing 3D Figures
 Enrichment Tasks: Cube Ninjas!
Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
 Background Info. & Guided Practice
 Check for Understanding: Area of a Circle  Area and Circumference of Circles  Radius, Diameter and Circumference
 Enrichment Tasks: Measuring the area of a circle*  Designs*
7.G.B.6
Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
 Check for Understanding: Area, Volume and Surface Area  Solid Geometry
 Enrichment Tasks: Sand Under the Swing Set*  Drinking the Lake
7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step problem to write and solve simple equations for an unknown angle in a figure.
 Background Info. & Guided Practice
 Check for Understanding: Complimentary & Supplementary Angles  Quadrilateral Angles  Vertical Angles  Solving for Unknown Angles
What are some signs of student mastery?

Tools & Technology
NCTM's Isometric Drawing Tool (requires Java) can be used to create dynamic drawings on digital isometric dot paper. Draw net figures using edges, faces, or cubes. You can shift, rotate, color, break into parts, and view in 2‑ or 3‑dimensions. GeoGebra is a dynamic math software tool that allows users to explore geometry, algebra, tables, graphing, statistics and other areas of math in one easytouse package. It can be downloaded for FREE on a computer or tablet device. 
More 4 U
Watch a video about "Finding the Areas of Triangles, Parallelograms, and Trapezoids." Watch a video of a seventh grade teacher extending the concepts in this unit to discovering the formula for the surface area of a cylinder.
Source: The Teaching Channel
