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 three-dimensional objects. In preparation for work on congruence and similarity in later grades, they reason about relationships among informal geometric constructions. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two-and three-dimensional 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 three-dimensional objects. In preparation for work on congruence and similarity in later grades, they reason about relationships among informal geometric constructions. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
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What will my child learn?
Students will:
Solve real-world 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 real-world 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 real-world 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 real-world and mathematical problems.
6.G.A.4
Represent three-dimensional 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 real-world 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 two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Solve real-life 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 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 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 real-world 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 real-world 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 real-world 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 real-world 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 three-dimensional 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 real-world 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 two-dimensional figures that result from slicing three-dimensional 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 real-life 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 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 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?
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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 easy-to-use 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
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