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KUD Organizer
Course: Junior High Mathematics (Grades 7-8)
Unit: Geometry
Approximate Days: 30-35 days
STANDARDS:
CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them.
CC.2.3.7.A.1 Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
2.3.8.A.1 Apply the concepts of volume of cylinders, cones and spheres to solve real-world and mathematical problems.
2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.
2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.
UNDERSTAND:
Geometry is the investigation of the relationships and patterns that exist within shapes.
Two-dimensional geometric figures are representations of our three-dimensional world. Experimenting with and investigating the
relationships between two- and three-dimensional geometric figures connects and integrates these concepts for problem solving.
That a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations,
reflections and translations. (Two-dimensional figures are similar if the second can be obtained by these methods and dilations.)
Geometric figures can be transformed, analyzed and measured in a variety of ways; an understanding of these processes is critical to
understanding the nature of shape and being able to solve real-world problems that involve shape.
KNOW:
DO:
How to describe and apply properties of
geometric figures.
Solve problems involving scale drawings of geometric figures, including finding length
and area.
How to identify, use and describe
properties of angles and their measures.
Identify or describe the properties of all types of triangles based on angle and side
measure.
How to determine circumference, area,
surface area, and volume.
Use and apply the triangle inequality theorem.
The properties of a circle (circumference,
diameter, radius)
The effects of scale factoring on the area
and volume of geometric figures
The characteristics of similar and congruent
shapes
The relationships between line segments
on geometric solids (parallel, perpendicular,
skew)
The relationships that angles in a diagram
or figure share (i.e., supplementary angles,
complementary angles, vertical angles,
adjacent angles)
The possible types of transformations on a
geometric figure.
How to use the Pythagorean Theorem to
find the length of a side on any right
triangle.
Describe the two-dimensional figures that result from slicing three-dimensional
figures.
Example: Describe plane sections of right rectangular prisms and right rectangular pyramids.
Identify and use properties of supplementary, complementary and adjacent angles in
a multistep problem to write and solve simple equations for an unknown angle in a
figure.
Identify and use properties of angles formed when two parallel lines are cut by a
transversal (e.g., angles may include alternate interior, alternate exterior, vertical,
corresponding).
Find the area and circumference of a circle.
Solve problems involving area and circumference of a circle(s). Formulas will be
provided.
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. Formulas will be provided.
Demonstrate constructing support to justify a figure’s volume, surface area, and area.
Demonstrate inductive reasoning to generalize perimeter and area of a compound
figure.
Given two shapes, describe a sequence of transformations that exhibits the similarity
or congruence between them.
Apply the converse of the Pythagorean Theorem to show a triangle is a right triangle.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles
in real-world and mathematical problems in two- and three-dimensions.
Apply the Pythagorean Theorem to find the distance between two points in a
coordinate plane.
KEY VOCABULARY:
Scale drawing, scalene, isosceles, equilateral, acute obtuse, right, cross-section, supplementary angles, complementary angles,
vertical angles, adjacent angles, parallel, perpendicular, skew, alternate interior angles, alternate exterior angles, corresponding
angles, transversal, sum of interior angles, circumference, diameter, radius, perimeter, area, volume, surface area, inductive
reasoning, deductive reasoning, similar, congruent, two-dimensional surface, three-dimensional solid, transformation, translation,
reflection, rotation, dilation, Pythagorean Theorem, hypotenuse, leg, converse