Download Document

KUD Organizer
Course: Pre-Algebra
Unit: Geometry and Measurement
Approximate Days:
STANDARDS:
CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.
CC.2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.
CC.2.3.8.A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
UNDERSTAND:
There exists in all geometric shapes and figures relationships between sides, angles, sides and angles, and measurement such that
formulas can be used to model and interpret these relationships.
KNOW:
How to apply properties of geometric
transformations to verify congruence or
similarity.
How to solve problems involving right
triangles by applying the Pythagorean
theorem.
The formulas for perimeter, area, surface
area and volume for geometric shapes.
DO:
Identify and apply properties of rotations, reflections, and translations. Example:
Angle measures are preserved in rotations, reflections, and translations.
Given two congruent figures, describe a sequence of transformations that exhibits the
congruence between them.
Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures, using coordinates.
Given two similar two-dimensional figures, describe a sequence of transformations
that exhibits the similarity between them.
How to apply area formulas for
parallelograms and trapezoids.
Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
How to apply the circumference and area
formula for circles.
Apply the Pythagorean theorem to determine unknown side lengths in right triangles
in real-world and mathematical problems in two and three dimensions.
How to apply volume formulas of prisms,
cones, cylinders, pyramids, and spheres.
Apply the Pythagorean theorem to find the distance between two points in a
coordinate system.
The reference triangles.
Apply formulas for the volumes of prisms, cones, cylinders, pyramids, and spheres to
solve real-world and mathematical problems.
The trigonometric ratios for sine, cosine
and tangent in right triangles.
The classifications and properties of
triangles.
Apply the reference triangles to find the lengths of sides of triangles.
Find the sine, cosine and tangent of an angle in a right triangle.
The total number of degrees in a triangle.
Apply the sine, cosine and tangent ratios to find unknown side lengths in a right
triangle.
The classifications and properties of angles.
Classify triangles based on their angle measures and their side measures.
The classifications and properties of
polygons and quadrilaterals.
Find unknown side lengths in a triangle based on given information.
Find angle measures in a triangle based on a ratio.
The total number of degrees in a
quadrilateral.
Classify a polygon based on the number of sides.
The classifications and properties of solids.
Classify a quadrilateral based on their special properties.
How to apply the surface area formula for
Find unknown angle measures in quadrilaterals.
prisms, cylinders, pyramids and cones.
Find the area of parallelograms and trapezoids.
The classifications of special pairs of angles.
Find the circumference and area of circles.
The relationship between angles and
parallel lines.
The formula to find the sum of the
measures of interior angles in a convex
polygon.
The formula to find the angle measure of
one interior angle in a regular n-gon.
Find the surface area of prisms, cylinders, pyramids and cones.
Classify special pairs of angles.
Find missing angle measures using special pairs of angles and angle relationships with
parallel lines.
Find the sum of the measures of interior angles in a convex polygon.
Find an interior angle measure of a regular n-gon.
KEY VOCABULARY:
Similar figures, corresponding parts, congruent figures, scale, scale drawing, scale model, parallel lines, perpendicular lines, skew
lines, Pythagorean Theorem, leg, hypotenuse, midpoint, acute triangle, right triangle, obtuse triangle, equiangular triangle,
equilateral triangle, isosceles triangle, scalene triangle, polygon, regular polygon, convex, concave, pentagon, hexagon, heptagon,
octagon, trapezoid, parallelogram, rhombus, diagonal, base(s), height, circle, center, radius, diameter, circumference, pi, solid, faces,
prism, pyramid, cylinder, cone, edges, vertices, net, surface area, lateral face, slant height, volume, parabola, complementary angles,
supplementary angles, vertical angles, transversal, corresponding angles, interior angles, exterior angles, alternate interior angles,
alternate exterior angles, transformation, image, translation, tessellation, reflection, line of symmetry, line of reflection, line
symmetry, rotation, center of rotation, angle of rotation, rotational symmetry, dilation, center of dilation