Download 3rd Unit

Common Core Curriculum Map 2012-2013
Common Core Unit Name: Geometry
Unit Number: 3
Enduring Understandings: 1. Verify experimentally the properties of rotations, reflections, and translations. 2. Show that I understand that lines
are taken to lines and line segments to line segments of the same length. 3. Show that angles are taken to angles of the same measure. 4. Show that
parallel lines are taken to parallel lines. 5. Understand 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. 6. Given two congruent figures, describe a sequence that exhibits the congruence between
them. 7. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8. Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. 9. Given two
similar two-dimensional figures describe a sequence that exhibits similarity between them. 10. Explain a proof of the Pythagorean Theorem and its
converse. 11. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and
three dimensions. 12. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.
13. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real world and mathematical problems.
Standard
Essential Questions

8. G.1 Understand congruence and similarities using
physical models, transparencies, or geometry
software.
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How will I verify experimentally the properties of
rotations, reflections, and translations?
How will I show that I understand that lines are
taken to lines, and line segments to line segments of
the same length?
How will I show that angles are taken to angles of
the same measure?
How will I show that parallel lines are taken to
parallel lines?
How will I understand 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?
Given two congruent figures, how will I describe a
sequence that exhibits the congruence between
them?
How will I describe the effect of dilations,
translations, rotations, and reflections on two-
Pacing Guideline
Key
Academic
Vocabulary
14 days
8.G.1,2,& 3
1.translations
2.rotations
3.reflections
4.lines of
reflections
5.center of
rotation
6.clockwise
7.counterclockwise
8.parallel lines
9.betweeness
10.
congruence
11.reading A as
“A prime”
12.similarity
13.dilations
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Common Core Curriculum Map 2012-2013


dimensional figures using coordinates?
How will I understand that a two-dimensional figure
is similar to another if the second can be obtained
from the first by a sequence of rotations, reflections,
and translations?
Given two similar two-dimensional figures, how will I
describe a sequence that exhibits similarity between
them?
14.pre-image
15.image
16.
rigid
transformation
17.exterior
angles
18.interior
Angles
19.alternate
interior angles
20.angle-angle
criterion
21.deductive
reasoning
22.adjacent
23.
Supplementary
24.
complementary
25.
Corresponding
26.scale factor
27.transversal
28.parallel
29.right triangle
30.hypotenuse
31.legs
32.Pythagorean
Theorem
33.Pythagorean
Triple
34.cones
35)cylinders
36.spheres
37.radius
38.volume
39.height
40.pi
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Common Core Curriculum Map 2012-2013
Common Core Unit Name:
Unit Number:
Enduring Understanding:
Standard
Essential Questions
Pacing Guideline
Key
Academic
Vocabulary
14 days
8.G.2 Understand the Pythagorean Theorem



How will I explain a proof of the Pythagorean
Theorem and its converse?
How will I apply the Pythagorean Theorem to
determine unknown side lengths in right triangles in
real-world and mathematical problems in two and
three dimensions?
How will I apply the Pythagorean Theorem to find
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Common Core Curriculum Map 2012-2013
8. G.3 Solve real-world and mathematical problems
involving volume of cylinders, cones, and spheres.


the distance between two points in the coordinate
system?
How will I know the formulas for the volumes of
cylinders, cones, and spheres?
How will I use the formulas for the volumes of
cylinders, cones, and spheres to solve real-world
and mathematical problems?
12 days
Suggested Resources by Unit
Location of these resources
Lesson Plans: Finding Missing Lengths of Similar Triangles
Lessons Plans: Finding Volume of Similar Figures
Lesson Plans: Identify Similar Figures
Modeling: Making Matchsticks
Proof of the Pythagorean Theorem Using Similarity
http://www.uen.org/Lessonplan/preview.cgi?LPid=23525
http://www.uen.org/Lessonplan/preview.cgi?LPid=23529
http://www.uen.org/Lessonplan/preview.cgi?LPid=23522
http://www.map.mathshell.org/materials/lessons.php?taskid=410#task410
http://www.khanacademy.org/math/geometry/triangles/v/pythagorean-theoremproof-using-similarity
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Common Core Curriculum Map 2012-2013
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