Common Core 8 (CCM-8) Unit 2 Starting Points
Unit 2: Geometry
Essential Questions:
o What changes do line segments in the coordinate plane undergo that have been rotated,
reflected, or translated?
o How do similar figures compare?
o What transformations can figures undergo that enable them to remain congruent to the
original image?
o What are the differences between rigid and non-rigid transformations?
o What special angles are formed from parallel lines cut by a transversal?
o What characteristics exist among all triangles?
o What is the relationship between the lengths of the segments of right triangles?
Common CoreStandards:
Understand and apply the Pythagorean Theorem.
8.G.B.6. Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in
real-world and mathematical problems in two and three dimensions.
8.G.B.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate
system.
Understand congruence and similarity using physical models, transparencies, or geometry
software.
8.G.A.1. Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.A.2. 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, describe a sequence that exhibits the congruence between them.
8.G.A.3. Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates.
8.G.A.4. 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, translations, and dilations; given
two similar two-dimensional figures, describe a sequence that exhibits the similarity between
them.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
8.G.A.5. Use informal arguments to establish facts about the angle sum and exterior angle of
triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles.
Approximate Length of Unit: 35 days
Standard(s)
8.G.B.6
8.G.B.7
8.G.B.8
Days
11-13
Notes
Big Ideas:
Prove if a triangle is right/given 3 sides determine whether or
not a right triangle can be formed (use converse Pythagorean
Theorem to prove if a triangle is right).
Determine unknown side lengths in right triangles in real-world
and mathematical problems in two and three dimensions.
Apply Pythagorean Theorem to find the distance between two
points in a coordinate system.
Note: Extend from understanding of exponents and solving in
unit 1 to Pythagorean Theorem
Resources:
 Lesson: Introduction to Pythagorean Theorem
 Task: Curb Appeal
 Task: Amazing Amusement Park
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed on
PARCC. Examples of Connections to Standards for
Mathematical Practices: The Pythagorean theorem can provide
opportunities for students to construct viable arguments and
critique the reasoning of others (MP3).
This standard is part of the major content cluster assessed on
PARCC. The Pythagorean theorem is useful in practical
problems, relates to grade-level work in irrational numbers and
plays an important role mathematically in coordinate geometry
in high school. By working in geometric contexts such as the
Pythagorean theorem, students enlarge their concept of number
beyond the system of rationals to include irrational numbers.
They represent these numbers with radical expressions and
approximate these numbers with rationals.
Assessment Items:
 Illustrative Mathematics: Is this a rectangle?
Illustrative Mathematics: Rectangle in the coordinate
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
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8.G.A.1.a
8.G.A.1.b
8.G.A.1.c
8.G.A.3
7-8
plane
Illustrative Mathematics: Applying the Pythagorean
Theorem in a mathematical context
Illustrative Mathematics: Bird and Dog Race
Illustrative Mathematics: Converse of the Pythagorean
Theorem
Illustrative Mathematics: Area of a trapezoid
Illustrative Mathematics: Two Triangles’ Area
Illustrative Mathematics: Points from Directions
Illustrative Mathematics: Running on a Football Field
Big Ideas:
Experiment with properties of rotation, reflection, and
translation.
Describe the effect of dilation, translation, rotation, on
reflections on two-dimensional figures on a coordinate plane.
Resources:
 Lesson: Transformations
 Lesson: Transformation Exploration
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed on
PARCC.
Assessment Items:
 Illustrative Mathematics: Point Reflection
 Illustrative Mathematics: Reflecting Reflections
 Illustrative Mathematics: Triangle congruence with
coordinates
 Illustrative Mathematics: Congruent Segment
8.G.A.5
5-6
Big Ideas:
Use informal arguments to establish facts about the angle sum
and exterior angles of triangles.
Use informal arguments to establish facts about angles created
when parallel lines are cut by a transversal.
Use angle-angle criterion for similar triangles.
Resources:
 Web Resource: Exterior Angles
Assessment Items:
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
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8.G.A.2
8.G.A.4
7-8
Illustrative Mathematics: Tile Patterns II: hexagons
Illustrative Mathematics: Triangle’s Interior Angles
Illustrative Mathematics: Find the Angle
Illustrative Mathematics: Find the Missing Angle
Illustrative Mathematics: Tile Patterns I: octagons and
squares
Big Ideas:
Determine whether or not two-dimensional figures are similar.
Understand similar two-dimensional figures can be obtained
through a sequence of transformations (reflection, rotation,
translation).
Describe the sequence used to generate similar figures.
Understand two-dimensional figures are congruent if the second
can be obtained through a sequence of transformations
(reflection, rotation, translation).
Describe the sequence used to generate similar figures.
Resources:
 Task: Graphic Art Contest
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed on
PARCC.
Assessment Items:
 Illustrative Mathematics: Partitioning a hexagon
 Illustrative Mathematics: Reflecting a Rectangle over a
diagonal
 Illustrative Mathematics: Triangle congruence with
coordinates
 Illustrative Mathematics: Congruent Triangles
 Illustrative Mathematics: Congruent Rectangles
 Illustrative Mathematics: Cutting a rectangle into two
congruent triangles
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.