Goddard: Eighth Gradecommon Core State Standards (CCSS) Mathematics

Goddard: Eighth GradeCommon Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.1
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: Verify experimentally the properties of rotations, reflections, and translations:
Depth of Knowledge:Level 1: Recall ☐Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Properties – a character or attribute that something has

Rotation - the act of rotating; turning around as on an axis

Reflections – an image or shape as it would be seen in a mirror

Translations – moving a shape without rotating or flipping

Be Able to Do (Verbs) / Level I / Level II / Level III / Level IV / Level V
List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square: / Knowledge/ Remembering
Memorize facts, definitions, & formulas / Comprehension/ Understanding
Perform Procedures / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Verify – to prove the truth of by presentation of evidence

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This standard means a student will know and be able to do…(use your own words)

Students use compasses, protractors, and rulers to explore figures created from translations, reflections, and rotations

Essential Questions:

Can I use a compass, protractor, and/or a ruler to explore figures created form translations, reflections, and rotations

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: line, line segments, coordinate plane, angles, parallel lines / I ☒ II ☐ III ☐ IV ☐ V ☐
2. / Identify: rotation, reflection, translation / I ☒ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Compass, Protractor, Ruler, Technology
Assessment Item Type: Selected Response☒Extended Constructed Response☒Technology Enhanced☒
Performance Task☒ Oral Response☒ Eligible as summative item☒
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Using a ruler or a protractor show that these figures are congruent.

Example 2: Use a ruler or protractor to show that these figures are congruent.

Example 3: Use a ruler or protractor to show that these figures are congruent.

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.1a
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: Lines are taken to lines, and line segments to line segments of the same length.
Depth of Knowledge:Level 1: Recall ☐Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Lines - straight, extends in both directions without end

Line segment – part of a line connecting two points

Length – line from end to end

Be Able to Do (Verbs) / Level I / Level II / Level III / Level IV / Level V
List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square: / Knowledge/ Remembering
Memorize facts, definitions, & formulas / Comprehension/ Understanding
Perform Procedures / Application
Demonstrate understanding of math / Analysis
Conjecture, Generalize, Prove / Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Are Taken – comparing two corresponding lines

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This standard means a student will know and be able to do…(use your own words)

The student can verify that after figure has been translated corresponding lines remain the same

Essential Questions:

Can you verify that after figure has been translated corresponding lines remain the same.

Can you identify corresponding sides?

Can you identify corresponding angles?

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: line, line segment / I ☒ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Compass, Protractor, Ruler, Technology
Assessment Item Type: Selected Response☐Extended Constructed Response☐Technology Enhanced☐
Performance Task☐ Oral Response☐ Eligible as summative item☐
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Using the model below, show that corresponding sides are congruent.

Example 2: Using the model below, show that corresponding sides are congruent.

Example 3: Using the model below, show that corresponding sides are congruent.

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.1b
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: Angles are taken to angles of the same measure.
Depth of Knowledge:Level 1: Recall ☐Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Angles – the amount of turn between two straight lines

Measure – to find a number that shows the size or amount of something such as meter or kilogram

Are taken - comparing angles to angles

The student can verify that after a figure has been reflected corresponding angles have the same measure

Essential Questions:

Can I verify that corresponding angles have the same measure

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: angles, corresponding angles, reflection, lines / I ☒ II ☐ III ☐ IV ☐ V ☐
2. / Measure angles / I ☐ II ☐ III ☒ IV ☐ V ☐
3. / I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Compass, Protractor, Ruler, Technology
Assessment Item Type: Selected Response☐Extended Constructed Response☐Technology Enhanced☐
Performance Task☐ Oral Response☐ Eligible as summative item☐
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Using the model below, show that corresponding angles are congruent.

Example 2: Using the model below, show that corresponding angles are congruent.

Example 3: Using the model below, show that corresponding angles are congruent.

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.1c
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: Parallel lines are taken to parallel lines.
Depth of Knowledge:Level 1: Recall ☐Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Parallel lines – two lines on a plane that never meet ; always the same distance apart

Are taken – comparing parallel lines to parallel lines

The student can verify that after a figure has been rotated corresponding parallel lines remain parallel

Essential Questions:

Can I verify that corresponding parallel lines remain parallel

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: parallel, rotation, angles, lines / I ☒ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Compass, Protractor, Ruler, Technology
Assessment Item Type: Selected Response☐Extended Constructed Response☐Technology Enhanced☐
Performance Task☐ Oral Response☐ Eligible as summative item☐
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Given that AB is parallel to CD, show that A’B’ is parallel to C’D’.

Example 2:

Example 3:
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.2
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: 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.
Depth of Knowledge:Level 1: Recall ☒Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Two-dimensional – a shape that only has two dimensions such as length and height and no thickness

Congruent – the same shape and size

Rotation - the act of rotating; turning around as on an axis

Reflections – an image or shape as it would be seen in a mirror

Translations – moving a shape without rotating or flipping
Sequence – the order of symbols and objects

Understand

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Describe

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This standard means a student will know and be able to do…(use your own words)

The student will be introduced to congruency; students examine two figures to determine congruency; students recognize the symbols of congruency

Essential Questions:

Can I explain how transformations can be used to prove that two figures are congruent

Can I perform a series of transformations to prove or disprove figures are congruent

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: sequence, two-dimensional, congruent, transformations / I ☒ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Three-dimensional models, geometry software
Assessment Item Type: Selected Response☒Extended Constructed Response☒Technology Enhanced☒
Performance Task☒ Oral Response☐ Eligible as summative item☒
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Graph each transformation of triangle ABC.
1. translation 4 units down
2. reflection across the y-axis
3. rotation of 180 about the origin
4. Show that triangle ABC is congruent to each of the other triangles.
Example 2:
Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.3
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Depth of Knowledge:Level 1: Recall ☒Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Dilations – to resize something

Translations – moving a shape without rotating or flipping
Rotation - the act of rotating; turning around as on an axis

Reflections – an image or shape as it would be seen in a mirror

Two-dimensional – a shape that only has two dimensions such as length and height and no thickness

coordinates – a set of values that show an exact position

Describe

Students identify resulting coordinates from dilations, translations, reflections, and rotations recognizing the relationships between the coordinates and the transformations

Essential Questions:

Can I describe the changes occurring to the X and Y Coordinates of a figure after a translation, reflection, rotation or dilation?

What learning progressions are needed to master this standard? Give specific, measurable skill statements.
Learning Sequence / Prior skill(s) needed / Check Level of Rigor/Cognitive Demand
(Depth of Knowledge
1. / Vocabulary: transformations, two-dimensional figures / I ☒ II ☐ III ☐ IV ☐ V ☐
2. / Prime / I ☒ II ☐ III ☐ IV ☐ V ☐
3. / Coordinate Plane: ordered pairs / I ☐ II ☒ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
I ☐ II ☐ III ☐ IV ☐ V ☐
Assessments: (What will be acceptable evidence the student has achieved the desired results?) / Instructional Resources/Tools:
Textbook, workbook
Three-dimensional models, geometry software
Assessment Item Type: Selected Response☒Extended Constructed Response☒Technology Enhanced☒
Performance Task☒ Oral Response☐ Eligible as summative item☒
Example: Provide possible instructional learning example/formative assessment item(s) for this standard:
Example 1: Draw the image of a triangle with the vertices (-1, 2), (3,3), and (1, -3) after a translation 2 units up and 2 units to the right.
Example 2: Give the coordinates of each point after a reflection across the given axis. (1,4); x-axis
Example 3: Dilate the figure by the given scale factor with the origin as the center of dilation. What are the vertices of the image?
scale factor of 2

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain: Geometry / Code: 8.G.4
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard: 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.
Depth of Knowledge:Level 1: Recall ☒Level 2: Basic Application-skill/concept ☒
Level 3: Strategic Thinking ☐Level 4: Extended Thinking ☐
Know (nouns) Definition
List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Similar –figures not necessarily the same size but the same shape

Two-dimensional – a shape that only has two dimensions such as length and height and no thickness

Sequence – the order of symbols and objects

Translations – moving a shape without rotating or flipping

Rotation - the act of rotating; turning around as on an axis
Reflections – an image or shape as it would be seen in a mirror

Understand -

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Describe

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This standard means a student will know and be able to do…(use your own words)

The student will understand that similar figures have congruent angles and sides that are proportional

Essential Questions:

Do I know that similar figures have congruent angles and sides that are proportional