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ALL

Geometry

• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Domain Description

Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.

Standards in this Domain

• MAT-08.G.01 - Verify experimentally the properties of rotations, reflections, and translations
• MAT-08.G.02 - 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.
• MAT-08.G.03 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
• MAT-08.G.04 - 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.
• MAT-08.G.05 - 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 angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
• MAT-08.G.06 - Explain a proof of the Pythagorean Theorem and its converse.
• MAT-08.G.07 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• MAT-08.G.08 - Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
• MAT-08.G.09 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-08.G.01

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.01 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.

Student Learning Targets:

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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

**MAT-7.2.5. Draw the result of a transformation in the coordinate plane; i.e., translation, reflection, and rotation

**MAT-8.2.6 Draw the results of a combination of transformations in the coordinate plane; i.e., reflections, rotations, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

MAT-08.G.01a

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01a Lines are taken to lines, and line segments to line segments of the same length.

Student Learning Targets:

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Product Targets

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Rubric - Resources

MAT-08.G.01b

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01b Angles are taken to angles of the same measure.

Student Learning Targets:

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Product Targets

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Rubric - Resources

MAT-08.G.01c

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01c Parallel lines are taken to parallel lines.

Student Learning Targets:

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Product Targets

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Rubric - Resources

MAT-08.G.02

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.02 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.

Student Learning Targets:

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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-5.2.7 Describe properties of congruent (BPS: and similar figures with proportionality) figures and use them to solve problems

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

*MAT-2.2.5. Identify congruent figures from a selection of similar figures

*MAT-4.2.4 Use motion geometry to show that shapes are congruent or similar

*MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

MAT-08.G.03

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.03 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

Student Learning Targets:

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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-9-10.4.2 Describe the effects of scalar change on the area and volume of a figure; eg., the effects of doubling one or more edges of a solid on its surface area and volume.

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

MAT-08.G.04

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.04 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.

Student Learning Targets:

• I can
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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

MAT-08.G.05

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.05 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 angle-angle criterion for similarity of triangles.

For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Student Learning Targets:

• I can
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• I can
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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-8.2.3 Identify the angles formed and the relationships between the angles when parallel lines are intersected by a transversal

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

MAT-08.G.06

Domain (G) Geometry
Cluster: Understand and apply the Pythagorean Theorem.

MAT-08.G.06 Explain a proof of the Pythagorean Theorem and its converse.

Student Learning Targets:

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Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark