Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: 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.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: Verify experimentally the properties of rotations, reflections, and translations:
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: 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 three angles appear to form a line, and give an argument in terms of transversals why this is so.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: 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.
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Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
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Learning Domain: Geometry
Standard: Understand and apply the Pythagorean Theorem
Indicator: Explain a proof of the Pythagorean Theorem and its converse.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: Parallel lines are taken to parallel lines.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: Angles are taken to angles of the same measure.
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Learning Domain: Geometry
Standard: Understand congruence and similarity using physical models, transparencies, or geometry software
Indicator: Lines are taken to lines, and line segments to line segments of the same length.
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Learning Domain: Geometry
Standard: Understand and apply the Pythagorean Theorem
Indicator: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
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Learning Domain: Geometry
Standard: Solve real-world and mathematical problems involving volume of cylinders, cones and spheres
Indicator: Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
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Learning Domain: Geometry
Standard: Understand and apply the Pythagorean Theorem
Indicator: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
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Learning Domain: Mathematical Practices
Standard: Mathematical practices
Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
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This is a lesson/assessment unit. There are many resources for the teacher to aid in the lesson. There are student handouts, assessments, assessment revisited, ppt, explorations for students, suggested questions and prompts for common issues. It is addressing CCSS 8.G.5 to use properties of triangles to identify similar triangles.