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: 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: Mathematical Practices
Standard: Mathematical practices
Indicator: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
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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 lesson is good at connecting from one transformation to doing multiple transformations. However, it asked students to do rotations and reflections that are above the Smarter Balance Consortium's specific item specifications for 8G. In the specifications the Target Specific Attributes say that that rotations should only be done around the origin in multiplies of 90 degrees, and reflections done over the axis. In addition, it does not use the coordinate plane notation.
This is a lesson/assessment tool. It has many teacher resources like detailed lessons, student worksheets, card sets for students to match, and tips to help students get started on the task. It is addressing CCSS 8.G.1. It does not have students explore all properties of transformations, reflections, and rotations, but it does connect a series of transformations to a single transformation.