unit 7 - Logic and Geometry
Lessons7.1 Patterns and Predictions
7.2 Conjectures and Counter-Examples 7.3 Deductive Reasoning 7.4 Fallacies and Problems 7.5 Geometry Rules 7.6 Polygon Rules 7.7 Geometry Proofs Learning OutcomesC1. Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.
1.1 Make conjectures by observing patterns and identifying properties, and justify the reasoning. 1.2 Explain why inductive reasoning may lead to a false conjecture. 1.3 Compare, using examples, inductive and deductive reasoning. 1.4 Provide and explain a counterexample to disprove a given conjecture. 1.5 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks. 1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs). 1.7 Determine if a given argument is valid, and justify the reasoning. 1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1. 1.9 Solve a contextual problem involving inductive or deductive reasoning C2. Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies. 2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g., guess and check, look for a pattern, make a systematic list, draw or model, eliminate possibilities, simplify the original problem, work backward, develop alternative approaches. 2.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game. 2.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game. |
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B1. Derive proofs that involve the properties of angles and triangles.
1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology.
1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.
1.3 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.
1.4 Identify and correct errors in a given proof of a property involving angles.
1.5 Verify, with examples, that if lines are not parallel the angle properties do not apply.
B2. Solve problems that involve the properties of angles and triangles.
2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning.
2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles.
2.3 Solve a contextual problem that involves angles or triangles.
2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used.
2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.
1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology.
1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.
1.3 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.
1.4 Identify and correct errors in a given proof of a property involving angles.
1.5 Verify, with examples, that if lines are not parallel the angle properties do not apply.
B2. Solve problems that involve the properties of angles and triangles.
2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning.
2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles.
2.3 Solve a contextual problem that involves angles or triangles.
2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used.
2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.