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Published byTheodore Lang Modified over 5 years ago
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Warm UP The length of a square is 5 cm. What is the measure of its width? What is the sum of the first 5 counting numbers? Solve the equation 2x + 1 = 5.
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A geometry proof (your choice, two-column, paragraph, or flow)
2. A Geogebra printout (fit to page, color if possible) with a written explanation of how the construction was made and what the problem or investigation demonstrates on note card paper clipped to the front. 3. A particularly challenging problem you completed, including a diagram and all work. 4. A challenging, satisfying, or impressive homework assignment you completed with a description of why you chose this assignment. 5. A piece of work from Geometry or some other class that demonstrates the connection between Geometry and other disciplines (art, music, history, science, language arts, etc.). Include a description of how/why you chose this piece.
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6. An in class assignment or quiz with corrections attached and work shown neatly. 7. A copy or digital image of a unit project (individual or if group project include an individual reflection of your contributions). 8. Your favorite piece of work from the quarter (it may be your most creative, most challenging, or best work). Include a few sentences which describe why you chose this piece as your favorite work from the quarter.
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An Introduction to Proofs
Section 2.1 An Introduction to Proofs
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What is a Proof? A proof is a convincing argument that something is true. Before you allow yourself to be convince by a supposed proof, make sure that it is sound. In math, a proof starts with things that are agreed on. Postulates or axioms. Logic is used to reach a conclusion
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Worksheet
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Types of Proofs Some proofs follow a prescribed form and are called formal proofs. Two-column Proofs (Lesson 2.4) Paragraph Proofs (Lesson 2.4) Flowchart Proofs (Lesson 4.4) Coordinate proofs (Lesson 5.7) Table Proofs (Lesson 9.3)
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Example Formal Proof 5x + 4 = 24 Given
5x = 20 Subtraction Property of Equality x = Division Property of Equality Each statement on the left is given a justification in the column on the right.
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Types of Proofs The proofs you did in the Activity did not follow any particular form but they are just as mathematically sound (if they are correct!) as formal proofs.
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Algebraic/Equivalence Properties of Equality
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Practice
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Practice
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