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Proof of the Pythagorean Theorem Using Transformations
Middle and high schoolers construct a triangle using Cabri Jr. They construct squares on each of the legs and hypotenuse of the triangle. Pupils show that the area of the squares on the leg equal the area of the square on the hypotenuse.
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Number Theory
Learners explore the concept of number theory. They discuss an assortment of number theory topics such as prime numbers, composite numbers, GCF, modular arithmetic, and others in a lecture style discussion. Pupils view videos about these...
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Discovering Math: Concepts in Geometry
Middle and high schoolers explore the concept of proving the Pythagorean Theorem. They research proofs of the Pythagorean Theorem. Pupils create posters of proofs, and research Greek mathematicians.
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Getting It Right!
Pupils construct right triangles, measuring the sides and recording the measurements in spreadsheets. They analyze their measurements for patterns and research the Internet for information on Pythagoras.
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Euclidean Direct Proofs
Learning how to prove theorems in geometry can be challenging. This resource explains what a proof is, and the different styles for proofs. It also contains links to web-based practice problems that help guide learners though example...
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Product + 1: Integers
In this integers worksheet, students solve 1 word problem using proof. Students prove their hypothesis of the result of multiplying four consecutive positive integers and adding one to the product.
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Proof That One Equals Zero (Using Calculus)
In this proofs worksheet, students evaluate the integral of 1 function. Students use uv-substitution to prove 0=1.
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A Different Proof of the Law of Cosines
In this proofs worksheet, students construct 1 proof of the law of cosines. Students construct a right triangle within a circle to prove the law of cosines.
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TI Workshop Presentation Guide for "Preparing for Proofs"
Pupils discover proofs using the TI in this geometry lesson. They collect data from newspaper and magazines and analyze their data using the TI, relating it to proofs.
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Prize Numbers
Students explore what a proof is, how and why mathematicians create them and compose essays on how reason and logic are employed in the workplace. They explore whether any three lines can make a triangle and attempt to verify Goldbach's...
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Easy Worksheet: Congruent Segments
For this congruent segments worksheet, high schoolers solve 6 short answer problems. Students justify steps in a proof by identifying the reason for various steps. High schoolers justify steps of proofs using the transitive property,...
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Proofs: Solving Equations
In this proofs worksheet, high schoolers solve 4 short answer problems. Students identify the correct reason for each step in solving each multi-step equation.
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Inductive vs. Deductive Proof
Twelfth graders differentiate between inductive and deductive proofs. In this differentiating between inductive and deductive proofs lesson, 12th graders compare strengths and weaknesses of each type of proof. Students discuss an...
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Geometry Proofs
In this geometry proofs worksheet, 10th graders solve and complete 6 different problems that include various proofs. First, they prove a triangle has equivalent angles as given. Then, students prove two angles supplementary as described.
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Congruent Triangles
In this congruent triangles worksheet, 10th graders solve and complete 10 different problems that include various forms of triangles. First, they name the method for proving each set of triangles congruent using the given information....
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Congruent Triangles
In this congruent triangles worksheet, 10th graders solve and complete 10 different problems to determine whether each set of triangles is congruent or not. First, they copy each diagram onto a piece of paper and mark up the paper with...
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Quadrilaterals
In this quadrilaterals activity, 10th graders solve and complete 10 different problems that include various types of proofs and quadrilaterals. First, they read the given information for each quadrilateral illustrated. Then, students...
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Quiz: Direct Euclidean Proofs
In this Euclidean proof learning exercise, students observe models and read given proofs. Students determine conclusions based upon the given information. This one-page learning exercise contains ten Euclidean proof problems.
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Pre-Proof Warm-Ups
For this pre-proofs worksheet, 10th graders solve and complete 10 different problems that include various proofs and their definitions. They use the diagram shown and the given information to write the direct conclusion for each case....
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Proofs
In this proofs learning exercise, 10th graders solve and graph 8 different equations. First, they prove that each triangle is either congruent or similar. Then, students use the concept of corresponding parts of congruent triangles to...
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Proving Triangles Congruent
In this proving triangles congruent worksheet, 10th graders solve 5 different problems that include proofs and proving congruence in triangles. First, they determine which postulate can be used to prove the triangles congruent and mark...
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Using Proof in Algebra
In this using proofs in algebra activity, 10th graders solve 2 proofs by applying the many rules from algebra for the Properties of Equality for real numbers. They name the property that justifies each statement as seen in the...
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The Proof Is in the Picture
Students select a geometric figure and find an example of the figure in their surroundings. They photograph the figure and write a proof to accompany it. They match photos to proofs.
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Mathematics
Twelfth graders explore a variation of proof. In this geometry lesson, 12th graders apply their knowledge of proof to different scenario. They use 3 different tiers to advance through the lesson.