Algebra Module 8: Geometry in Algebra

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Lessons Lesson Summary
For virtual manipulatives for algebra and geometry, please see: (scroll down) http://matti.usu.edu/nlvm/nav/grade_g_3.html

Alg 8.1 Solving with Square Roots
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Students find sight-distances and heights a formula involving square root.

Alg 8.2 Discover and Write an Ancient Theorem
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Students build puzzles involving the Pythagorean Theorem, write their version of the theorem, compare their version to textbook versions, and use the theorem to solve problems.
Alg 8.3 The Distance Formula
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Students problem solve for a hiking distance, relate the distance formula to the Pythagorean Theorem, and use the distance formula to find distances on real-life maps of their own areas (internet maps).
Alg 8.4 Solving for the Midpoint
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Students fold paper, draw and measure line segments to understand what a midpoint is and derive the formula for finding the segment midpoint.

Alg 8.5 Squares and Square Roots
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For a great follow-up lesson, see:
http://math.rice.edu/~lanius/Geom/irrat.html

Students draw squares on dot paper, build a table comparing the areas of the squares to the side length. use square root notation to describe the length of the sides of the squares drawn on the diagonal, find the radical numbers to describe the length of the sides of squares whose areas are known. They use the Pythagorean theorem to check answers.
Alg 8.6a Comparing Rational Numbers

Alg 8.6 A Question of Order

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Students problem solve to order rational and irrational numbers in different group configurations.
Alg 8.7 Developing Circle Formulas      PDF

Students derive and practice the formulas for finding the perimeter and area of a circle.