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Table of Contents with Lesson Purpose and Essential Question KG Shafer 2017 Book 1: Segments, Angles, Circles and Programs Lesson 1: Line Segments (1246 words includes math and code and 4 graphics) Purpose: This lesson introduces the basic commands and vocabulary used in Geometry. Essential Question: How do you tell someone how to move from one place to another place?

Lesson 2: Iteration (790 words includes math and code and 6 graphics) Purpose: This lesson introduces the idea of iteration. Iteration is the act of doing the same commands over and over again. Essential Question: How do you create a Logo design with the Repeat command?

Lesson 3: Introduction to Angles (840 words includes math and code and 3 graphics) Purpose: This lesson introduces the definition of an angle and the common ways in which we classify angles. Essential Questions: What are the different types of angles? What are a few of the common mistakes students make when discussing angles and their measure? Materials: Protractor and straightedge

Lesson 4: Angle Pairs and the Coordinate Grid (880 words includes math and code and 12 graphics) Purpose: This lesson introduces a classification system for pairs of angles. You will also learn about the coordinate plane and how to position the turtle in the plane. Essential Questions: How can you use Logo to position the turtle in the coordinate plane? How are angles related to each other?

Lesson 5: Regular Polygons (1156 includes math and code and 9 graphics) Purpose: This lesson introduces regular polygons and the location of an exterior angle. Essential Questions: What does it mean for a polygon to be regular and why is this word so important? What is true about the sum of the exterior angles of any polygon?

Lesson 6: Logo Circles (1070 words includes math and code and 4 graphics) Purpose: This lesson introduces the relationship between a polygon and a circle to draw “circles” and “arcs” in the Logo workspace. Essential Question: How can Logo be used to draw “circles” and arcs of given dimensions (circumference or diameter). What is the difference between arc measure and arc length?

Lesson 7: The Pythagorean Theorem and Triples (1720 includes math and code and 11 graphics) Purpose: This lesson introduces the Pythagorean theorem. A related concept is the Pythagorean Triple. Essential Questions: What is the Pythagorean theorem and how can it be used to find a missing side length in right triangles?

Lesson 8: Color and Procedures (1550 words includes math and code and 9 graphics) Purpose: This lesson introduces Logo color commands, sub-procedures, and calling procedures. Essential Questions: How can you add color to a Logo design? How can you store Logo code so it is saved from one work session to the next work session?

Book 2: The Sine Function, Quadrilaterals, and Transformations Lesson 9: The Sine Function (58- words includes math and code and 6 graphics) Purpose: This lesson introduces the sine function, which is used to find an unknown side length in a given right triangle. Essential Question: Given a right triangle, three known angle measurements and one known side length, how can the sine function and the Pythagorean theorem be used to calculate the missing side lengths?

Lesson 10: Obtuse Scalene Triangles (800 words includes math and code and 8 graphics) Purpose: You will use the sine function and the Pythagorean theorem to find missing side measurements in obtuse scalene triangles. Logo will be used to check your work. Essential Questions: How can an obtuse scalene triangle be decomposed into two right triangles? How can the sine function and the Pythagorean theorem be used to create the Logo code for an obtuse scalene triangle?

Lesson 11: Inverse Sine Function (1130 words includes math and code and 10 graphics) Purpose: This lesson introduces the inverse sine function, which is used to find an angle measure in a given right triangle. Essential Question: Given a right triangle and three known side measurements, how can the inverse sine function be used to calculate the missing angle measures?

Lesson 12: Acute Scalene Triangles (610 words includes math and code and 6 graphics) Purpose: This lesson focuses in decomposing acute scalene triangles into right triangles. You will use what you know about the Pythagorean theorem. The 45-45-90 and the 30-60-90 triangles are introduced in this lesson. Knowledge of the sine function is necessary in the problems marked with an asterisk. Essential Question: Can you apply what you have learned about the sum of the measures of a triangle and the Pythagorean theorem to solve complex problems?

Lesson 13: Parallelograms (1600 words includes math and code and 6 graphics) Purpose: This lesson introduces the definitions and properties of parallelograms. The Logo program provides an excellent environment to explore different types of parallelograms. This lesson uses a procedure with three variables to efficiently draw a given parallelogram. This lesson contains optional information on how to set the dimensions of the graphic window. Essential Question: Can you apply your knowledge of interior and exterior angle measures to code and investigate the properties of parallelograms?

Lesson 14: Kites (600 words includes math and code and 6 graphics) Purpose: This lesson introduces kites and should be a review of what you have learned about the Pythagorean theorem. Knowledge of the sine function is necessary to complete Example 2. Essential Question: Given a convex kite with a few measurements provided, can you use the Pythagorean theorem and the sine function to calculate the missing angle measures and side lengths? Can you use Logo to test your calculations and code? Can you use these calculations to make generalizations about Kites?

Lesson 15: Transformations (1052 words includes math and code and 12 graphics) Purpose: This final lesson in Learning Mathematics with Logo, introduces the transformations; rotation, reflection and translation. Polar coordinates are introduced in the discussion of a translation vector. Essential Questions: What information is necessary to turn, slide or flip an image and how can these movements (transformations) be coded in Logo?