By Scott J Smith (ssmith@mtbaker.wednet.edu) Mt. Baker JH Deming, Wa 98244 Dramatized by Doug Harkness, Nazario Garcia,

2. By Scott J Smith (ssmith@mtbaker.wednet.edu) Mt. Baker JH Deming, Wa 98244 Dramatized by Doug Harkness, Nazario Garcia, and Joey Martinez Mt. Baker Junior High School CIRCLE GEOMETRY With a Fractional Twist ● ●

3. GLE 1.3.2Understand the characteristics of polygons and circles. • Identify, describe, compare, and sort figures. • Draw polygons and circles with specified properties

4. GLE 5.1.1 Apply concepts and procedures from a variety of mathematical areas in a given problem or situation.

6. Find a center to the circle. • Pinch (not a fold) to find the center. • What is a circle and its relationship to the center?

7. Continue, by pinching again to find the center

8. Can you see our two “pinches” that will define our center?

9. Mark the center. • All points that are exactly the same distance from the center is the circle. • What is that distance called?

11. Fold your circle to the center. We've created a chord. A chord is a line segment with its endpoints on the circle.

13. Fold the circle to the center again, but this time use one of the endpoints of segment for the endpoint of your new segment. • What is two (or more) segments sharing a common endpoint?

14. What is an inscribed angle? measure of angle? Cut arc (minor arc) Is there a relationship between measure of the arc and the angle?

16. Now, fold the last segment to the center. • What is the shape? Be specific. • What are the attributes of this shape? (mention the angles and the lengths of the sides) • What is the sum of the angles of any triangle?

17. Find the midpoint of a side Pinch (don’t make a hard fold), then fold the opposite vertex to that midpoint.

18. What is this shape? and what are its attributes? Fold another vertex to its opposite midpoint.

19. What is this shape? and what are its attributes? Fold the last vertex to its opposite midpoint.

20. What is this shape? and what are its attributes?

21. Now, bring all of the folded vertices to meet at a single point. What is this shape? Are there two names?

22. Fold a vertex to the center.

23. Fold another vertex to the center

24. Now fold the last vertex to the center.

25. Unfold, and tuck one of the vertices into the flap of another.

26. A truncated tetrahedron

27. If this is 1, then…

28. How big is this?

29. How big is this?

30. How big is this?

31. If this is 1, then…

32. How big is this?

33. How big is this?

34. How big is this?

35. How big is this?

36. Let’s do the math…and check the reasonableness or our thinking. minus = OR = minus 3

37. How big is this?

38. How big is this?

39. If this is one: , How big are these: (In the dark lines) A B 1 1/3 1 1/2 1 1/6 D E 19/24 C 5/24 Share your ideas that make sense of these parts of a whole or fraction.

40. Killers: if this is one: , Then, how big are these: A B 1 4/5 7 1/5 4 3/5 4 4/5 3 4/5

41. The Golden Apple* A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded a payment of one-half of the apples and two more. The prince gave him the apples and set off again. A little further on, he was stopped by a second troll guard. This troll demanded payment of one-half of the apples the prince now had plus two more. The prince paid him and set off again. Just before leaving the enchanted orchard, a third troll stopped him and demanded one-half of his remaining apples plus two more. The prince paid him and sadly went home. He had only two golden apples left. How many apples had he picked? *From Make It Simpler by Carol Meyer and Tom Sallee, 1983