1. Angles in pattern blocks

2. Diagonals Joining two nonadjacent vertices of a polygon

3. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid Parallelogram Rhombus Rectangle Square Kite

4. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogram Rhombus Rectangle Square Kite

5. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombus Rectangle Square Kite

6. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectangle Square Kite

7. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Square Kite

8. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Squareyes Kite

9. For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoidmaybe Parallelogrammaybe Rhombusyes Rectanglemaybe Squareyes Kiteyes

10. Sum of the angles of a polygon Use a minimum of five polygon pieces to create a 5-sided, 6-sided, 7 sided, 8-sided, 9-sided, 10- sided, 11-sided, or 12-sided figure. Trace on triangle grid paper, cut out, mark and measure the total angles in the figure. 2 13 4 5 7 6 9 5 8 1 2 3 4 6 7 http://www.arcytech.org/java/patterns/patterns_j.shtml

11. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 NthN What patterns do you see?

12. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

13. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

14. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

15. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

16. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon8 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

17. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon9 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

18. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon10 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

19. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon11 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

20. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon111620 Dodecagon12 Triskaidecagon13 nth n What patterns do you see?

21. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon111620 Dodecagon121800 Triskaidecagon13 nth n What patterns do you see?

22. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon111620 Dodecagon121800 Triskaidecagon131980 nth n What patterns do you see?

23. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon111620 Dodecagon121800 Triskaidecagon131980 nth n? What patterns do you see?

24. Sum of the angles of a polygon Polygon # sides Total degrees Triangle3180 Quadrilateral4360 Pentagon5540 Hexagon6720 Heptagon7900 Octagon81080 Nonagon91260 Decagon101440 Undecagon111620 Dodecagon121800 Triskaidecagon131980 nth n180(n-2) What patterns do you see?

25. Total degree of angles in polygon

26. Area Formulas: Triangle  http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 http://illuminations.nctm.org/LessonDetail.aspx?ID=L577

27. Area Formulas: Triangle 1. Using a ruler, draw a diagonal (from one corner to the opposite corner) on shapes A, B, and C. 2. Along the top edge of shape D, mark a point that is not a vertex. Using a ruler, draw a line from each bottom corner to the point you marked. (Three triangles should be formed.) 3. Cut out the shapes. Then, divide A, B, and C into two parts by cutting along the diagonal, and divide D into three parts by cutting along the lines you drew. 4. How do the areas of the resulting shapes compare to the area of the original shape?

28. Area Formulas: Triangle

30. Area Formulas: Trapezoids  http://illuminations.nctm.org/LessonDetail.aspx?ID=L580 http://illuminations.nctm.org/LessonDetail.aspx?ID=L580

31. Area Formulas: Trapezoids Do you have suggestions for finding area? What other shapes could you use to help you? Are there any other shapes for which you already know how to find the area?

32. Area Formulas: Trapezoids 24 cm 18cm 15 cm 13 cm 11cm

33. Connect Math Shapes Set http://phcatalog.pearson.com/component.cfm?site_id=6&discipline_id=80 6&subarea_id=1316&program_id=23245&product_id=3502 http://phcatalog.pearson.com/component.cfm?site_id=6&discipline_id=80 6&subarea_id=1316&program_id=23245&product_id=3502 CMP Cuisenaire® Connected Math Shapes Set (1 set of 206) ISBN-10: 157232368X ISBN-13: 9781572323681 Price: $29.35

34. Area Formulas: Trapezoids When triangles are removed from each corner and rotated, a rectangle will be formed. It’s important for kids to see that the midline is equal to the average of the bases. This is the basis for the proof—the midline is equal to the base of the newly formed rectangle, and the midline can be expressed as ½(b 1 + b 2 ), so the proof falls immediately into place. To be sure that students see this relationship, ask, "How is the midline related to the two bases?" Students might suggest that the length of the midline is "exactly between" the lengths of the two bases; more precisely, some students may indicate that it is equal to the average of the two bases, giving the necessary expression. Remind students that the area of a rectangle is base × height; for the rectangle formed from the original trapezoid, the base is ½(b 1 + b 2 ) and the height is h, so the area of the rectangle (and, consequently, of the trapezoid) is A = ½h(b 1 + b 2 ). This is the traditional formula for finding the area of the trapezoid. A = ½h(b 1 + b 2 )

35. Area Formulas: Trapezoids 24 cm 18cm 15 cm 13 cm 11cm

36. Area Formulas: Trapezoids Websites: http://argyll.epsb.ca/jreed/math9/strand3/tra pezoid_area_per.htm http://argyll.epsb.ca/jreed/math9/strand3/tra pezoid_area_per.htm

37. Parallelograms

38.  A = Length x width  http://illuminations.nctm.org/LessonDetail.aspx?ID=L578 http://illuminations.nctm.org/LessonDetail.aspx?ID=L578

39. Area of Parallelogram Can you estimate the area of Tennessee?

40. Area of irregular figure?

41. Find the area of the irregular figure.

42. Area of irregular figure?

44. Circles Area = π r 2 Circumference = 2 π r or or Circumference = π d

45. Circles Otis is drawing a circle with a 4 inch radius. He wants to double the radius. How will this affect the area of the circle?

46. Circles Su is selling 12 inch diameter pumpkin pies for $6.50. How should she adjust her price (if she wants to be fair) when she reduces her pies to a 10 inch diameter?

47. Circles Javier’s bicycle tire has a 12 inch radius. How far will he travel...... in one rotation of the tire?... in 10 rotations of the tire?