Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 5, Part B:
Cutting Up (50 minutes)

 You can solve each of the following problems in more than one way. Try to find several solutions; then pick the one that you like best. Jot down notes about each solution so that you can reconstruct your work later. Print out these figures to use in Problems B1-B6. For each problem, start with the figure described. Find a way to cut that figure into pieces you can rearrange to form the second figure described. You have to use all the pieces from the original figure and put them together like a puzzle -- no gaps or overlaps are allowed. Pay attention to how you can justify your cutting process. Use the properties of your beginning figure and the cuts you made to explain why you ended up with the second figure. Note 2 Problem B1 Start with a parallelogram. Find a way to cut your parallelogram into pieces you can rearrange to form a rectangle.

 Problem B2 Start with a right triangle. Dissect the triangle so that you can rearrange the pieces to form a rectangle.

 Problem B3 Start with a scalene, non-right triangle. Cut it into pieces that will form a parallelogram.

 Video Segment In this video segment, groups of participants work to transform several shapes into new figures. As they progress toward more difficult problems, they are able to make increasingly complex justifications for why their cuts work. Were you able to make similar kinds of justifications? If you are using a VCR, you can find the first segment on the session video approximately 5 minutes and 45 seconds after the Annenberg Media logo. The second segment begins approximately 8 minutes and 52 seconds after the Annenberg Media logo.

 Problem B4 Start with a scalene, non-right triangle. Cut it into pieces that will form a rectangle.

 If you've solved Problems B1 and B3, you can put those solutions together to solve Problem B4. Alternately, you can divide the triangle into two right triangles and apply your solution to Problem B2 twice.   Close Tip If you've solved Problems B1 and B3, you can put those solutions together to solve Problem B4. Alternately, you can divide the triangle into two right triangles and apply your solution to Problem B2 twice.

 Problem B5 Start with a trapezoid. Dissect the trapezoid into pieces that will form a rectangle.

 Problem B6 Start with a trapezoid. Dissect the trapezoid into pieces that will form a triangle. As a challenge, see if you can do this with a single cut.

Problem B7

In several of the problems above, you had a rectangle as a final result. For each of the following shapes, start with a rectangle and dissect it into pieces you can rearrange to form that shape:

 a. An isosceles triangle b. A right triangle c. A scalene triangle d. A non-rectangular parallelogram e. A trapezoid

 Problems B1-B5 and the Video Segment problems adapted from Connected Geometry, developed by Educational Development Center, Inc. p. 164. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math
 Session 5: Index | Notes | Solutions | Video