tag:blogger.com,1999:blog-6172532982347376290.post8242428558491230478..comments2017-07-21T19:14:22.336-04:00Comments on CCSSI Mathematics: The concept of area – Part 3Five Trianglesnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6172532982347376290.post-62802425191581731882013-08-13T00:09:21.561-04:002013-08-13T00:09:21.561-04:00The five triangles problem is nice, a perfect sort...The five triangles problem is nice, a perfect sort of problem for seeing if the student understands how and why the (1/2) b h formula works.<br /><br />The one given above on this page is a bit harder, you have to draw in the diagonal from upper left to lower right, then you have (1/2) b h for each of the two resulting shaded triangles so the answer is 3x8/2 + 5x6/2 = 27 cm^2. This is more like a Math Olympiad problem than one I would expect to see in class, certainly not for a non-gifted class. It's nice to talk about encouraging thinking, but if you can actually get average students to be able to do such problems, you are a remarkable teacher!Unknownhttps://www.blogger.com/profile/02736747311303236634noreply@blogger.comtag:blogger.com,1999:blog-6172532982347376290.post-67746416460978677002013-08-12T23:51:56.553-04:002013-08-12T23:51:56.553-04:00Cleverness is required, but the point is that in g...Cleverness is required, but the point is that in going around all three corners, 360 degrees will be traversed. So the total distance there is the circumference 2*pi*r . During that pivoting, the role of the circle and its center switch, where the center rotates around the point on the circle that is "stuck" to the corner of the triangle. This might be hard to explain to a 6-8 y.o. but it may not get much easier as that student gets older, if he or she has trouble visualizing in two dimensions.<br /><br />So the total distance traveled by the circle's center is the perimeter of the triangle plus the circumference of the circle.Unknownhttps://www.blogger.com/profile/02736747311303236634noreply@blogger.comtag:blogger.com,1999:blog-6172532982347376290.post-58237518725346212522013-05-01T21:35:13.528-04:002013-05-01T21:35:13.528-04:00This is the problem the commenter refers to:
http...This is the problem the commenter refers to:<br /><br />http://fivetriangles.blogspot.com/2013/04/59-path-of-wheels-axle.htmlCCSSI Mathematicshttps://www.blogger.com/profile/12318317536740240935noreply@blogger.comtag:blogger.com,1999:blog-6172532982347376290.post-91942300899517718402013-04-11T20:30:09.610-04:002013-04-11T20:30:09.610-04:00On 5 triangles how do you solve problem 59 in a wa...On 5 triangles how do you solve problem 59 in a way that 6-8 yo can understand and account for the length of the curve point 0 traces as it goes around a corner?Mathius1978noreply@blogger.comtag:blogger.com,1999:blog-6172532982347376290.post-80067875168058765242013-04-11T20:26:54.339-04:002013-04-11T20:26:54.339-04:00Thank you for posting your series. For those of y...Thank you for posting your series. For those of you stuck on the problem, look in the math subreddit for a discussion of this. I am not posting a link to encourage you to spend some time trying to solve it on your own.<br /><br />At the author, glad you found my reddit post. I am sorry if you did not want an answer posted. Feel free to delete this if you do not want a guide to out there.<br /><br />Again thanksMathius1978noreply@blogger.com