We are working our way through the Level C Lessons concerning triangles, circles, and fractions (lessons 69-74).
Concerning the dividing of a triagle into fourths, is he supposed to know how to find the midpoint of a number such as 7 inches or 3 1/2 inches or is he just supposed to "eye it"? This is pretty easy to do when the triangle is cut out and can be folded but is more difficult when using a pencil and ruler. Any tips to help my child find the midpoint with difficult measurements such as half of a 3 1/2 inch equalateral triangle...or is this not expected at this point for an 8 yo boy?
Concerning the dividing of equalateral triangles into thirds, is my son expected to know how to divide 3 1/2 inches in half to find the midpoint or is he just supposed to "eye it"? I think I understand that he is to use the 30- 60 triangle point to draw the straight lines to divide the triangle in half 3 times (at each point) but is he supposed to know WHY he uses the 30 degree angle?
Concerning the dividing of the circle into thirds, is he just supposed to "eye" this as well or is there a trick to dividing the circle into thirds correctly? I know that it is supposed to resemble the triangle as divided into thirds but don't know if it is to be more precise.
As far as finding the midpoint of the triangle goes -- no measurement is needed if you use your drawing tools. You can use your T-square and 30/60 triangle to get the midpoint. If you line the triangle or T-square with the point (apex) of the triangle (depending on which way the triangle is pointing), this will give you the midpoint, much the same way that folding the triangle in half gives the midpoint.
I am not sure how much of the "why" he needs to understand about why he uses the 30 degree triangle -- later he will use the 60 degree triangle. We took the try it and see which one works better approach!
Concerning dividing the circle into thirds -- you start by dividing it in half, much like he did with triangle (use the dot in the center of the circle, so that he knows where the line is supposed to go through). Then, using the triangle, he can draw the other two lines, both of which are to end in the center of the circle at the dot (the dot is pre-drawn on the worksheet).
Note on lesson 71, there are two ways to divide the triangle into thirds -- one way gives triangles, the other way quadrilaterals. I missed this at first and had a difficult time figuring out final part of the lesson, until it was pointed out to me -- maybe I was going to fast!
Thank you for the help. I still have a question, though. After dividing the circle in half with a straight edge, if I use the angle of the triangle to divide it into thirds, the angles aren't correct to make it into 3 equal thirds. Am I just supposed to eye it or am I missing something here?
These lessons are to train for critical thinking/problem solving skills. The child is not expected to already know this, they should be exploring and discovering this.
With great encouragement, we should be allowing them time to figure out how they can solve this problem. This is one of the great parts of RS, it teaches children to think and not rely on "set-up" problems. Of course, for those of us that were taught math in the usual manner this will scare us because we are used to being told how to do everything in a formulaic way, so we can pass the test. Here at RS, the idea is to teach to the child to think outside of what they are used to and it will help them to think when they come across new math concepts.
So be prepared this happens often
To answer your question... After dividing the circle in half with a straight edge, if I use the angle of the triangle to divide it into thirds, the angles aren't correct to make it into 3 equal thirds. Am I just supposed to eye it or am I missing something here?
The 30 degrees should be correct if you are resting it on your T-square, and have your paper taped to the drawing board.
You should have one vertical line going from the top to the center of your circle, then a second 30* angle from the center to the circumference, then a third 30* angle by flipping the triangle and having it go from the center to the circumference. He might do it slightly different, but the idea is the same and it should be fine.
He should be seeing the pattterns in dividing a triangle and a circle in thirds.
Please let me know if you have any more questions. You can email me directly at Carissa@alabacus.com .
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