Nart Posted January 16, 2015 Share Posted January 16, 2015 My son is finishing up Beast Academy 3A. On a few occasions he is able to solve the harder problems only by using cuisinaire rods, but not by drawing pictures. For example, yesterday the problem was (page 77, number 50, two stars). "Grogg cuts the square below [it is 8x8 but that information is not given] into two congruent rectangles. Each rectangle has a perimeter of 24. What's the perimeter of the original square?" So after thinking about it, he said he wanted to use cuisinaire rods, so my son got two oranges (10) and a purple (4) and lined them up for the 24 then said he needed two of the same color and two of half the color, so he started with black and realized there is no half, then tried 2 dark greens (6) and two light greens (3) and lined them. Too short so he got two browns (8) and two purples (4) and realized he figured out the perimeter of the rectangle, then from there he got four browns lined them up and got 36 and said "duh, of course 4 times 8 is 32 and I could have looked to see 16 plus 16 is 32" When I looked in the back of the book for the solution, it suggests drawing rectangles of different sizes and then figuring out which one has a perimeter of 24 as the first step. A few days before he understood the triangle inequality by taking C-rods and trying to make different triangles. On the balancing weights section instead of skip counting and writing down the answer he used the rods to figure out the smallest number of weights of two sizes to balance an object. So my question for people whose kids have used BA. Should I continue to let him use the C-Rods, insist that he only draws, or I guess I could have him do it with C-Rods then make up a similar problem for him to solve by drawing. Any advice? Quote Link to comment Share on other sites More sharing options...
wapiti Posted January 16, 2015 Share Posted January 16, 2015 Thinking out loud, wouldn't both his c-rod method and the drawing method be trial-and-error in this case? If that's true, then I don't think it makes a bit of difference mathematically which one he uses. If there were some other mathematical goal for the problem (e.g. maybe the skip-counting one), then I might reconsider, but generally I'd allow him to solve this one any way he wanted, with extra points for creativity in using the rods :) Quote Link to comment Share on other sites More sharing options...
Miss Tick Posted January 16, 2015 Share Posted January 16, 2015 So he is using the c-rods to discover solutions his own way, gets the right answer, and then seems to be able to translate between what he did and what the book authors did. I wouldn't mess with that! Perhaps I'm reading between the lines, but he does some problems without c-rods, right? So if something seems tricky this is his go-to tool. I'm not sure I understand your concern. Quote Link to comment Share on other sites More sharing options...
Minerva Posted January 16, 2015 Share Posted January 16, 2015 Awesome! Any lightbulb moments should be encouraged. There are so many ways in math (and life) to get the right answer. As long as he is stretching his thinking, let him use whatever works. Quote Link to comment Share on other sites More sharing options...
kateingr Posted January 16, 2015 Share Posted January 16, 2015 I agree with eveyone else--that's a terrific solution, and an innovative way to solve a trial-and-error problem! The C-rods are very appropriate for those spatial problems. My only concern with using the C-rods would be if he were using them as a crutch because he doesn't have very good mental math skills--but if he recognizes quickly that 8x4=32, I think you're fine. :) Quote Link to comment Share on other sites More sharing options...
Nart Posted January 16, 2015 Author Share Posted January 16, 2015 So he is using the c-rods to discover solutions his own way, gets the right answer, and then seems to be able to translate between what he did and what the book authors did. I wouldn't mess with that! Perhaps I'm reading between the lines, but he does some problems without c-rods, right? So if something seems tricky this is his go-to tool. I'm not sure I understand your concern. I am concerned that without concrete objects he couldn't do the problem by writing out pictorially. It is the whole concrete-to pictorial-to abstract progression that SM is based on. Also once the numbers get bigger he can't use c-rods. I am concerned that as he moves on in BA he perhaps is supposed to be picking up the skill of drawing some problems so in 4th grade BA he won't be able to solve problems. Quote Link to comment Share on other sites More sharing options...
kiwik Posted January 17, 2015 Share Posted January 17, 2015 I think after a while he will need the rods less. Quote Link to comment Share on other sites More sharing options...
Rosie_0801 Posted January 17, 2015 Share Posted January 17, 2015 Does he have a ruler? Quote Link to comment Share on other sites More sharing options...
Farrar Posted January 17, 2015 Share Posted January 17, 2015 We used the rods for the triangle inequality. I think it's totally fine, especially since it sounds like he's using the rods in a really creative way, not in a, oh, I can't remember how to add these two numbers sort of way. Quote Link to comment Share on other sites More sharing options...
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