beansprouts Posted October 27, 2008 Share Posted October 27, 2008 Page 41 inthe Textbook "Review A" problem #10: 3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile? Up to this point, I have been very comfortable with the math and not found a need for the teacher's manual. There have been a few problems like these, and I am not seeing how they relate to the preceding lessons. I know how to solve the problems algebraically (pile #3 is x, pile #2 is 2x, pile #1 is 2x+10) and this is what I taught dd. She caught on to this and was able to finish the problem. However, if she was supposed to learn an entirely different skill, I don't want to skip it. How would you handle this with a 9 1/2 year old 5th grader? As this program becomes more advanced, am I going to run into more situations where the TM would be helpful? Quote Link to comment Share on other sites More sharing options...
KAR120C Posted October 27, 2008 Share Posted October 27, 2008 3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile? <----------------> pile 1 <-------------> pile 2 <--------------<-> ten books (difference) <-----> pile 3 So if you go with pile 3 as your "unit" there are 5 units plus ten books total... so the 5 units (5x "pile 3") is 2090, and one unit (the amount in pile 3) is 2090/5, or 418. Algebraically works fine too, and if she doesn't have any trouble with that then I don't really object, personally, to your using that method, but I do like the rod diagrams for laying out a problem first, even if you end up using algebra to solve it in the end. I believe that is what Singapore expects the kid to learn here... not the math as much as the layout. Quote Link to comment Share on other sites More sharing options...
beansprouts Posted October 27, 2008 Author Share Posted October 27, 2008 <----------------> pile 1<-------------> pile 2 <--------------<-> ten books (difference) <-----> pile 3 So if you go with pile 3 as your "unit" there are 5 units plus ten books total... so the 5 units (5x "pile 3") is 2090, and one unit (the amount in pile 3) is 2090/5, or 418. Algebraically works fine too, and if she doesn't have any trouble with that then I don't really object, personally, to your using that method, but I do like the rod diagrams for laying out a problem first, even if you end up using algebra to solve it in the end. I believe that is what Singapore expects the kid to learn here... not the math as much as the layout. It sounds like they are expressing the problem concretely for now to lead into the algebra later. I will show her the rods. That should help her understand the algebra. Thank you :001_smile: Quote Link to comment Share on other sites More sharing options...
KAR120C Posted October 27, 2008 Share Posted October 27, 2008 (edited) It sounds like they are expressing the problem concretely for now to lead into the algebra later. I will show her the rods. That should help her understand the algebra. Thank you :001_smile: That'll teach me to do math in my head without coffee -- it's not 2090 it's 2990... so 2990/5 or 598. Double check that though. ;) And yes -- it's the concrete (or pictorial) representation of what algebra will be later. Basically the beginnings of learning that you can manipulate numbers without knowing what they are first. Edited October 27, 2008 by KAR120C Quote Link to comment Share on other sites More sharing options...
at the beach Posted October 27, 2008 Share Posted October 27, 2008 I posted a reply on the other thread. Not sure how to move it! Quote Link to comment Share on other sites More sharing options...
beansprouts Posted October 27, 2008 Author Share Posted October 27, 2008 That'll teach me to do math in my head without coffee -- it's not 2090 it's 2990... so 2990/5 or 598. Double check that though. ;) That was what we got :001_smile: I do try to introduce algebraic concepts whenever it is appropriate because I don't want it to be totally new when she begins studying it in earnest. I am pleased that she was able to catch on to solving the problem this way. However, I don't want to miss any lessons by skipping ahead. Thank you for showing me how these problems should have been presented. I am thinking that HIG will come in handy for the future. Quote Link to comment Share on other sites More sharing options...
beansprouts Posted October 27, 2008 Author Share Posted October 27, 2008 I posted a reply on the other thread. Not sure how to move it! No problem I saw you :001_smile: Quote Link to comment Share on other sites More sharing options...
mcconnellboys Posted October 29, 2008 Share Posted October 29, 2008 I agree. This is what we try to do, too. I think learning to really see how the problem works before you move to the abstraction of algebraic formulas will help them understand math more clearly down the road. Quote Link to comment Share on other sites More sharing options...
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