happycc Posted July 16, 2012 Share Posted July 16, 2012 (edited) Singapore 3A in my teachers guide/ standards edition page 70. Enrichment problem Ann and Amy have $42 altogether. Ann has $12 less than Amy. If Amy gives $3 to Ann, how much more money does Amy have than Ann? Now here is the part that stumps me: They say " A straightforward way to solve this is to find the amount each has, (2 units = 42-12=30; one unit =15.; Ann has 15, Amy has 15+12 =27 Where are these units they are talking about.... I get the pictures.....but the whole units part is stumping me and kids. UGH! Pregnant brain! Edited July 16, 2012 by happycc mistyped.12 for 2 sorry guys Quote Link to comment Share on other sites More sharing options...
zoo_keeper Posted July 16, 2012 Share Posted July 16, 2012 Singapore 3A in my teachers guide/ standards edition page 70. Enrichment problem Ann and Amy have $42 altogether. Ann has $12 less than Amy. If Amy gives $3 to Ann, how much more money does Amy have than Ann? Now here is the part that stumps me: They say " A straightforward way to solve this is to find the amount each has, (12 units = 42-12=30; one unit =15.; Ann has 15, Amy has 15+12 =27 Where are these units they are talking about.... I get the pictures.....but the whole units part is stumping me and kids. UGH! Pregnant brain! In SM's bar chart approach, each bar is a unit. So the bar chart way would be to do the following: Amy: [XXXXXX][12] Ann: [XXXXXX] [XXXXXX][XXXXXX][12]=[42] >>> [XXXXXX][XXXXXX]=[30] >>> [XXXXXX]=[15] Quote Link to comment Share on other sites More sharing options...
Dealea86 Posted July 16, 2012 Share Posted July 16, 2012 I'm no expert on SM methods, but since no one's answered you yet I'll give it a try. It looks to me like they're defining the $$ Amy has as one unit, and it was a misprint in the book. It should read 2 units = 42-12. That gives you 2 units = 30. Dividing by 2 gives you 1 unit = 15. So they're defining Amy's money as one unit. That's pretty much the same thing as saying "Amy has X dollars. Let's solve for X." If anyone knows more than me about SM, though, please feel free to correct me. :) ETA: I knew I should have waited longer for someone to jump in. ;) Quote Link to comment Share on other sites More sharing options...
Trez Posted July 16, 2012 Share Posted July 16, 2012 Yup, I agree with both of the previous posters.... Anne [---------][12] } Amy [---------] } 42 So a unit is what Amy has and 2 units equal 42-12=30 so 1 unit is 15. Quote Link to comment Share on other sites More sharing options...
happycc Posted July 16, 2012 Author Share Posted July 16, 2012 why we had to use the unit and the point of doing that. What do I say to her? Quote Link to comment Share on other sites More sharing options...
kalanamak Posted July 16, 2012 Share Posted July 16, 2012 why we had to use the unit and the point of doing that. What do I say to her? I draw the bar diagram and call the working amount a "unit". Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted July 16, 2012 Share Posted July 16, 2012 I draw the bar diagram and call the working amount a "unit". This non-SMer is curious .. is the bar (/unit) diagram way of solving a problem a visual .. perhaps less abstract .. version of algebra? Quote Link to comment Share on other sites More sharing options...
Zoo Keeper Posted July 16, 2012 Share Posted July 16, 2012 This non-SMer is curious .. is the bar (/unit) diagram way of solving a problem a visual .. perhaps less abstract .. version of algebra? Yup, you got it. :) I'm hoping this helps ME finally understand some algebra better. The kids are already making these jumps...:lol: Quote Link to comment Share on other sites More sharing options...
Incognito Posted July 16, 2012 Share Posted July 16, 2012 I think that using the word "unit" was just a short way of describing the problem. You don't need to use the word if it confuses you or your child. Quote Link to comment Share on other sites More sharing options...
kalanamak Posted July 16, 2012 Share Posted July 16, 2012 (edited) I think that using the word "unit" was just a short way of describing the problem. You don't need to use the word if it confuses you or your child. You could call it the "base amount". It can be confusing with units such as feet, pounds, grams. Edited July 16, 2012 by kalanamak Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted July 16, 2012 Share Posted July 16, 2012 I call it "x". :D Quote Link to comment Share on other sites More sharing options...
Dealea86 Posted July 16, 2012 Share Posted July 16, 2012 A foot is a unit, right? It's a unit made up of 12 inches. A pound is a unit made up of 16 ounces. A kilometer is a unit made up of 1000 meters (or 100,000 cms, or 3,280 ft, or whatever). Similarly, in upper level algebra we use a unit vector - a vector where the length is 1 'unit'. Depending on the problem, we pick the unit that makes the most sense and that will make the math easier for us. So instead of measuring the length of a room in inches, we choose to measure it in feet. Saying that the room is 11 feet long is easier than saying that it's 132 inches long. In the same way, this problem is using a 'unit' made up of however many dollars Amy has. It doesn't matter that we don't know right away how much money she has. By calling it a unit, we can solve the problem much easier. It's algebra with pictures, and it's completely brilliant. I would have loved to learn algebra this way in elementary school. Not because I hated algebra (it's my favorite math :D), but because it's just so cool. Quote Link to comment Share on other sites More sharing options...
Trez Posted July 16, 2012 Share Posted July 16, 2012 This is also one of my favourite things about Singapore. It took a little while to get used to with my elder son coming from public school but now whenever they are stuck on a problem, I ask them to draw the diagram before they ask me. Many times seeing it visually in this way helps a great deal. It is also a great way to introduce algebraic concepts before actually doing "real" algebra. Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted July 16, 2012 Share Posted July 16, 2012 How do you decide how big to draw the unit in relation to the known amounts when you don't know it's value? Do you estimate? Quote Link to comment Share on other sites More sharing options...
boscopup Posted July 16, 2012 Share Posted July 16, 2012 How do you decide how big to draw the unit in relation to the known amounts when you don't know it's value? Do you estimate? The unit is an unknown quantity. It's not drawn to scale compared to the known values. Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted July 16, 2012 Share Posted July 16, 2012 The unit is an unknown quantity. It's not drawn to scale compared to the known values. Are the known values drawn to scale? Quote Link to comment Share on other sites More sharing options...
boscopup Posted July 17, 2012 Share Posted July 17, 2012 Are the known values drawn to scale? We make 12 bigger than 5, but that's about it. Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted July 17, 2012 Share Posted July 17, 2012 We make 12 bigger than 5, but that's about it. Okay. I found some app once for this stuff and I couldn't work with it. Im trying to figure out if I'm not really getting something or if my brain is just wired differently. Sorry if my questions sound silly. :001_smile: Quote Link to comment Share on other sites More sharing options...
boscopup Posted July 17, 2012 Share Posted July 17, 2012 Okay. I found some app once for this stuff and I couldn't work with it. Im trying to figure out if I'm not really getting something or if my brain is just wired differently. Sorry if my questions sound silly. :001_smile: Pick up a CWP book... maybe grade 3 would be good? Look through the examples there, and it will teach you how they're used. The challenge problems will show some problems where they're super helpful (sometimes making the problem easier than algebra would). Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted July 17, 2012 Share Posted July 17, 2012 why we had to use the unit and the point of doing that. What do I say to her? "Unit" is just what Singapore math calls any unknown amount --- especially if the same amount is used more than once in the problem. For example, if they said that Amy had three times as much as Ann, then they would draw four units: one for Ann and three for Amy. Quote Link to comment Share on other sites More sharing options...
kalanamak Posted July 17, 2012 Share Posted July 17, 2012 I call it "x". :D I'm starting to, after we introduced X and Y as angles of unknown degree. Quote Link to comment Share on other sites More sharing options...
kalanamak Posted July 17, 2012 Share Posted July 17, 2012 Are the known values drawn to scale? By eyeball. When we very, VERY first started I did it on big graph paper, to scale, but now he knows that the biggest bar goes all the way across my Boogie Board (which I use instead of a white board) and we work from there. About all I get is the smaller part of the total is a smaller bar than the bigger part. I sweated about this at the beginning, but kiddo seems to catch on with eyeballing. Quote Link to comment Share on other sites More sharing options...
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