Visualizing Two Word ProblemsDate: 03/12/98 at 23:54:18 From: Sherilyn Subject: word problem Sandy has thrice as many beads as Wendy. Ann has half as many beads as Wendy. If Sandy has 180 beads more than Ann, how many beads do the 3 girls have in all ? My solution comes in this way : Sandy o........o........o........o........o Wendy o........o Ann o....o I take 180, divide by 5 parts (Sandy has 4 parts plus 1 part from Wendy). It will give the quotient of 36 for each part. Looks like I am unable to proceed further. Please help! Date: 03/13/98 at 12:23:30 From: Doctor Lim Subject: Re: word problem Hi there, You were almost there. Let us go over your problem. >Sandy has thrice as many beads as Wendy. Sandy [____________][____________][____________] Wendy [____________] >Ann has half as many beads as Wendy. Sandy [____________][____________][____________] Wendy [____________] Ann [_____] This means that: Wendy [____________] Wendy [_____][_____] Ann [_____] This also means that: Sandy [____________][____________][____________] Sandy [_____][_____][_____][_____][_____][_____] Wendy [_____][_____] Ann [_____] We finally get: Sandy [_____][_____][_____][_____][_____][_____] ---> 6 units Wendy [_____][_____] ---> 2 units Ann [_____] ---> 1 unit >If Sandy has 180 beads more than Ann, Sandy [_____][_____][_____][_____][_____][_____] Ann [_____] <----------- 180 ----------------> Do you see the relationship now? Yes that is right. 5 units ===> 180 beads. The total number of units that the girls have are 9 units. So 5 units ===> 180 beads 9 units ===> 180/5 * 9 beads = ?? I am sure that you will be able to get the answer now. Now change the problem a little and see if you can get the method right: Sandy has four times as many beads as Wendy. Ann has half as many beads as Wendy. If Sandy has 210 beads more than Ann, how many beads do the 3 girls have in all? If a word problem looks difficult, read it sentence by sentence. You will find that the problem is not that difficult after all. -Doctor Lim, The Math Forum http://mathforum.org/dr.math/ Date: 03/14/98 at 22:51:36 From: Sherilyn Subject: word problem Thank you for helping me in my word problem which you have answered on 14 Mar '98. Your explanation is very clear and this gives me more confidence in tackling such sums in future. Meanwhile, I have this problem sum; please tell me if my answer is correct. The question is: If Paul gives 20 of his marbles to Simon, he will have three times as many marbles as Simon. If he gives 10 of his marbles to Simon, he will have five times as many marbles as Simon. How many marbles does Paul have? My working is : [10][10][10][10][10][10][10][10] Paul's original no. of marbles [10][10] That's for Simon 80 minus 20 = 60 60 minus 10 = 50 Meaning Paul will have 50 marbles. (Is this the answer?) Please help!! Date: 03/16/98 at 16:12:16 From: Doctor Lim Subject: Re: word problem Hi there, I am glad to be of help. Let us try to work out this one. > If Paul gives 20 of his marbles to simon, he will have three times as many marbles as Simon. Model A At first, Simon has [___] When Paul gives 20 marbles to Simon, Paul [_______][_______][_______] Simon[_______] To make this in relation to Simon, Paul [___][20][___][20][___][20] Simon[___][20] >If he gives 10 of his marbles to Simon, he will have five times as many marbles as Simon. How many marbles does Paul have? Model B At first, Simon has [___] When Paul gives 10 marbles to Simon, Paul [______][______][______][______][______] Simon[______] To make this in relation to Simon, Paul [__][10][__][10][__][10][__][10][__][10] Simon[__][10] Your working is not right, as the two models you drew are not of the same unit, so you cannot just take away from them. From my two sets of models, I still cannot find an identical unit, so I must redraw them. Instead of having: Model A Simon[___][20] I have to change it to the following to suit the second statement: Model A Simon [__][10][10] This is to make this model the same unit as the first and second statement. ================== Model A Paul [__][10][10][__][10][10][__][10][10] Simon [__][10][10] Paul [__________][__________][__________] Simon [__________] ================== Model B Paul [______][______][______][______][______] Simon[______] Paul [__][10][__][10][__][10][__][10][__][10] Simon[__][10] ================== Now I have to compare the two models. I'm going to call Paul and Simon "Paul A" and "Simon A" when working with Model A, and "Paul B" and "Simon B" when working with Model B. Paul A [__][10][10][__][10][10][__][10][10] Simon A [__][10][10] Paul B [__][10][__][10][__][10][__][10][__][10] Simon B [__][10] I shall return [10] from Simon A to Paul A. This is to make Simon A and Simon B the same. Paul A [__][10][10][__][10][10][__][10][10][10] Simon A [__][10] Paul B [__][10][__][10][__][10][__][10][__][10] Simon B [__][10] ================== Paul A [__][10][10][__][10][10][__][10][10][10] Paul B [__][10][__][10][__][10][__][10][__][10] ================== We rearrange them: Paul A [__][__][__][10][10][10][10][10][10][10] Paul B [__][__][__][__][__][10][10][10][10][10] Paul A has 3 [__] and 7 [10] Paul B has 5 [__] and 5 [10] We take away from those that are the same: Paul A [__][__][__][10][10][10][10][10] [10][10] Paul B [__][__][__][10][10][10][10][10] [__][__] We now know that [10][10] is the same as [__][__]. That means that [__] is the same as [10] ================== Simon has [__]. This means that Simon has [10] or 10 marbles. Let us go back to Model A: Paul [__][10][10][__][10][10][__][10][10] Simon [__][10][10] If [__] means 10 marbles, then Paul has [__][__][__] + [10][10][10][10][10][10]. So Paul has 10 + 10 + 10 + 60 = 90. But Paul gave 20 to Simon. That means that Paul has 90 + 20 = 110 marbles at first. ================== This problem is difficult, as you have to compare both the models that you have drawn. You have to make sure that the units you draw are identical. Otherwise, you cannot compare them. The difference in my m models is that I had broken up the 20 marbles that Paul gave to Simon as 10 and 10. In this way, I can break up the models easily. Don't worry about these kind of word problems. You have to play around with the statements and think of the possibilities of the type of models that you get. Once you have understood these concepts, word problems are no longer a "problem." Have fun working it out. How about trying it with other numbers or working your problem backwards? You can then give that word problem to your friends and get them to solve it. This will be another way to revise. It will be fun for you and your friends to think that you, not just your teacher, can make difficult word problems. -Doctor Lim, The Math Forum http://mathforum.org/dr.math/ |
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