Monday, July 21, 2008

An answer to an anonymous challenge question

Anonymous said...
Would you like a challenge?
Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?


I think I have it figured out!

Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?

First things first, read the problem sentence by sentence underlining the who and what

Alan saved $115 more than Ben. After Alan gave $17.50 to Ben, the ratio of Alan's money to Ben's money was 3 : 1. How much money did each of them save?

Step two: List the varibles:

Alan's savings

Ben's savings

Step three: draw a unit bar to model each varible, make these all the same size
Alan's savings[][][]

Ben's savings[]

Step four: determine what each unit bar represents and where you need to place a question mark.

In this problem we need to determine how much money Ben started with, and how much Alan started with.

Alan's money [][][] + 17.50?
Ben's money []?

Step five: compute the problem
I went with what I knew:
Alan's $ to start with was = Ben's starting $ + 115
Ben's $ + 115 + 17.50 = 3:1
Alan's $= 22.50 + 115 - 17.50 = 120/4 = 30

Alan's money [30][30][30] + 17.50?
Ben's money [30]-17.50?

Alan's money to start with would have been $137.50, Ben's money to start with would have been $22.50.


I used a lot of guess and check on this problem to get the answer. I knew that I had to add

1 comment:

Anonymous said...

Good job, you got the correct answer.

The point of drawing models is to eliminate the guess and check, though. The problem with the step by step process you were taught is that it breaks down when you get to more complex problems that don't lend themselves to those particular steps. This one is from a primary 5 book. The "follow the steps method OK for the easier problems in grades 1-3 Primary Math, but you can't follow specified steps with problems from the later levels - you have to apply more problem solving and logic to the problem as a whole rather than following a sequence. You can follow steps with a lot of them, but not all. Perhaps following specified steps is helpful, though, to start out with. I don't know what grade you are teaching, and maybe they will teach you how to solve more complex problems later. But don't get stuck on one procedure with these. A different approach may work better, like working backwards.