Proportion-1512

I posted this because it is funny and because it reminded me of the age problems we worked on in our Teaching Math to Elementary Students 1512 class. It also gives a taste of the confusion over proportion and ratio. Sometimes what seems to make sense in our minds may not work out on paper. We do need to teach basic facts along algorithms that work every time in order to avoid raising students who have an Abbott and Costello understanding of math.

So, let's take an example of the age problem from the "other" math class. I will use it to illustrate my take way from Chapter 7. The following story problem is based on actual people, only the names have been changed to protect the aging.

Agnes, Gertrude, and Prudence are three sisters who live in a decrepit Victorian mansion.  Agnes is the youngest and Gertrude is one year older than Agnes,  Prudence is one year older than Gertrude.  Together their ages add up to 294.  Find their ages.
The first step is to determine what the problem is asking us.  And clearly the question asks us to expose their ages. Rude? yes. But that's what they want.

Agnes is the youngest so we will start with her and use X to signify her age.
Gertie is one year older so we can call her X+1
We're going to call Prudence X+ 2 because that is easier than calling her one year older than Gert which would look like this     X+ 1+1 which means the same but takes longer to write and may end up being confusing. So Prudence is X+2
We know that altogether the three add to 294 so we'll put that number on the other side of the equal sign, all by itself.

Our plan looks something like this

X + (X+1) + (X+2) = 294

We have a plan- now we should put that plan into action-

We can add all of the X's together which equals 3X and then add the whole numbers together which gives us 3- this changed the left side of our equation this way

3X +3 = 294

The idea is to isolate the variable- or the X so we expose what is means.  To do this we have to take three away from each side -

3X = 291

We're almost there (for the first part anyway) - divide each side by the 3 and that will leave us with the value of just one X (or Agnes' age)

X = 97

But wait!! Finding X is great and all but was that all we needed to do?  Don't spike the ball just yet...LOOK BACK and see what the question really was....oh yeah, they wanted all the ages, not just Agnes'.

Since we know that Gert is one year older than Agnes we just add one to 97 giving us 98.  We can then add one to Gert's age to find out Prudence's age of 99.



The thing I like best in chapter 7 is the chart illustrating how to approach a problem and work towards a solution. I would take this idea and create a poster to hang in the classroom to help students during work and test time.
It goes a little something like this...

I know that using this process during instruction will help give students a structure to rely on when approaching a new problem. If I hang this poster in the room and allow it to remain during testing it may help trigger the students memories from the lessons.