Final Project
Part 2
One thing that all people (including children) are interested in is
money. So to involve children in the classroom, why not do problems related
to things that they like? For instance, anyone who has entered a classroom
lately would realize that students do not like word problems. Do we know
why this is? Maybe it is because they must think some before jumping in
and using an algorithm to solve the problem or possibly the words get in
the way of the mathematics of the problem. In any case, word problems are
important and it is very necessary for educators to teach the students how
to deal with these real-life problems. Let's take a look at this a word
problem dealing with money.
Problem:
Jessica and Sally are juniors this year and they want to go on the senior
class trip next year with all of their friends. Both of their parents have
agreed that they can go, but they must pay for the entire trip themselves.
Sally already has $150 saved from her summer job. Jessica has $20 saved.
Sally's savings account earns 2% interest (compounded monthly) and Jessica's
savings account earns 3% interest (compounded monthly). The girls must
have the money for the trip in 11 months. If the total trip costs $600
for each person, how much will each girl need to deposit into her saving
account so that they will have enough money to go on the trip.
First the students need to identify each piece of information that they
will use in the problem. Once they have done this, there are many ways
to approach the problem. One of the easiest ways for students to complete
this problem is using a spreadsheet. With a spreadsheet, the students can
see instant results when they change a single number or a formula without
having to recalculate everything themselves.
Below I have used Microsoft Excel, a spreadsheet package to find the solution
to this problem. I developed columns for each value that I needed from
the original problem. When using a spreadsheet it would be best to try
to do each girl's account separately to avoid more confusion than necessary.
Once the basic frame of the spreadsheet ready, the students must decide
which formula to use. Presumably, this has been discussed in their mathematics
class. In this scenario, I needed to use a formula for compounding interest.
So I chose:
In the column with no label, I calculate the amount in the savings account
after the interest is added. The formula used in the spreadsheet looks
like the following:
Then I added another column. The amount above the label is the amount
that each girl will add to her account at the end of each month. So the
formula looks like this: = unlabeled column + monthly amount.
Now the amount in the first row and "Added Monthly" column is
used in the second row and "principle" column. Then the formulas
are dragged down. Some of the values must be fixed, so it may take a little
time to get the formulas entered correctly.
From this point, the students can play with the amount added monthly until
each girl has at least $600 in 11 months for their senior trip. The students
can also change the amount each girl had originally saved and see how that
effects the total amount earned.
To answer the question at hand, Sally must deposit $34 a month into her
account. However, the question asks how much each girl must deposit per
week. If we assume that there are 4 weeks per month, then Sally must deposit
$8.50 per week into her account.
Jessica must deposit $40 a month into her account. This means she must
deposit $10 per week.
Please see the spreadsheets below .
These word problems can be tailored to fit any classroom situation or
let the students develop their own word problems for other class members
to solve. Spreadsheets are very useful tools for the classroom. Sometimes
it may take some time to teach the students the "ins and outs"
of using formulas and some of the other features, but this will definately
save time in the end.
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