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In this
lesson we will play the game
"Guess My Number"
This is a
terrific way for you to use knowledge
that you already have to arrive at a new solution.
Let's look at an example.....
Take this set of numbers....
11, 3,
41, 16, 25, 10, 17, 12, 9
Now...what if I tell you
that the secret number is odd...
Well, we know what odd means...don't we?
Of course we do!
So now our set looks like this...
11,3, 41,
25, 17, 9
Now....what if I tell you
that the secret number is less than 30..
That would eliminate some more...wouldn't it?
So now the set looks like this....
11,3, 25,
17, 9
The next rule is...the
number is a perfect square...
and the set gets even smaller....
25,9
and if the final clue
says it's a multiple of 5....
then we know the secret number is...
25!!!
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Now let's think about
what you just did to find the secret number.
Well...you certainly had to know a lot of
math vocabulary didn't you....
Odd, Less Than, Perfect Square, and
Multiple....
Knowing what these terms mean was the key to you
finding the number.....
In mathematics we call this having "prior
knowledge".
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Let's look
at a little different kind of problem.
But, as we work through it together, think about the "guessing" game
and see how this problem relates to that one.
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Jane has
$3.05 in nickels, dimes and quarters....
We know the following information...
1.) the number of quarters is one-half the number of dimes.
2.) the number of nickels is greater than the number of quarters
3.) the quarters total $1.50
Find the number of each type of coin.... |
Well... let's think....
First...do we need to follow the rules in order?
Not necessarily!
If one of the rules gives some very specific
and helpful information, then go for it!
In this problem, knowing that the quarters total $1.50
gives us the number of quarters in one quick step!
After all, we know that a quarter equals $.25, so in order to get
$1.50
we would need 6 of them...so there are 6 quarters.
Next, since the number of quarters is one-half the number of dimes,
if there are 6 quarters...there must be 12 dimes!
What we have so far....
6 quarters = $1.50
12 dimes - $1.20...
So we have accounted for ($1.50) + ($1.20) = $2.70!
That leaves $3.05 - $2.70 or $.35
Finally, the clue above says that the are more nickels than quarters
so that means more than 6...which works out nicely since
7 nickels totals $.35
So the solution is:
7 nickels, 12, dimes and 6 quarters
What was the prior knowledge
you needed for this problem?
Well, you needed to know the value of each of the types of coins.
You also needed to know that if the smaller number is one-half the
other,
that's the same as saying that the other number is twice the
smaller.
To practice some of these on your own....
CLICK HERE
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