Saturday, October 25, 2014

Dividing with fractions, using pennies

Yesterday, I was going to use the height of a penny in a math question on a quiz so I googled "width of a penny".  It said it was 3/4 inch.  That wasn't what I wanted, but I liked the number.  I went to bed thinking about it and woke up with this....

Maybe an actual original idea for the #MTBoS?

There has been recent discussion on blogs and twitter about how to teach dividing by fractions besides just telling the kids to multiply by the reciprocal - the why part.

It got me to thinking: how many pennies would line up on a ruler? A penny's diameter is 3/4 inch, so I did 12 divided by 3/4 but really multiplied by the reciprocal 12 times 4/3 and I got 16.  Sixteen pennies should fit on a ruler.

So, then I thought about it some more:
In just looking at 4 inches of the ruler and putting one penny in each inch, I then thought this:
So, in four inches there would be 5 pennies because four fourths makes one whole.
Next I multiplied by 3 and got 15 - what the heck?!  Now, mind you, I woke up thinking all this at 6 am on a Saturday morning.  I knew I was wrong but it seemed to work.

It lead me to a joke (again early morning):
What does 1 penny plus 1 quarter equal?  An inch  :)  I like it - that's original too!

So, then I was thinking about 2 pennies.  Two pennies would be an inch and half so four pennies would be three inches, but then I have a whole inch left over and a penny is only 3/4 inch so I would have room for 1 penny with 1/4 left over -ahhhhhh - there it is.  I would have three 1/4's leftover and that equals my sixteenth penny.

I went wrong in thinking that four fourths makes the whole.  Only three fourths makes a whole penny