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. 

Pumpkins, Ghosts, Paper Clips, Barbies, and Flowers

I have a couple of review activities, fun for this time of year, a Dan Meyer activity and some flowers.

These are not original ideas and I have blogged about them before.

Ghosts in the Graveyard:   I took 12 problems and put them onto worksheets so that each team member is working on a problem and then checking with me.  If they get it correct, they get a ghost and can tape it to the board in one of four places around town.  They don't have their points assigned yet, so they just guess where they want to put them.  Before the end of class, I give 25, 50, 75, or 100 points to the different places and we see which team wins.  (I forget who I borrowed this review game from)

Trick or Treat:  I took 12 problems and wrote out all the solutions and answers.  Some were correct and some were incorrect.  I was the student.  The students play teacher.  I put the half pieces of papers in a pumpkin and call it Trick or Treat.  If they are correct, the students provide feedback and each one is worth 4 points.  If the problem is incorrect, they have to find the mistake, correct the mistake, and explain the mistake.  Then, they provide the feedback and decide how many points it deserves.  The kids are much harder graders than I am. (Again, another borrowed activity, but forgetting the original owner, sorry)

Paper Clips:  Did you know Dan Meyer is a World Record holder?  Check out the paperclip challenge to see his first attempt.  I asked the kids what they would need to know if they wanted to try and break the World Record for the length of a paperclip chain.  Then, we practiced.  They really liked the practicing time and were getting good at it.  We did 1 minute, 2 minutes, and 3 minutes.  Their hands were shaking during the 3 minutes.  We read about Dan's journey trying to break the record and felt his failure the first time.  But, then he tried again and we read about that here.  We watched this video about it here.

Barbie Bungee:  I did Barbie Bungee for the first time last year (blog here) and loved it.  I have four boys at home, so I didn't own any Barbies.  They are expensive, so I bought some cheap ones at Kmart.  They worked but lost their arms, legs, and heads and they were really lightweight.  Read about where I got my Barbies this year here.  I definitely recommend the real Barbies.  What a difference!  The kids had a lot of fun.  One girl was leaving and I heard, " I wish we could do stuff like that every day."  I am trying :)

And, flowers.  Below are some violets (I think) the Foreign Language department brought me this week.  It was a tough week at school and I loved coming in to find these one day and then the next day they had already grown taller.  It is a dark, rainy, and raw week and I think these flowers look like they are standing tall and trying to stretch their little heads towards any hope of sun. 

Cups and Mistakes

We did cup stacking again this year in Algebra 1.  I love it.  We did it with big whiteboards and their work was great:

And, in a different class we are working with integers.  This was an interesting mistake I have not seen before.  Makes sense but it is still not correct.