## Wednesday, August 6, 2014

### Proportional Reasoning and Peach Jam

Today I am linking up with
 A monthly REAL WORLD math blog link-up hosted by

I love when I can connect real life stuff to my students' math education.  A few weeks ago, I was lucky enough to be able to give a very fun real world math lesson to a few middle school students who I was doing summer tutoring with.  We had finished working on proportional reasoning problems and their rides had not yet arrived.  A few days prior to this session I had purchased a bunch of peaches and one of my tutoring students asked if he could have one.  He noticed that several of them had developed soft spots and I really didn't want to throw out all those peaches so I made a spur of the moment decision to make peach jam.  I had never made it before and did not have a recipe so I did a quick online search and found this.
 We used this recipe from food.com

It seemed like more peaches than I had but I had all the ingredients.  My two students seemed very concerned that it wouldn't work without enough peaches.  Little did they know that we were about to get majorly involved in a proportional reasoning problem.  A few phone calls to parents and they were both granted permission to stay an extra hour so we got right to work.

 We peeled, and diced the peaches and did not follow the recipe where it says to let them sit an hour and it seems to have come out fine!
After all the peaches were cut up, we had 6 cups.  It was nice that it was a nice whole number, because these kids are just getting the hang of proportional thinking.  If these kids were a bit more advanced, I would have loved to see it be 6.25 cups or another number involving a fraction or decimal.

We started trying to figure out how to change the recipe.  The recipe calls for 10 cups of peaches and we were short of that amount.  I asked them to make an estimate about how much sugar we would need.  They noticed that we had a little more than half of the peaches we were supposed to and would therefore need a little more than half of the sugar.  Because jam can be super tricky and will often not set of the right proportions of ingredients are not used, I explained to them that we would really need to figure out the right amount.  The estimate ended up being a good jumping off point for them along with the fact that six tenths is a friendly number to work with.  They quickly figured out we needed 3 cups of sugar and about 1.75 teaspoons of lemon juice.

They were so tickled that they used what they had been learning in our tutoring session to make this jam.  Of course, I could not stop there because these kids also need to review some multiplicative reasoning concepts so I jotted down a few notes and sent them home with the challenge to figure out how much it cost to make each jar.

Here is the information I gave them

Peaches were \$0.77 per pound.  We used 3 pounds
Sugar I bought a 10 lb bag for \$3.99.  We used 3 cups.
Lemon Juice 99 cents for 200 mL
Canning lids \$1.99 for 12.  We used 5.

They had to use multiplication, division, measurement conversion and addition to solve this problem.  Multi-step and multiple ways to approach this!  We had the best discussion a week later when they returned with their costs per jar.  They got the sweet reward of a jar of jam and I got kids thinking about math and not just doing it which really is the best reward of all!

How do you help your kids see that Math IS Real Life?  Please respond in the comments below or head on over to the linky and check out other teachers' ideas!