# Cooperative Problem Solving: Discovering Fractions with Quesadillas

This is a great centers activity for students 4th grade and up.    It is a real-life problem solving activity using cooperative learning and manipulatives.  It takes about 30 minutes.  Even if you normally don’t use centers, you can come up with a few other activities for students to rotate through to practice previously learned skills, or, all the students could do this at once, but you will loose some of the benefit, I think, if you do it that way (see below).  If you pre-cut the circles,  it will go faster.  I rotate my more advanced students through first so they can cut the circles if they finish early.  Make an attractive hallway display out of your final results, if desired.

You will need:

• Pre-copied paper circles – size is not crucial.  I used legal size paper and fit 3 circles on each paper.
• scissors – 1 pair per group of students
• markers
• chart paper – at least two pcs total for a classroom with 20 students or more (for display to discuss as a class and post in the hall)
• Practice circles on a handout:  Provide students with some small (quarter size) practice circles so they can decide how to work the problem before cutting the paper circles.  I provided six small circles at the bottom of my direction sheet and told students that they could draw more of their own circles on the back if they needed them.

Tell Students (or create handout or transparency):

THE SITUATION:  Your have invited three friends over to watch a football game.  You want to provide some snacks during the game.

THE PROBLEM:  You discover that you only have enough ingredients to make three quesadillas!  This is a problem since there are four people!  How will you divide three quesadillas for feed all four people equally?

DIRECTIONS:

• STEP 1:  As an individual, think of how YOU might solve this problem if you were in this situation.   Use the practice circles tot think of a way to divide the quesadillas so that each person will get the same amount.  Be ready to discuss your solution with your group.
• STEP 2:  Meet with your group (3 or 4 students).  Each person will take turns talking about how they solved the problem.  There are several solutions.  Talk to your group about each solution and decide which ones will work and which ones won’t and why.

INTERVENTION:  If the lower-level groups are confused, allow them to look at what previous groups have put together by allowing them to look at what has already been posted on the chart paper (see step 6).  Tell them the need to come up with a different solution, but looking at a other solutions should help.

• STEP 3:  Decide on ONE solution as a group.  You may choose one of the ones that someone suggested in your group or come up with a new one together.
• STEP 4:  Color the parts of your quesadillas in four colors to show what parts of each quesadilla that each of the four people will get to have.
• STEP 5:  ONE group member should now use the scissors and cut the large paper circles (representing the quesadillas) to show how you decided to divide the quesadillas.
• STEP 6:  Now take the peices and tape or glue them to the large chart paper to show the class how you have solved the problem.
• STEP 7:  Now write an explanation for your model on the chart paper.

Teachers:  You could make this fill in the blank, i.e.:  Each person will get  (insert fraction) of each quesadilla.  Keep in mind that some groups might split the three quesadillas into different fractional amounts and might show it as an addition problem, i.e. Each person will get  X of one quesadilla and X of the other two quesadillas.  If you have already studied adding fractions in previous lessons or grades then you can expect them to add them as well.

I found that my 5th grade students had a good time working out this problem in groups of four.  I think it was good that my more advanced students did the problem first to provide a model for the lower level students.  All of my groups successfully  posted examples on the chart paper.

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