How to Encourage Critical Thinking with Fun Size Statistics

We all know that critical thinking skills are extremely important in the modern world.  Math is more than just being able to move the numbers around.  In order for the math to be useful, you have to be able to understand the meaning behind the numbers.  This summer I wanted to give my children a project that was a little more interesting than our normal habit of using candy to drill arithmetic.  This project is an introduction to the concept of statistics.  The only prerequisite is being able to count, and it would be a great way to help students practice the analytical skills that they will need for their science investigations. 

We used Mott's fruit snacks for our project. (No affiliation, we just like it.  If they'd like to send us more, we would be happy to use it for something else!)  Since we have a habit of using candy at lunch time to practice math, my kids weren't surprised that this treat came with a catch.  One of them was especially drawn to this project, but they both worked on it happily.  

Materials

package of snack size bags of candy

paper

markers, one color to match each color of flavor of candy

How we gathered our statistics

For the first several days, each child simply counted how many of each flavor was in their snack pack, and recorded it on their sheet.  We used matching markers to make dot for each piece of candy.

After several days we realized that some flavors were definitely more prevalent than others. 

Learning to Analyze

Once they had eaten all the bags of of fruit snacks except two (one per child), I gave them a second worksheet with questions about what they had found.  

1.  What color was most probable? (Probable=most likely to occur)

2.  What color was least probable?

3.  What was the mean number of snacks of their favorite flavor? (Mean is commonly referred to as average.  Add up all of the pieces, and divide by the number of packages.)

4.  What was the mode number of snacks of their favorite flavor? (Line up all the numbers and find the one in the middle.)

5.  What combination of flavors would they predict to find in the next pack they opened?

6.Open that last package, and see what you really find.

This time, my children gave exact predictions about the last pack of fruit snacks. Next time I plan to encourage them to give each flavor a range of expected values, and see if they can successfully predict a range that includes the correct values.  You could also calculate percentage error.

Our findings showed that some flavors were much more prevalent than others. This begs the question why?  Also, is that always the case, or would the numbers even out if we investigated a greater number of fruit snacks?

The value in this project was that it gave my children a sense of how quantifying what has happened in the past allows us to make predictions about what will happen in the future.   It also introduced some math vocabulary, and encouraged further questioning.  My kindergartner was easily able to understand this project, but some of the concepts would be appropriate for middle or even high school students.   

What candy would you try with this activity?

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