Chocolate Fractions

Here in the Upper Mississippi River Valley we are under the cover of snow, and the temperatures are frigid. After a bit of snowplay who doesn't want to come in for a little warming up with a cup of cocoa. Following on the theme of using food for math manipulatives, here is one of my students' favorite math lessons.

(This lesson can be done with a piece of construction paper cut into the appropriate shape, but how much more fun is the tactile experience of chocolate, and therefore more memorable.)

Each student needs his or her own bar of Hershey's chocolate (standard size, without almonds). I have my students draw each stage and label the picture accordingly.

One whole bar. 1/1 Note three rows (top to bottom) and four columns (left to right).

Then break the bar in half between the second and third row. One half. 1/2 Ask how many halves make up one bar. Go back to the whole bar to note 2/2 make one whole.

Break the halves in half between the columns. One fourth aka one quarter. 1/4 Ask how many fourths make up one whole bar. Go back to the whole bar to note 4/4 make one whole.

(For older students point out 1/2 times 1/2 = 1/4. Note that the multiplication sign can be translated as the word "of" in English. Half of half is one quarter (or one fourth). Also point out that 1/2 divided by two represents the same thing. This leads naturally to the discussion of how the saying, "Ours is not to reason why, just invert and multiply." pertains to dividing with fractions. Show how multiplying by 1/2 is essentially the same as dividing by two.)

Now break all the fourths into twelfths. At this point we will be rearranging and drawing the different combinations.

Put the twelfths back together to resemble the original bar, but leave a small gap between the rows. This shows three thirds. Draw a third lengthwise. Rearrange to show that there are the same number of pieces in drawing the thirds in columns (this means stacking four twelfths on top of each other). 1/3 Ask how many thirds make one whole bar. Go back to the whole bar to write 3/3 equals one whole.

Rearrange the whole bar and group the pieces in groups of two. This shows 1/6. Ask how many of these fit into the whole bar. Go back to the whole to write 6/6 equals one whole.

Have the student count how many separate pieces of chocolate there are. Draw the piece and label it 1/12. Ask how many of these pieces are in whole bar. Go back to the whole bar to write 12/12 make one whole bar.
Now go through all the other groups to see how many twelfths are in half, one fourth, one third, and one sixth. Do this for all of the fractions. This will show the equivalent fractions.

Regroup the pieces to represent three fourths, five twelfths, seven twelfths, ten twelfths, and eleven twelfths.

http://www.amazon.com/Hersheys-Milk-Chocolate-Fractions-Book/dp/0439135192
Have the student write down all of the equivalent fractions on a number line.

___________________________________________________________________________
0 1/2 2/2

1/3 2/3 3/3

1/4 2/4 3/4 4 /4

1/6 2/6 3/6 4/6 5/6 6/6

1/12 2/12 3/12 4/12 6/12 8/12 9/12 10/12 12/12


Future post: Adding and subtracting fractions with chocolate fractions.