For our Problem of the Day, I asked the children, “Which is a better deal? Two pieces of candy for 3 cents, or 3 pieces of candy for a nickel?”
Motivated by the idea of buying candy, the children eagerly jumped into the problem. I showed them how to organize their information on a table. The first row was labeled, “Assorted candy” and the second row was called, “Coins.” I helped them get started by showing them how to draw 2 candies for 3 pennies in the top chart, and 3 candies for a nickel on the bottom table.
Kimberly saw the fractions and had correct ratios, but did not know how to compare numerators to see that 6 candies for 9 cents was a better deal than 6 candies for 10 cents.
The children enjoyed pretending that the pattern blocks were their assorted candies and several used protractors to help them trace circles that represented the coins.
Since some were struggling with correctly building the ratios, I told the students to pretend that the candies were sold in bags of 2 candies for 3 cents or bags of 3 candies for a nickel. This helped them make sense of the problem and better organize their ratios.
Jessi helped his classmates see that 2 bags of 2 candies each (or 4 candies) would cost "3 cents + 3 cents." This helped some who were confused about how to use the table for organizing their information.
Finally, Ediverto was the only one who correctly label his work with the right answer. He wrote, "I can prove 9¢ for 6 candies is a better deal."
Pleased with his efforts, I had him come up to the front of the class and share his discoveries. Ediverto beamed with great pleasure and did a little "victory dance" to show his delight.
He is a child with autism and never speaks a word, but he is well accepted by the class and a brilliant mathematician.
Here Ediverto is showing the other students that "6 candies for 9 cents" is a better deal than paying "10 cents for 6 candies." The class clapped and cheered for him. We were all very proud of Ediverto!!
Below you can see the back side of his candy chart.
4.NF.A.1 The next day I followed up with a related activity and showed the children why 2/3 and 4/6 and 6/9 and 12/18 were equivalent fractions. Here are two different student samples. In each case, we multiplied by the big "1" and proved that multiplying a fraction by n/n may change the name of the fraction and the size of its parts--but not the total area. 2/3 times 2/2 = 4/6 and 4/6 is an equivalent fraction of 2/3.