For Easter, the Hershey's Chocolate Company makes Kisses® wrapped in colored foil. The Easter Bunny has a bag containing the following candies: The Easter Bunny is making up Easter baskets for Flopsy, Mopsy and Peter Cottontail. If he does his best to share the Kisses® evenly among the 3 bunnies, show what each of their baskets will contain.
The week after Easter the students are full of stories about their Easter egg hunts and the Easter basket they received. This week as part of a reading unit, we read The Tale of Peter Rabbit by Beatrix Potter. This problem featuring Flopsy, Mopsy and Cottontail very nicely tied those two activities together. This task enables students to apply their knowledge of charts and tally marks. It challenges their organizational skills and their ability to keep track of a lot of data. It shows those students who have persistence and industry to complete the task in one work session and those who are overwhelmed by a lot of data. With the use of manipulatives to represent candy, the problem is accessible to students with different levels of calculation skill. Some students will solve the problem by grouping manipulatives and counting. Others will be able to draw on their knowledge of basic multiplication facts, their growing use of the addition algorithm and from their knowledge of coins (3 x 25 = 75). How students approach the task reveals their grasp of division as "even sharing". 45 minutes As noted, the problem is related to the Easter season. It can be related to reading The Tale of Peter Rabbit, which is a classic for this age level. A similar task could be written about a different group of three characters. The task also relates to many other occasions during the year when materials must be shared evenly for art projects, math activities involving manipulatives and the sharing of snacks. In solving the problem students were shown a bag of the kind of candy that is wrapped in different color foil. They were told to read the problem through with a partner and then I read the problem aloud to the class and asked if there were any questions. Everyone in the class understood the use of tally marks. Some students were unsure of the meaning of the word "contain". This was explained. I told the students that they would be working on their own and that they could use math manipulatives. They thought bowls of rainbow cubes would be most helpful and many students used these. However, I told the class that they all needed to show and tell with a "math drawing" what the bunnies' baskets would contain and to try to use equations to prove their solutions. The class was familiar with the term "math drawing" from our work this year. I contrast "math drawing" with an art drawing. The former needs to be clear, quick, helpful and often has labels, numbers and symbols. Some students will simply want to add the total number of candies and divide by three. These students will need to be encouraged to share each color evenly among the bunnies. A bag of color foil wrapped candy such as Hershey Kisses® or chocolate eggs and manipulatives to represent the candies. 25 eggs in each basket: 5 light pink, 3 dark pink, 7 silver, 6 green and 4 blue.
The Novice will be unclear about how to go about the task or once started, will only deal with one part of the task. Notation will confuse rather than clarify and the use of diagrams will be rudimentary or unconnected to the solution.
The Apprentice will have an understanding of the task, but will make calculation errors or obtain only a partial solution. These students may determine that each bunny gets 25 candies, but do not identify how many of each color each bunny gets. The mathematical language the student uses will be basic, relying mostly on equations to communicate.
The Practitioner has a full understanding of the problem and an approach that addresses all aspects. The solution will be free of computation errors and will be systematic in the approach. The use of mathematical language and diagrams clarify the solution.
The Expert has a sophisticated understanding of the problem, along with an efficient approach. These students demonstrate their developing calculation skills by calculating mentally. These students tend to use paper and pencil as a way to verify their mental calculations. These students will also make mathematically relevant observations such as, "All candy amounts are multiples of three," or that, "There are twice as many green than light pink."
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