The purpose of this activity is to engage students in equally partitioning a set of objects among four parties.
The background knowledge presumed for this task is outlined in the diagram below:
This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.
The procedural approach (show more)
- The student uses appropriate calculations to find the share that each friend receives.
Students who are in the early progressions of algebraic thinking favour closure. That means they prefer to know in advance the quantities they are dealing with rather than treat those quantities as an unknown. The least sophisticated strategy is to calculate the total number of jellybeans then divide that total by the number of shares. There are likely to be variations in the methods student use to calculate their answers in this way.
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Students will desire closure may carry out the operations in the opposite order. They might share each jar among the four people then combine the three amounts.Click on the image to enlarge it. Click again to close.
Other strategies include giving a whole jar to three people then compensating the fourth person from each jar until equal numbers are reached.Click on the image to enlarge it. Click again to close.
Students might also alter the number of jellybeans in each jar so that the number is easily divisible by four. Then they may compensate to allow for the rounding.Click on the image to enlarge it. Click again to close.
The conceptual approach (show more)
- The student attempts a variety of approaches to find the equal shares and describes the similar structure in those approaches.
Students who operate without closure tend to be more interested in the process by which answers are obtained than their closure preferred classmates. They will look for diverse ways to solve the problem by procedures. These students may recognise that the same operations are performed in different orders without changing the answer. In the first method (3 x 64) ÷ 4 = 48 was calculated and (64 ÷ 4) x 3 = 48 was calculated in the second method.Click on the image to enlarge it. Click again to close.
Conceptually focused students are also more likely to apply the quotient theorem, j÷p = j/p where j represents the number of jellybeans and p represents the number of people. Students using this approach find the fraction of a jar that each person gets first without the closure of knowing the total number of jellybeans.