We could continue to cite examples from many areas of mathematics that are best solved by using proportional reasoning. A big idea empowers students by revealing that a common pattern applies to a broad variety of applications. From these examples, it is clear that mathematics seen through the eyes of big ideas such as proportional reasoning is simplified, connected, and filled with potential for mathematical empowerment. In preparation for this activity, copy onto card stock a sufficient supply of the selected numbers to be used by five students. Cut and distribute one set of the numbers to each student.
Students can store their set in an envelope or plastic bag for future use.
This is a four-part activity in which students will use different sets of whole numbers. They will discover interesting information about how the results differ with different sets. Encourage students to find and make a record of as many patterns as possible. After they think they have found all possible sums along the two arms, challenge them to give reasons why they believe that is so. Students will utilize a diversity of ways to find all possible solutions.