Students will try to determine a pattern for expanding binomials by using the expand command. Students will then make a conjecture about the expansion of a more complex pair of binomials. Students will then use SMG to take a closer look at how two expand binomials. The last page can be include or left out.
Before the Activity
Students learn to simplify expressions (like terms) and multiply monomials using algebra tiles. CAS can be used to consolidate the work they do with the tiles. Virtual tiles can be found at http://nlvm.usu.edu/en/nav/category_g_4_t_2.html.
During the Activity
Students will work through the first page and try to determine a method for expanding two binomials by using CAS. Most of them will use the sum and product pattern and believe that all binomials are expanded in this manner since the expand command leaves out the intermediate step.
The top of the third page presents two binomials that challenge that pattern. Students will then use the Symbolic Math Guide to expand and simplify binomials and thus will see the intermediate step. Students will generalize this into a process and try to revise their previous conclusions.
After the Activity
A selection of concept problems could be given as practice.