Implement the Core-- A binomial activity with connections

Twitter Problem 10-13-14

(ax+b)(cx+d)
List the different trinomials which result from assigning 1,2,3,5 to a,b,c,d in all possible ways.
List as follows:,
(3x+1)(5x+2)=15x^2+11x+2

Explain why there are 12 possibilities!

COREFLECTIONS...

1) Do you think this type of activity will facilitate factoring? OR factoring involves different skills/reasoning?

2) Activities which connect algebra to other content areas like discrete math (combinations, multiplication principle,etc) are fundamental to the Common Core. While students are practicing multiplication of binomials ( a lower-level algorithm) they are also exercising higher-order reasoning. Do you feel this is overly ambitious for students who struggle with distributive property?

3) Students need to understand that listing the 12 possibilities is not the same as **EXPLAINING WHY** there are 12!

You might challenge them to explain the flaw in the following reasoning:

There are 4 choices for 'a'.
Then 3 remaining choices for 'b, so there are 12 assignments for a,b. For each of these there are two assignments for c, etc. Thus there are (4)(3)(2)(1) = 24 outcomes.