Monday, November 7, 2011

The Lifeguard Rescues the Distributive Property in Algebra

Visual learners, who need stories to help them understand math,  might enjoy the story about the lifeguard saving swimmers to understand the use of the distributive property ﻿to remove grouping symbols in algebra.

In the first example:  2(x+ y),   I tell students that the numbers in the parentheses are the swimmers in the pool.

The children in the clipart above would represent the x and the y.   The 2 outside﻿ the parentheses represents the lifeguard.  I then tell the students that the lifeguard needs to dive into the pool to rescue each of the kids (using the distributive property).  First he dives in and attaches himself (herself) to the x  making 2x.  Then he dives back into the pool and attaches himself to the y making 2y.  Because there was a positive or plus sign in the parentheses, the result is 2x + 2y.  There needs to be a LOT of reinforcement of this idea before any other signs are involved.

In this next example:  -3(x-5) can be very confusing to a visual learner.  Just tell the students that this time the lifeguard -3 has a lifesaving board with him.  This takes some of the scariness away from the negative number and replaces it with a visual image.
So, the lifeguard and his board dive into the pool.  He attaches himself to the x making
-3x.  But, when the lifeguard dives into the pool a second time, the second swimmer already has his own board.  Isn't that handy?  He really doesn't need rescuing, and what a POSITIVE thing that is.  But, he rescues away anyway.  So he attaches himself to -5 and the result is +15
(Remind the kids that a negative sign ALWAYS goes with the number or variable behind it).

The result of this lifesaving simplifying experience is -3x + 15.

﻿
﻿
﻿