# Day 33: Mixture Mania

Today in Precalc we looked at various ways rational functions can appear in real world situations.  One of the more common ways is mixture problems which we talked about yesterday, you know give the problem and look at all of the different approaches students take and then help them compare strategies to determine the most efficient approach.  So as our opener problem today, the kids did this problem:  How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?  One student presented his solution on the board, but it was apparent by the student discussion that many students weren’t getting why the 0.7x was added to the numerator and a 1x (instead of a .3x) to the denominator.  So we made a model of the situation and “experimented” with a couple of friendly values to see what happened, followed by relating it to the problem.  I tried to use color to enhance the connections, but am not sure if it helped.  I do love, Love, LOVE my laminated CCSS magnet signs for the 8 practices….so convenient for highlighting how students used the practices!!  How do you help students understand the concept underlying the idea of mixture problems?