There are two levels of accomplishment with understanding and fluency. The first level: students slowly solve problems with understanding and accuracy. The second level: students quickly solve problems with understanding and accuracy.

Many think that the job is done when students have reached the first level. After all, they got the problems right, and understood what they were doing—does it really make a difference if they were fast or slow? It does. Students who instantly know that 9 + 5 = 14 have a clear advantage in more complicated contexts: 49 + 65 = ?   91 + 52 = ?   98 + 57 = ?  976+458 = ?  9x + 5x = 280   (x+9)(x+5)= ?

As students grow older, 9 + 5 and all the other basic facts do not go away. They are used repeatedly throughout the upper grades.

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