[Dragon photo above by monkeywingand treasure chest by Tom Praison via flickr.]
Let’s play around with a middle-school/junior high word problem:
Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?
[Problem set in the world of Patricia Wrede’s Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]
How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:
![x - \left[\frac{1}{4}x + 0.6\left(\frac{3}{4} \right)x \right] = 48](https://s0.wp.com/latex.php?latex=x+-+%5Cleft%5B%5Cfrac%7B1%7D%7B4%7Dx+%2B+0.6%5Cleft%28%5Cfrac%7B3%7D%7B4%7D+%5Cright%29x++%5Cright%5D++%3D+48&bg=ffffff&fg=303030&s=0&c=20201002)
…or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (called bar models or math models or bar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use.
Edited to add: Oops! I missed the 
Denise Gaskins' Let's Play Math 