I tell my math-teacher sister that they need to drop the word "algebra" and call the class "what if?". Almost all of algebra can be taught by asking "what if" and discovering a method to determine the answer.
What if your car gets 9 mpg and you have 2 gallons of gas? Once they see how that one works, then generalize the question. What if your car gets 9 mpg ... how would you determine how much gas it needs to get somewhere?
What if you are at the south-west corner of a section of land (1 mile square) and you need to get to a point that is in the center of the section ... how far will you need to travel to get there by the shortest path?
What if Obama is re-elected and the national debt takes off in an exponential rate. How much will your generation owe in 12 years?
Start off asking "what if" and discover a method. Hopefully, discover two or three and learn that there are usually multiple ways to get to the correct answer ... and, most importantly, how to determine which one is the better method in this problem.
Of course, all this might explain why I'm teaching computers and not math.
Here’s one:
What if you have enough money to buy $30 worth of groceries per week for one month? If you follow the servings guidelines for good nutrition, i.e., fruits, dairy, meat, vegetables and cereals, what would you buy and eat?
Unfortunately, your approach is too close to how basic math is now being taught: here’s a problem, break into groups and come up with ways you could solve the problem (preferably using estimation).
That all, except for the group bit, would be fine if the students had already been taught how to solve such problems, but they’re supposed to be coming up with approaches on their own. Needlessly confusing and time wasting for average and below-average students especially. They first need to be taught the tools and when and how to use them. That is elementary algebra.