Whiteboard Problem: Algebra
Below is a typical algebra problem. Keep in mind - word problems are tools to generate thought, not tasks to be completed.
Water is being drained out of a tank through 2 pipes at the rate of 330L/min. We know that one pipe releases 50L/min more than the other. How much do the 2 pipes drain each?
Solution below if you want it - but remember, the joy is in the struggle.
Reasoning. If one pipe releases 50L/minute more than the other then the difference between them is 50L/min. If I subtract the 50L/minute from the higher capacity pipe, both pipes will be releasing the same quantity. This will also remove 50L/m from the total. So together both release 280L/m. That means I halve 280 to get 140 for each pipe. Now we add 50L/m to one pipe bringing it to 190. So 140 plus 190 equals 330L/m.
This is harder to follow than actually do! Hope that makes sense. A good activity would be to get the learner (and you) write your own approach in your own words. Quite difficult!
330= 2x + 50
Cancel 50 from both sides
140 + 50 = 190
You will discover that it is the written explanations that make mathematics daunting. The concepts are actually pretty easy to grasp, it's translating the concepts from other people that's the real challenge.