I have been examining sites that illustrate the use of the block model for solving problems. I am an adult with a degree in math and I have an interest in seeing how math can be taught.
From what I have seen, block modeling can be a useful introduction to algebra. The blocks provide a visual way of working with unknown variables. However, there are cases where the illustrated use of block models requires more ingenuity and abstract reasoning than simple use of algebra.
I saw one problem given as follows: The ratio of money between A and B is 5:4. If both A and B spend $45 then the ratio is 13:10. How much money did they have originally?
This is the solution that was given. To solve the problem, observe that 5 is one greater than 4. If we multiply both 5 and 4 by 3, giving 15 and 12, we now have the same ratio but now we have a difference of 3. This allows us to form 13 out of the 15 and 10 out of the 12 with 2 left over for both. This common difference of 2 blocks represent \$45, so each block is \$22.50, so A and B started respectively with 5 x \$22.50 and 4 x \$22.50.
Anyone able to think of that would have no problem parameterizing the original values as 5x and 4x and solving (5x - 45)/(4x - 45) = 13/10.