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 each of A and B spends $\$45,$ then the ratio of the money they have left is $13:10.$ How much money did each 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 each. This common difference of $2$ blocks represent $\$45,$ so each block is $\$22.50,$ so A and B started respectively with $15 \times \$22.50$ and $12 \times \$22.50.$
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.
Here is an example of the Singapore block model that I think works well. A person spends 1/6 of the money in their wallet and has \$15 dollars left over. How much did they start with? Create 6 blocks. Color one to represent the 1/6 that was spent. The remaining 5 blocks must add to \$15, so each block is \$3. Add the \$3 in the colored block to the \$15 to get \$18. Someone learning algebra may have a little trouble setting up the equation even though it is a relatively simple problem. The block model makes it easy to see how everything relates.