17. I am thinking of a number. When I multiply it by 5 the product is 0. When I multiply it by 6 the product is ?
23. The product of 2 different whole numbers is 7. Theirs sum is ?
24. The sum of 2 positive whole numbers is greater than their product if one of the numbers is ?
27. If paper clips cost 48 cents a dozen then ? paper clips cost $1.
Some of the problems that I did not list are in fact algebra and some I did not list because they were either definition problems or basic arithmetic problems. Those (except the actual algebra problems) are important as well but I chose these because they require solving, yet at the same time, don't require algebra.
I think a lot of students and teachers fail to comprehend algebra because they are clueless of its purpose. It might be better said that they have been rendered immune to its purpose. This is the problem with curriculums that are based on procedure only and lack the cleverness that defines higher mathematics. Putting algebra early into an arithmetic curriculum is no fix because the student is even less likely to appreciate it.
My solution is, in addition to the steady diet of fractions and decimals, to begin exposing my son to these types of problems so that he develops an appreciation for the mechanics behind cleverness with the idea that they will be easily recognizable and accessible when he sees them organized and extended in algebra.