In education we departmentalize teaching multiplication of decimals, then percents, then adding fractions, then dividing fractions.... By the time we have moved onto prime factorization the average student has forgotten how to find 15% of 30. There are many strategies such as reviewing, warm ups, spiraling that can help. One of many teaching strategies of not compartmentalizing math is KRYPTO. Putting 4 random digits on the board such as 5 0 7 4 can keep students reaching for new methods mixed with old. Just because factorials are not taught in 6th grade does not mean students shouldn't be introduced. The more strategies you learn the more chance you have of success (for example 4 divided by .5 equals 8 confuses students but being able to use it as a "weapon" in KRYPTO empowers the student), not to mention KRYTO is endless (using a little creativity and math knowledge 0 0 0 0 can even be done) and can teach the rule attributed to various chinese philosophers, "The journey of a thousand miles begins with one step" or perhaps "The journey of a thousand KRYPTO's begins with ones first attempt".
KRYPTO Rules: You must use all 4 numbers only once and any mathematical symbols and letters are fair game. I tell my students that a math teacher walked in they must be able to evaluate the expression equal to 15, and of course 3 + 5 + 8 - 1 is the same as 5 + 3 + 8 - 1 of course this is a good teaching opportunity to discuss the commutative property.
Here are some answers to 5 0 7 4 can you find more?