Week of April 13th

This week the "easy" idea of reciprocals will be used to divide by fraction divisors. This is conceptually about as abstract as we can get, and these ideas will be seen again in 6th grade. The concept of division is our starting point to help us see that when you divide a number into smaller and smaller parts, you are able to get more of them. There are several kinds of fraction divisor applications, but we will limit our focus to one type. If I have a 24 inch long piece of wood for my science project, and I need to divide it into 1/2- inch pieces, how many pieces can I get? The answer is 48, which is actually larger than my dividend. This strikes students as odd, since with whole numbers, division makes things "smaller." Some students may actually make the connection that we approached dividing with a decimal divisor in the same way! (A great time to review that 24 divided by 0.5 is also 48.)

Even though the concepts are abstract, the algorithm is very straightforward, although keeping track of the many steps can be a problem at times. (How many parents remember "invert and multiply"? That's it!)

There will be a quiz on fraction divisors this Friday, April 17th. Then it's off to geometry land!