
Re: whole number computational fluency articulated to decimal computation
Posted:
Dec 11, 2001 5:39 PM


In today's world I would not be the least bit opposed to having a student find the answers to 3.45 x 2.8 or 0.453/2.6 using a calculator. However, let's assume that the student MUST be able to demonstrate paperandpencil computation for the 3.45 x 2.8 problem. Why can't the student use whole numbers 345 x 28 to find the answer to the number crunching and then locate the decimal point using the lesson learned in CMP's Bits & Pieces II, lessons 6.3 and 6.4? Or using methods learned in Investigations, the student could draw a rectangle and write 300 + 40 + 5 along the top and 20 + 8 along the left side and then proceed divide the large rectangle into 6 smaller areas to find the answers to 20 x 300, 20 x 40, 20 x 5, 8 x 300, 8 x 40, and 8 x 5 and add up those 6 answers and then locate the decimal point a la lesson 6.3. This method will still work in algebra when they have to multiply binomials and trinomials. OR maybe it is now time to introduce the standard algorithm. I don't think that Investigations is OPPOSED to learning the standard algorithms; they just want the students to understand why those algorithms work before they blindly use them. The division question is far more interesting. I know that Bits II has a new 7th investigation on dividing fractions. I am not sure if it includes dividing decimals as well. This question is asking how many 2.6's will go into 0.453 and I guess the answer is "not many." I know that I personally would reach for my calculator on this. I suppose that if I HAD to use paper and pencil, I might try guess and check. 0.1 x 2.6 would be 0.26, too small. 0.2 x 2.6 would be 0.52, too big. Since 0.453 is considerably closer to 0.52 than 0.26, I would guess an answer of about .17 or .18. But since the answer on my calculator is 0.1742308, I don't think that guess and check would be very efficient for much more than estimating! But then, I don't think the long division algorithm would be very efficient in this case either and I certainly wouldn't want to take the time in today's packed math curriculum to spend the necessary time to make sure my students could do 0.453/2.6 by hand. If I think of where in the world outside of school a student would have to find the answer to 0.453/2.6, I imagine it would be in a highly technical field that would require precision and I am sure that student's boss would encourage the use of a calculator and discourage the use of finding the answer by hand.

