# Justifying moving the decimal

I need your help. I’ve been thinking of ways to better connect decimal multiplication with fraction multiplication, especially in terms of justifying moving the decimal point. Sixth graders may recall counting the number of decimal places, but do they really know what they are counting and why they are counting it?

The following is work in progress and I would appreciate your input. How can my attempt at creating curiosity  be improved upon? Are the examples sufficient or should they be revised? What am I missing? I’m anticipating students will say, “Count the decimal places,” so my follow up is this question. I don’t think students will connect fraction multiplication with decimal place value so my next move will be to ask them to compare the two expressions. Some students may recognize the two expressions are equivalent, but will they make the place value connection? I prepared a second example that “culminates” with this slide. Since the above problem has numbers in the ones place, some students may recognize 2 x 2 = 4, so it would be reasonable to place the decimal between the 5 and 6. I would certainly accept that, but my point is to discuss powers of ten. Yet I need to be careful. My sixth graders haven’t been exposed to negative exponents. Would it be appropriate to describe it as powers of tenths? Is this they best way to address the mathematics? I’ll likely begin with establishing a pattern before I present these slides.

I’m also thinking of creating a similar lesson which connects dividing decimals with dividing fractions using the common denominator method.  The students are familiar with the common denominator method, but I wonder if it will be too messy?