Cheryl wrote,

Do you know of any good activities that are appropriate for 6th graders that help explain/show why you divide the numerator by the denominator to convert a fraction to a decimal?

Cheryl,

What a great question. And I’ll answer in the most roundabout of ways. We get numbers from counting, measuring and performing operations on those numbers.

- Counting usually gives us whole numbers
- Measuring with the metric system or money gives us decimals
- Measuring with the standard system gives us fractions
- For operations like division, we can choose—when we divide 7 by 2 we can stick with whole numbers 3 with remainder 1, use fractions 3 1/2, or use decimals 3.5—it just matters what you want your units to be wholes, halves, or tenths. BUT, and here’s the segue to your question—they are all just equivalent representations for the same number.

So, if I think of fractions, decimals, and percents as equivalent representations, then I get use my favorite equivalent picture to think about this idea. Have you ever met the ratio table?

There are strategies to getting from one column to the next, * or ÷ by a number or + or – two columns. In this case, I am using the * or ÷ by a number strategy.

If I have a 1 as the whole, the part is represented in decimal form

If I have a 100 as the whole, the part is represented in percent form

If I have any other number as the whole, then we get a fraction form.

I could share a podcast with you or a reference to more ratio table materials and applets if you aren’t familiar with this one.

Share your thoughts if you try any of it….