This morning I had an epiphany about fractions. Why do we teach students fractions with denominators of 5, 7, 9, 11 or possibly even 12. I tried to think of an occasion I used any of those in my life and couldn't think of a single possibility. None. You might use those when you gamble but the context is different.
In the past, I had students make those strips showing equivalent fractions such as 2/2 or 7/7 = 1. I've had kids adding fractions with denominators of 33 or 75.
In reality, why don't we just teach fractions using the fractions we run across in real life. For instance fractions with denominators of 2, 3, 4, 8, 16, and 32 as those are the most common ones we use. I might even include 10 and 20 for money as there are 10 dimes in a dollar and 1 dime is 1/10th of a dollar or ten cents.
I do see the point of teaching equivalent fractions, of adding, subtracting, multiplying and dividing fractions but do we have to include pages of fractions that may be filled with denominators they will never see in normal life? In fact, why am I teaching them to multiply or divide mixed numbers by mixed numbers when most of the time we use whole numbers.
Yes, I see that they need to manage all sorts of numbers in a theoretical situation but in reality when will they use it?
All of the situations I can think of only use a limited numbers of fractions.
1. Gas is sold by in increments of 10th or 100ths with a price that is usually a dollar amount with 9/10 at the end.
2. Recipes use denominators of 2, 3, 4, or 8. If we increase or decrease a recipe we do it by whole numbers such as double or triple.
3. Hand tools are usually have sizes with denominators of 8, 16, or 32.
4. Distance that is listed on roadside signs usually have denominators of 2 or 4 while mileage signs between wholes might be in tenths.
5. Building materials are in often bought with denominators of 2 or 4.
I could not think of a single example that used some of the odd numbers of 5, 7, 9, 11, 13 etc except for the fifth of liquor. So I still wonder, why am I spending all this time to teach students to use fractions with denominators that they will never see or use in their lifetimes.
If anyone has suggestions on where these types of fractions would be used, please let me know.