The other day I pondered fractions. What are they and how do we teach this to students? Although students should know the topic well by the time they start high school, many of my students do not.

I have taken time to show students that the parts need to be of equal size within the figure but I have never explained the size is not important when showing one fractions.

By that I mean, the figure could be large or small, it does not matter as long as 1 part is shaded in. You can see I have two different sized shapes, both illustrating 1/4th.

The other way to show a fraction might be using this formation as one out of a group. The size of the individual circles should be the same but I could have used individual squares.

I do not use this representation as much because the teachers in the elementary use the first representation. I don't think they ever teach it the second way.

I know I need to include the second representation more often so they develop a better understanding.

However, when we show students addition and subtraction of fractions, we need to make sure students understand both shapes have to be the same size with equal subdivisions.

From what I've seen in the elementary classes, teachers do not take time to teach this because most of the elementary teachers I know are afraid of math and do not have an understanding themselves.

I remember years ago, one of my students had an "ah ha" moment when she realized the subdivisions within the shape had to be equal. Up to this point, she would draw the divisions any old way so they were not equal.

Imagine getting to high school, a senior at that, and having no understanding of that basic idea. This coming year I have two pre-algebra classes and one foundations of math class. I know I am going to include more illustrations in the class when teaching fractions.

I also plan to create drawings to help reinforce the idea that when adding or subtracting fractions, the size of the shape or group has to be the same so they "see" it. I've read that our brains do much better remembering material when there is a visual illustration to go with a concept.

Sorry, I'm running lazy but I had to take something into town to be cleaned, ran errands, and forgot I hadn't done this column yet. I hope everyone has fun this weekend and let me know what you think.