Fractions

For the past two weeks we have been playing with fractions.  Fractions can be a lot of fun when you get to play with materials and you feel you master them. For some fractions may look frightening. Fraction concept is probably one of the hardest ones to truly understand. Even though children see pizzas and cookies shared, and are able to find a half or a quarter of a rectangle already in reception, the full understanding of part-whole-relationship idea, and what the numbers in written form of a fraction mean, may stay hazy for years. I am a firm believer in strong foundations, therefore I'd rather spend longer time building the conceptual understanding than quickly introducing new terms and galloping through curriculum.

This Wednesday we had a lesson where we looked at shapes divided into multiple parts and the students had to decide whether these were or were not models of fractions.

The idea was to decide whether all the shares were fair or not.

The students had to explain and justify their thinking.

When I first showed this model, majority of the students were convinced it was not a fraction. After some thinking and a student clearly explaining that on both sides of the middle line the shape was divided into halves, just in a different way, the class was able to see that this was a model of fraction.

The next model allowed very interesting discussion. Some students saw halves and quarters (see the green lines) and said this was a model of fraction. Some students cut the circle into pieces and proved that some pieces were smaller than others (see the colored section), therefore this was not a model of fraction.

The third model allowed varied approaches to problem solving. Cutting the pieces clearly shows that not all shares are fair. One group decided to alter the shape to make it into a model of fraction. This kind of creative thinking is very welcome in math. 

If initially everyone was convinced this was a model of fraction, then after the explanations, many students changed their opinion, but not all. As I said earlier, truly understanding fractions can be challenging, and some students may not be developmentally ready, yet.

We also played a quiet game of sorting and grouping fraction models. Again, some models are straight forward and easy, others required deeper thinking and understanding.

One of the students walked out after a math lesson and started looking at the flags thinking out loud whether they were or were not models of fractions. 

I hope that the students keep their eyes open outside school too, noticing fractions and thinking of possibilities to model fractions.