I am posting late today; classes were good not to cover everything that happened.
All the Algebra teachers in my department decided to spend a few days review fraction operations. So I started digging in the Blogosphere. I came across Fawn Nguyen’s Post on dividing fractions and built off the same idea for addition and subtraction. The lesson went something like this:
Take a minute to solve this problem.
I have an issue here; it confuses me that we add the numerators and not the denominator AND that we need to make the denominators the same. Can anyone explain to the class why that is?
“We have to make the bottoms the same so it is easier to add”
Why is that?
Let’s go ahead and look and look at what 1/2 and 1/3 look like, sketch both fractions in your notes.
I am still not seeing where the 6ths come into play, let’s use some grid paper so we can be a little more accurate.
We already know that the common denominator is 6 in this case. Are there any other rectangles we can draw to show the same fractions?
“2 by 3”
Go ahead and draw them, shade 1/2 in the first and 1/3 in the second.
When we add we combine numbers or in the case the shaded pieces.
I kept repeating throughout the lesson that it was important when we add fractions or in this case a rectangular representation that we were working with the same sized figures. Trying to push the idea of why this shows that we need common denominators and all.
Let’s try another.
One more on your own.
Here is some student work.
Most students had a solid grasp on the idea after this point, we checked each problem with an online fraction calculator along the way. After we had a short discussion on how subtraction would differ then we moved back to the algorithm. They worked through 8-10 problems and that wrapped up the day.
I have a hard time throwing 20 fraction addition and subtraction problems at students without at least trying to explain a different representation or WHY we need common denominators.
In Geometry we started constructions, this was pretty chaotic, but we will spend more time tomorrow bisecting angles and what not!