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.*

A student then walked the class through it, some students had the correct answer, others were struggling.

*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.*

Interesting…

*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.*

I use my ipad to take pictures of various representations then put it under the document camera and we looked at them all.

*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.*

*Now we see both rectangles are made up of 6 squares. How many pink do we have? How many red?*

*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.

Common denominator of 28… does this 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!

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Mr. PMet with a peer teacher today. I am about to reteach adding fractions to 7th graders. In regard to your “why,” he said to start with this:

“What is 1 apple plus 2 apples?” 3 apples.

“What is 1 banana plus 2 bananas?” 3 bananas.

“What is 1 fourth plus 2 fourths?” 3 fourths. This gets the students seeing that they are not changing the denominators. The he said:

“What is 1 apple plus 2 bananas?” Kids will hem and haw a little, but it’s obviously not 3 apples or 3 bananas, but a student will say “3 fruit.” Exactly! In order for you to add them you need to find what they have in common. When they have different denominators, they cannot be combined as they currently appear, but you find how they are the same.

Now your rectangle grids here can lead into making them the same. Thanks for your post!

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danburfPost authorThat is a great way of starting off and addressing the why. Hope the lesson goes well, thanks for stopping by!

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