Day 9: Pairs of Angles

Today in Algebra we went over multiplying and dividing fractions. I followed along with Fawn, the day went OK. We used rectangles to model addition, subtraction, multiplication, AND division and I believe students were overwhelmed with using the same representation for all four different operations.

Next year I will probably use rectangles only for addition/division. It was also difficult for students to shift from the rectangle representation of division to the algorithm. I explained to them that the goal for today and yesterday was to look at how fraction operations worked rather than just memorizing algorithms.

In Geometry we started with a Visual Pattern.

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Student did an awesome job on this, it was really interesting to see which students counted the upside down triangles and the reactions when other students listen to a method they had not thought of. I have been doing visual patterns around once a week and LOVE them.

Students took a few notes on Adjacent Angles and Linear Pairs and worked through Pairs of Angles from Math Teacher Mambo. This was a great way for students to practice identifying and talking about different types of angles.I showed students a short proof on vertical angle congruencey and they went back through the worksheet and starred which angles were vertical.

 

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Day 8: Adding/Subtracting Fractions

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.

day7.7A 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.

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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.

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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.

day7.8Now we see both rectangles are made up of 6 squares. How many pink do we have? How many red?

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When we add we combine numbers or in the case the shaded pieces.

day7.11I 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.

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One more on your own.

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Here is some student work.

Common denominator of 28... does this work?
Common denominator of 28… does this work?

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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!