Flip Flopping Inequalities

As we have been working on inequalities in my Algebra 1 class, my students have been having trouble understanding the concept that if 1 > j, then j < 1. To me, it makes sense. If 1 is greater than j, then that means that j has to be less than 1. But for my Algebra kids, that abstract reasoning is just not quite there.

But then, I had a brilliant idea! Height! I picked two students – one really tall, and one really short. We’ll say their names are Chris (the tall one) and Jane (the short one). We made an inequality. If Chris is taller than Jane, then C > J. From that, since we know that Chris is taller than Jane, it made sense to the students that Jane HAS to be shorter than Chris, so they wrote an inequality for that! J < C.

Then we talked about age. If Chris is older than Jane, then C > J. Since Chris is older, than Jane MUST be younger than Chris, so J < C.

We did a few examples like this, and it then talking about flip-flopping the inequalities. When you flip-flip the side of the inequality, then you also have to flip-flop the sign!

This really helped the students to understand the ‘Flop Flop Order Matters’ sheet that we did, which you can find the link to in my previous blog post.

This definitely helped though!

It is such a great feeling when students are struggling with something, and you just don’t know what to do, then you switch it up, and students start getting those ‘Ah-Ha!’ moments! I LOVE seeing Ah-Ha moments!

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Graphing Inequalities

In my Algebra 1 class, we have just started working with inequalities. I actually got some really good lesson ideas from Sarah Hagan at the Math = Love blog. I used a lot of her material for my own lesson, and to put in our own Interactive Notebooks. One thing, though, is that I didn’t realize she had PDF copies to download. I spent forever trying to make a foldable to copy hers. I think that I finally got the hang out of it, but it would have been way easier if I hadn’t spent all that time trying to create a similar one, only to find out that I could download her’s right at the bottom!

One thing that we are really working on is graphing the solution set for inequalities. I started to put meaning to it that I had never learned before. I was taught to memorize that we use an open circle unless it has the ‘or equal to’ part, then we use the closed circle. My students seem to be trying to memorize it this way, also, but I have been really trying to help them to understand why that is. When we are graphing the inequalities, we circle the number that we are given. So, we have been starting with the open circle every single time. Then, we shade in all of the numbers that are possible solutions. We first start by checking the number itself. When we have the ‘or equal to’ along with our inequality symbol, then we shade in that number, because it is included in the solution set. Every time one of the students says “So we up the closed circle when its ‘or equal to’ and the open circle the rest of the time,” I agree with them, but then I make them explain why that is.

It seems like it has been working well for my students. Hopefully, this unit goes great after we just spent the whole first quarter on solving equations! This is so similar, it should be a good confidence booster for the students, as well!

It’s Been Awhile…

So, it has been a long while since the last post! Over the summer, I had no idea what I was going to be teaching this year, so I really had no idea what to post.

Last year, I started teaching at a school halfway through the year. But now, I am officially through the 1st quarter of my first full year of teaching. In my own real classroom! Boy, have I learned A LOT! It has been good, bad, and ugly. I have definitely learned a ton already, but I have also learned just how far I have to go.

This is my first-ever experience with freshmen – they are like a different breed of people! I am figuring out this breed, though! This year, I am also in a school with a very different culture, which I am still getting used to.

I am going to start making posts regularly, and the things that I do that work, I will post up here for everyone else to use! One thing that I tend to do a lot of, though, is use other peoples’ lessons, foldables, templates, and ideas. There are so many good resources out there, and I wish that I had the time to sort through all of them and find all of the amazing ones to use!

I am going to get back to my search now! I promise that I will be back soon!

-Emily