Algebra 1 - linear equations review

I think Ms. Haley showed me this one. It's got pretty much everything you need to know about linear equations.

The source for this foldable is also from I Speak Math - NAGS Foldable. She has a file you can print up but do this well ahead of time as your printer may offset the result. I tried to print that morning and thought things were ok, until we went to write on the inside and everything was upside down. There was some reprinting involved and it took away from the time we should have been writing things down. "I Speak Math" used this for notes, I used it for review. The students liked all the information that was on here, but in the end, didn't like this foldable much saying it was too busy and hard to find information. "I Speak Math" also had her students write notes on the back for review but since this WAS my review, we used that side to paste down in our notebooks.

Since I like the info on here, I think some modifications we can do would be to make it a multi-page booklet so the info is broken up. You should probably check out the "I Speak Math" site to see what she wrote seeing as yet again, I didn't write anything down. (Don't worry, one day I actually do!)

 

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Algebra 1 - slope

During the unit where we studied slope, we did this foldable as review. I got this from "I Speak Math". She also used it as a review but had plans for using it for notes. It's not a bad foldable but our class didn't quite put the components together like they ought to. If this could be used for notes instead, I think it would be more effective. Still, it's better than what I could put together on my own.

As you can see, mine is blank. Always write what your students are writing or the questions they have later may not make sense!

 

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Algebra 1 - problem solving

In between the solving equations and solving inequities we did a lesson on consecutive numbers problems and using Cross Products. As a way to make things easier, we cut the reference section of the worksheet out and pasted it in our books. This isn't the worst idea (use what you've got) but I think we lost connection by not showing some examples. I'm becoming a believer of drawing and writing as much as possible instead of using pre-fabricated foldables. This idea will come into play in some future posts.

I liked this reference for the students and think they would reference it more if we had used our own handwriting, had examples and we were consistent with journals.

 

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algebra 1 - solving equations and inequalities

I've been trying to get this posted for a day or two now. I couldn't remember the source for the foldable that I used though so I didn't want to officially post until I could give credit where it was due. The foldable we used comes from "Mrs. MATH"'s site on Teachers Pay Teachers. The official title was:

Solving Linear Equations and Inequalities Foldable

It is a free download and worth checking out. She's got some other Algebra 1 materials but I haven't checked those out just yet.

We used this foldable to help us with multistep equations and inequalities. I believe we went over the concept in class and then before we moved on, we did this foldable with all the steps written out. It took some time to write everything out and more time to fold and cut. I recommend having the tabs pre-cut unless you're kids are pretty quick with foldables.

Keywords on the outside:

Description of steps on the left side with example problem on the right.

A couple days later we worked on inequalities and did a similar foldable.

 

The students liked having the example but near the end of the unit, they weren't referencing it as much as I'd hoped. I will probably try something else this year along the same lines. You know, I like the idea behind this foldable and am grateful someone put it together. My finished product is a bit busy and some of my dyslexic kids had a tougher time with it. To modify, I would probably have fill in the blanks for the descriptions and then have a more structured problem solving area to help them put things in the correct places. I really think I'll try something else this upcoming year though. If you know of some other foldable, please let me know!

 

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Algebra 1- multiple representations

In this entry, some time has passed in my algebra class. we've studied linear functions through various activities and have worked through various forms of solving equations. The lesson this was for was the multiple representations for functions. We needed to show a concrete model, the algebraic model, a graph, table and then the solution check. Instead of creating something, we cut out an example from our worksheet and glued it in. Well, they glued it, I just threw something in there to hold its place (again with the "not doing what they're doing" problem!) What you will see in the picture is my attempt to show the page we pasted in but as I looked closer, turns out I had the wrong worksheet. Since we've addressed my failings in previous posts, lets move on to picture.

 

As I reminisce about my journal, I shake my head. I know I can do better. The thought "what is the purpose of this?" has crossed my mind a lot lately. When I started my journal, I had some purpose but lost it along the way or that purpose became less meaningful (when the journal became a review at the end of the unit instead of it being a useful tool through the unit). That's not to say that I lost total purpose in algebra, I just didn't have follow through in journaling. That brings me to looking at my choices. If I continue to journal, I now know I need to stick to it and make sure the journal has purpose. If I don't journal, it's not the end of the world. There are many great teachers out there that don't journal and their students are successful as well. The main thing I need to remember is making sure my kids leave with a better understanding of algebra so that they are ready to take on the world, and hopefully have a better attitude towards math in general.

Back to multiple representations, I should have just used the four corner foldable. In one corner I could do the concrete model (algebra tiles), in another corner, algebra method with solution check, another corner has the table and the last have a graph. It could have been that simple. This year I will try the four corner since the kids will be used to it anyway.

As you go through my blog, keep in mind, I'm not an expert teacher. I chronicle my failures because I hope you see that not everyone is a great journaler but, that with some thought and a willingness to try again, you can be successful at what you chose to do.

 

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Algebra 1 - algebraic properties

For algebraic properties I did a layered foldable. Seemed like a good idea. Still is, but I think I need to define the steps better. For this one, we just wrote what we did to simplify the expression but now that I look at it again, it could be better.

On a quick tangent, as I look over what I did/didn't do this past year, I'm trying harder to ask myself "what is the purpose of my doing this?" I think that for most of this, I had good intentions. But some of the things I chose to do weren't very transparent or didn't feel purposeful. With the push of helping the students be career and college ready, I need, we all need, to have purpose for what we teach.

Off my soapbox, here is Algebraic Properties. Top flap has our title and then an expression to simplify (I just used an expression we had worked on).

 

Next flap has the distributive property. We wrote an explanation out with some key things to remember but I think it would be better if we had defined actual steps for simplifying.

Commutative property comes next. Same scenario with instructions. Needs better step by step.

Last but not least, associative of addition property. Made sure to emphasize the addition since signs matter.

Overall, it wasn't the worst foldable and with better clarity I think it will be useful. I think with my new approach, I can make this a bit better.

 

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Algebra 1 - Unit vocabulary

At the end of the first unit (maybe 2nd?) we did a review where we highlighted the vocabulary from the unit. To go faster, I typed the vocabulary on my laptop after we'd decided on what words we needed to clarify. Fantastic idea... Until I deleted the file as the next class came in. You know, I wish I could say I was that teacher who always looked fantastic, always had everything prepared with no printing problems, every student left my class thinking my lesson was fabulous, who never accidentally deleted files... But I'm not there yet. Nope. Not yet. So I delete the file, smack my forehead and then moved on with a blank page. This vocabulary lesson put most of my class off track with page count (not everyone writes the same size) which in turn put our table of contents off and so this is why I am not fond of a table of contents.

In the meantime, here is my vocabulary page in all its blank glory-

Let's talk about how I could make this all better. The first thing I can think of is to have some pre-printed worksheet with vocabulary spaces to fill in. I don't know that id have everything typed in, maybe just an open page with bullet points in place. I don't know that I would do a shutter fold. OR better yet we would make a pocket and do flash cards instead. Hmm. Either way, instead of typing like I did this time, I will be writing along with my students because I have a document camera now. Life is better with a document camera. I don't know why. It just is.

 

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Algebra 1 - exponential functions

Exponential functions turned out to be my students' favorite functions. I think it was because the pattern was so easy to figure out and it applied to Science (they really liked Science.) They were disappointed when we moved onto linear functions. Go figure!

This first picture is our example of exponential growth - Blooming Bacteria. I drew the graph on the whiteboard so I have another transfer issue :(

This next picture is of exponential decay - Indestructible Isotopes. Again, missing graph since I drew it on the whiteboard.

By this point, the students are beginning to like the four corner foldable but this is also where our units ends. We didn't work on just the one example per function. We actually had other practice problems but did not use the four corner model. I'm thinking this might be a part of my inconsistency. In fact, I know it is. Here I am getting kids used to a way to represent and I only did it once per function instead of having them do it every time. Note to self: if you start it and it works, keep going.

 

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Algebra 1 - inverse functions

At the beginning of the year, CScope has you introduce inverse functions. I forget the reasoning behind this (its summertime, I'm not at my peak like during school) but I know it does help us compare domain and range and study different functional relationships. The kids didn't like inverse functions at first, but once they saw the characteristics that helped them identify inverses, they were all about it.

Here is the four corner model we did as an example of inverse functions. This one is actually complete (woo!) and that is because we worked on it near the end of class. I finished the model during my prep period and then took a picture of it so the kids could finish theirs. If I had a promethean, I'd do a slow reveal as they worked on the different parts but instead, I posted and we discussed as they compared their copy to mine.

The kids are starting to get kinda fuzzy as to whether or not they like doing the four corner at this point but I press forward explaining the different representations and how they are all modeled for us on one sheet instead of being all over. They agreed to give it a try again for the next function model.

If you'll notice, in the bottom right corner, I have more information this time. This is because we are studying the actual function and not a comparison between relations and functions so there is more involved with the analysis.

 

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Algebra 1 - functions vs relations

To help the students remember the difference between relations and functions, we created a foldable that depicted characteristics of each. On the front we drew a Venn diagram that showed the entire oval as a relation and then inside the oval we had a circle with functions labeled. This was a two flap front so the kids could open up each flap and see the characteristics/definitions inside.

Inside we drew graphs and tables of examples and non-examples. This seemed to help the students see the similarities and differences between the two.

The students liked this one because they had visuals as well as definitions. It helped later when we reviewed for state tests because they knew what foldable to refer to if their peers got stuck answering relations vs functions questions. Not sure how I could clean it up but am open to suggestions. :)

 

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Algebra 1 - functions

This is the part where we started examining functions. The unit lesson had us talking about the special relationship (linear) between two variables using Ticket Prices. We did a four corner model where we wrote the question and identified the variables in the upper left corner, drew our table in the upper right corner, graphed in the bottom left corner, then did a verbal summation in the bottom right corner. In the middle, we wrote the title, function rule and the type of function or main idea for the lesson. The kids liked doing our function study this way and it helps the kids with seeing the different representations. I did this same thing for the relations page, but didn't use the four corners. This lesson was the first time i utilized the four corners. Thr four corners model was something I wanted to continue for the rest of the year but didn't due to the transfer issue. I cannot stress how helpful a document camera is for journaling. If I had a SMARTboard or other interactive board, I might sing their praises. As it is, I have a projector, a regular whiteboard and a recently purchased document camera. I'll go into technology later, but y'all need to know I am not provided the latest and greatest technology due to small district size.

So here it is, the four corners representation model. You can modify as you wish. Some have suggested writing domain and range with the graph instead of with the summary. I think you should do what fits your teaching style and what helps the kids remember.

 

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Algebra 1 - relations

The first couple weeks, we studied the basics of relations and functions (doing my best to follow the required CScope). Since the freshmen and I were new to each other and it was a nice morning, I took the kids outside with a jump rope and I had the kids jump for as long as they could. The main question was "does the amount of time determine the number of jumps I can do?" It wasn't my best work but it did get us out of the classroom and got the kids laughing and interested. All I wanted them to see was that there was a relation, but wasn't focused on it being a function. It wasn't a bad idea, but it wasn't well put together so I need to work on having a better purpose and questioning.

Here's the bad part. This was our first journal entry and I wrote on the whiteboard but didn't copy anything down in my own journal. Bad move. My suggestion to new journalers would be to do what your students are doing WHEN they are doing it. Having a document camera really helps (I didn't have one for most of the year so I attribute much of my failing to the lack of equipment) because the kids can see what you're doing in your own notebook and you avoid transferring from whiteboard to journal or forgetting to transfer. My bad.

So here's the page I created, but didn't remember to fill out. Lesson for this entry- whatever you want the kids to do in the journal, you do it too right then!!!

 

 

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Algebra 1 notebook part 1

Finally got some of my stuff together to show you what I'd attempted this past school year. It really isn't all that much but it's something.

First off, I did use a table of contents. Here are my thoughts on this- by the end of the year, due to the size of my students handwriting, we were all on different pages so the TOC was a pain to have synchronized. Ms. Haley showed me how she does a pocket fold for each new unit and then she makes a tab by putting duct tape on the lower right hand side. Rather than having her students reference the TOC, they just count the tabs until they get to the unit they need. If you are using the journals daily, then I can see how kids can memorize the units and know where to turn, thereby causing the students to internalize what is in their journals. Just for kicks, here is a picture of the TOC I did. If you'll notice, I didn't keep up very well.

This upcoming year, I will avoid doing a TOC and try Ms. Haley's method instead.

 

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