Made 4 Math #19 Parent Functions and Transformations

I'm really proud of myself for a couple of reasons that all pertain to the blogosphere. One is that I at least feel like I'm more on track this year based on what others are posting. It seems like every idea that comes up is either something I taught last week or something I'm planning for next week. That just makes my teacher heart happy.

Second, I took some ideas from other good bloggers and made two really good activities for my students. Teacher heart smiles again.

Third, my students really liked those activities. They said it forced them to read attention. They said they learned more than listening to me talk because they actually had to do all of the work themselves. They even said that students talked less because they were more engaged...they actually used the word engaged! Teacher heart passes out.


For my first activity, I shamelessly stole Pam Wilson's file Function Families Investigation. Her description reads: "modified through the years – this small group investigation allows students to learn how to enter different types of functions in graphing calculator; students group functions based on shapes of graph, then give a description of similarities in the functions’ equations."

With her permission I have modified it and will link to it here. The changes I made was to first type out very clear and very thorough directions on how to graph equations on the calculator because I knew my students would need it.

I also created a sheet of 16 graphs for students to sketch their answers on. I modified the equations so that there were 4 equations for the 4 parent functions I had in mind: linear, quadratic, exponential, and absolute value.

I basically used the same reflection questions at the end but I changed the graphs and added a couple of questions to the end.

Last but not least, I added a foldable at the end of the document. It lists the name and equation of the parent function as well as a description of what the graph should like. The space below gives room to glue 2 of the 4 graphs from each group. It works best to glue above and below the type. Then I had students fold the bottom up until it hits just below the parent function name. Then we cut the bottom half so that we have a 4 window foldable with tabs. I did not pass these out until students had completed the investigation and reflection questions.

The activity was awesome and very few people screwed it up. Here are some things to look out for: students graphed exponential functions as linear functions because they either ignored or didn't realize that the x was an exponent. Also, some students ignored the absolute value bars or thought that they were 1's. This resulted in students having 12 graphs with straight lines and 4 with parabolas...which made the sorting and analyzing next to impossible.

Also, students can't read. They would ask a question that was literally answered in the next sentence. Some just sat there waiting for me to tell them what to do. I warned them from the beginning that I was going to be a jerk and answer almost every question with "Read the directions". Then I proceeded to do so.

I made up a slide of the right answers but it just wasn't needed. And since students were working at their own pace, there was never an appropriate time to show it without ruining it for another student. Once they finally caught on...it was beautiful.


And so I proudly present:

Function Families Investigation


The foldable was printed separately on colored paper and made for a really nice transition into the next lesson...Function Transformations.

I planned this lesson to be an individual activity as well. You read the feedback from my students at the beginning of this post and that encouraged me to continue in that vein.

For transformations, I looked at several different bloggers' post but ultimately still created my own. I created a set of 8 transformation cards for the 4 parent functions with 6 sets to a page. The eight transformations were left, right, up, down, skinny/steeper, wider/flatter, flip, and then more than one combination of those.



For linear, I couldn't figure out if there was a transformation for left and right so I just didn't include those. Therefore, each student should have 30 transformation cards. I labeled them Transformation 1, Transformation 2, etc so that I wouldn't give away what the transformations were and I printed each transformation on a different color of card stock which greatly helped in the sorting.

From there students used their foldable to write in the parent function names and equations on all 32 graphs...which they hated and a lot of them skipped. I thought maybe I should just type them in but since I wasn't lecturing at all, I think this was an easy way for the students to commit those four function names and equations to memory.

They then sorted and found the cards for Transformation 1 and matched them to the correct graph shape (again reinforcing what they analyzed the day before). They wrote this new equation in the 'new equation' box and graphed it on their calculator. I plan to have students go back with a highlighter and highlight the part of the 'new equation' that is different from the original.

Next they graphed the new equation on their calculator and sketched it with a colored pencil on the graph. Now the parent graph is already on there and I did that on purpose so they could easily see what happens to their colored graph.

Therefore, the next step was for them to finish by answering the question "What happened to the graph?" This process is repeated throughout all 8 transformations.

And that ladies and gentlemen is Function Transformations:


The whole class hasn't finished yet but after they do we will go back and use the foldable to write down the transformations and the equation with the part that is causing the transformation to happen written in colored pencil.

My plan after that is to do a review game where I give students the equation and have them sketch the graph without a calculator and maybe vice versa where they have a picture and must write the equation. More to come on that...

My one annoyance is this...what do you do with the students who get done before everyone else? Oh wait, that's the same problem I always have. Maybe the real question is how do we get everyone else to speed up?

Made 4 Math #17 Relations and Functions Foldable

First, I made a very basic grade sheet for my students to keep track of their grades. I'm tired of looking it up over and over or seeing the looks on their faces when they realize I don't have every single one of their grades memorized...similar to the look they get when they realize I can do mental math. *gasp*

This is nothing fancy at all but maybe there is someone who can't figure out how to make tables yet, or who doesn't want my grade sheet but is now inspired to make their own, or who just happens to need this file on the exact day they read this post (love when that happens!).

Behold:


Now to my real creation. I loved Nora Oswald's post about a relations and functions foldable. I had just finished that in Algebra II and realized how nice a foldable would have been to tie all that information together. Since I am now teaching functions in Algebra I, I modified her foldable so that it works for our interactive student binders.

I typed in the main stuff (text stolen from Nora) so that the real work of the students is to create the examples and non-examples which to me, seems like the higher order thinking I want to accomplish. If you decide to use this, when you fold the top down, do not fold exactly in half. Instead only fold to the bottom of the dotted line. Then you have space to write the title and everything fits nicely.

The students also label the outside flaps, which are created by cutting on the top dotted lines only. This gets them thinking a bit because they have to decide the difference between each flap.

My student teacher is using this today in her first lesson so I will try to update my post later tonight with pictures and whatnot. She will be teaching domain and range so we went ahead and put those blanks on the foldable as well.

Now presenting:

Made 4 Math #15 Foldables

I wanted to share two foldables I've used so far.

One is ripped off of Sarah Rubin's Words into Math foldable that I modified to fit on a regular piece of paper rather than into a composition notebook.

I displayed this slide with key words in it and we wrote them in the correct places.

I like the idea of keeping this all year and adding more words to it as we come across them. Here's the download:


In Algebra II we made a foldable for Operations with Functions. On the outside flaps we wrote how to do each operation and things to remember (i.e. don't add exponents when combine like terms).

We made this after I taught those concepts so I had students go back to their notes and pick out two examples of each to write  on the inside. Just one small way to show that our notes have a purpose. Here's the download:

If you notice, function composition is on here as well. I haven't taught it yet but I noticed when I folded the foldable, the back was split up nicely into four squares as well. I threw the title on there and now we can add to that this week.

Yay.

Made 4 Math #11 - Diamond Foldable and EOC Review

Although this isn't the first foldable I've ever used, it's the first one I put any effort into designing. I stole the idea from Nora Oswald's Discriminant Foldable. I liked the way she folded hers so that it formed a diamond. I printed out a blank one to attempt writing examples in the boxes. I wanted two per box so I was trying to decide the best way to fit them into each box. I went ahead and folded it to make the diamond. When I unfolded it, I now had to even spaces to write in. Success!

I altered the original foldable by adding the diagonal lines as separators and as a guide to folding. They don't fold exactly right but it  works for me. I used this for solving equations: multi-step, variables on both sides, distributive property, and fractions. I did two examples each, one with integers and one with decimals and we used two different colors- one on the outer flaps and one on the inner.

Here's the results.

And here is the file.

Next up, I created a 50 question Powerpoint that serves as an end of course review for Algebra I. The first 40ish questions are straight from our EOC exam except with different numbers. The last 10 or so are some overarching themes from Algebra that I want students to pick up. I finished this when I was tired so it might not be the most excellent thing you've ever seen but I think it could be really helpful.

We are having a schoolwide movement to try out the L to J program which basically works like so. I use the powerpoint once a week and ask 2-3 questions randomly from it. As a class, we graph our results. No grades. Just graphs. We do this every week and it exposes students to things we will learn or have already learn continuously throughout the year in order to improve retention. We celebrate all time bests of the students as individuals and as a class. Students start to look forward to our 'weekly competitions' and attendance and test scores improve. Miraculous, right? I'm not really bitter toward this, I like the idea, a lot actually. I'm bitter that I procrastinated making these powerpoints this summer and now have it piled up on my never-ending-should-already-be-done list.

But at least I have accomplished one out of three.

Here are some cute things I bought at Wal-Mart- everything under $7 and nothing that I actually need or have a plan for.

And here are my binders with glittery stickers in my favorite colors that were on sale at Hobby Lobby.

Last but not least, I made this gift for my teacher friend by using a Sharpie to write on a Dollar Tree mug and then bake it at 350 degrees for 30 minutes. Hand-wash only! Then I filled it with suckers. Simple and sentimental. And cheap. :)