Math 2 Function Transformations

With the change in Math 2 standards this year in NC I'm revamping a lot of my Math 2 material. I'm finally enjoying teaching this course as I feel it is so much more coherent now (although still way too much in the course). We conclude our algebra journey with function transformations of the major functions studied in the course: Quadratics, Square Root/Cube Roots, and Inverse/Reciprocal functions. 

At our 1st Southern #MTBoS tweetup, Tara (@chatelet0211) shared a document she had refined over the years for transformations and I knew I needed to use it this year. I did the graphs electronically and changed it to fit with the transformations and functions we needed to cover in Math 2 (we don't do horizontal dilations or reflections until Math 3).

The document is missing the equations of the new functions because I'm lazy and didn't want to type them all in so I printed and hand wrote them in. Maybe in my next life when I have time I will go back and add them electronically. It is 8 pages and I plan to fit 2 to a page and have students work in groups of 4. Each student will get a sheet with 6 graphs on it. The dotted lines show the parent function and the solid the transformed function. They are to identify how the new graph is related to the parent function. Then students will cut out their six functions to participate in the group activity. As a group students will decide which functions moved to the right, left, up, down etc. etc. and gather a list of those equations and notice what is similar in each equation for that particular transformation.

I included: quadratics, square roots, cube roots, and inverse functions
Transformations: Left, Right, Up, Down, Vertically Stretch/Compress and Reflect over the x axis.

Enjoy!

Also in the link is my practice for quadratics and square roots separately. Some problems give them the graph, some the equation, and some the transformation and they must fill in the missing information and sketch the graph if not provided.

 Quadratics:

Square Roots:

Here are the files!

Structure and Restructuring

In case you haven't noticed from the name of my blog or interacting with me in person, I am extremely oriented towards structure. Give me something to organize, color-code, or sort and I'm your girl. Every year as the beginning of school approaches I re-orient myself and take considerable time to think about how I structure the time in my classes. I think that having routine really helps my students know what to expect and I've seen that we are all a lot happier when we are on the same page.

On of the challenges for me this year is going back to an alternating (A/B day) block schedule. If you are unfamiliar with this then it is seeing half of 6 classes every other day for 90 minutes. I did my student teaching on this schedule so already know some of the pitfalls (lots of time between lessons) and what that means I need to change. Here is my current thinking on "structuring" my 90 minutes.

One of the shifts I need to make with my new schedule is the "Warmup" or "Math Maintenance". I love Math Maintenance (MM) (check out iisanumer for a description). I've used it successfully the past two years. I had the pleasure of rooming with her this year at #TMC16 and we talked about recent research on block scheduling and students being most focused during the first and last 30 minutes of class. At her school they are going to be keeping Math Maintenance but moving it to the middle. This works great because it is essentially spiraled review, and I do actually need to start with something related to what we did the class period before since it will have been a *minimum* of 48 hours before...

So I'm going to have students answer one or two clicker questions to review the prior lesson. 

I'm still not 100% decided whether I'm going to do the new lesson during the first 30 or practice from the class before. But either way these are just broad categories for introducing and summarizing a topic and then practice (usually whiteboards) on the topic. 

The middle 30 minutes is where we will focus on honing prior skills and answer any lingering questions on HW. I am going to try and do a combination of Julia's circling red incomplete questions and Nate's folder HW collection and see if that works. ALL students must turn in the assignment even if it is blank. They keep their HW in the front pocket of their INB. I'm hoping that checking this daily will help me spot problems for the class and as a whole more clearly. 

I also am considering treating MM more like an open notebook quiz....hm...

None of this is rigidly fixed but rather just denotes the flow of the class and gives me and the students a framework to work in. 

I think I've decided to keep doing my HW packets by "week" but instead number them by Days (Day 1, 2, 3, 4, 5) not MTWTF since I won't see the same preps on the same day. Homework will be checked everyday in class but scored/collected every other week on test days. (I had been testing every Friday so I think I will keep to every 5 periods).

I know this is probably a random post, but I thought it might provide some food for thought since it seems many of us yet again are asking "what about HW?"

Make It Stick #TMC16 Presentation

Here is the copy of my #TMC16 presentation. Sorry for the delay but #honeymoon. If anyone is able to add it to the wiki, I'd <3 you! I'm having issues...



Link to add your ideas to implement:
www.tinyurl.com/makeitsticktmc

My Favorite: Vertical Non-Permanent Surfaces (#VNPS) aka - Whiteboards!

Two things have drastically changed my classroom this semester: 1) VNPS and 2) Spiraling my homework.

There has been a lot of discussion in the past year about the research behind whiteboards and how to implement them in the classroom (a la Alex Overwijk). I hope this post can highlight some of the nitty-gritty "how can I do this?" to make your implementation go smoother.

First, should you do this? Yes!!! You wouldn't believe what a change it will make. Some reasons to do it:
1) I teach on block so I have kids for 90 minutes/day. You'd be surprised how long they will work at the boards (I'm talk 40+ minutes on task in a normally rowdy class).
2) The kids BEG to do whiteboards and get excited to do math on them (Yeah, you need to see it to believe it)
3) It gets them up out of your seat.
4) You can immediately identify who needs help or if the whole class needs to pause and receive a mini-lesson on something they are all missing.
5) Use random grouping to get students working with others they don't normally work with
6) It dramatically increases student talk.

Here are my #VNPS hacks:

1) Buy 4'x8' white tile board and get it cut in thirds at the store. Should be pretty heavy - not flimsy. Ran about $14/board for me and I got 5. I only had room for 14 pieces though.

2) Decide how to attach. My walls are really annoying and have been painted over with the wrong type of paint, so I had issues with falling boards at first - fun stuff. See if your school will let you drill into the wall to attach. But I like to fly under the radar so here is my method:

3 strips of velcro command strips along the top of the board and two command hooks on the bottom to support the weight from below. Bonus tip: AC Moore has a slew of them, use a 40-50% off coupon to save some $$$.

4) I had students taking push pins off my posters to put up the problems they were working on which annoyed me to no end. Solution: Duct tape a binder clip to the top of the whiteboards that can hold whatever the prompt or problem is they are working on.

5) Doubles as a holder for Expo Marker!

6) Cut pieces of felt and add a book ring to the end. Superglue a hook to the board to hand it on. Now kids have the supplies they need at the boards already.

7) Add numbers to the boards. Then if you use a random generator for groups like the one at My Instant Classroom they go straight to the board number that is generated.

I hope that some of these hacks will help you! This is a great and relatively inexpensive (<$200) change to make in your classroom that will radically change the level of talk, communication and quality of work you see just by getting them up out of their seats and at the boards. What are you waiting for? =). 

PS - 

Cleaning: Just use water. When you need to get a more thorough clean use Totally Awesome from the Dollar Tree BUTTTT....rinse the board off with water after using it so the expo's don't stick to the residue. #liveandlearn. 

#onegoodthing: When Students Come Back for Help

Amidst the hustle and  bustle of the end of semester and all its craziness with finals, I had several opportunities to stand back and celebrate #onegoodthing but this is the one that stands out the most.

I had an opportunity to tutor former students before their Pre-Calc state exam. I had several students who wondered if they could stop by after school one day to get my help on PreCalc. I have only done student-teaching in Precalc, but they knew I loved the topics and wanted to get some help to review. We had a great afternoon and I loved getting to delve into a class I hope to teach some day. I particularly loved the moments when I talked about how the other trig identities come from sin^2+cos^2=1. They hadn't made those connections and seeing those light bulbs go off is why I love doing my job. We also had some fun looking at patterns in polar equations to help remember what the graphs look like. Overall it was just a great chance to spend time with some lovely former students in a relaxed way and talk about some awesome math. What gets me the most is that a couple of the students weren't always super responsive in class (i.e. I didn't get the vibe they totally loved my class), but they were practically gushing about how much they missed my class, interactive notebooks, and the way I taught overall. They also talked about various things they still remember learning (!!) and that a lot of the beginning of Precalc was review from what we talked about. There were also shout outs to dividing polynomials with the box ;-). All in all - a win win and something to celebrate.

It All Started With "She Told Me to Stop Asking 'What If?'"

Today I had one of the best classes so far in my career. And it happened when I went completely off book.

We were working on writing equations for systems of equations word problems. I want them to solve without a calculator but these particular problems were gross without one, so I just had them ID their first step and we talked about the different ways to solve particular problems. Which led to a conversation about which numbers were "easier" to multiply by hand...

I of course mention in passing that I had been thinking about why I don't like multiplying by 7 the other night when I couldn't sleep. (I then clarified that I do have a life sometimes...). So I wrote some numbers on the board and we talked about the patterns that made numbers easier to multiply.

Some ones that they hadn't heard of were 11 (10 +1), 9 (10-1) and 5 being (10/2) which then makes 15 easier.

My students had so many ah-ha moments and were so engaged in the conversation. They wanted me to go back and teach the third graders to see math this way. We talked about how I never learned math this way and have only recently (thanks to the #mtbos ) begun trying to think of numbers this flexibly. It was amazing to see their eyes light up as we talked.

I've already digressed before in this class (basically 9th grade Algebra I) about different ways to subtract. But I think this is important for several reasons
1) Allowing them to build number sense
2) Seeing multiple methods to solve
and 3) Help them see math as creative and flexible

And when half their state final is without a calculator...these skills are even more valuable.


But back to the title...
We also perhaps digressed even more briefly into the concept of bases. To me this brings up the "why?" and "what if?" which I believe are the central questions in mathematics.  One of my very inquisitive students said her last math teacher asked her to stop asking "what it?". I can't even begin to convey to you what my face looked like. It literally brought tears to my eyes (which of course they noticed) as I emphatically begged her to keep asking that question. "I have taught you that is a great question to always ask, right???" "Yes, Ms. Hester...don't worry" *whew* Good...

And what followed was a great conversation about math, the beauty and patterns in math and the importance of asking questions.

It might not be on my pacing guide, but I hope that later students will remember today as a day that they really experienced and saw math in a different light.

So Many Good Things #onegoodthing

So after my less than happy last post, I wanted to take a minute to highlight some of the happy things going on in my school year. I'd call it one good thing, but there are so many.

In no particular order:

1) I'm no longer considered a beginning teacher...which means: Less paper work (!!), less annoying mandatory meetings, and only two formal observations
2) Vertical Non-Permanent Surfaces (#vnps ie...whiteboards on the wall) are changing my classroom so much. Future posts pending about details.
3) Forming great relationships with students. I did several of the youcubed videos with discussion the first week of school and had students write a lot at the beginning. Students are so much more open and have a more positive attitude towards class and learning and I think those discussions really are paying off.
4) Getting to use activities from Desmos Activity Builder. 'Nough said.
5) No benchmark testing! Yay for not giving up so many days of my teacher for a pointless test.
6) Using MyInstantClassroom to do seating charts and groups for whiteboards. I hate seating charts and would always procrastinate sending them out
7) Folders for each group and each class to put their warmups and misc other papers for day to day. Solved my problem of students needed a binder and INB
8) Spiraling Warmups and HW has a huge impact and student attitudes and feeling that they still have a chance to learn material
9) In class time to correct tests...every single time
10) Keep scores on a separate piece of paper so students are only looking at comments until they have corrected their test.
11) Mu Alpha Theta (Math Honor society) is taking off. I've had over 10 students at every meeting. Yay for fun math.
12) Former students and parents going out of their way to thank me for their experiences in my class
13) Former students coming to my room, seeing the whiteboards, and wishing they were in my class this year so they could use them.
14) Students telling me they are teaching others in their new classes things we learned.
15) Students telling me they still have their "math Bible" and use it.
16) Totally embracing myself as the energetic, obsessed with math teacher that I am
17) Making up songs for mundane tasks in class...ie my warmup song.
18) A colleague starting to use the box method only to divide polys.
19) Some of my colleagues finally using some of my activities/materials

And that's what I've got after a few minutes of a brain dump. Part of me hates to leave the list at only 19...but hey, those prime numbers need some love too and not just composites like 20 that are nice and round ;-)