Instead of going in order of my units, I decided to start with some of my faves first. I love factoring and I love how I progress through factoring. Hopefully eventually I'll do a vlog (never done one)/video talking you through how I build coherence through multiplying, factoring, and dividing - but until then, here's how I initially progress through factoring. I use the box/area/partial products method for factoring, so students are already used to using that framework.
Finding a GCF
Factoring out a GCF ("skinny box" AND intro factoring GCF from a 2x2 box)
Difference of Squares (this could also go at the end after trinomials)
Factoring trinomials where a = 1 ("X factor", aka just sum/product puzzles if you know those)
Factoring trinomials where a isn't 1 ("X Box" originally inspired by Julie at ispeakmath.)
First thing is we need to establish what a GCF is and how to find it, which is part of a class period. The rest of the day we talk about factoring out a GCF from a polynomial by putting each term into a compartment of the hence forth "skinny box".
The same day and the beginning of the next we talk about factoring out of a 2x2 box. I think this is one of the key elements that helps my students be so successful later when we do trinomials. Hint: I used to teach this part as finding the GCF of each row/column but now just have them find the GCF of the first row and then go around saying what times (GCF) gives me whats in the box? Works SO much better now and works seamlessly with the intuition for dividing polynomials with the box in Math 3 (coherence!!!)
The next day we move onto Difference of Squares - next semester I might move this to the end. Stole the note form from Sarah Carter at mathequalslove. My twist with this is my "Difference of Squares" rap. While I haven't video taped it. I guess someone in my class recorded this and entitled it "When Math Teachers Try to Make Class Fun" <3 . Before direct instruction I have them multiply out several difference of squares to notice/wonder about the pattern.
Me doing it (slower than I usually do so they can see the steps)
Brave student then doing it for the class (LOVE HER!)
It's ridiculously cheesy but one of the best feelings later when the students learn it and you have a whole class getting into it with you. =)
Next up is trinomials where a is one which I affectionately call the "X Factor"...because you use an X, and you are factoring...and I love puns, especially if they are terrible.
I give students a sum/product puzzle where at first all the numbers are given and I ask them to find a pattern that works for all the Xs. (Love introing things as a puzzle, because isn't that really all factoring is?! and you get more interest/buy in from students when you present it this way). We then talk about how to use this method to factor. Once we move onto where a isn't 1 we talk about why it always starts with (x ) (x ) if your a is 1.
Then we move onto X Box. To start this off, I give them a filled in box and have them find the GCF and all the sides like we did Day 1. How was that? "Easy" then I have them do an X Factor problem. How was that? "Easy" I then write up the original polynomial we started with and ask them to notice/wonder about where the different numbers and terms are coming from in the original polynomial so that they practically discover the process for themselves. Thanks to Elissa @misscalcul8 for typing up my notes!
By the way, throughout all of this I'm constantly emphasizing that factoring is just rewriting a problem as multiplication.
Last, we factor completely. For that I made a handy dandy flow chart because, let's face it, I <3 flow charts.
Here's the link to my documents that I've actually created. I will add others to the same link as I get around to typing them up! Sorry for the awful handwritten copies for now, but hey - something is better than nothing!
Here are my old youtube videos explaining it if you are still curious. Notes: I was still doing the GCF for all rows/column method in the X Box Video =/
Difference of Squares:
SIDE NOTE: I actually am changing things up a bit by introducing solving by factoring/zero product property first and then practicing with every new method. I found this semester that it really helped students distinguish between what "factor" and "solve" meant!
Hey you, yes you! I have a secret...are you ready??
I hate paper. I know, I know...how could @TypeAMathLand, one of the queens of the INB hate paper? I know...but really, I can't stand the paper management of teaching. Things to file, papers to grade, master copies to organize (or as you may have seen on Twitter, leave alone for a semester and take a whole day to organize).
Another confession: I'm horrible about passing out papers. I'll even write it down but still forget once I get caught up in actually teaching the humans entrusted to my care.
So pretty much anything that limits the flow of paper in my classroom makes me happy.
At my previous school, I almost never collected classwork and didn't grade at all homework. I could create my own grading system. But it's my first year at a new school so not trying to rock the boat in every arena and choose my battles. Overall the department is about 80% assessments and 20% classwork/homework/notebooks. This had been driving my SBG self a little crazy, oh well. But since I need to do it, I had to find a more efficient, time-effective way to handle this. I just did the typical collect, grade, and return (or not) and even though I was doing this - students couldn't see the effect of doing work (gasp) and their grade.
So enters: the stamp sheet. I feel so middle school/elementary school for this. But, work completion is improving. I'm getting a lot more work turned in period (both on time and late), and thus test scores are improving since we are actually starting to see a relationship between doing the work and not doing the work.
That's a lot of words so here's the nitty gritty of how it works.
1) Each period is a different color (mine is 1st: green, 2A: Red, 3A: Yellow, 2B: Blue, 4B: Purple). All the folders for the class are the same physical color.
2) My groups are color coded as well. The folder is labeled with the color group.
3) Students turn in work to the left pocket. This is also where I put no name papers (no more wondering who those go to) and assignments that I don't consider satisfactory that they need to redo/finish
4) Stamp sheets for the group go in the prongs
5) Once I've stamped their sheets for the assignments, I put the assignments in the back and they can take them out and do whatever with them.
I can then see at a glance certain students are consistently not turning something in and try to have a conversation with them and parents about that. I also put an A for absent if they weren't there that day.
I cross off any time I didn't collect something for that box.
Red Folder so I know this is my 2A class. Purple Group.
What it should look like:
Oops, we have some missing work.
There ya go! Hope that helps someone. Also, I'm only going to enter the scores every week or every other week. I can't find my excel spreadsheet where I made the actual sheet, but will link it when/if I do =).
Edit to answer some questions from Twitter:
1) I change groups every 5 class periods
2) Students turn in assignments at same time, so already pretty aware of who is/isn't turning in assignments. Things are only checked for a valid attempt, so no "scores" being shown. And assignments can be turned in late, so it is really just communicating what is missing.
3) Every student gets their own stamp sheet (I laid out the whole quarter on it) that is kept in their folder. There are 4-6 sheets per group because I different sized groups.
4) I only stamp the stamp sheet, not the paper. If they care they can just look at the stamp sheet ;-). But once again, I'm just looking for valid attempts and any ? marks they put on their work which I respond to on their paper.
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.
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?"
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? =).
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.