So I recently blogged… mainly because my head was too full of things I couldn’t sort out but also because Annie Fetter (@MFAnnie) pushed me a little.
Then, without thinking about it much, I said – OUT LOUD on twitter – that I was going to blog once a week. What was I thinking?
So… we’re at the end of week one of school for me so here’s the week one blog.
I had a really good summer – at least by my standards. Didn’t really go anywhere but got lots done around the house so I didn’t get my usual – “UGH, I have to go back to school” blues. I was as ready as I was going to get.
This summer we’ve had some construction going on in our school so many of the rooms weren’t ready on day 1. That meant that day one back for teachers meant some short meetings and then hunting down various places in the school to work. Honestly, it was kinda fun. Forced folks to see each other and work together rather than hunker down in their rooms.
Week one also means lots of meetings and professional development here. Our PD this year has been mainly focused on our fairly new learning management system, CANVAS. I’ve been in on the pilot for a couple of years now and really like it. The division has been great about rolling it out in a way that teachers aren’t feeling too stressed. Because I’ve been in on it for a while, I did a lot of teaching this week. It was great to see our teachers really excited about it. Even those that weren’t super excited were at least not too stressed! I’ve had lots of questions come my way and been thrilled to be able to answer most. I also had the opportunity to work with one of my CTE colleagues that I don’t get to work with much. WIN-WN
I finally got into my room on Friday and, like Sarah (@mathequalslove) I concentrated on just making it neat. Kids arrive on Wednesday so I still have a couple of days to pretty it up! Just have to steal some pretty ideas!
This year I’m teaching Algebra 2 and Algebra 2 Honors – both of which I really love.
If you read my last entry you know I’m still using SBG and INB but hope to do more problem solving. I have a student teacher from the University of VA and am working with three colleagues from my department on both courses. I love collaborating with others and am super excited having so many folks to work with. Three of us met today – yes, on a Sunday – and planned our first few days of Algebra 2. The fun part – ALL about mindset and “Making it Stick”! I’m a little nervous about it… very different from my usual day 1 … but also excited.
So – week one done. Kids come this week (secretly can’t wait – hunted down some at pre-school band practice last week!)
Seems I only post once a year these days! At any rate… here’s where my mind is going right now. Hoping that writing it down will help my mind focus a bit more! I am quite anxious for thoughts, comments and ideas – so please feel free!! You all are my PLC! I’m depending on you to clear my fogginess!
Standards Based Grading at all levels – I can’t begin to describe how liberating this process has been. My kids love it – they know exactly what they need to work on and they really appreciate the opportunity to improve. I love that I can look at their work with new eyes. No more – “should I take off a point for that silly error?” Looking at their work from this perspective has actually helped me focus more on their overall understanding and less on the individual pieces.
Math Forum Problems of the Week and peer-to-peer mentoring – I actually want to use these even more this year. Hopefully add them to my academic level (maybe this should have gone under “change”.) My kids last year reported that the peer-to-peer mentoring really helped them understand and better express their mathematical thinking and I saw a big improvement in their writing from the beginning of the year to the end. (See our presentation materials on this project HERE!) Super excited that NCTM has partnered with Math Forum too! Anxious to see where that partnership will lead!
Interactive Notebooks for my academic level – I’ve used INB for the past two years but this year I let them slip. I didn’t check them as often and that didn’t force kids to keep up. I also want to add in more practice within the notebook as opposed to on separate sheets of paper.
Homework – kids just don’t do it…. at almost any level. How can I changeit so they might actually do it? How can I limit it so it seems more doable but also gives them enough practice to solidify ideas and (unfortunately) procedures? How can I set up homework to spiral content? I think practice over a longer time would help the content “stick” better – just my thoughts.
Grading homework – Do I grade it? Not grade it? Kids assure me that if I would grade it they would do it – that’s a bunch of hogwash? Do I give them just a work ethic grade for it? Check it only if they want to reassess. Or focus on classwork in their INB for a work ethic grade? I know …lots of questions that I think we all have.
Group work – perhaps this should be expand instead of change. I already do some of this but I want to expand it. Similar to last years goal of “Talk less.” Perhaps using Math Forum problems, Exeter problem sets, classwork and homework review as the bouncing off point for this work.
A review at the beginning of the year – preferably one that doesn’t suck!
Interactive Notebooks in my honors class – How do I approach this with my honors kids? Many already know how to organize at least somewhat. How do I not make this seem like an “elementary” task? I’m really drawn to this idea but want it to be a great resource for them but not make a ton of more work for me.
Big Blue Button Hangout office hours – I want to use our learning management system, Canvas, to host some Online office hours for my kids in the evenings. Can someone add some hours to the day?
Homework review in class – spending 10 – 20 minutes reviewing homework that many kids haven’t done is just a waste of everyone’s time. They aren’t getting anything out of watching/listening to me solve problems. They need to solve problems. I think I’m going to provide answers and give them 5-10 minutes to review in groups. Perhaps having them decide on 2 or 3 problems that they want to review and assigning them to the groups to present.
As I mentioned previously, I have so much running through my head that its a little overwhelming. I have lots I want to start and change but I know, from more experience than I care to admit, that I can’t do all of these. I must prioritize and focus otherwise I’ll do none of them well. HELP! Kids come back in two weeks! Can’t wait and I’m not ready all at the same time!
Again – would love your thoughts, comments and ideas!!
The beginning of the school year is always a time of turmoil for me. I’m so excited to get started and so nervous at the same time. You’d think, after 30 years, that I’d be used to it. NOT!
This year I was particularly excited to get started. I get to work with Kate Nowak (@k8nowak) – YAHOO – and Arlene Smith (@smitee60ne) and I have decided to expand our project from last year and have even been accepted to speak at the NCTM conference in Boston in April about the project and peer-to-peer mentoring in general. We’re using a new learning management system in our school and I’ve been pretty involved in that too. All these new adventures made me anxious to see the kids and hopefully get them as excited.
On top of these, I had some goals for myself – 1. Do less talking. Have students working in groups more and talking to each other more. 2 – Work on NOT repeating students answers. Letting them own their answers and encouraging them to listen to each other. 3 – Getting students to be willing to share their answers and look for different ways to solve problems.
And that was where this post stopped a month ago and its been sitting in my drafts folder since! To say I’ve been a little busy is an understatement. I’ve done it to myself – I’m just too interested in too many things. But I’d rather be that way then to be bored and doing the same old thing all the time. So I,m back to this post finally and wanting to put this out there so my goals are public. Working on holding myself accountable for what I said I wanted to do – so there it is.
How am I doing so far? Well… so, so….
1. Less Talking – did pretty well at this in the beginning of the year but have slacked a bit lately. Some content feels like it lends itself better to discovery than other material does. I also am coming to believe that some productive discussion isn’t a bad thing. Just yesterday I felt like I talked more than I would like but they talked to and it was more about leading them in a discovery than telling them. Maybe I need to reword that goal – Less of me TELLING them stuff. More about that lesson later.
2. NOT Repeating their answers – this is still my most challenging area. My reasoning is that I always want everyone to hear whats said but that can be accomplished by them repeating. I just need to remind myself constantly!
3. Getting them to share their answers – again, not bad at the beginning but they are still a bit afraid. I don’t necessarily think they are afraid of what I’ll say but more what others will say. They don’t want to appear dumb in a class where they perceive that everyone is smarter than them. We’re still working on building a community of trust there. I’d just pluck some out and share them without names but then we’d miss the interesting part of asking the person what they were thinking and how they approached the problem from the beginning. Ideas for building this trust?
Anyway… almost a nine weeks in (how did that happen) and that’s where I am. Where are you?
Since I became an EnCoMPASS fellow two years ago I’ve probably been asked those questions about 100 times. I always struggle some with the answer. Its hard to put into words exactly what EnCoMPASS is – at least to me. But, here goes….
Formally, EnCoMPASS stands for Emerging Communities for Mathematical Practices and Assessment and its a grant project started by the Math Forum at Drexel University. That’s defined a bit more on the EnCoMPASS site – “The EnCoMPASS Project is developing an online professional teaching community of mathematics educators focused on understanding and improving mathematical thinking through work with formative assessment rubrics and feedback to student problem solving.” But, after the one week institute in Philly and two whirlwind weeks home starting school, I’m still thinking about the fact that it means so much more to me.
So, here is what EnCoMPASS means to me…
- Thinking – lots of it
We analyze, talk about, tear apart, and talk some more about student work. “So what”, you say. Well, its a huge “so what.” As teacher, I hope we’ve all analyzed our students worked. We’ve probably thought about what made the student do what they did and we’ve then assigned a grade or taken off the points we thought they deserved for whatever error they made. We’ve probably even adjusted our instruction based on that analysis. But, in many cases, we haven’t had the time or resources to sit down with our peers and analyze it from start to finish. To discuss the problem before giving it to a student, to think about what possible strategies the student might take and then to look at the work once its done to really try to get into the head of the student and analyze their thinking. EnCoMPASS means that…
It means giving feedback to students rather than just a grade. Giving valuable feedback that makes the student explore another option, revisit their solution, think about their own thinking or just express themselves more clearly. That’s definitely not as easy to do as it is to write here. It stretches your teacher brain too!
- Providing resources for other teachers
The EnCoMPASS project is working on a platform where teachers will be able to share work with other teachers to allow that analysis to build. Other teachers will be able to look at, analyze and see others analysis of student work on problems that they either plan to use or have used with their students. A true online PLC (professional learning community.) A way to provide teachers with that resource in a way that they can access it at a time that’s flexible for them. And the coolest part, that platform is being developed by teachers for teachers!
One of my assistant principals called this my “geekcation.” And it really was. This group of teachers is one of the most dedicated, talented and passionate I’ve ever had the pleasure of knowing. I am truly honored and
humbled to be included among them. The stream of cool ideas, thoughts and suggestions that come out of this team daily is almost overwhelming. They are risk takers who aren’t afraid to fail and try again and they encourage that in their students. They ARE the teachers that we all want our kids to have. They provide inspiration to their students, their colleagues and their students daily. Just fills the heart to be around them.
I know that sounds weird. But this group really has become a family. We talk to each other via Facebook, Twitter, EnCoMPASS discussion forum, Google hangouts, text etc…. all year long. We know about each others kids, happenings in our lives and the day to day stuff that all families talk about. I love this group!
EnCoMPASS family – I miss you all so much… feels like its been a year when its only been two weeks! Google Hangout soon?
(Credit to Vivian Klotz for almost all of the awesome photos! Aren’t they great?! )
(Credit to Lisa Henry for this wonderful “selfie.” Frisbee photo bomb by Andrew Stadel and Michael Pershan)
So I love to teach… I don’t mean like “love” to teach, I mean I passionately LOVE to teach to the point where I’m annoying to others that aren’t maybe as crazy about it as I am. Folks wonder about me. “How could she really love to work with those obnoxious teenagers everyday?” “Why would she work for a week or more on a lesson when she could just use what she did last year?” I don’t hear people actually say it out loud everyday but I know that many folks are thinking it. I can see where they are coming from. When I’m overwhelmed (which is often – I’m not good at saying no) I wonder myself. What was I thinking redoing that lesson that was perfectly fine and successful before? Here’s the bottom line – I love to teach because I love my kids, want them to learn and I love to learn myself.
Redoing a lesson or working with “those” teenagers requires that I look at something in a new way, learn new things. No year is the same as any other, no day like the one before and, in order to not completely stink (I don’t pretend to be awesome), I have to keep learning. As Max (@maxatmathforum) just reminded us, Teaching is hard. Rarely a day goes by that I don’t learn something – even if its just that that kid can’t sit next to this one. I love the feeling when a lesson works out and my kids “get” it. When the kids have that ‘ah-ha’ moment. I love those moments because I love it when I have those moments.
So where does Twitter play into this – after all the post is “Why I Tweet…”? I was reminded of why I tweet today. I traveled to Richmond (about an hour from me) to have lunch with two of the best tweeps ever. Mary Williams (@merryfwilliams) and Mark Sanford (@hfxmark.) We had lunch at 1 and didn’t leave until 4! It was AWESOME! We had never met “in real life” but immediately gave each other hugs and felt right at home sitting and chatting. (The waitress wasn’t too sure what to make of us.) How could that be? Because we’ve been collaborating for well over a year – via Twitter. Whenever I need to find a new idea, reflect on a lesson or just chat – they are there.
As teachers we are often so busy during the school day that we don’t have time to collaborate with our own teammates. At the end of the day we pack up and run home for some peace and quiet. I wish, as do many others, that we could give teachers more time in the day to truly collaborate with each other. But since very few seem to be clamoring to do that – I turned to Twitter. I didn’t know that’s what I was doing at first. Someone suggested a Twitter account, I jumped on (I like to learn) and thought – no way is this helpful. But I stuck around and now I have a whole world of colleagues that I can turn to for advice, ideas and reflection. I have my “tribe” – the folks that feel the same way I do about teaching. We are the teachers but we are also the learners.
There has been some talk on Twitter recently about whether or not teachers are actually making changes in their classroom based on their twitter conversations. I wonder if maybe we’re thinking of “changes” in such a big way that it will never seem like enough – and is that a bad thing? I know I haven’t changed everything I’d like to about my teaching.. But I also know though, that I have changed small things (and a few bigger ones) that have made me better today than I was yesterday thanks to all those fellow “department” members on Twitter. And I am grateful for that. Grateful to my collaborative department of 300+ Grateful to have the ability to collaborate at all hours of the day (not blocked at my school) and night (Fawn @fawnpnguyen and Shelli @druinok will answer me!)
Teaching is hard and sometimes we’re even harder on ourselves. As I mentioned to Lisa (@lmhenry9), I think she’s awesome because she’s worried about how totally un-awesome she thinks she is. We’re learning and whatever we learn via twitter, or blogs, or our colleagues at school, or our students, impacts our teaching whether its in a big way or a small one. Every little bit matters even if its only 140 characters long.
I’m ready for the next “Tweet-Up” …see you online later tonight!
So back in April, my mouth opened and this came out…
“Wouldn’t it be great to have a week of summer school of sorts to help kids get ready for
Algebra 2? Sorta of an Algebra 1 Review – Algebra 2 Preview type thing. I think it could really help all of our kids. Thoughts? “
Well, of course, everyone thought it was a great idea and they especially thought it was a great idea since I was willing to do it.
So invitations went out and enrollments came in (not many but enough) and today was day #1. We didn’t have many show up but we’re at it anyway. Very lucky to be in a small division that is willing to fund and try anything we think will help kids.
Now, in the meantime I’ve dipped my hands into WAY too may pots – I tend to do that (that’s a subject for another post another day) – and I’m overwhelmed (yes, I know its summer.) But, not wanting to ever waste an opportunity I’m jumping in with both feet. The cool parts of this – I get to spend some time with students without the stress of grades etc. AND I get to try out some things I’ve been meaning to try and either haven’t been teaching that or seemed to run out of time.
So today it was Mr. Stadel’s 3-Act on Styrofoam Cups. You can find it here. (Side note: If you haven’t visited his Estimation 180 site you should go there immediately! Its awesome!! AND I get to work with him through EnCoMPASS – I’m so lucky!) I was working on tying this in with solving equations and connect it to arithmetic sequences that we talk about early on in Algebra 2.
The basic premise behind this 3-Act task is that students have to determine how many cups, stacked up, it will take to fill the inside of the door. In case you’re not familiar with 3-Act lessons or tasks, they usually start with a video showing kids a scenario and leaving it open-ended so they ask their own question. Then you can give them some information, they answer the question they had and the third act sums up the activity by showing them the answer (or an answer based on what they think the kids questions might be.) Its very engaging for students and they really love that its “real-life” even if they don’t really have a reason to stack cups in a doorway.
I presented the video to my kids and asked them “What do you want to know?” I thought I’d immediately get – “How many cups would it take to reach to the top of the doorway?” Nope…. I got “How many cups would it take to reach that line on the door?” (there was a green line with a big 40 on it in the video on the door.) Then I got – “How many cups would equal his height?” Wasn’t surprised at that one… and it gave me an “in” to something else! Love those moments. I did have a small group so I might have gotten the one “I wanted” had I had a larger group. Mine sat there and looked at me and I told them to keep thinking and they finally said – “OH, how many to the top of the door?” So off we went.
They needed more info and I gave them the images that Andrew shared on his page. They completely missed that they had to do a conversion between inches and cm until I asked them to look carefully – “What do you notice?” They struggled more than I thought they would with what to do with the height of the first cup. One student just divided by the “lip” of the cup (amount added each time – was thrilled that they saw that) and had an answer that was too big. Another student questioned why she didn’t use the height of the cup and this generated much discussion and lead to eventually writing down the height of 1 cup, 2 cups etc. (and a nice intro into arithmetic sequences for me!) They were finally able to write a rule and get an answer!
They anxiously awaited the video answer and they were thrilled when they found out that they had gotten the correct answer. Made perfect sense to them to round down – a definite win!
Then came Act 4!
Yes, an Act 4 – I mentioned that Mr. Stadel had another video stacking cups up to his height and they immediately wanted to know how tall he was. I had mentioned that he was TALL! I paused the video of the doorway cups and let them take a guess. Now that they knew how many were in the doorway they guessed how many matched his height within 2 cups! So… we actually watched his last video for the “How many cups stack to Mr. Stadel’s height?” question so they could see how many cups. They were super excited that their guess was so close but it still didn’t answer their question. “We want to know how tall he is … in feet, not in cups!” So … I said… figure it out!
AMAZING!! LOVE THOSE MOMENTS!!
Ok… Mr. Stadel – my kids think you are about 6’4″. (But .. in our opinion the 142 cups don’t quite come to the top of your head.) How close are we?
Tomorrow we throw Barbie off a balcony! FUN!!
Full disclosure – this is a long post (even though I rewrote it to try to make it shorter!) Much of it is me thinking out loud with some questions/thoughts at the end.
Standards Based Grading as its looked for me so far….
- Year 1 – Used in my Algebra 1 class. The learning targets were pretty good but could have been more specific. Averaging grades was a pain – used a spreadsheet but not perfect. Students rarely did review and reassessment work. I struggled with how or whether to count classwork.
- Year 2 – Used again in my Algebra 1 class. Learning targets were more specific. Spreadsheet was easier to use but overall grading was harder to figure out with our school wide gradebook package. We used a department created grading scale to match the 1 – 4 with our 0 – 100 scale on the report cards. Had no D grade – only A, B, C and I (Incomplete) Students were a little better with review and reassessment. Classwork was still a struggle.
- Year 3 – In Algebra 2 class this past year. Learning targets started out clearer and we refined as we went along. Spreadsheet had a nice report for students but still have to be printed individually. Added the D back into the grading scale to help parents understand better. Review and Reassessments started to take off but still not super. Classwork was added in as a learning target but only 1 of 40 targets so it didn’t have a huge impact.
What I LOVE about it…
- I know (and the students know) exactly which skills or concepts they understand and which they don’t.
- Students feel that they have some control over their grade (they always did but this seems to make that very clear.)
- Students can review and reassess! I was one of those students that didn’t always “get” it right away. I would have loved this opportunity.
What I DON’T LOVE so much…
- Motivation to do practice and classwork isn’t always where it should be.
- Our computer gradebook program doesn’t really support it (although our new LMS does support it to a degree.)
- Parents aren’t always clear about what’s going on. They are used to traditional grades and don’t always understand these.
Here are my questions……..(warning – some of this is the thinking out loud piece)
- Should I expand this to my Honors level (pre-AP) classes?
I actually said NEVER when we first started using SBG but I think my focus was on the reassessment and I thought my kids would take advantage of that. They just wouldn’t study and expect a retake. These kids tend to be very grade focused. It felt like using SBG here would be lowering my standards rather than raising them. I didn’t really think about the fact that I can customize the learning targets to level of the course. I also didn’t fully appreciate how valuable it would be for both my students and myself to be able to determine exactly what they understand and are able to do and how this might make them more learning focused than grade focused.
- What grading scale should I use if I use this with my Honors kids?
We’ve been using one where we “adapted” the 1 – 4 into 0 – 100. A (3.5 and above) = 87.5; B (3 -3.49) = 75; C (2.7 – 2.99) = 67.5; D (2.5 – 2.69) = 62.5. For other courses we use a 9/10 pt scale (91 – 100 etc.)The issue that I’m personally having with this is that the standard is lower for A – C but then higher for the D. I feel like parts of this would appeal to parents/students but then I’d get push back from the kid with the 61. It makes it confusing for parents to understand why an A in my course is an 87.5 while an A in every other course is a 90.
- And speaking of parents, what might I expect there?
My parents this year were fine because they had been through 2 years of this already. These parents haven’t had much if any experience with this method of grading. I would hope they would like how specific this is with regards to exactly what their child understands and is able to do but I also think the grading scale piece would be confusing to them. How can I get them to see the positives and calm their fears?
- Anyone else out there using SBG with pre-AP kids in a school that’s NOT all SBG?
Suggestions? What road blocks did you run into? Might there be a way to use SBG that’s less intimidating to parents/students and would help them bridge the gap between what they are used to (traditional grading) and this new method?
So there it is… If you made it this far, thanks so much for reading! Believe it or not this is shorter than the original! I’d love to hear thoughts and suggestions.
Any of you that know me personally know that the 2012-2013 school year was a rough one for me so I was less than sure about how this one might go and what that might mean for my future in education and at my school. So a year after that challenging one, here’s where I am – no proofreading from my English teacher friends, just the raw facts grammatical errors, dangling participles and all!
I’ve learned lots of little things that have been great – how to do a vlookup in Excel, how to use interactive notebooks in class, how to navigate the online course world of Canvas. All of those things have been great but here are the BIG things I’ve learned this year….(or really knew but somehow had forgotten)
- As the amazing Larry Clarke says, “You can lead from the back seat!” – Leadership is about so much more than a position. Its about stepping up when you’re needed. Its about mentoring others by just doing your own best work. Its about listening and collaborating. You can lead from anywhere and often folks are looking to you for leadership even when you’re not intentionally leading or in a leadership position. I have been blessed to have been reminded of these opportunities this year and I’m so grateful.
- I often give others too much power over how I feel about myself and the job I do. I’m not saying that I’d be ok with never hearing good things or always hearing critical things about what I do. What I am saying is that I need to consider each within the context of what’s good for me and my kids. I want to keep that growth mindset and continue to learn but also work on not letting critical things effect how I feel about myself and shake my confidence. Last year I wondered if I had stayed too long at the party. I wondered if my time had come. My confidence was shaken.
But I am happy to report…. I still have some “party” in me.
- You can move forward and learn by moving backwards. Giving up a leadership position that just wasn’t working for me has allowed me to find my passion again. I refocused on my classroom and my kids and its been a wonderful year full of learning for both of us. It wasn’t perfect – there were ups and downs but they seemed so much more doable. I found time to try those ideas that I so selfishly stole from my CHS, Twitter and Math Forum/Drexel friends and turned to them when I felt like I was at the end of my rope. I got to have those conversations with other teachers that I’d been needing so badly. My kids supplied the affirmation that I had made the right decision. They reminded me why I went into education to begin with. I expected a lot, they worked hard and learned a lot of math and hopefully a lot more. I completely loved them and many gave me tons of love right back. That is worth so much more than I can describe.
They are it! That’s why we’re here! Not a title or a position or a job. And WE are so much more IMPORTANT than even we realize sometimes. Its an enormously hard job that is so amazing. So this veteran will keep at it a little longer hoping to continue learning, helping others and having fun while I’m at it. Would you believe I’m already looking forward to next year?
But first … a nap… maybe a summers worth!
Completing the Square always seems to be one of the toughest concepts for Algebra 2 kids to do and understand. I always seem to be looking for a new way to tackle it with my kids.
A few years ago I started with the vertex form of the equation – teaching the transformations and showing my kids how to write the equation in vertex form by finding the vertex on the calculator. While I hate teaching calculator “methods” before the algebraic methods this did have a benefit. Pretty quickly my kids saw the pattern between the middle term (b) and the x-coordinate of the vertex and then they figured out that they needed to subtract the square of that from the constant to get the y-coordinate. At least it worked pretty well when the leading coefficient was 1! When we had an “a” value that was more than 1 it was a bit more problematic. They saw the pattern but it was harder. I showed them algebraically what was happening but to say they weren’t buying it was an understatement. The idea of a perfect square trinomial just seemed hard to grasp even though we had done factoring and looked at the pattern before. With no other way present I stuck with this one.
Then, a few months ago I posted about using boxes to help students with Polynomial Long Division. At the time I asked the question – “Could we use this for completing the square?” Bob (@bobloch) replied with a great post showing how to use the boxes for completing the square. I just recently taught this concept in my Algebra 2 Honors class and my kids loved the boxes. I started by showing them how that might work with a = 1. They got it! Made sense to them. Then we went to a = 2 and I actually had them make 2 boxes. Then I went to 3.
That’s when one of my kids brilliantly asked – “What happens when a = 40? I don’t want to make 40 boxes.” So we had a great discussion about how to make one box but multiply it by our coefficient and several kids actually commented on how that helped them see what was going on in the algebraic form. Whoo Hooo! Win!
Now for the crazy part – as I was discussing how this lesson show go with my student teacher, she said, sorta jokingly… “Since they understand the ones where a = 1 its a shame we couldn’t do something like slide and divide with this. ” (I just learned about slide and divide for factoring about two years ago – amazing! Found a proof online too!) Well, this sounded like a challenge to me so I tried it. With some weird tweeks it works and I can explain why I think it works but I can’t prove it yet. See what you think. Anyone will to try to tackle a proof?