Backing up… we are getting ready to begin the unit with linear functions. You know the one, the one in Algebra 1 where we work on graphing lines and writing linear equations. Where slope and rate of change are formally introduced. I know my students are already aware of y = mx + b from 8th grade. I’ll be doing a pre-assessment this week to confirm what they already know how to do. But already knowing they’ve at least been exposed to y = mx + b does change some things.

So, these are the Common Core State Standards that I am planning on working with in this unit:

F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.7a: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (a: Graph linear and quadratic functions and show intercepts, maxima, and minima.)

A-REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F-LE.1a: Distinguish between situations that can be modeled with linear functions and with exponential functions. (a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.)

F-LE.1b: Distinguish between situations that can be modeled with linear functions and with exponential functions. (b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.)

F-BF.1a: Write a function that describes a relationship between two quantities. (a: Determine an explicit expression, a recursive process, or steps for calculation from a context.)

F-LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F-LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

S-ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

My list of learning targets I used last year:

*I can calculate and interpret the average rate of change of a function. (F-IF.6)

*I can graph a linear function and identify its intercepts. (F-IF.7a)

*I can graph a linear inequality on a coordinate plane. (A-REI.12)

*I can demonstrate that a linear function has a constant rate of change. (F-LE.1a)

*I can identify situations that display equal rates of change over equal intervals and can be modeled with linear functions.(F-LE.1b)

*I can construct linear functions from an arithmetic sequence, graph, table of values, or description of the relationship. (F-BF.1a and F-LE.2)

*I can explain the meaning (using appropriate units) of the slope of a line, the y-intercept, and other points on the line when the line models a real-world relationship.(F-LE.5, S-ID.7)

As I am ready to embark upon this unit, I find myself struggling. I want to incorporate more activities. Mary Bourassa has gotten me thinking. I was catching up on blog posts and I began reading her blog from the beginning of the year. I like the idea of bringing in activities. Barbie Bungee, Stacking Cups, and Vroom Vroom are just a few activities that other teachers have done that may fit in line with the standards.

Some of the questions bouncing around my head include:

How do we do the activities and ensure that students learn what they are supposed to from the standards? As I write that, it sounds goofy, but I have some semblance of confidence that when we work through examples and practice problems, I’ve done something to ensure that what the standards are asking me to teach, I’ve taught.

The follow up to that is how does assessment look? Is it a test? Is it another activity like one of the ones listed above? If it’s an activity, how does that fit into the Standards Based Grading world I operate in?

How do you decide which activities to do? There are lots of good rate of change / writing linear equations activities out there. How do you decide which one(s) and how many?

How do you know it’s “working?” Even if student engagement (at face value) seems higher because you’re doing activities, how do you know they are getting what you want them to get out of the activity?

The bottom line for me at this moment is that I know where to find the activities. If you think you’re ready to make more of a shift from a “traditional” teacher, how do you start? If you are choosing a unit to change, how much of it do you change to give it an honest go at it?

I look forward to reading your comments.

]]>I had thought about going and creating a Polygraph at the Desmos Teacher website, but when I got to school, I saw the chromebooks were already taken for my Algebra 1 classes. (I may still go back and do this, though). The idea popped into my head to have students create their own arithmetic sequence. It would give me a chance to make sure they understood what an arithmetic sequence was and it would give them a chance to practice writing them and creating the equations, which is what I needed them to do.

These are the directions I projected on to the Smart Board:

I did modify them a bit after the first class. Originally, I did not have them write their work for their sequence on their paper, I had them write it on a separate page. It worked easier for them to have it on the other side.

So, this is what their papers looked like:

I thought that the activity went fairly well. All students participated. Those students who were not here yesterday for the notes were able to get some additional help and get on the right track. I could see which students understood what an arithmetic sequence is and which ones could successfully write the equation for an arithmetic sequence. There was still time for students to start practice problems in class, but not so much that they would finish the practice. All in all, it was a good day.

]]>(Created from Creative Commons Pictures)

I hate to say it, but Kate started me down the path today.

```
```@Mythagon @MrCBRobinson I use the “share” icon and then save to Pocket. I <3 pocket.

— Kate Nowak (@k8nowak) November 3, 2015

@Mythagon @MrCBRobinson That allows me to use Favorite for “like” or “I acknowledge your tweet” without cluttering up my read-later list.

— Kate Nowak (@k8nowak) November 3, 2015

```
```@Mythagon @MrCBRobinson and and AND, when you read articles in pocket app, it strips out all the annoying ads and gizmos.

— Kate Nowak (@k8nowak) November 3, 2015

@Mythagon @MrCBRobinson This: @Pocket

— Kate Nowak (@k8nowak) November 3, 2015

```
```@MrCBRobinson @Mythagon it’s pretty magical. And it plays nicely with other apps and the browser plug in works easily.

— Kate Nowak (@k8nowak) November 3, 2015

OOH Shiny! Squirrel!

And off I went looking at Pocket and thinking about how cool it would be to read stuff I saved for later on my device while waiting to pick up my kids from wherever it was they were and I could use Twitter better and…

Crap. I already have set up for my favorite tweets to go to Evernote. And there they sit. Part of the reason they sit is ANY tweet I favorite goes to Evernote. Even if it’s a pithy comment by Sam which doesn’t show up in my Evernote because he’s locked down his tweets.So there they sit because I don’t feel like cleaning it all out and sorting *why* they are my favorited tweets.

I used to have it set up that my favorite tweets go to Diigo. (Oh, wait! It looks like some of them still go there.). But I ran into some of the same frustration with Diigo as I have with Evernote – the tweets go there, but they’re categorized under Twitter or Favorite Tweets and I have to go back and categorize them to where it’s meaningful to me. But then, how do I decide what goes in Diigo versus what goes in Evernote. I like that Diigo just saves the link and a brief description and I can go there in a click. But sometimes, websites change or go away and the link I thought I was favoriting isn’t what it is when I go back. I like that Evernote takes a picture of the page or can just save a snippet of a page. But it’s not quite as quick to get to the webpage (although it’s not a *huge* deal to get there).

Pinterest is like Diigo where it saves the bookmark to the website, but it adds a picture. But in Pinterest, I have to categorize into boards and I don’t have the flexibility of tagging with whatever tag I want like I do in Diigo or Evernote. Digg Reader is where I keep track of the blogs I am reading and can do some saving in that website as well.

PHEW! Way too many places for way too many things!

I’d like to think Evernote is my answer. I can make folders and put things wherever I think it makes sense. But sometimes, I don’t want to comb through all of what’s on the page. Diigo is great for keeping track of all sorts of websites, but it doesn’t link in well with Twitter sometimes. And because this is such a mess, I don’t want to go to either one of them to fix it. I really should. I know I should. It would be way more helpful in planning and other stuff if I would just fix it.

But how? How do I fix it? There is a part of me that doesn’t want to throw anything out. Each has it’s place. I need Digg Reader to keep track of who has new blog posts even though I tend to get most of the blog posts I read anymore from Twitter (when I’m on Twitter – which hasn’t been a lot recently, so I guess I need Digg Reader anyway…). I like Pinterest, but it is just too cluttered for me. Too many pictures and it’s too distracting. Pinterest has a good purpose, but it’s not working for me for a lot of things right now. I like Kate’s idea of saving Twitter links to Pocket to read later, but I’m not sure how that will play out for me. Will they just sit there or will I actually do something with them? And if I start with reading stuff via Pocket, that will help to take the clutter out of my Evernote/Diigo links.

But that doesn’t answer the question of what do I do with Diigo? Or Evernote? And how do I clean up the mess so one or both of them are useful? Do I keep things in *both* places? Do I try to get everything into Evernote and move on from Diigo entirely? Or if I use both, how do I decide which one get the link? Such hard questions to answer right now, but I feel like if I can’t answer those questions, I can’t clean up the mess or stop the automatic moving of the Twitter Favorites.

Thoughts from the audience?

]]>This is my third year teaching Algebra 1 under the Common Core State Standards for Mathematics. Although I am getting more comfortable with the standards, I am, by no means, a master of teaching them. I have made some improvements, but I don’t feel I’m at the point that I absolutely have gotten *there*.

As my 3rd Algebra 1 class walked in yesterday, they told me, “Mrs. Henry, I heard this test was hard.” My heart sank. I had not gotten far in grading the assessments, but what I had seen so far looked great. I had more students than usual not finish (so I have several who need to finish tomorrow), but from what I saw on paper, it looked like they had gotten most or all of what they should have.

Here are the (partial) results:

Class 1 | Class 2 | Class 3 | |

Graphing with a Table | 9.6 | 9.5 | 9.9 |

Confirming a point on a line | 9.4 | 9.4 | 9 |

Comparing graph, equation, table | 8.9 | 9 | 8.6 |

(scores out of 10 – I use SBG where 9 is proficient and 10 is mastery)

These are the best results I have had to date in Algebra 1. They are the best results I have had on these learning targets since I began teaching the course. So now I am sitting here trying to comprehend what went right. I have some preliminary thoughts:

- The 8th grade math teacher was on his second year in our district last year.
- Last year was the first year our middle school taught specifically Common Core State Standards for Mathematics.
- This year’s group of students seem to have been more receptive to the Warm Ups I’ve been doing (a combination of Which One Doesn’t Belong, Visual Patterns, Estimation 180, Would You Rather, Balance Benders and so on.)
- This year’s group of students seem more willing to communicate mathematically.

As I reflect upon it more, this year’s students have been taught under Common Core previously whereas my last two year’s groups were not exposed to it. I suspect that is the strongest reason why they had more success. Although they may have found it difficult (aka “hard”) to reason through the comparison problems, they persevered through them (and some still are…). They were able to do what was asked even though it was not easy for them because they practiced and prepared. And, although I would like to take a lot of credit here, I honestly think that because this was not the first time they were exposed to problems that made them think a little harder (whether in my class or the year before), they were more comfortable with pushing through.

I guess what I am saying is this: for as much crap as Common Core has taken in the last year (due to the standardized testing), it works. If we want our students to think through and reason better, teach the standards the way they were intended. It takes time, but it will work. Are they perfect? Probably not. Are they an improvement? Yes. Will kids be able to meet the standards? Yes, given time. It’s not fair to them or teachers to yank out the standards after a handful of years to change them because things aren’t going perfectly at the beginning. They won’t. It takes time for everyone to adjust. Give it time.

]]>By third period (9:20 am), we still had no internet or connection to the server. While it wasn’t a huge loss for my Calculus students (we certainly had a lot of ground to cover in 50 minutes), my Algebra 1 students have come to expect and do the warm ups each day. What to do, what to do.

It dawns on me that I have a bag of Smarties that I just opened this morning. Maybe I can use that…

So, I walk around with the bag and ask them to estimate the number of Smartie rolls in the bag. At some point, one of my students notices that there are 3 1/2 pounds of Smarties in the bag. Another student asks how much a roll of Smarties weighs (7 grams from the label).

We go through our normal Estimation 180 process (I don’t use the exact form, but the gist of it in my weekly warm ups). My students ask how many are in the bag. I ask them how we could figure that out and they suggest looking at the label.

However, we took it farther. We recently worked through converting units, so I ran with the information my students picked up on and we worked to figure out how many Smarties there should be by weight.

We talked about why there was a discrepancy (the bag being filled by weight versus someone estimating). However, my students weren’t satisfied (and really, neither was I). So, while they worked on a worksheet, I counted them. Knowing I had eaten 2 rolls of Smarties that morning, I knew the count would be off by 2 Smarties rolls.

There were 225 Smarties rolls in our bag. And that led to discussing why the weight estimate was more accurate than the serving size estimate. Such estimation fun today!

]]>At TMC13, I went to Megan Hayes-Golding‘s 2 hour INB Extravaganza. It was a little overwhelming at first, but by the end of the session, I was convinced that it would help my Applied Algebra students. They don’t historically do a good job of taking notes and I felt this was going to help them organize things better for them. I thought for Algebra 1 it might help them compile their notes and maybe encourage them to hold on to their notebooks. Little did I know…

It started about 3 weeks ago. I had an Algebra 2 student who had me last year for Algebra 1 tell me that they were so glad they had held onto their interactive notebook. The student in question had been referring back to what we had done in Algebra 1 last year and was using it to refresh their memory about how to complete the square. A few days later, another student stopped me in the hall and made a similar comment. And then another. And another.

I had told my Algebra 1 students to hold on to their INBs so they could refer back to them in Algebra 2. I had made the same comment to the previous year’s students, but I didn’t hear these types of comments from them while they were in Algebra 2 last year. I’m not quite sure what the difference is, but it is very obvious that they held onto them last year.

I’ll be honest here, I don’t do INBs like some do. I am certainly not the foldables queen that either Sarah Hagan or Julie Reulbach is. In all reality, I do mine very similar to how Jonathan Claydon does. I don’t check them. I guess it’s not something I’m overly concerned with in the grand scheme of things. But I do insist they put things in it and I clearly show how I would like them set up. My students, for the most part, comply and have a great resource at the end of the year.

Was I reluctant to start doing INBs with my students? Definitely. Would I do them again? Absolutely. It is well worth it and I think my students find them to be helpful later on. That is a good reason in my book to do the INBs in the first place.

]]>My students like doing “Around the World” (the link is to an early version of it) and I wanted something similar but I knew some students would fly through integer operation problems. I decided to get some problems from Math-Drills because they had several pages of 30 problems and they were mixed. I printed off enough for 20-30 problems for each student. I then cut them into individual problems as pictured above.

When we got to class, the directions I gave were:

- Pick up a problem from the pile. (I gave them the first problem face down so everyone wasn’t as the desks at the same time).
- Work the problem.
- When you think you have the correct answer, raise your hand.
- Wait for either myself or my co-teacher to okay your answer.
- Then get a new problem.

We did this for about 20 minutes. It went surprising well. My students all worked on problems and waited patiently for us to check answers. It allowed my co-teacher and I to help students who still needed help. The students got to get up and move around a bit, which always helps. Many of the students practiced 15-20 problems in the time frame we allotted.

I would like to try this again with a larger class and with problems that would take a little longer to complete. I’ll have to think about how I would want to execute that.

]]>But, September, I just don’t like you. The first assessment, where my freshmen realize that they don’t know how to properly prepare for an assessment and they don’t do well. Going through the growing pains of doing Standards Based Grading, where my students realize that I’m not going to grade their homework, so they don’t do it. Then, when the assessment rolls around, they realize they don’t know the material as well as they should and they try to cram-prepare and it backfires on them. Then, after having the talk with my classes about the disadvantages on not doing outside of class work, waiting to see who it sunk in with.

And I don’t like going through the whole “training” bit of getting my students to write all of their thinking down, even the stuff they put into the calculator (*especially the stuff they put into the calculator*!). Don’t get me started on the goofy things freshmen do behaviorally. Definitely high up on my not favorite list.

Nope, I just don’t like this feeling out period at all. You all know the time, where the students are still trying to figure out how your class is going to go, where you, as teacher, have to get them going in the right direction. Last year’s group just had it down so well, your brain reminds you. How quickly it forgets that you went through the *same* thing with last year’s group too. And the year before, and the year before that, and so on.

But at some point, past September, I’ll get into that just right rhythm with this year’s classes, too. With one of my classes, this is the second time I’ve had them, and it was so easy to fall into that rhythm with them this year. At some point, I’ll get there with the rest of them. But could it just get here soon? Please?

]]>When someone says that to you, and you know they are saying it because you explained things well, how does that make you a good teacher? Some say that the best teachers are the ones who help teach their students to think. How does explaining something well do that? If all or most of what a teacher does is lecture or explain how to do something, but they do it well, does that make him or her a good teacher?

If you look at evaluation rubrics, there is NOT an emphasis on explaining things. It’s all about differentiating and meeting all students needs and keeping the students active in the classroom. Is that a good teacher?

If you look at PAEMST teachers, what do they do that distinguish them from all of that other math and science teachers?

What makes a good teacher?

]]>Fast forward to TMC15, and the Formative Assessment morning session with John Scammell. We did Plickers as part of responding to a question about formative assessment and feedback and I was reminded of their awesomeness. I used them (for the first time) with our staff as I shared a little bit of what I had learned from the session. I had decided at TMC15 that I was going to try them this year and had opted to print them and put them on the back of my students’ interactive notebooks this year (with matte contact paper as Julie Reulbach had suggested).

After using Plickers today, I have to say, I’m sold even more than I was after the first time I used them. Students are more engaged with the problem and trying to come up with a correct solution. Designing the choices to reflect what are common errors help me to identify where students are at with the concepts. The detailed reports let me see not only how many students answered each choice, but what each student answered. With the most recent update, I can now file questions into folders, sorting them by class.

As I work with Plickers more, I have figured out that it makes sense to show the list of students, so they can see if their Plicker has registered. Both the iPad and Android versions allow you to see not only if a student’s Plicker registered, but if the answer was correct or not. With Math Type, I can save an equation in gif form and bring it into Plickers for students to see (although it is not as crisp as I would like) – thanks to Eric Martin for the pro tip.

I will continue to use Plickers as part of my teaching arsenal. Thanks to Pam and John for sharing it!

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