I put together a card sort with various types of situations that would result in setting up a quadratic equation and then learners would have find the correct equation and then solve the equation. None of these problems are looking for a maximum or minimum (i.e. the vertex). I realize that many of these problems may be considered pseudo-context, but they were what I could find to get close to what I thought the standards were looking for.

This card sort was designed to work with the following Common Core State Standards:

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. *Include equations arising from linear and quadratic functions, and simple rational and exponential functions*.

F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

]]>By TMC17, one of the really difficult decisions I had to make was what morning session I was going to attend. The math teacher in me wanted to attend Cal Armstrong, Bill Thill, and Peg Cagle‘s Rich Tasks Morning Session. The “I wanna play math” person in me wanted to attend to attend David Butler and Megan Schmidt‘s Mathematical Yarns Morning Session. (Recap: Rich Tasks won) **But**, I really wanted to learn how to crochet.

Tina Cardone organized time in the evenings to learn crochet and help work on creating a square that would eventually be assembled into a blanket and donated (I forget to whom). So, I thought I would work on learning crochet that way. I tried to learn. I really did. But I’m not sure if my brain was really ready for it Wednesday night of TMC and Tina had a specific way she was teaching crochet and for whatever reason, it just wasn’t clicking for me.

I wanted to give up. Not a frustration I wanted to have during TMC. But, my grandmother used to crochet and I really wanted to learn.

(Here is the blanket she made for me as a high school graduation present:)

By Saturday night, I had decided that I couldn’t give up. The Mathematical Yarns group had displayed their creations (thanks to Sam Shah for sharing this:) and my curiosity was really piqued. So I sat down by Megan and asked for help. She got me going in the right direction. Both she and David gave me some ideas for patterns and off I went. I kept working on learning single crochet on the way home from TMC and got the rhythm of crocheting.

@Veganmathbeagle I made a Math yarn thing. Thanks for all of your help. pic.twitter.com/TnO34uXRxf

— Lisa Henry (@lmhenry9) August 2, 2017

.@DavidKButlerUofA @Veganmathbeagle I made another #mathyarns item. Started with a circle. Single crochet 9, chain stitch 6. Repeat. pic.twitter.com/qC7aBDjCEc

— Lisa Henry (@lmhenry9) August 7, 2017

.@DavidKButler @Veganmathbeagle Take 2 on #mathyarns – start w/circle. Every 9 single crochet, add branch of 6 chain stitches. (1/2) pic.twitter.com/iBKzV07kLf

— Lisa Henry (@lmhenry9) August 8, 2017

Coral (finally!) completed. Circular start. Branch as long as the color goes. Single crochet until color change. Repeat. #mathyarns pic.twitter.com/8hcSltuEtv

— Lisa Henry (@lmhenry9) September 4, 2017

New #mathyarns: Circle of 5, one single crochet, then 2 in one, then 3 in one. (Increases) Repeat. pic.twitter.com/MLOdwXH1Ul

— Lisa Henry (@lmhenry9) September 9, 2017

Most recent #mathyarns – single crochet 4, increase 1. This one started w/ a row of 4. pic.twitter.com/qlWA2owQMg

— Lisa Henry (@lmhenry9) September 17, 2017

Most recent #mathyarns– increase every color change.

Cc @Veganmathbeagle @DavidKButlerUoA @mathinyourfeet pic.twitter.com/zvUHnsaZ6r— Lisa Henry (@lmhenry9) September 23, 2017

It has been a lot of fun. Crocheting has been therapeutic for me in a busy time. I can get into the rhythm and just work the yarn. It has been neat to see what comes out when I am done. As I am crocheting, my mind thinks of other patterns to try with the specific yarn I am working with. I want to learn more, starting with another stitch than single crochet. I would love to find someone who can help me in person (maybe one of the older ladies at my church…). I am borderline obsessed with crocheting. So far, here’s my yarn collection as proof (although the yarn in the upper right (starting with the 2 circles that are arranged vertically I had from trying knitting):

Here are some of the pictures I have as I have crocheted.

If you are interested in the “how to,” here are some links:

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I have been guilty of referring to a whole group of people as “you guys,” even when the group is not all male. I hadn’t really ever thought about it. I have been working on deliberately not using this term in my daily language. I am generally successful. I have taken to referring to the group of people in my classroom as “ladies and gentlemen.” I’m not really sure why I have stuck upon this phrase – maybe it is hopeful in that they will live up to the title (as opposed to boys and girls), but it is working for me at this point. I noticed today when I was a parent observing my son’s sixth grade band class that the teacher referred to the whole group as children (which is true…), but again, not “you guys.” I am liking not using “you guys,” and am continuing to work on my language.

When Glenn was talking about using “learners” versus “students” in his work, I really liked the idea. It made sense to me. The individuals in my classroom should be learning, not just studying, mathematics. So, I started trying to change that language in my own vocabulary.

I am having trouble with this.

Find and replace in Word is incredibly helpful with this. **However,** you have to remember to use it… I keep forgetting to change my own language. Other teachers use students, not learners. It feels kind of “high and mighty” to use it. I’m not sure why. It just doesn’t feel right to me. I keep trying, but it just isn’t clicking with me yet.

In all of this, I have noticed how important it is to use proper mathematical language. It seems like it’s not a big deal. I got thinking about it one day as I was teaching the same material for the third or fourth time. When I use informal language in the classroom, while it may seem to help ~~students~~ learners to grasp the material better, it can also cloud understanding. For example, when we use FOIL in class to explain multiplying a binomial expression by another binomial expression, it does explain the mechanics of doing so. But, if I give a ~~student~~ learner a binomial expression and a trinomial expression to multiply, FOIL no longer works, So I use the phrase “double distribute” to indicate what to do, so when a learner encounters the binomial expression multiplying a trinomial expression, he or she will have a better idea of how to begin expanding the multiplication.

Now, while I’m not at the point of using “additive inverse” (one of my, now retired, colleagues used this every time properly and I used to think it was stuffy…), I am finding that I am more of a stickler on using proper language. Language is important. All of the time.

]]>So, what’s different this year? I think my mind was ready to receive the learning and implement it in my classroom.

For years, (yes, you can go back and look if you really want to), I have been saying I want to implement (more) Rich Tasks in my classroom. I haven’t. Or at least I thought I hadn’t done any, although I learned that I have been doing some of this already in my classes. I had pretty much decided that I was going to the Rich Tasks morning session with Cal Armstrong, Peg Cagle, and Bill Thill. Cal, Peg, and Bill have taught at PCMI. They did not disappoint my anticipation of this session and far exceeded whatever it was I expected from my learning. Some high points for me from the 6 hours I spent with them:

The first day, we took one of the Visual Patterns similar to what’s on Fawn Nguyen‘s website, but rather than asking the question “How many are in the 43rd one?,” Peg asked us to complete the following statement as many different ways that we could:

“As the step changes, _________________ also changes.”

We came up with a rather lengthy list – some obvious, some not so much so. Then we were directed to find someone who wanted to explore the same attribute the we did. I chose to work with Andria Kelly and Bob Batty on what was termed the “Modified Minesweeper” (how many squares shared an edge). Here is what we created:

It was a lot of fun to explore this and I would have happily spent another couple of hours doing more math with the pattern given. What I liked about it was that we were not restricted to a specific pattern and worked with others who wanted to work on the same thing that I did. I haven’t quite figured out how I will implement this specifically into my classes, but I’m thinking of some possibilities.

On the second day, we worked through various teacher moves while discussing rich tasks. We also looked at participation quizzes, which intrigue me.

On the third day, we looked at how we could work with existing materials and modify them to be richer. This was also very powerful for me. I realized that I had been doing some of these rich tasks already in my classroom (and here I had thought I hadn’t done anything!) and found many more ways to improve upon a worksheet. I left feeling empowered to implement rich tasks into my classes and with resources (website and people) to help with my journey.

Another useful session to me was Henri Picciotto‘s Reaching the Full Range. Henri talked about several strategies, but the one that I absolutely wanted to learn about was Lagging Homework. This is also something that has been on my list for a few years and, while I have implemented it a little, I haven’t gone to the lengths that Henri has. I am also considering assessing material multiple times (not just once) and these two strategies work hand-in-hand. Henri has posted quite a few resources on the linked page, so if you are interested in Lagging Homework, you can check it out. Steve Leinwand also talked about this in his session Practical Ideas on the Coaching We Need to Provide and Demand – although his variation is a little different (2 problems on today’s topic, 4 review problems – 1 from yesterday, 1 from last week, 1 from last month, 1 other review, and 2 thinking problems – explain how you got your answer). I am leaning towards the way Steve does it, but may modify a little.

There were several My Favorites that I had made notes about, but probably my favorite one was by Jonathan Claydon titled “Let’s Buy a House.” What struck me about it was the practical tone of the whole unit. I had taught something similar last year in my Senior Applied Class but I struggled with it. It was boring – and if I was bored, my learners had to be also. I am hoping this will help me revise the unit in a positive way.

While there are other sessions I attended and other My Favorites that I liked for various reasons, these speakers stuck with me for the same reason: my mind is ready to receive what information I learned from them. While intellectually I liked or wanted to implement many concepts over the years, I honestly felt that when I left TMC17 that my mind was ready for the seeds of these sessions. I am open to trying these things in my classes this year. I feel ready to do so. The seeds are planted. Let’s see how well they grow this year.

]]>For the past several years, I have used a form of Standards Based Grading. Assessments have grades for each learning target. Learning target scores are out of 10 points and students earn a score of anywhere of 5 (did not attempt) to 10 out of 10 points. In any given grading period, I have between 10 and 15 learning targets (so 100-150 points). Students can reassess any individual learning target.

Score |
Level |
Meaning |
In Gradebook |

5 | No attempt | I did not answer the questions and/or I did not show any of my thinking to answer the questions. Also given when I don’t show up for an assessment. | 5/10 (50%) |

6 | Limited | I don’t get it. I don’t even think I am starting this problem right. | 6/10 (60%) |

7 | Basic | I think I don’t get it. I can start the problem, but I cannot get very far in solving it. | 7/10 (70%) |

8 | Competent | I get the idea. I can start the problems but I make some mistakes along the way. | 8/10 (80%) |

9 | Proficient | I have a good idea of what I am doing. I make some minor mistakes or one major mistake along the way. | 9/10 (90%) |

10 | Mastery | I know what I am doing. I can answer problems without making any mistakes. I can help other students with this kind of problem. | 10/10 (100%) |

I wasn’t happy with how things worked out. Students were not completing practice problems (homework) and did not do as well as they could have. Students did not reassess. So, revisions were needed. Things that I have tried:

- Since students were not doing homework, I added in a 20 point homework learning target. I would mark whether students completed (1), partially completed (1/2), or did not really attempt (0) homework assignments. I would total up the number of points a student had, divided it by the number of homeworks the student was assigned and multiplied the decimal by 20 to get their homework learning target. While this did create accountability, I don’t think it really changed the behavior of most students in terms of whether or not they did the assigned problems. I did like that it did not put a heavy weight on homework.
- I have tried corrections in class the day after assessments. While this helped students’ grades, I don’t feel like they learned or retained the material well. Benchmarks and semester exams show that is true for many students.

This is my current brainstorm for the upcoming school year. I would appreciate any feedback in the comments.

I am looking at 3 components to student grades:

1) Individual Learning Targets – same as before. 10 points per learning target, scores between 5 and 10. Students may reassess as I had done in the past (they would need to come in outside of class and complete problems on that particular learning target). No corrections in class.

2) Homework – most grading periods, I have approximately 20 homeworks that I check. Rather than do the percentage deal, make each homework worth a point. Students can earn 1/2 point for partially completed assignments. Basically do the scoring the same but not make the final grade out of 20 points. Add them up and have one homework grade. Rather than having a grade like 17.5/20, a student’s homework grade would be 6/8 or 19.5/21 or whatever the total was at any point in the grading period. I think it will save hassle for me in the long run and be clearer to everyone where that grade comes from. As much as I would like to be rid of this grade, I cannot see doing so. It does provide accountability and gives some incentive to the students who were borderline on attempting it.

3) (This is the area I’m struggling with the most) I would like to add an additional section on assessments that would be previously taught material. Students still seem to feel that they need to learn the material for the assessment and then they can forget it. Although in Algebra 2. it seems like previous material comes up more, I want to make sure I continue to assess that material so that students will hopefully work to retain it better. I am thinking of having 2-3 problems from previously taught material and assess it similarly to the individual learning targets part of assessments. It would be a 10 point section on their assessment. However, unlike the learning target section, they could not reassess this portion of their assessment. I am still debating whether I would grade it on the same rubric I use for the Learning Target section (5 – 10 points) or if I would make each problem worth a certain amount and then give a score for each problem (i.e. problem 6 is worth 5 points, problem 7 is worth 2 points, and problem 8 is worth 3 points). I tend to give anywhere from 3-5 assessments in a grading period, so this would add an additional 30 to 50 points on the grading period. It would also lessen the affect of the homework points as a part of one’s grade.

If I add this additional component, something else I am debating is whether everyone would get the same kind of problems in the review portion. I usually make up 3-4 versions of the same assessment (to discourage wandering eyes). Would all versions have the same type of problems – for example, would all versions have factoring problems and a graphing quadratics problem? Or, would I choose different types of review problems for each version – for example, version 1 would have a factoring problem and a graphing quadratics problem, version 2 would have a solving quadratics problem and a vertex form problem, etc.? I think the latter may be perceived as not fair but I’m not sure I want everyone to know what the review problems would be so that they would be prepared. I’m still thinking that through.

Thanks for any feedback you can offer. I appreciate it.

]]>Day 1 –

We went over what made a good “Which One Doesn’t Belong.” Rather than providing them the exact WODB I chose, I had them either sketch or write what each option was. Some of them we did as a whole class, others they filled out the tables in their small groups and then we discussed them as a class. It took about 40-45 minutes to go through all 7.

Day 2 –

We worked through some of the incomplete sets using the same tables I used with them the previous day. We looked at what all three had in common first, then we started to look at what each pair had in common to determine possible 4th items. If I were doing this again, I would not have the trigonometry example second – it was the most difficult for my students to work with.

Days 3 and 4 –

I gave the students the assignment above. For some of them, they finished the first day. For others, it took them into the second day (either because they were stuck or the creation process of the items took a while). A completed one looks like:

I really wanted them to do the charts so as they were coming up with items, they could see if something did not fit. Towards the end of the fourth day, I had students do a gallery walk with a post-its to offer commentary – I told them to focus on something they saw differently than the creator and to check to see if they were accurate. There was enough time for students to adjust their creation before turning it in if there was a mistake (although, surprisingly, many of them left it rather than try to fix it). I think I would have given some other guidance before the gallery walk because I didn’t feel like they made helpful comments.

Here are some of my favorite WODBs (only – no charts).

It was a worthwhile activity. I thought they did a nice job looking for good choices and some of them really tried to make them a little challenging.

]]>Generally what happens is I start to think about who I am going to sit with sometime on Wednesday. Sometimes I touch base with a student who sits at the table (which is what I usually do with the group of sophomore boys I sit with sometimes), sometimes I just show up at the table. What I found is if I wander around without knowing who I want to sit with, I usually end up wandering around and it is harder for me to decide where to sit. Once I decide on where to sit, I ask the group of students if it’s okay if I sit with them. I haven’t been told no yet, which has been refreshing.

Once I get settled at the table, I try to listen to whatever the students are talking about. Sometimes they’ll continue whatever conversation was happening before I sat down. Sometimes they’ll ask me a question. But generally, I try to spend more time listening to them rather than talking. I try to ask questions of them to spur on the conversation. When lunch is about over and I am getting up to leave, I thank them for allowing me to “crash” their table.

Some general observations:

With being out of the classroom for a couple of months, going to the cafeteria and having lunch with the students has allowed me to stay connected with the students. I have really appreciated this and looked forward to Thursdays because of this. Thursday lunches have also made being out the classroom a little easier.

For a while, students were requesting to have me come to the their table. That was really cool and made me feel pretty good as well. It gets harder to remember who I’m supposed to have lunch with when I have a couple of requests, but fortunately, the students will remind me.

When I’m at lunch with the students, I try my best to ask questions that aren’t about math or my class. I want to hear about what’s going on in their lives and learn a little more about the students as people. I’ve learned that one of my students is learning to be a blacksmith, that another is an absolutely amazing writer, and yet another loves to cook. We just don’t have enough time during class to have these types of conversations. I love that I have gotten the opportunity to learn more about my students this way.

I feel like I am more connected to my students than in years past. Part of that may be that I have now had most of my Algebra 2 students for two years and I have had more time to develop relationships with them. I feel that part of it is due to going to the cafeteria for lunch and connecting with my students in a different way. I am really glad that I’ve done this and I think I will continue to do Thursday lunches in the future.

]]>Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

The learning target this time is:

I can describe the transformation(s) that changed a graph of f(x) by replacing with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). (LT20 for me)

I began with establishing the Parent Functions we were going to work with, as Rebekah Peterson had set up with her classes previously. We completed this in our interactive notebooks on the first day.

In the past, I would have done something like this to set up where the descriptions come from:

While this accomplished what I wanted (students had to explore how the rules were determined), it was rather time consuming. I had already kind of decided that I may not have students graph every piece by hand and then this gem of a post came from Julie Reulbach about an activity she put together in Desmos Activity Builder. (Go ahead and read it, I’ll wait while you do.) As I read it, I thought about the notes I had done in the past and was planning to do something with when I got there a month or so later. And Julie had already done it for me (without even knowing I needed it!)! YAY!

Yesterday, we did Julie’s Introduction to Transformations Marbleslides. It was my students’ second experience with Marbleslides and their first real experience with using Desmos Activity Builder in an instructional manner. My students were engaged with the activity. In one of my loudest classes, you could just about hear a pin drop as they begun the activity and worked through the first part on their own. WIN! For the most part, my students completed the notes that Julie had set up (and I adapted to fit in their interactive notebooks), although I did notice that some were caught up in working with Desmos and sometimes forgot to write down the notes.

Today was the day we were going to put it all together. Today was the day I had been thinking about and rethinking about over the last two weeks as I tried to best figure out how to help students put it together. I had started from some of Julie’s previous transformation activities which happened to come up when I read her post. Yesterday, as I was putting things together, it had dawned on me that I could use Desmos to create graphs that would be included in student notes so they would have a lasting record of how transformations work. I was pleased with that and went to bed pretty comfortable with how I set things up. I was still troubled with how I was going to explain the difference between horizontal and vertical dilations (compressions and stretches), but I had a basic idea of what I was going to do. The graphs were going to help.

As I explained how stretches and compressions worked, I used the graphs but I was physically illustrating pushing and pulling the graphs in the proper directions. That’s how it made sense in my head. About the third time through, I thought to myself that there has to be a way for Desmos to show this dynamically. And it does, with sliders. At the moment, the sliders go two ways and one way forward. I needed it to go one way backwards to show the horizontal stretches and the vertical compressions. Enter gifsmos. With a little bit of work, I got it to show what I wanted:

I was able to insert these into my notes and all I needed to add were arrows indicating the direction the stretching or compressing was happening. And, instead of me looking a little goofy showing the stretching and compressing, the graph and Desmos did most of the work, which was really neat.

(Update 12/7/2016:) Here is the blank PDF of my Smart Notebook file:

The next I see my classes are Thursday, so I will be sharing the gifsmos with the other three classes that didn’t get to see them. Hopefully that helps some more students.

What I what I truly appreciate about what Desmos has done is that it is has taken away what appears to students as the heavy lifting – the creating of the graphs. Students can focus on what is happening to the graphs rather than the act of determining the points and plotting them. Both of these can be rather time consuming and by the time students are done with this, I believe that they have lost focus on what is really the issue I want them to grapple with in this case, which is how the graphs change and the description of those changes. Julie took the ideas behind something I have previously done (and in all honesty, had not shared with her) and created a series of activities in Desmos’ Activity Builder that not only allowed students to explore how the graphs change, but then allowed them to try to create equations to show they understand how those changes appear in equations. What I had done on paper took most of 2 class days (50 minute periods). Julie’s activity took about 30-40 minutes in class to complete and was way more elegant and was definitely more effective.

I am so glad that I have taken the time to work with Desmos more in my Algebra 2 class this year. I think that it has helped enhance my students’ understanding of the material. I know I’ll continue to use Desmos in my classes this year.

]]>To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC17-1). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Thursday, July 27 and 48 one hour sessions that will be either Thursday, July 27, Friday, July 28, or Saturday, July 29). That means we are looking for somewhere around 70 sessions for TMC17.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is **January 16, 2017 at 11:59 pm Eastern time**. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Thank you for your interest!

Team TMC17 – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Daniel Forrester, Megan Hayes-Golding, Cortni Muir, Jami Packer, Sam Shah, and Glenn Waddell

]]>So, on one Thursday towards the end of October, I decided to go to the cafeteria and sit with the kids.

(No, this isn’t me or my students. But you get the idea.)

It was a little nerve-wracking at first. I didn’t know if I would find a table to sit at or students who were willing to share their lunch time with me. Fortunately, a couple of my students had an empty seat at their table and were very welcoming when I asked if I could sit at their table. We had nice conversation, some about class and some about other things going on. It was a pleasant lunch.

The next Thursday, I went back to the cafeteria and found a different table of students to sit with. This time, it was a small group of my sophomore boys. They had several seats open because a few of their friends were absent that day. While the conversation didn’t flow as easily, it was still a good way to spend lunch. So the following Thursday, I went back. This time I chose a group of my freshmen boys to sit with. One of the sophomore boys who was at the table I was at the previous week came to the table to ask why I wasn’t sitting with them. I explained I was trying to sit with different groups each time. I asked if he wanted me to come and sit with them next week, to which he said yes. It was kind of cute that the sophomore boys seemed to be a little jealous that I wasn’t sitting with them and that they wanted me to come and sit with them.

And then I heard about it most of the next week – that they were looking forward to sitting with me the following Thursday. The following Thursday, I sat with a (full) table of sophomore boys and had a very enjoyable lunch with them. We didn’t talk about classes very much and they did most of the talking, which was perfectly fine. They were behaved and gracious and I was glad I had lunch with them.

I have a new Thursday routine now. While I’m not sure who I’ll be sitting with on Thursday this week, I do know I’ll be in the lunchroom. It’s nice to see my students in a different atmosphere and to share conversation not related to math. I’m looking forward to it.

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