Group Quiz–Maiden Voyage

I’ll start with the goods…student and collegue comments:

This is great.
I could have never done this alone. (from an uber high level student)
Can we finish with the same people on Monday?
I feel really good about this.
I want to see this with your OpenUp students. This a great. (my principal)
Did you hear what they are saying? They are really talking math! (curriculum facilitator)
Telling them they can kick a kid out of the group if they are not part of the process is gold. (math coach)
Did you come up with this yourself? (sixth grade teachers that came to watch)

So here’s how this came about.

I was in math club this morning and we had a group competition where each team of 4 had two problems and 6 minutes in there rounds. (Modified @mathcounts target round combined with team round) With math club you need the time con-straight because you are preparing for competition. I stole the two questions per sheet idea, the score only one sheet, and the group collaboration. I added…use 1 calculator for the group if you need it, graph paper and patty paper are permitted as are compasses and protractors, sadly, no desmos. Students choose the tools though. Tools are in the room, but students need to get them. They are figuring out what tools they need. That’s a mathematical practice, you know.

I bought a book at a used book store last weekend called something like The Humongous Book of Geometry Problems (I left it at school soI don’t have the exact title.) I was attracted to it because it had problems as well as solutions. Thank you. I modified some problems from there and used some pretty much as given. I also used problems from the quiz bank I was recently turned onto by David Wees. Thank you.

So, each group got a pack with two problems per sheet. Each student had their own sheet plus a colored sheet that had to have the final solution on. Group stapled all work papers to the colored sheet and turned it in as which time they got another pack with two questions. I had a total of three packs for 6 questions. There was notice limit. Here’s a copy of the instructions posted for the class.

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Here’s a pic of the problem packs. I’ll attach the files if you want them. By the way, we are studying transformations.

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The students were more engaged than I have seen them all year. I know part of it is that these students are motivated by grades. That got them going since it was a quiz grade, but the learning and the sharing and the teaching one another is the goal. I hate grades, but these students will work for them. This quiz was actually getting them ready for their unit test as they taught and reviewed with one another.

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My last class ends at 3:50. This quiz had kids engaged at this level at 3:45 at the end of a week where they had county interim assessments for three days. IMG_2763

Her’s a montage of photos from the two classes.

At my principal’s request I am going to try this with my Math 8 students (they are using Open Up Resources). They are motivated in different ways than the groups I show here. I too am curious at the levels of learning and engagement I will get. I am hopeful.

Here’s the problems if you want them. group quiz transformations

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Opening Up about My Affair with Open Up Resources

I feel like a first-year teacher drinking from a fire hose. A couple days before school started, we were offered the opportunity to pilot the Open Up curriculum in our county for mathematics in grades 6 through 8. Because I had taught math 8 with zero resources for the past 12 years, other than what I harvested or created myself, I jumped at the opportunity.

There are many things I love about the Open Up Curriculum.

  • I love that I have to be more organized, focused and deliberate.
  • I love that I learn and see math differently each and every day.
  • I love the warm-up and learning routines and structures.
  • I love trying new things.
  • I love that the materials are already prepared.
  • I love that my kids are challenged and then they still have second chances if they don’t get something the first time around.
  • I love that they finally respect my kids and me enough to develop some real resources.

Struggles:

I cannot get ahead. I barely keep up. Each day I rush to get ready for the next. I prepare a PowerPoint to keep the class and me on topic. I snip screen shots into a PPT and prepare Student Task Sheets using what Open Up provides. Problem is, I frequently have to heavily edit so the information fits nicely onto a printable document. Mastering Textboxes has helped enormously in this area. I am saving all of these edited documents, so hopefully next year will be better. If that holds true, it will be the first year I have ever used what I made the year before. I have always created everything new each year in response to what my kids need.

I know that Open Up is integrated with OneNote and I even spent a couple hours being trained on how to do that. On my own, I cannot for the life of me figure it out though. I have to get ready for the next day. I don’t have time for trial and error where it is mostly error. I want to learn how to do all of that, but I also must be ready for the next day. I cannot sacrifice my kids for my learning curve. I also know there are Google slides for many of the lessons, but I have no idea where those are. I had them in the last unit, but can’t find the link now. There’s just too damn much to keep track of. I have to use what I know I can pull off now. I must survive.

Adjustments:

I am working on pacing myself and my class based on the recommended time estimates for each activity. I have a hard time not getting each and every comment and contribution out of students before I move on, but a timer is helping me. I hate leaving a kid unheard, but we need to move.

Many kids are used to waiting you out. They will copy what you do, but they will not venture out on their own. I am now waiting many of them out, but I can’t wait them all out. There just isn’t time. I love mistakes that kids learn from, but too many won’t even try until the bitter end. Working in extra supports and re-teaching is tough. Where? When? With what?

I struggle with formal assessment as well. I hate grades and love learning. Unfortunately, we are required to take a minimum number of grades a quarter. On what? There are only end of unit formal assessments, but that is not enough. There are no quizzes. I collect daily work and cool downs periodically, but are they really formal assessments or are they just part of the learning process? I started the year doing my own quick quizzes, but have gotten away from that. I need to get back to that. Now.

The formal assessments created by Open Up are really great, but they are a bear to evaluate. If we were doing standards based grading, I could see where this type of assessment would be really helpful. We are not though, so making the grey into black and white is a challenge for sure.

 Misconceptions about conceptual understanding:

For years I was told to dig deeper to get students to better understand. Problem was, nobody showed me what that meant. I was left to my own devices. I thought I was doing that when I insisted students understand why certain math algorithms worked. Turns out, I missed the mark. I am finally starting to understand what conceptual understanding means. If somebody was writing about it, I wasn’t reading it. Open Up Resources is actually showing me what it means to have/get/show/teach conceptual understanding of mathematics topics.

What I worry about now, is what my NC Math 2 kids are missing along the lines of conceptual understanding. These are the kids who have done well so far because they have been able to get away with memorizing stacks of mathematical algorithms. My only evidence that I am actually teaching for understanding in Math 2 is that I have a few kids that have historically gotten all As now struggle to get Bs because they do not truly understand what they are doing. I digress. This is about my experience with Math 8, Open Up Resources. I long to crack this conceptual understanding nut though.

I confess, I tell my Math 2 kids everyday how excited I am about what I just learned in Math 8. The ones that truly listen to what I am saying are very curious and want to know more. How I wish I could teach them this Math 8 goodness as well. I know next year I will work much of this into the Math 2 warm-ups. I do a bit know, but not like I wish I could.

Sharing:

I want to share with others, but I am slow. I know I should put all my stuff on Google Slides and share that way, but I haven’t learned all of that yet either. I need help figuring out how to efficiently share my stuff. I am re-creating all this and I am not sharing. That’s not who I am. I need help figuring out how to do that without spending an additional thirty minutes a day. My biggest problem is that I stink at asking for help. I will do anything for anybody, but I am not good at asking for help for myself. I’m getting better, but I still have a long way to go.

Goals: (These are actually wishes because I do not have actionable steps for them—yet.)

  • Create a Desmos activity of each lesson. I experimented with a cool down, but I want more. I think the tasks could be adapted pretty easily in Desmos.
  • Figure out how to use the parent resources created by Open Up. I am not even sure how to show parents that they are available. What I print stinks, so there must be a better way.
  • Figure out how to get students to utilize the reflection piece created by Open Up. That looks pretty deep and by deep I mean valuable.
  • Design a notebook or filing system for students to organize work papers so resources are available for review.
  • Figure out how to work training into my schedule. I teach Math 2 second and last periods. Math 8 is first and third. Trainings are half days. This takes me out of half of each of my classes. We have a dozen cross-teamed kids so adjusting the schedule is not practical.
  • I want to find or develop a group of learning tasks that show kids that their efforts matter even if they don’t get to the end. Too much of math is about the end and we need to start to praise and celebrate the middle because that is where the learning happens. I think this will help that perseverance piece a great deal.

Closing:

I hope I don’t sound like Debbie Downer. I am really digging this curriculum. I even showed my pharmacist brother-in-law how cool it was over Thanks Giving. He said, “I don’t fully understand, but I can see how it would be exciting for a math teacher.” Now, granted, he is above average intelligence. The point is he appreciated what Open Up is trying to do for kids’ understanding. He also enjoyed how excited I was about it.

Completing the square completes me

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My favorite topic to teach is completing the square. Weird, right? I just love it. I start by having kids solve radical expressions. I say “what cha gonna do?” and then say “square both sides!” We then move to solving equations where we need to square root both sides and I catch them in the chant! “what cha gonna do?” “Square both sides.” Really? Then they think. And then they think some more. “Oooo,” they say. X squared = plus or minus the square root of x. Major deal of course. So now the chant becomes, “what cha gonna do?’ and they say, “square root both sides.” Many forget the plus and minus no matter how many we do it. I do this before solving quadratics, which may be unconventional, but it works.

We solve equations with a squared term, a linear term and a constant or two and we discover how to complete the square in order to be able to take the square root of both side after some massaging. It’s awesome. It’s magical. It has absolutely nothing to do with quadratics as far as students know. We are merely balancing equations.

Then we do go into quadratics. There is always some smart alec that wants to dive into the quadratic formula. I hate this, but soldier on. They may NOT use the quadratic formula until they can prove it. End of story. We go into vertex form of a quadratic. They dig the structure and can assemble the vertex form of a quadric if they know the vertex and the multiplier. We then look at discovering coming up with a quadratic equation with far less information. We know the structure of vertex form because that is taught in Math 1 (supposedly). Of course the structure is re-taught. But, now we have a reason for knowing how to complete the square. Yeah! It’s so similar to coming up with the slope intercept form of a linear equation. Plug in what you know (what you are given) and chug away. That there must be a perfect square trinomial to make the square root of both side s of the equation is the secret weapon. All must balance. No illegal moves. Taking the multiplier into consideration is a challenge, but we get there.

Because I introduce completing the square multiple times and early, it sticks by the time we prove the quadratic formula. It gets revisited when we do geometry and prove the Pythagorean theorem. The sparks and light bulbs that go off are so fun!

I tell my kids when we first complete the square that this is a skill that could make them a hero some day. When I first started teaching algebra 7 years ago, my daughter was in a college chemistry class. Her class had a problem that looked unsolvable until a student suggested that they complete the square. That student was a hero. I tell my students that some day they too can be a hero with completing the square. They are instructed to notify me the day this happens. Sadly, no notifications so far.

I think that success in teaching completing the square comes from students being exposed to it over a period of time, even before they really need it. If you wait until they need it, the mind is too clogged with other ways to solve quadratics. I tell my kids, too frequently solving a quadratic via the quadratic formula is like taking a barge down a river. Completing the square is a kayak. Have fun! Use it. Be a hero!

 

Making It Real

So, I went TMC16 and for whatever reason, I kept running into Denis Sheeran @MathDenisNJ. It was almost annoying. For both of us. I did get his book Instant Relevance https://www.amazon.com/Denis-Sheeran/e/B01JAWZQIE this fall and he told me he would love to hear what I think. So here it goes.

When I ordered the book, I thought, “crap that’s a lot of money at this time of year.” See, I just set up my classroom. Then the mail came and I thought, “Are you kidding me? This is the shortest book since Jonathan Livingston Seagull!”

So now I think this. ALL BOOKS THAT ARE MEANT TO HELP TEACHERS BE BETTER SHOULD BE THIS LENGTH!! I am so serious. I’m beat at night. I can’t do much more than 5 pages. I want to learn more and become a better me. I really do. But some books are so boring and so long and I have the attention span of a gnat. I teach middle school for crying out loud.

So, thank you Denis. I never felt bad or distracted or loserish as I read your book. And this happened.

I took pictures. I had a bag if rolled up coins in the mud room that have never made their way to the bank. I wondered what I was missing out on so I figured my kids could help me.

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I showed them a pic of the sac of coins. They guessed high and low. Then the best thing ever happened. One girl who I just moved from math 8 to math 1 (thank you county for being so great at giving us quality tools to place kids properly when they move in—sarcasm intended) said, “hey that’s like one of these things we’re working on. Can I show you?” She walks up to the board and does this.

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I am blown away. I should be smart enough to see all the connections, but I don’t. I need my students to do that. I love this gal. I love my job.

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My 1st class, math 8, worked as a class to figure out how much $ there was. I introduced the problem to my math 1 kids (periods 2 & 3) and then they pursued it to the end in small groups after they finished another task in class. They totally dug it.

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Math 2 kids are a bit harder to impress, but they finished the entire task as an opener as I progressed through fotes.

All of this is just my way of saying, thanks Denis. It works. I get it. I dig it. I’m doing it.

Practicing on real kids!

You have to love a PD where you get to watch other teachers as they hone their craft as well as get to practice yourself…on REAL live kids!!! The kids were on fire as they made models of houses. I wanted to take one home, but I didn’t. (I mean a kid, not their house. The house was swell and all, but talking with these kids was a treat!)

This set-up the need for area and scale and unit conversion in order to make cost estimates of building materials.

The problem created the need for the content. The content did not set the stage for some hokey, convoluted, boring application.

Kind of getting excited for Aug 29!!!

Oh linear functions–please don’t be boring!

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This month I was going to change the world, or at least change the climate in my 2 math 8 classes. It’s been miserable lately. I took responsibility for that and decided to make major changes in class as the second semester began. I changed the daily organization, the look of the room and most importantly, the lessons. Of course, I wanted everything to become perfect all at once, but that didn’t happen. Here’s how change began lesson-wise.

Two weeks ago I started by using a hundreds board and chips to revisit linear equations. We looked for patterns using 5 transparent plastic chips placed in the shape of a plus sign on the numbers on a hundreds board. We added the numbers under the chips; we looked at how we could get the greatest sum in a given pattern, the smallest sum, etc. We moved the plus sign around. We added by decomposing numbers. It was good.

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(I modified an old Illuminations lesson that I found in an old notebook and I forgot it at school. Sorry. I’ll copy and edit into here Monday or so.) The lesson was good. I was happier, the kids were happier. Students were noticing patterns. We made a table of ordered pairs by using the middle number in the plus sign as the input and the sum of all five squares as the output. Students graphed individually. Then I gave each student a smiley face sticker to place on a big graph locating one of the ordered pairs they found. The goal was for students to see that even though they each did the activity alone, their points all made a pattern that graphed as a straight line. Since some of the points weren’t too close to the straight line, we also were able to notice parts of a pattern that don’t come out the way we expect. This was a time for self-correction. By giving each student the exact same type sticker, there was no way to single out a particular kid as being the one who didn’t get it. This activity allowed us to work with linear equations –again– without the students realizing it.

The next day we extended the 100s board activity onto a calendar. We did some calendar math using four by four grids. We saw patterns in diagonal sums, four corner sums, and center four sums. This was then extended to the abstract as I had students choose any day in the four by four region to be n. All other days were then defined in terms of that n by adding or subtracting.

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(My students struggle with turning concrete math into abstract math so this was a good exercise.) Sums were then found again. Setting these sums equal to one another or setting a sum equal to the original concrete sum yielded the original date on which the n was placed. I preferred this to choosing the first box as n and simply adding to get subsequent dates in terms of n. Students who persevered were delighted when the solved equation yielded the original n value. It was cool that n was different for various students, but n stilled tied to the original n-date the student picked. That was much more fun when n wasn’t 1! When the students would each get their respective n values, I said to them individually, “where have you seen that number before?” Their eyes lit up when they realized it was their original n value. Any opportunity to link the concrete to the abstract is a win.

Students then worked with squares with only one number and completed the rest of the squares relative to the given square’s value according to patterns that would occur on a calendar.Screenshot 2016-02-06 16.32.17

For the final assessment activity, I had the students solve missing squares for a calendar that was from the fictional planet Crayon…they only have 5 days in a week on Crayon! (I didn’t even steal that part from anywhere, btw!)

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That was probably the best two consecutive days if school so far this year in math 8.

I have tear-stained pages of lessons that I tried this week using geo boards to create linear equations and simple systems of equations. That seemed like a great idea. I extended that to equations with one solution, no solution, and infinitely many solutions. The students weren’t nearly as impressed as I was, so I’ll try to polish that up and post geo board-graphing at a later date.