I was clued in to the existence of The Story of 1 a couple of weeks ago from my twitter PLN. I had my sub show it to my algebra 1 classes when I was out of town, and it seemed to go well. Then, one of my colleagues was sick this week and did the same lesson. Her sub said that the students were really engaged with the movie. I couldn't find a question guide on-line for it (though I didn't search all that long), so I made one up.
Here is a puzzle activity for reviewing equation solving. I found that it worked better when I made an answer mat for students to put their pieces onto (I indicated a couple of pieces on the mat to help them align the rest of their pieces).
In the last couple of years, I've worked to really clarify exactly what skills I expect my students to learn. The assessment system makes it crystal clear what skills students know and don't know. And then I realized: Oh wait - it's only crystal clear to me. Students focus on their test scores, and come in to retake and improve tests, but they really don't think about what mathematical content they need to develop - only what test number they need to retake. I still have a few students who insist on retaking skills tests even though they haven't done any work to learn the skills that they got wrong the first time. Even when this fails to produce the results they want, they still resist actually working with me to learn the skill.
I think that helping students really understand what the individual skills consist of, and what their personal ability level is on each skill, is really the next step. I want students to understand the connection between their level of numeracy and their success in mastering algebraic concepts. I also want students to make connections between their behaviors in class and their growth (or lack of growth) in the lesson's objectives. Finally, I want to provide students with greater differentiation so that all students can both feel challenged and successful.
So, I put all of that together into a new plan for beginning and ending class. Students will start class with a 10 minute Do Now that has three parts. Part 1 is a Numeracy Skill Builder that targets a specific elementary math concept that is either key to the specific lesson, or something that students have been struggling with. Part 2 consists of one or two algebra concepts that are the lesson objectives. These are broken into basic, proficient, and advanced levels. The proficient level is the form in which the concept will be tested on a skills test. Students are told to solve only one problem in each concept, at the level they feel most comfortable at. Part 3 is a multiple choice test prep question. The purpose of this is obvious, as we need to get students ready for state tests, ACTs, placement tests, and so on.
Students have 10 minutes to complete these problems individually and silently. No helping is permitted here (in general), because the purpose is for students to really get a sense of what they know at the beginning of class on their own. At the end of the 10 minutes, I show the answers so students can see how they did, but we don't spend time actually reviewing these specific problems. I quickly collect the papers.
We have the lesson. Ok.
Now, in the last 5 - 7 minutes, I hand back the papers. On the back, students complete the Exit Slip / Reflection. They are supposed to go back to the Do Now problems, pick one algebra concept, and try a higher level problem. The idea is for them to see how much they can improve in an objective over the course of the class period. So, even if they are only able to accomplish the basic level (when they couldn't before), they can see growth in themselves and feel good about that. Students who already could do the advanced concepts at the beginning of the class have a shot at doing a harder challenge problem, so that they too can push their thinking (my advanced students really like this).
I just started doing this today, so I don't have too much to report about it yet. It seems to have gone well, though it took longer than the 10 minutes because I needed to explain the process a few times until they all got what I was talking about. As it becomes part of the routine, I'll know more about what impact it is really having.
Here is the first one we did, in pdf and word formats.
I'd love to get any feedback on any part of this.
Edit
We decided to make the reflection portion into a progress tracker, instead of copying it individually on the back of each Do Now. This log will be kept in a binder in the class. This will allow students to see how they did in previous classes as they are filling out the current reflection. It will also be a very useful document for discussions during grade conferences.
I made a review lesson for my Algebra 2 students on these topics, to make sure they are really ready before we start performing operations on complex numbers.
Some instruction, some board races, and there you go. Hope you like it.
Lesson
Keynote
Quicktime
I also updated my Algebra 1 box with unit 2 files and the first four lessons of unit 3.
I am beginning the planning stages of our unit on solving equations in Algebra 1. In my past experiences, some students pick this up very quickly, no matter how you teach it, while other students struggle mightily. I want to try some alternate approaches this year, to really reach those students who have not been able to learn this skill in the past. I remembered an order of operations approach that I read about in the NCTM magazine a few years back. I can't recall the name of the article, but a little google searching found me this document that is even better than what I remembered.
Our students in Numeracy already work with bar modeling to solve word problems, so this seems like a natural extension to solving equations. I like this approach because it helps focus on the idea that the variable is a given quantity that must be determined, instead of focusing on the steps that isolate the variable. It also might help with those difficult to master "converting verbal sentences to algebraic equations" problems. Here are a few examples of how this might look. I know the diagrams are a bit confusing at first, but I think they would make more sense to students as they watch them get created and do them by themselves.
I also like the other representation discussed in the article. This is the original order of operations process that I had been searching for. I like this because it gives a very clear framework for solving equations - reversing the order of operations.
When you look at each stage, you can draw equal signs between the boxes. These would be equivalent to the intermediate statements in the traditional "do the same thing to both sides" approach.
So for the unit, I am thinking that we would spend two or three lessons on bar models to build the concept of what we are actually trying to do (find the value of the unknown amount). Then, spend a couple lessons on the order of operations representation to build an understanding of the process for isolating the variable. Finally, transition to the traditional approach, which is clearly the fastest and cleanest way to solve an equation of the three. This would take more time, of course, but the hope is that it would build a more enduring understanding.
Has anyone tried these methods with their students?
Edit:
I wonder now if it would make more sense to start in with modeling sentence/word problems with the bar model method, and not start by saying that we are "solving equations". That way, more students would be engaged with the material, and we could eventually use the bar models to develop the equations.
This way, the unit doesn't start with the problem "solve (3/5)x = 45", which will stop most kids dead in their tracks, but maybe with something like "It took Sandra 45 minutes to finish 3/5 of her homework. How long will it take her to finish it all?", which kids might have more of an entry to. After we solve it, we can then discuss how to represent it as an equation.
Edit 2:
I also need to think about how to incorporate the balance idea and preserving equality... Kids don't always know what the equal sign really means. Maybe in the transition time from the box method to the traditional method?
Edit 3:
(Written on 10/27 - at the end of the unit)
On reflection, the problem was not having enough time to really devote to the two alternative methods. Both did show a lot of promise, but we weren't able to really practice either enough for it to really stick with students. The bar model method really worked to help students set up and solve word problems, so I think I will stick with that next year. Give it some more time so that it really sinks in and can be used to get a deeper understanding of fractional coefficients. I will probably save the GERMDAS method for individual tutoring with students who are not having success with the traditional balance method. Less fights... more differentiation.
All of these lessons have been added to the box widget on the left.
My goal for this weekend was to complete a rough draft of all the skill items that will be assessed on the first semester final exam. These items are assessed in chunks on the weekly skills tests, and in larger chunks on the 6-week benchmark exams. After each benchmark exam, the plan is to spend a lesson or two on targeted reteaching - any ideas that people have on how to make this effective would be very much appreciated.
I've finished the list, and am interested to hear what other Algebra 1 teachers think about the scope and detail of the items. What would you add? Take away?
This student finished all of the simplifying expression problems on paper (correctly), and then used the algeblocks for the following:
But can I blame him? Why would a student who can already do a procedure well bother trying to figure out a slower, less portable method?
But then, the students around him who really do need to use manipulatives to help them understand the difference between 2x and x^2 don't want to use the blocks either. They feel stupid and they want to do it the faster way too.
This seems impossible without fully differentiating instruction in the classroom. Which also seems, you know, impossible.
We have our Numeracy class, in which students spend time working on ALEKS. The Numeracy teacher this year is doing small group pull-out during that time to work on specific skill building. I am starting to think we should use the manipulatives in that setting only.
I've resisted it until now, but it seems like a lot of good stuff is happening in the twitter world. No point in shutting myself out.
My algebra 2 students needed more practice solving equations with rational exponents. I was trying to think of an interesting and yet still effective way for them to keep practicing, and then I thought about how the errors they make tend to be the same again and again. That reminded me that I hadn't done an error analysis activity in a long time - and just like that, the lesson was created. I assigned each table pair one problem, where they had to find the mistake, explain it, and do the work correctly. Then each pair was called to present their findings to the class; the class then worked out the problem and if they all agreed that they had found the correct solution, I allowed them to move on.
Students were generally good at finding the mistakes I had made. Will this activity help keep them from making the same mistakes in the future? We'll find out next week.
Here are the twelve problems plus homework.
Ok, so it was more than a month. But at least I'm finally writing again. I don't think I will be able to post about every lesson like I did last year, but I am still going to put my files in the box.net account for you all to look at, use, critique, etc. This year, I am reworking our Algebra 1 curriculum, so I'll be trying some new things, and hopefully be getting lots of ideas from all you other teacher bloggers. If you are reading this, and you are not blogging your ideas or posting your work online, I highly encourage you to give it a go. You will get a lot out of it, and you'll give a lot to the community.
We just finished our first unit on evaluating expressions, including order of operations and working with square roots. Up next will be simplifying expressions, and we're going to be using Algeblocks to model combining like terms and the distributive property.
I'm going out of town for a few weeks, and with any luck, I won't be thinking about school. Posting for the new school year will start up again probably at the end of July or beginning of August. I'll be teaching Algebra 1 and Algebra 2, and will be redeveloping lots of Algebra 1 materials and posting them like I've done with Algebra 2 this past year. So come back and have a look around - I'll be looking forward to your critiques and comments.
I finally got around to posting my old Numeracy curriculum on my box. This is by no means a final draft of what I think our 9th grade basic math support class should look like, but it is where I left it last year. I didn't decide to start using Keynote presentations until the third unit, so that's why there aren't any Keynote files in the first couple of units. This year, I am not teaching this class, so I haven't had the opportunity to keep developing these lessons. I'm sure I will get around to reworking this stuff at some point. For now, I'll throw it out there for people to look at, borrow, critique, steal, and so forth. I hope someone finds it helpful.
We are nearing the end of the quadratics unit, which got chopped up by the STAR test and all the associated hoopla. I don't have too much to say about it right now, except that I think it needs a good deal of revision for next year. Feel free to peruse and comment. Lesson 5 is missing because that was just a midterm review day.
Instead of linking all of the files individually, here is the folder:
I've also updated the skills tests from units 5 - 7 in the Box.
When we get back to school next week, we have a week of classes, and then we have the STAR tests. Instead of trying to jam in a few more concepts, we're just going to review what we've already learned, in game form. I've got "Who wants to be a millionaire?", "Tic Tac Toe Battle Royale", and "Big-L Bingo" ready to go, as well as a triage lesson (when you look at a problem, should you Guess it? Try it? Kill it?) I hope that this will yield an overall positive result. And when the test is complete, my students won't have to see another multiple choice question for the rest of the year.
I haven't had much energy lately to post, but I've still been updating my box.net account. We ended unit 5 with polynomial division and we are starting unit 6 (quadratics) with completing the square. We are having our midterm before break this Friday. Over break, I'll post in more detail about some of the recent lessons. For now, feel free to download stuff from the box widget on my blog. As always, feedback on what you find there is much appreciated.
I'm not planning our Algebra 1 classes this year, so I have not been producing much for it. But I did put together a scaffolded introduction to inequalities. The objectives are for students to:
