Start a Lesson With a Question

Whenever possible I try to start any lesson with a question to lead into what we are learning that day. This is a real shift from when I started teaching in the 80s - teaching training then focused on "tell tell tell" while students listened. Being the kind of learner that needs to understand I was never a big fan of that and figured out how to make questioning a bigger focus of my teaching. Marilyn Burns was a great mentor for this and I used her book

Collection of Math Lessons, A: Grades 6-8  a great deal when I taught middle school.

Anyhow back to this blog post...Here I am focusing on the 3rd week of the MTSoB blogging initiative

So to repeat myself - Whenever possible I try to start any lesson with a question.

Algebra One last week we were starting systems of equations. I knew that students had dabbled in this in 8th grade - they had solved systems of equations using graphing and perhaps had been exposed to some algebraic methods. But did they really know what a system was? I love really knowing what certain math concepts ARE and what they are good for (not always real life applications, just how they interconnect with other things I know about math), It's really the only way I can learn math. 

So I started class with this question..

What are some mathematical models that we can use to solve problems?

Students came up with great responses (almost like there were cue cards or something) - Graphs, Tables, Equations.  Yay! But this wasn't really the question to lead the lesson, this was the warm up. Next I asked them

 You have a bunch of quarters and dimes. 

The value of your coins is $3.00. 

How many of each coin do you have?

My students sit in small groups so I let them work on that. They gathered up some graph paper and made beautiful linear graphs of this situation with a lovely equation to accompany it. We talked about whether this graph was continuous or discrete and whether we would consider values in all four quadrants. Also with some prodding they came up with a table showing the possible solutions. Great work!

Then I told them that this question presented them with a situation that had two unknowns (number of quarters & number of dimes) and one condition that established a relationship between the unknowns. It resulted in a number of possible solutions. What if I gave them another condition to partner with this information?

 What if the number of dimes is two more than the number of quarters?

Then students worked on narrowing things down with this condition. They added on to the models they already created (another line on the graph, another equation for that condition). They found that this second condition resulted in a unique solution. Cool.

These initial questions allowed us to explore situations with two unknowns and two conditions that would have a unique solution. From here we could define systems of equations (after we did a few more examples) and keep in mind that is what drives a system of equations in two variables. Two unknowns and Two conditions. 

I put all our questions on a powerpoint. I also have a homework sheet to accompany this. We created a cool foldable for our notebook of an example (this was used the next class block as our warm up).  All supporting materials can be found at this link.

Here's the foldable I used with my students to illustrate these models. It's a cool "4 square fold" that my student teacher found last year (thanks Tess!). So it allows you to get a lot of information down in once place.

Here is the front all folded up into 4s (see how it folds up to use only half the page?):

Open it once and you get two places to have information:

Completely open it up and there are 4 places to have information:

Graphing Calculator Pictures - PreCalculus Project

Many teachers in our department had projects in their math classes long before the common core curriculum had us having students do performance tasks. I hate grading projects but love having students do them because they show me that they can really apply what they have learned to something interesting and different from what we are able to do in class. I've taught PreCalculus (honors level) for about 10 years and this particular project is sort of like the pinnacle of all the projects I have students do. It's absolutely amazing what students are able to create on their graphing calculator.

So what's this incredible project? Students draw a picture on their graphing calculator using functions they've learned and restricting the domains (essentially creating piecewise functions on their calculators).  By the time students are in PreCalculus they have learned all the basic parent functions. By December we've reviewed all those types (& have just started graphing sine, cosine & tangent) and reviewed transformations. The bare minimum requirement of this project is to use 10 equations and three function types. As you'll see in my rubric the minimum only results in a maximum grade of a C. I tell students they should aim for about 40 equations. And they should realize and plan for the fact that this project can take anywhere from 8 to 20 hours. And that the "write up" can take 2 hours on its own. My students are terrible at time management, waiting until the last minute to do most things. That will not work with this project. It takes a lot of time and most students have to have me transfer their images from their calculator to the computer with my trusty old graph link (although they can do it themselves with the cord that comes with the new calculators and some software from TI).

So I had the idea to have students do this while sitting in a really boring professional development worksheet many years ago (like 10 years ago) so started playing around  on my graphing calculator and came up with Bob the Dog:

I was pretty proud of myself, but of course after 10 years of seeing fantastic pictures done by students this is not a really a great picture. Oh well. I am so impressed by what students have done and it's time to share in a blog post.

At this point, everyone knows this project is coming up in PreCalculus. So in early December I get them started. I tell them to find a horizontal image they would like to draw. They need to print out this image in the size of 7.5 inches by 5 inches.  And I show them this fish as an example:

I give students a few days to come in with a picture and then we spend about 30 minutes going over how to start the project. I did my "Bob The Dog" freehand without this step but students prefer to have a starting point and this is a great way to get started visualizing how to transfer an image to a coordinate plane and then their calculator. They trace their image onto graph paper that has a [-15,15] by [-10.10] "window". This will match the square window they will use on their calculator [ZOOM] 5:ZSquare.

From there they look at the image and work with a major shape part of it (like the top of the fish) and consider what functions they would use to create those lines. I remind them of the general transformation form of any function y = a (x - h) + k and of the many parent functions they've studied in Algebra 2 and PreCalculus. 

     

We don't devote any full class blocks to working on this and we still have regular lessons going on. I do give them the day before Christmas break to work on it in class. And I am available to help after school. Some students do this entirely on their own, some need 10 minutes of help getting started, some need an hour of one-to-one help to get started. But everyone comes up with a cool picture!

Students also have to do a write up of their work. This is time consuming too! But they do a great job. I've included files below that have the rubric and project info, tips for the project, a sample student write up and a powerpoint of images submitted by students over the years (oh about 50 or so slides).

            

They are not that difficult to grade. I've gotten the rubric down to a very quantitatively calculated grade with only one piece that can vary according to "creativity".

After they are all collected and graded I print out everyone's final pictures and create a graphing calculator gallery in the hallway for the school to enjoy. I invite school officials, the superintendent and the members of the board of education to stop by and see the gallery. It really is impressive.

        

Probably the best part of this project is how much students like it. They all say it takes a lot of time but they learned a lot and really enjoyed working on it!  Yay, success!

      

Go to all documents related to this project HERE. 

            

            

My Favorite

Welcome to week 2 of the blogging initiative!  The week two blogging challenge is to simply blog about one of our favorite things.  Called a “My Favorite,” it can be something that makes teaching a specific math topic work really well.  It can be anything in teaching that you love!  It can also be something that you have blogged or tweeted about before. OK sounds great!

I've been teaching for many years and over the years there have been many favorite things. I especially love working with teenagers (most of the time) and love teaching math (especially when we delve into the "why" of things). So I'll try to keep my favorite list short but I can't just write one thing....

One of the best parts of teaching is seeing how students think and how they break down a problem/concept. I've always worked hard at asking open ended questions a lot and asking why a lot in class. This is just an every day favorite thing for me about teaching math. It can be hard work holding back and not explaining things to students, certainly if they get stuck i give hints or suggestions on some path they can try. It's something I've always done and in the early years got some resistance from other teachers. So I love that all the latest common core math practice standards naturally promote this type of teaching.  Yay!

And my new favorite thing has a few sub-topics (will try to keep this short). I LOVE using interactive student notebooks (ISN) in my classes! I don't use them to "drive" my lessons. Instead they are used to summarize topics after we've explored and figured things out. We no longer have a textbook in my Algebra classes (waiting to see what becomes available for the new common core curriculum) so these are invaluable reference tools for students. My PreCalculus students do have a textbook but the ISN is still a great supplementary resource for them. It also appeals to my creative side. And to my student's creative sides. I don't get too fancy with foldables, just creative enough.

Managing the ISN in my lessons is made so much easier by a few things that are also FAVORITES:

Document Camera - great for displaying what we are filling in. Most of our teachers do not have one so I had to beg to get this and it's only on loan from our school library. They are so wonderful about doing this for me.

Supply Baskets - any supplies we might need (scissors, colored pens, highlighters, tape) I have at the ready for students in little baskets.

Group seating in my classroom - so each group gets a basket of supplies with one student in each group grabbing what they need for the day. This group seating is also great in encouraging students discourse in exploring new topics and problem solving.

GLUE SPONGES - a neat, permanent way to glue in any foldables we use in our ISN. I blogged about them here in this post.

I've blogged a bunch about using the ISN in my classroom and a lot of my posts on certain topics show how the ISN supplements the lesson. I just started blogging in June 2015, here is my first post that highlights my use of interactive student notebooks.

A Day in My Life as a Teacher

Week 1 of the 2016 Blogging Initiative!

We often get caught up in our day teaching, and often don’t take the time to be in the present. So we have two options that with that goal in mind. Choose whichever floats your boat and blog about it!

Option 1: We rarely take the time to stop and smell the roses. Even on the most disastrous of days, good things happen. And these good things, when you’re on the lookout for them, pop up. All. The. Time. So for one day (heck, do it for many days), keep a lookout for the small good moments during your day and blog about them. We bet that by keeping an eye out for the good, your whole day will be even better!

Option 2: A few years ago, some people in the #MTBoS wanted to share what their teaching lives were like. Partly because we all work in different schools, and so we wanted to get a glimpse of our friends-in-action. At the same time, we also wanted to battle against the idea that teaching is easy. We wanted to share what it is like to be a teacher with non-teachers! So we all blogged about a single day of teaching — from start to finish. So for the first week of the blogging initiative, we thought you blogging about a day in your lives would be a great way to start getting to know each other!

Okay a blog post all about a day in the life of a math teacher - how exciting! (LOL). Certainly easy to write as I've lived it. So yesterday January 11, 2016. 

5:20 AM Phone alarm goes off (I've got to find new wake up music - this is sooo annoying). No snooze for me, this is the latest I can sleep....

5:25 - 6:40 Shower, get dressed, feed the cat, make my morning smoothie (today it's a healthy caramel apple smoothie) & assemble my lunch and then head to school.

6:50 Arrive at school - check my mailbox and head up to the third floor to my classroom.

7:00 Students start arriving, one in particular from my Applied Algebra class for extra help on what he missed last class (others are there for my first block class with quick questions about the test they'll be taking once class starts). 

7:33 to 8:55 -  First block - PreCalculus.  We're having a test on unit 3 "Circular Functions". After the test students are working on mid-term exam review (they have an outline of topics with suggested review problems in their textbook) and their graphing calculator design project (which I promise I'll be blogging about soon - such a GREAT project). While students take their tests I correct their study guides (mostly just for completion but some perusal for correctness).  After the test I walk around and give assistance on projects. One student is making the slinky dog from toy story and needed help with the functions for the feet. 

She decided to use log functions and I was helping her with the transformations to get them in the right position in her image (she had already established the stretches and reflections needed but couldn't get the shifts exactly as she wanted). I will include her final result in my pending blog post about this project.

9:05 to 10:29 Second block class - Algebra One. This class also has an assessment. Unit 5 end of unit quiz. It's a short unit, only one week. Focus is on creating scatter plots and trend lines (by hand & using graphing calculator) and analyzing the results (linear regression, interpolation, extrapolation, correlation, causation?, outliers & influential observations). We go over the homework first (basically I check to see if there are questions - I post the homework answers on my website so I don't have to read all the answers. Students have to check their answers but only about 1/3 of the class did). After the assessment students work on their midterm exam packet and I start to answer questions. We got through a little review of unit 1 (sequences) and students told me things they had questions on so I could prepare some problems for next class. Exams are coming up this Thursday.

10:35 to 11:03 I actually went to lunch with the math department today! I usually only make it about once a week but things are a little lighter this week with exams coming up (no lessons to really prepare until classes start again on January 21). The big talk in lunch was about powerball lotto - the jackpot is huge this Wednesday, over a billion $! So of course everyone is buying tickets and/or contributing to a pool. I wish I had time to go to lunch more often but often use that half hour to get a few things done (use bathroom, run copies, clean up classroom and set up for next class on A days). So today was a treat to hang out and talk with grown-ups.

11:08 to 12:20 This block is my prep block for the day. A nice long prep I know. I usually devote my prep to parent communication & planning. We don't have textbooks for Algebra & Geometry at this points so we are creating materials for our classes. Since I've been teaching my Algebra Ones for a few years I have a lot of materials created but I'm always tweaking them. I save all my correcting for outside of school (at home in evenings or weekends). Today I had to do some exam modification work for my Applied Algebra class. It's a small class but 12 out of the 14 students have an IEP (individualized education plan) that calls for a variety of modifications. In general I create all the materials for the class so that the modifications are covered and everyone gets them. But then I have to create packets for the "exam proctors" - most of the students start/take the exam in an alternative setting. So I organized that. And finished sending out exam materials to my math department coordinator. And gathered data on my latest assessments in Algebra One (unit 4 test and performance task) for my coordinator. And took care of some parent contact tasks. Checked email. And double checked what cupcake recipe I'm going to use for the cupcake baking contest our faculty does at a faculty luncheon the first day of exams. This year I'm going with Lemon Meringue Cookie Cups.

12:20 to 12:32 set up my classroom for my next class. This is my Applied Algebra One class and I have a special seating set up for them. I put 15 desks around in a squared off horseshoe facing the main whiteboard with three smaller groups of desks behind them. We start in the main horseshoe to go over homework and have general whole class discussion. then the smaller groupings are used for independent or group work. Generally my classroom is set up with 6 groups of 5 desks each. But I learned this class needed the horseshoe set up to help them with focus and attention. It works really well with them and once they can work independently on a concept they can move to a "table" grouping. Some stay in the horseshoe grouping the whole time because they need constant monitoring. I have a teacher's aid in that class. He's great but doesn't know the math so I give him answer keys with my lesson plan. I work more closely with the kids who need that constant one-on-one while he just monitors that the rest of the students are staying on task and checking answers.

12:38 to 2:00 Last block of the day - my Applied Algebra One class. Today we wrapped up the "rate of change" concept with a quick review of the homework and a quiz. Then we came back as a full group to review more for the exam. Today we focused on unit 2 expressions & equations.

2:00 to 2:15 Run down to guidance to check in with a counselor about a students, stop by the mailboxes to distributed the Applied Algebra One exam packets to the special ed teachers.

2:15 to 3:15 Math Department Meeting - today we learned more about the whole school SATs that we are just starting in CT as our high school "standardized test". All juniors will take the SATs on March 2. So we learned about the logistics of that schedule. And talked about the PSATs (all 10th & 11th graders took that in October and scores are out) and how we can help students use information about their scores to guide their SAT preparation. I'll be spending more time on learning more about the new SATs & using collegeboard.com and Khan academy in my classroom on our next PD day February 12th.

3:15 to 3:30 head home

3:30 to 5:00 some home "stuff" including a 30 minute fitness walk around the neighborhood. Brrr it was cold - in the mid-30s with a lot of wind. Gotta do my exercise to keep up on #FitBoS! 

5:00 to 6:00 some correcting of quizzes. Not much time to do this tonight as I have book group later and I'm hosting. Most of the food is all partially prepped but once book group starts I won't get any more work done. So I didn't get much done.

6:00 - 10:00 set up, book group 7 to 9:30 and clean up. Our book was The Nightingale. 

10:00 to 11:00 read to unwind, then finally to bed (to start all over again the next day....)

Pretty busy, but probably pretty boring to read about. This was a lighter day really because of midterm exams coming up and not having to do much prep right now. Fortunately with exams we get the afternoons "free" (no students) so we can correct exams and I get a lot of prep done then for the first weeks of the new term.

Blogging Initiative

Time to dust off the blog....I find it pretty difficult to keep up during the school year. The primary purpose of my blog has been to share the materials I've created. Especially the ISN (interactive student notebooks) materials. Most of my materials have been adapted from things I've found from the internet - so in the spirit of passing on and sharing the "wealth" I started my blog last June (2015).

There's a pretty amazing group of math education bloggers out there - many of them stay connected through the Math Twitter Blogosphere ( #MTBoS). And now there is a blogging initiative for 2016 led by  #MTBoS. You can learn more here. 

So here is my official statement for this initiative:

I, Mary Anne Hardy, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the January Blogging Initiation hosted by Explore MTBoS.

You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!