Mathsational

One of my favorite resources is the  Mathematics Assessment Project .  These are scripted lessons, which at first was off-putting to me.  However, once I implemented a few lessons (with modifications as I saw fit), I accepted them as exemplary lessons.   While I don't always follow the script, I do believe that the lessons have been vetted and shown to be well thought out.  I like the script as a starting point and I like having a model to work with.  I especially like the common misconceptions and the suggested questions that could be posed to students. Here are two of the most recent lessons that I have used in my classroom. Defining lines by points, slopes, and equations My favorite part of many of these lessons is the collaborative section.  This lesson contains a matching activity where various information is missing from some of the pairs.  Students can more easily match the pairs with all the information given and then expand t...

Here are two more activities that I have tried in class recently. Linear Inequality TIC-TAC-TOE: I borrowed this activity from @MathBerts and adjusted the directions to make it work in my classroom.  Since I teach in a hybrid/station based classroom, students need to be able to complete their assignments without a teacher leading the activity.  Most of my students enjoyed the activity.  I had just one problem in that I had small groups of kids all using the same game board.  I would recommend possibly copying each board on a different color of paper to alleviate this issue. Domain and Range Go Fish: This activity is a real winner.  The kids LOVED it.  I can't explain it, but every time we play go fish, they go nuts (in a good, on task, highly engaged sort of way).  Shockingly, the first time we play Go Fish, I have to do a mini-lesson on how to play.  Kids can be so deprived these days :(  This activity really helped my...

We all know that it is important for students to understand content deeply and be able to apply what they have learned.  However, there is still a need for basic skill practice from time to time.  My students hate worksheets as much as I do, so I've tried to come up with some more creative ways to practice skills. Some of my favorite alternatives to worksheets are board games, color-by-numbers activities, and task cards.  Here are some examples that I have used recently. Angle Addition Board Game:   Directions and Questions    I put out the directions and the cards and allow students to choose one childhood board game.  Right now I have snakes and ladders, trouble, and candy land. Angle and Perpendicular Bisector Color-By-Numbers   I have collected some color by number images here that I pull from for these activities.  Then I just copy and paste some worksheet problems to create the activity. Area and Perimeter Task Cards ...

Here is an activity that I tried recently.  I try to incorporate card games into my class whenever I can.  I find it somewhat sad that  need to teach my kids how to play card games but once they know how to play, I can repeat the activity with various content throughout the year.  Rummy games work well with anything where you can come up with 3-4 representations of the same item.  In this case I used vocabulary words, diagrams, and notation to create sets. I have also used similar Rummy games for various graphing practice (match the table, function, graph, verbal description). Once the students know how to play Rummy (or any other game), they enjoy the game aspect more than a traditional worksheet for practice.  I typically have kids yelling with excitement when they complete a set.  I even occasionally have kids bending the rules of Rummy to help their classmates form the sets that they need since they will sometimes play with their cards visi...

I tried this activity today.  The kids took turns being the reader and the drawers.  The reader read the the symbolic phrase using proper vocabulary then the drawers tried to sketch the described diagram.  The reader used the image on their card to check their teammates responses. I found this idea on Sandra Miller's blog . Here is a sample of the student work. The kids really seemed to enjoy it.  There was a lot of laughter and learning while solidifying their understanding of notation and vocabulary.  The kids finally started to see the importance of the differences in segments, rays, and lines.

I'm am teaching in a hybrid learning environment again this year.  You can read about that here . Here is how I have arranged my stations: direct: independent: collaborative: I used a bunch of posters that were shared by Sarah Hagan and Meg Craig So excited for the new year!!

3 Act Math lessons are a great way to introduce a unit.  It is especially cool when you can create a real need for the math that students are about to learn either by making it possible to find a solution or by making the solution easier to find. The basic concept is  Act 1:  Show some sort of media image or video and let kids ask questions.  Choose a question to try to answer.   Act 2:  Have kids tell you what other info they need to answer their question.  Research or provide that information. Act 3:  Reveal the solution. The whole process takes quite a while, so you can't do this every day and make it through all of your content.  However, I like to use these on the first day to introduce a new chapter.   Here are some of my favorite 3-act collections Dan Meyer 101 Questions Andrew Stadel Dane Ehlert Kyle Pearce

The only 'bad' thing about the MTBoS might be that there is soooo much out there and it can be hard to keep up with it all.  OK, really it is impossible to keep up with it all.  Here are some of my go to resources that I search when I have a lesson coming up but I don't have anything interesting to do with students on that particular topic. Common Core Problem Based Curriculum Maps - Geoff Krall of Emergent Math has organized thousands of problem based tasks.  He has sorted them by grade level, Common Core standard, and subject.  Seriously, so much good stuff that my mind explodes every time I visit the page. Desmos Activities - Interesting activities that are ready to use in your classroom.  Until recently there were only a few activities posted, all of high quality of course.  Lately however, new activities are being posted more often. Yay! The Math Projects Journal Lessons/Curriculum Maps - Chris Shore has organized projects for middle...

Reason and Wonder is great resource for engaging lessons.  Each lesson starts with an interesting image.  Students are asked what they notice about the image and what they wonder about the image.  Michael Fenton, writes the lessons in such a way as to promote student curiosity and the tasks are inherently interesting. These follow a 3-act set up in which the teacher allows students to generate questions about the topic.  The question to be explored is predetermined, but students will likely ask the desired question if they are encouraged to ask as many questions as they can. The thing I like best about Michael's lessons is that they are classroom ready.  Many of the other 3-act lesson collections are great too, but these are very complete with lots of media files, desmos files, and presentation slides. I have only tried the Charge!  lesson in my classroom so far, but I look forward to exploring more of Michael's lessons.

Open Middle is one of my favorite resources.  Most of the tasks could take 20 minutes to complete but I usually start by using one as a warm-up. The key characteristics of these problems are the beginning and ending are closed (all kids start with the same prompt and arrive at the same result) the middle is open (there are many paths to the correct solution),   the problems have a low floor and high ceiling (it is easy to understand and find one solution but harder to find the best solution) they involve finding the maximum/minimum values (kids see this as a competition to see who can find the best solution) My students seem to really like these because they feel successful in finding one solution even if they don't find the best solution.  After giving the kids time to think on their own and then work as a team, I ask for one team solution.  I praise that team for finding a solution that works.  Then I ask if anyone can top their performance. ...

*singing* One of these things is not like the others.  One of these things just doesn't belong... Which One Doesn't Belong is a fairly new resources.  As usual, I stumbled upon this jem while catching up on tweets one day.  I use these as warm-ups about once per week in my 9-12 classroom.  I am not concerned that the topic we are studying is represented in the set, but rather that students think of multiple solutions.  That is my favorite part of using these sets.  I encourage students to come up with a reason why any of the 4 pictures could be the one that doesn't belong. I love that there is often an obvious solution so all students can find success but there are multiple answers for students who are ready to think more deeply.  I have not tried the incomplete sets yet, but I think those would be awesome for higher order thinking skills as would making up your own WODB set.

Kelly Turner has this great site .  I can not find her on twitter, so if you know her personally, convince her to join.  Then tell me about it so I can follow her. She posts a graph with reflection questions every week during the school year.  I like to use these as warm-ups with my 9-12 students.  She asks students to look at a new, relevant, and interesting graph.  Students practice reading the graphs to answer questions like:  What is the topic of the graph? What do the axes represent? What observations can you make? What do you think will happen in the future? Reading graphs is always a frustrating topic for me to teach.  It seems like something that high school kids should be able to do, but  it turns out they can't.  I like to use this resource once a week to give my kids extra practice.  We also discuss misleading graphs and bias.

AOD is another site that I love. These usually take the entire period to get through so they may not be just a warm-up. I could certainly see starting the activity at the beginning of a unit and then asking students to draw a conclusion. When they indicate that they don't know how to justify their position, it creates a need for the unit that you are starting. Then you can come back to this activity again at the end of the unit and do the math to support or dispute their original claim. Tim McCaffrey, the creator of this site has asked engaging questions that require 3-acts to reach their conclusion.  The 3-acts typically involve posing a problem, giving more information, and finding a solution.  Other tweeps have their own 3-act databases that are awesome too.  I'll write about those in a later post.  For now, enjoy these.  This is a good place to get started with 3-act math because it is not too overwhelming.  

Graphing stories are probably one of my favorite ways to start class.  The kids love it too.  I use it for all of my 9-12 students.  I don't match the graphs to the type of function we are studying, we just have at it.  Something about the videos is just very engaging for students. Here is how I use the site. 1)  Give students this handout . 2)  Play the first part of the video pausing as the y-axis is labeled so that students can write their title and labels. 3)  Play the full speed and half speed part of the video. 4)  Pause the video and ask the students to sketch the graph. 5)  Ask if anyone wants to see the video again (sometimes they do, sometimes they don't) 6)  Ask students to compare their graph with an elbow partner and discuss any differences. 7)  Take a pic and project one student's answer (I use Doceri on iPad) 8)  Ask the student to explain what is happening in their graph and how it matche...

The next resource that I like to use to start the class period is visual patterns .  I use these about once a week with my 9-12 students.  My ninth graders start the year not knowing anything (or remembering) about linear equations so they are really just trying to make a table of values and look for a pattern.  After we learn (review) how to write equations of lines we discuss how we can use that new knowledge to make our visual patterns easier to find.  Some of the patterns are quadratic or even exponential, so you will want to discuss this with students.  They should check to see if their pattern really is linear before beginning. The quadratic and exponential patterns are good for my algebra 2 kids, you just need to look through the list to find them.  The creator of the site, Fawn, will send you an answer key if you want a quick reference to tell what type of function each pattern is.   On this page , you can find several worksheets that ca...

My Second MTBoS favorite is Would You Rather .  This is another resource that I like to use to start my 9-12 classes.  Some of the questions are quick enough to use as a warm-up while others are long enough that you could spend an entire class period researching, calculating, and arguing.  I like these activities because they are interesting to students and require a low level of math knowledge to get started.  Of course, students can get very in depth with some of their answers.  I especially like to use these at the beginning of a unit before students have the skill to answer the questions.  An example of this might be using this probability task before learning about compound probability.  In this case the students might try to solve the problem with the brute force method, creating a sample space.  Then I can share with them the short cut and they would have a better appreciation for it.  The most important thing about these tasks i...

One of the reasons that I wanted to start a blog is that I had been an MTBoS consumer for about a year.  It all started last summer at a conference when I was encouraged to live tweet during the event.  I thought the idea was a little silly and I was not really interested in keeping up with the Kardashians.  However, I did learn something that I considered to be tweet worthy.  So I joined and tweeted.  After a few months, I had found about 50 math teachers from around the world that had great ideas.  These teachers were sharing their resources at no cost.  Twitter became my go-to lesson planning resource. Eventually I started to notice questions on twitter for which I felt I could contribute to the solution.  I tried to reply with 140 characters, but I often wanted to share links.  So, I decided to start a blog.  So far I've blogged about standards based grading and hybrid learning.  This next series of posts will be about my...

The process of planning for a hybrid classroom is not drastically different form planning from a traditional classroom.  You will need to consider that students will be progressing through the stations in different orders so you will need to be careful not to assign something at one station that can not be done without completing another station first.  You also want to be careful about over planning for the direct station.  The direct station should be different for all three groups.  It should be based on the questions that students have when they come to you.  If you find yourself doing the exact same thing all three times, you are probably doing something wrong.  To help you get started, here are some of my favorite resources. Direct station: I start off by preparing a traditional lesson.  This way if students do not ask questions, I have a variety of practice problems available to get them started.  Once we do one or two problems toge...

As with any teaching and learning strategy, teachers need to make it their own to get the most out if it.  In this post I’ll describe some of the modifications that I have tried as well as some that I know other teachers have tried. My classroom during year 1:  I am a rule follower.  When I learned about hybrid learning, I knew that the people who developed it spend tons of time trying different variations.  I understood that the training sessions that I was attending were based on what worked best out of thousands or trials.  Therefore, I tried to do everything by the rules. So, during the first year, students rotated through all three stations each day.  The problem with this was that I was teaching on a traditional schedule.  I had just enough time to run three 15 minute stations each day.  I had no time for warm-ups or closure.  This really bothered me.  I missed these opportunities to whole class pre- and post- asses...

Accountability is another important piece of hybrid learning.  I teach high school, so maybe my view of students is a little jaded.  Most of my students do not like school, do not like math, and only come to school so that they can see their friends.  There is very little intrinsic motivation.  Even my honors students are motivated purely by grades.  They almost never see that value of productive struggle.  They do not get a sense of satisfaction after solving a challenging problem.  This is a whole other concern that I do not have an answer to, but I am always looking for possible solutions.  In the meantime, since my students do not buy into learning for the joy of learning, I need to include accountability at each station every day.  This is easy at the direct station.  With so few kids in each group, it is impossible for them to hide or not participate at the direct station.  The other stations can be a little trickier. ...

The biggest challenge with teaching in a hybrid classroom is that students have much more freedom than they have ever had before.  This means they will need a lot of modeling and direct instruction on how to work at each of the stations. Here is a secondary example of what a hybrid classroom should look like. Here is what my typical first week of school looks like: Day 1:  Welcome students to the class, introduce myself, begin to learn student names/faces, begin work of a review packet covering material from the previous math course, explain hybrid learning Day 2:  Practice direct station, do this by learning about objectives based grading and continuing review, model classroom routines like signing out, use of electronic devices, turning in assignments, etc. Days 3 & 4:  Practice independent station, do this by getting all students registered for all computer programs that we will use such as Edmodo, edpuzzle, manga high, etc.  Give...

 In this post I’ll discuss what a typical hybrid classroom looks like.  I’ve made some modifications to make it work in my classroom and I know of other changes that other teachers have made that I will discuss in a later post. In general, hybrid learning works best on a block schedule and with a co-teacher or teacher’s aide.  I have neither of these for every period that I teach so it can certainly work if you do not have these things.  There are 3 stations direct, independent, and collaborative.  The teacher starts by creating a lesson plan for these three stations and then assigns students to each of the three stations.  Students then rotate through all three stations. One benefit is that the stations help to reach all preferences for learning.  The direct station is for small group instruction.  It often appears to look like a traditional classroom.  However the teacher should not be repeating the exact same lesson three times ...