Mathsational

I am about to start my 13th year of teaching high school math.  Every year, I buy way too much stuff for my classroom.  (My school does not provide us with very much in terms of physical supplies). This year, I am actually buying only a few things.  Of course there are some things that I will make as well.  Here are my must haves for the new year. 1)   Patty Paper  - for paper folding constructions and other activities from Patty Paper Geometry .  I already have the book, I just need to refill my paper supply.  This book is great for discovering geometry in a low tech, hands-on way.  Sure Geometer's Sketchpad is great, but sometimes physical is good too. 2)   The Classroom Chef  - I received this order a few weeks ago but was finishing a grad class.  I have a conference this week, so I'm hoping to start reading next week.  I follow both Matt and John on twitter, so I have high expectations.  I think their boo...

I especially like activities that are self checking, but don't totally give away the solutions.  For examples, a worksheet with a answerbank, but the answers are scrambled.  This allows students to have an idea that they are on the right track. Chains simply involve using task cards in such a way that the solution to the previous question is on the next card.  Some people makes theirs with a start and end card.  I typically create mine in a loop and students start with any card. Most often, I create them in powerpoint, print the 4 slides per page in landscape, then cut in half twice to create the cards. Here is an example from geometry on properties of parallelograms. Here is an example from algebra on finding the vertex of a parabola.

One of the pre-service teachers that I mentored introduced me to the free Tarsia Software .  It is one of the coolest things ever.  You have probably seen puzzles like this online.  You may have bought a premade puzzle or slaved in a word processing program with tons of text boxes and graphics to create your won.  The Tarsia software just does this for you.  It has an equation editor, which is amazing.  You type in your questions and answers and the program creates a table with the problems/solutions, a puzzle to be printed out (mixed up pieces) and a solution puzzle (pieces put together).  It's mind blowing really. I have not found a way to upload these to google docs with out printing to pdf :(  However,  Mr. Barton has made lots of tarsia puzzles and uploaded them on his website. When I use these in class, I typically give each group of 3 their own puzzle.  I usually print them one the smallest output and then copy 2 ...

The next practice structure that I'd like to share is having kids play board games.  This is just another alternative to a worksheet.  I take the problems from a practice worksheet and put them onto powerpoint slides, print them in landscape four to a slide, and cut the printed page into quarters with one problem per piece. For the board games, I have purchased a few cheap childhood games from stores like 5 below or walmart.  Right now I have Candy Land, Trouble and Snakes & Ladders.  You can also find lots of free printable game boards through a quick google search.  I have printed some of these out in color and laminated them to be used multiple times. For accountability, I usually just give the students a place to record their work.  I also try to provide an answer key so that students can check their work. In general I have all students try the same problem at the same time.  Then they check the answer and anyone that got the proble...

The next practice structure I'd like to share is a card game called My Ship Sails.  I had never played this game as a child, but came across it while looking for ways to gamify my classroom more.   Here is a link on how to play the traditional game. This game would work well for any topic where kids need to be able to categorize or differentiate similar concepts.  Traditionally, there are four suits in a deck of cards, but I suppose you could create a game with three or five suits just as easily. Basically, after dealing the cards, the idea is for kids to pass one card to the left while at the same time receiving one card from the player to their right.  The object of the game is to collect all cards with the same suit/type/category. Here are two examples that I recently created for next year. This game is for geometry.  Each card has a conditional statement and then one of the following:  the hypothesis, the conclusion, a counterexample, or the conv...

Practice Structures - Error Analysis Error analysis is one of my favorite practice structures because of the conversations.  My students typically find it very difficult.  They sometimes think that problems that have been done correctly are incorrect if steps are skipped in the written solution.  Other times they think incorrect solutions are correct because I try to make common mistakes.  One of the most interesting things that happens is that kids end up appreciating the work done by their teachers while correcting quizzes.  They almost always express that the toughest part is trying to figure out why the fictional person make a certain mistake in the work. In the past, I have typed up my error analysis problems.  However, I have switched to handwriting the work.  It seems more authentic and for some reason it is easier for the students to differentiate between the question and the solution.  I use Doceri to create the document.  It is ...

Another practice structure that I use about once per chapter is color-by-number.  I typically find the coloring pages on Pinterest.   Here is the board that I have been using to collect images for future activities. I usually choose with the problems by using Kuta software or by pulling from a pre-existing worksheet. I number the problems to match the numbers in the color-by-number picture.  Then I match the answers to the appropriate color.  Students solve each problem, locate the matching answer and color the numbers in the picture with that matching color. Somewhat surprisingly, these activities are well liked by my students.  If too much time passes, they ask about when we will do another.  I personally like the pictures that you can not identify until after they are colored, but my students seem to prefer cartoon characters. Here is one example that I used last year to have students practice factoring trinomials in quadratic form. Here is...

My goal during the summer is to blog at least once a week.  I've failed pretty miserably with this so far this year.  One of my goals was to blog about my favorite practice structures.  Let's be honest, a lot of the content in high school math is either inapplicable (I'm looking at you polynomial long division) or requires lots of practice to build fluency.  So, although I do like to try to do one project with honest to goodness real world application for each unit or marking period, I still need something engaging to do with kids to help them practice. The practice structure that I am sharing today is Old Maid. I love having my kids practice the most basic skills (ones that require little to no writing) by playing card games.  One sad side note is that I usually need to give directions on how to play these games because apparently, parents don't play games with their kids anymore. So, I just now created a new version of Old Maid for my first unit in algeb...

I borrowed this lesson from John Stevens .  As a quick side note, this is what I love about the MTBoS community on Twitter.  You build a network of creative educators from literally all over the world and your own lessons improve because of the sharing that happens. Now, my students and I live in central Pennsylvania.  We have the occasional earthquakes, but they are they type that only the most observant people even notice.   Here is a link to our most recent earthquake. This is  John's original lesson.  On his page, you will find links to his Slides presentation, lesson plan, and student handout as well as notes about how he implemented the lesson. I started with showing a San Andreas movie trailer. I asked if anyone had seen the movie.  I asked is any of them felt the earthquake that we had the previous summer.  These questions lead to some lively conversation. I showed them some maps from the USGS website that show intensity in ...

I was inspired by  @samjshah  to create an activity using logarithms and earthquakes for my algebra 2 classes.  Sam wrote about Earthquakes, Richter Scale, and Logarithms here . I did a little googling and ended up with this activity.  I still had some questions, so I emailed USGS and got a quick and through reply.  The reply resulted in this activity.  I have not tried it with students yet, but I'm really excited to do so next year.  Please feel free to check it out and give me feedback before I try it in the classroom. Here is the student document if you'd like to use it. Enjoy.

The origins of Barbie Bungee seem to be unknown, at least according to this twitter conversation. Looking for the earliest known copyright on Barbie Bungee. WHO INVENTED THIS THING?! https://t.co/CIayCEHJVC — Dan Meyer (@ddmeyer) October 21, 2015 I've seen it done in classrooms since I started teaching circa 2004, however, advancements in technology have made it soooo much more fun.  Many students have smartphones capable of taking slow motion video which adds to the engagement. Here is what I did on my most recent go-round. I did this lesson with a class called Survey of Math.  It is our remediation class for students who did not pass our state exam on algebra 1.  Most of the students seemed to enjoy it, especially the end when they dropped their dolls. This group even wanted to try to get closer to the floor and wanted to add the new data point and recalculate their regression line. Some of the interesting things that happene...

I modified this activity from one done by Matt Vaudrey and John Stevens .  I believe that they used the activity to study Pythagorean Theorem and the distance formula.  Here is a write-up of John’s lesson.  I used it to have students practice solving simple trigonometric triangles involving angle of elevation. I started the lesson with the same video that John did.  I asked the kids if they had ever been on a zipline and if so where.  A few kids had stories to share.  I asked them about what would make a zipline ‘good.’  This led them to the safe and fun metric.  They knew that the zipline needed to be both safe and fun if people were going to enjoy the ride. I set up a mini zipline in my classroom.  The starting height was fixed at some random value because I already had a command hook stuck to one of my cabinets.  It was at about 147 cm.  The zipline was just fishing line.  I used a carabiner and velco me...

I came across this activity in the #MTBoS community through twitter.  The activity seemed very outside the box for me and my students and I was nervous to try it.  Many teachers have written about their experiences with implementing this lesson, but Jenn's is the most detailed and helpful that I found.  The basic idea is this:  Students make a set of parallel lines and a tranversal with masking tape on the floor.  You review the angle pairs alternate interior, alternate exterior, same side interior, same side exterior, corresponding, vertical).  Have students place their feet on the appropriate angles in their tape diagram. In the post mentioned above, Jenn shares some awesome videos with fun music and angle pairs.  It works just like Dance Dance Revolution from there.  I tried it with my 11th graders as a review before we started parallel line proofs.  They had a grand time and really got into it.  I recorded one of the dances ...

Recently, my honors algebra 2 class studied radicals.  Among other things, we needed to build fluency in using operations and using radicals to solve equations.  Here are a few of the resources that students used during class to practice. Simplifying radicals board game:   I can not remember where I got this board game template.  At one time, I googled something  like “free printable board games” and downloaded a bunch of them to use once each unit.  In general, I print some practice problems using Kuta Software and cut up the worksheet to make problem cards.  I print and laminate the board game to use year after year.  I use dice and bingo counters that I purchased online.  This is a simple alternative to a worksheet that the kids always seem to enjoy.  The board games work best when the problems are quick.  The game part is not fun if the kids can only complete 2-3 problems and don’t actually get to move their gam...

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.

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