Mathsational

  This post is part of an ongoing book study series on Nix the Tricks by Tina Cardone. Each week, a group of math teachers meets to reflect on one chapter of the book and discuss how we can move away from shortcuts and toward true mathematical understanding. You can find our reflections from prior chapters in previous posts, and follow along as we continue through the book. Chapter 4, “Geometry and Measurement,” took us into one of the most visual and language-rich areas of mathematics. For many of us, geometry is where we first learned to “see” math, but it’s also a place where shortcuts and memorized formulas can overshadow the reasoning behind them. Our discussion this week revolved around three major themes: definitions, sense-making, and vocabulary. Rethinking Tricks and Formulas When reflecting on the “tricks” in this chapter, several teachers admitted they’ve used them in the past, especially when teaching CP (College Prep) Geometry classes. It’s easy to fall back on formul...

Draw what I say is an activity where students can practice using vocabulary.  It can also be used to practice reading and writing mathematical notation.  Here are the rules for this activity: Place the cards in a pile, face down, at the center of the table.  One person draws a card, without showing to the other people at the table. The person who drew the card should read the verbal description aloud to all the other people at the table. The other people at the table should attempt to draw a diagram that matches the description that the first person just read aloud.  Each person should do this individually on a recording sheet. The person who drew the card and read the card aloud should check the other people’s drawings.  If the drawing matches what is on the card, write a checkmark next to the diagram. If the drawing does not match, write an x next to the diagram. Continue the steps above, taking turns being the reader. Each person should tu...

I recently wrote about how I would like to incorporate robotics into my geometry classroom.  I followed all of the classroom robot companies on twitter and started asking questions.  The folks at  @OZOBOT  were quick to reply and they became one of my top contenders.  Several weeks later, Ozobot tweeted that they were partnering with  @Tryazon  to sponsor 200 parties.  Of course I jumped at this opportunity and was fortunate enough to be chosen to host. I have never hosted a Tryazon party before but they are a company that matches innovative new products with potential customers.  As a host, I had to host a party where adults would get to play with and experience Ozobot.  In exchange, I received an Ozobot Starter Pack .  I also received a second robot to give away as a door prize.  Additionally, I was provided with a detailed party planning guide, coupons, and support along the way to ensure that I was able to pull o...

I recently posted my algebra 2 scope and sequence.  I am also teaching geometry this year, so I figure I might as well post that too.  I am using standards based grading.  I number my objects as #.#  The first number is the unit number and the second number is the objective number within that unit.  The first year I did this, I just numbered from about 1 to 120.  It made making changes to the list more difficult.  Now when I need to add or subtract a topic, I don't need to renumber all of the objectives, just the ones in the same unit. I would love feedback on this list.  Our students take geometry after algebra 1 and 2.  The course seems very easy and I feel like I need more rigour in the class.  Please share your list on your blog and leave a comment here so I can check it out. Geometry Part 1 Chapter 1: Tools of Geometry 1.1 Use basic geometry terms and notation including points, lines and planes 1.2 Use basic postulat...

Oh how I wish I could be seriously planning for my first few days of classes.  I just got summoned to district jury duty.  This will be the fourth time that I have had jury duty.  Last year, I actually got called to local court twice in five months.  I was not all that worried about the second call because I know I was excused for a year.  When I called to let them know that I had just served, the lady on the phone was surprised to find that my name was in the pool three times.  I'm under the impression she fixed that, but who knows.  I wrote to the court to request a postponement until next summer.  At the very least, any time that is not during the first few days of school.  I certainly don't want to leave a substitute in charge of building a classroom culture for me during those very important first few days of class. I also have a jam packed curriculum, especially in algebra 2.  This past year, I messed up with pacing and had ...

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...

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...

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...

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 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 ...

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.