The Best MAP Yet.

9/12/17 EDIT: I haven’t taught Geometry since the Fall 2015 semester and this is still one of my favorite activities from the last three years. I also enjoy Classifying Solutions to Systems of Equations and Maximizing Profits: Selling Boomerangs.

Any time I talk about MAPs on here it’s almost always going to be referencing the The Mathematics Assessment Project. I love this resource. Some of the tasks and lessons have worked better than others – sometimes I have poor classroom management, my students aren’t engaged, or the concepts are too abstract for them – but I try to do at least one a month with one of my classes. This MAP was the best one we’ve done yet.

We had been talking about nets, surface area, and volume for 4 days. During those days the students did problems involving surface area and volume of prisms, cylinders, cones, pyramids, and spheres, as well as compound solids. They were cruising right along using their formula sheet and were mostly able to figure out when to use trig ratios or the Pythagorean Theorem to help them complete their calculations. The next day life became a little more difficult for them:

What are similar solids and how do we know that they are similar?

We have already learned about similar triangles and polygons, so we only spent half a class period discussing what similar solids were and how we can check their scale factors (or ratios or whatever it is that you call them) to see whether or not solids are similar.

But then we started to get more abstract. What if I double a rectangular prism’s length? What happens to the surface area and volume? Is this going to be true for ANY rectangular prism whose length gets doubled? It was like the world was ending! After I encouraged them to draw some pictures and try to come up with a statement as a group, the ball got rolling.

The MAP lesson that we did is titled Evaluating Statements About Enlargements. A brief overview of the MAP (the MAP itself has very explicit instructions, including questions/prompts for teachers to ask whole group and small group):

  1. Students were in groups of 3-4. You are supposed to group them based on their responses to the pre-assessment, and I do that to an extent.
  2. After some whole group discussion about the previously mentioned questions, each group received a piece of butcher paper, glue stick, and statement cards.
  3. As a group, the students had to determine which of the statements were always true, and which of the statements were false. They had to provide either a pictoral or written explanation on their butcher paper for each choice once they agreed as a group. MAP2
  4. If they believed a statement was false, they were challenged to alter it to create a true statement. MAP3

After all of the groups worked on this, we did a gallery walk where students made comments and asked questions. I need to get better at helping my students be a productive part of the feedback process! Then we reviewed the statements together as a class and worked through any misconceptions that still existed. MAP1

From the beginning of the MAP, students were engaged. There were drawings. There were calculations. There were arguments. It was great! Most of my students were not at a point where they could extrapolate using their own words to the idea of a:b, a^2:b^2, and a^3:b^3 but I didn’t mind that. We discussed that together as a class at the end and I think they understood well enough to remember it, or at least well enough to take the time to figure out these types of problems every time.

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Zombie Graveyard

I haven’t posted in a couple of weeks due to some traveling but I wanted to make sure that I posted about one of my favorite (and my students favorite) review/practice problem games.

The last day of our unit on Polygons in Geometry was spent on area and perimeter. Students start learning about area and perimeter in elementary school, so most of this is review. The only new thing is the formula for area of a regular polygon. We did two problems using this formula together, and discussed the important of units before beginning the game.

Zombie Graveyard is pretty simple. The goal of the game is to be the last student alive (or the student with the most lives left if you run out of time).

  1. Write down each students name on a white board that is easily accessible to the students. Give each student an X to represent each life you want them to have. The number of lives will depend on how long you want the game to last and how many student you have.
  2. Students, on individual whiteboards, attempt to find the answers to a problem displayed on the board/screen. I gave my students 45 seconds to complete perimeter problems and 1-2 minutes to complete area problems. This is a faster pace than what I normally play at because this is an advanced-pace course and the nature of the topic was review.
  3. Call on students randomly to show you their answers. This year I used the Class Cards app to select 5 random students. Last year I used the random number generator on my calculator and called students by their seat numbers.
  4. Students who have gotten the answer correct get to go up to the white board and take away a life from anyone.
  5. Once you’ve lost all of your lives, you’re dead. But that’s not the end of the game! Oh no. You have become the undead – a zombie – and zombies, should they get a problem correct when they are randomly selected, now get to take away TWO lives.
  6. Keep completing problems until you only have one person left alive!

My students love this game every time we play. I think it’s by far their favorite way to do simple “plug-and-chug” practice problems, and I try to play it once a month with at least one of my classes. It does require lots of student and teacher control, but the students know that the game can end any time it gets too out of hand and we will go back to individual practice problems that are turned in for a grade.

Last year I played this for the first time with simplifying powers in Algebra I. I plan on playing it again later this month for Surface Area and Volume, and am always looking for more concepts that it can be used for!

Discovering Polygon Angle Theorems

There are people who say “discovering” theorems and properties and relationships help students create and remember connections. There are people who say it’s a waste of time. I think that for students who are committed to an activity and able to understand the task at hand, discovery activities are one of the more powerful learning tools that teachers can use. I am trying to not only incorporate some of these into my Algebra I and Geometry classes, but also tweak them each time we do them so that the students get as much out of it as possible.

This year, our district has the ability to use Gizmos and this has been a great tool, especially for my Geometry students. On Friday we spent the lesson discovering the polygon angle theorems. Students were able to see the relationship between the number of sides and the number of triangles within a polygon, and then translate that into the interior angle sum theorem as well as the individual interior angle theorem. They also figured out the exterior angle sum and individual exterior angle theorems! These were done with very little prompting or clarification on my part – I had to explain what the worksheet meant by n-gon a few times but that really was about it.

IMG_0175 IMG_0176

In the first unit of the year the students derived the distance and midpoint formulas. They figured out the relationships between the size of an angle and the size of the opposite side of a triangle. We played around with side lengths to create triangles and not-triangles. I believe that taking the time to do all of these activities has given at least some of my students a better understanding of the concept and better ability to apply that knowledge when solving problems.

Rounding Out The First Marking Period

Next week is the last full week of the first marking period, and here’s what I’ve thought so far.

  • I’m not sure that homework is helping any more than it did last year. I am going to start making sure I post answers to all assignments online and assigning mostly odd problems from the textbook so students can check their solutions.
  • My Algebra I students overall have continued to rock functions. We still need to work on making sure they know the proper ways to write domain and range and not mixing up the x- and y-intercepts though.
  • There was not enough time to teach congruent triangles in Geometry. I needed more days for that unit.

Looking forward,

  • I can’t wait for a seating rearrangement at the end of the marking period. It’s my favorite arrangement that I’ve discovered thus far, and hopefully it will decrease the off-task conversations in two of my classes.
  • I have officially applied for my first grants! I applied for one on my own, and two more as a part of teams. I’m still going to be applying for one this week as well, so hopefully we’ll get all of them!
  • I still don’t know how I’m going to spend 6 week teaching about the equation of a line, so if anyone has really awesome suggestions please let me know.
  • After reading this reddit post, I’m really interested in creating a similar environment for my classroom and it might be a major project of mine over the next summer. I’ve already determined some possible jobs: garbage/recycling people, calculator keepers, board cleaners, paper passer, banker…

I’m going to be posting pictures of our Algebra I INB pages from the first three units of the year soon!

Time to try this blogging thing out.

My profile says I’m “fresh out of college” but that’s technically not true. I’m currently in my second year of teaching after graduating from Robert Morris University in 2014. I “joined” the #mtbos on twitter in 2013 and frequent blogs such as Kate Nowak’s Function of Time and Sarah Hagan’s Math = Love. After one year in the classroom, I feel like I’m ready to give blogging a shot myself.

So now,  to introduce myself. My name is Rose Roberts, and I am a math teacher. I currently teach at Warhill High School (Go Lions!) in Williamsburg, VA. I grew up in Adrian, MI (Go Maples!) and went to college at RMU (Go Colonials!). Our school has a block schedule right now, meaning I teach 3 out of 4 blocks each day and the math classes are seen on both A and B days. Last year I taught two sections of year-long Algebra I with a collaborating teacher, and semester-long Geometry. I’m currently teaching the same things this year, but next semester I’ll be switching from semester-long Geometry to Algebra, Functions, and Data Analysis (AFDA, an optional precursor to Algebra II).

My biggest goals this year are:

  • have increased classroom management
  • involve students more in goal-setting and keeping track of their grades and achievement levels
  • expand concept-based grading from semester-long Geometry to AFDA (haven’t implemented it in year-long Algebra I yet, but that will be a goal next year if I am teaching it again)
  • have a higher Algebra I pass rate
  • blog once a week

As a end-note, we’re one month in to school and some of the new things I’m implementing are really trying my patience (and sometimes the patience of my students) but I have faith that by June it will all work out.