Reachable, Teachable & Applicable

We’re in the seventh (yes 7th!) week of school and I’m exhausted. I haven’t posted in forever and a day, I know. We have a new schedule this year which forces lil’ spoiled ol’ me to see all of my students almost every day. We only have 2 block days now and I’ll be the first to admit that I work much better with longer chunks of time in which to work with my students.

You see, I have what I think is a long, laborious method of introducing topics. Laborious, that is, for me not the students. I feel that it works though because by the time I’m done with the introductory lesson many of my students are pretty comfortable with the material. Notice that I used the word ‘comfortable’ and not the word ‘masterful’. My method seems to be effective, but I still don’t believe that my lessons give the students a real reason for learning geometry.

My goal for this year was to find ways to make my students use the math. I wanted them to put their hands and their brains to good use. I had an idea that, by the year’s end, I could get all of my math-haters and math-phobes to realize that they could have a good deal of fun while learning their most dreaded subject. The key to this, I knew, was to find applications that the students might actually use. I teach Algebra 2 also, but for some reason it’s easier for me to find applications there. Hmmm ... Maybe I’m an Algebra person.

I’ve been using dy dan as an inspiration for my lesson presentations. His lessons stem from a book titled Discovering Geometry. That text takes a much more hands-on approach. I’d like to extend that idea. Possibly outside of the classroom. Possibly using technology. A colleague of mine went to a conference and listened to a presentation about a geometry program where the students actually built a house. How cool is that? Unfortunately, house-building-knowledge aside, I have neither the funding for such a project nor colleagues who would dive into such an endeavor with me. Ahh, such big dreams!

So now what? I still need all of my students to feel like learning math is within their reach. I don’t want to be bored as a teacher either. I guess for now I'll continue with my hands-on-activities-sometimes-play-some-games-but-mostly-lecture way of teaching. That is, until I find the time to create a more robust course. It’s funny. It’s like I have to get their butts out of the seats to keep their butts in the seats, if you know what I mean.

Cool & Creative Survivor Tribe Tags

Survivor Geometry just finished its 2nd week and I just wanted to mention how proud I am of my students and their very creative flow. The students were asked to do some research and use it to create a tribe name that somehow related to mathematics.

Here are my top picks.

#10 The Radicals

#9 Faces

#8 The Equalizers

#7 Loco Cuatro

#6 Plutonic Rulers

#5 Manhatten Project

#4 Ray-Men

#3 QTπz

#2 The Solve for X-Men

Drum roll please!
And my #1 pick for the coolest Survivor Geometry tribe name:

#1 Charlie's Angles

Ideas From Other Really Cool Professionals

This is the last post of this series on exam prep activities.




Review Activities to Make Real Students
Predicting Exam Questions
Expert Study Teams
Problem Trees: A Graphic Organizer
Round Tables


I was originally hoping that more of my colleagues would comment on this blog with some of the review activities that they use, but alas there is only one. Thanks to Tracy S for her suggestion! She has her students create 3 x 5 cards for use on each exam. She checks for the cards a few days before the exam and gives the students "study points" for completing them. I may have to steal this one for some of our more vocab/theorem dense chapters in geometry.

We did have a conversation the other day at lunch though. What follows are some of the things other teachers in my department do with their students to review before an exam. These are more game-like however.

• Trash Can Basketball is a favorite. Divide the students into groups and give each student a whiteboard, dry-erase marker, and an eraser. Each student (aka player) writes his group number and player number on his board. Then post a problem for the class to do. Each student does the problem on his whiteboard and raises the board when finished. Pick one of the player numbers at random and check each group for the answer. If the player has the correct answer he gets to shoot. Have all of the shooters attempt their shots and record the points. Points are only scored if the player gets the correct answer and makes the shot. Thanks to MW for this idea! I tried it for the first time last week. Like MW, I created two types of questions, 2-pointers and 3-pointers.

• I've used the game board for Trivia for Dummies to run a review called Math Trivia for Smarties. I combine the board and game pieces with a powerpoint presentation that displays the problems. I divide the students into teams and each player takes a turn rolling the dice when it's his team's turn. This seems to keep the students' attention for the entire hour because it takes that long for someone to get their piece all the way around the board. To win, they have to land on the last spot with an exact roll and get the question correct.

• BI created a game on his SmartBoard with balloons that pop when you touch them. Again, the students are divided into teams. When a student gets the answer to a review question correct he gets to throw a rubber ball at a balloon on the Board. When the balloon pops it reveals the number of points the team gets. Way to combine math and PE in this era of budget cuts, BI!

Students can get really competitive. Some students get a little impatient with their classmates, but generally most are willing to help their teammates learn the material. I'm sure these games are just a drop in the bucket that contains the plethora of activities one could use to help students review before a test. I like the idea of balancing games with learning activities that help us develop the "real" student. That is, a teen who values the art of preparing for exams. In the land of Perfect they would do this automatically. Unfortunately, we live in a world where a long list of standards leaves teachers with little time for the extras that are needed to ready our young people for life post secondary.

Round Tables

This is part 4 of 5. These posts discuss possible activities for math reviews that can also teach test-taking skills.



Review Activities to Make Real Students
Predicting Exam Questions
Expert Study Teams
Problem Trees: A Graphic Organizer



Disclaimer: The title of this post reflects the name of a math review activity and should not be confused with the round table associated with Arthur and his knights.

Well, actually, I've never been able to think of a better name. The idea is that the students rotate from one group of desks to another. The size of the group is usually 4 so the desks are arranged in a spiral with each desk facing a different direction. I guess I could have called it spiral tables, but here's how it works.

Each group is given an index card with one or two review questions on it. The students are given 5 - 8 minutes (depending on the type of problems) to answer the questions. At the end of the time, the students rotate to the next set of desks where they will find the answers to their questions on the back of the next card. Simple.

I like this activity because it gives the students immediate feedback. My students also seem to ask more questions during this type of review. When I started writing this post I didn't think the activity had much to do with test-taking strategies. Then I realized that the students are doing problems and assessing themselves right away, which is what they should be doing as they study for an exam. The problems on the cards are also a nice preview of what the test will look like. Now the trick is to get my students to understand and better utilize these very rudimentary procedures.

Problem Trees: A Graphic Organizer

This is the 3rd post in a series of 5 on review activities that also teach test-taking skills.



Review Activities to Make Real Students
Predicting Exam Questions
Expert Study Teams


When I arrived at UC Davis as a youngster, I was under the impression that I had study skills. I can tell you now that I did not. I knew how to take notes, but studying effectively was something I had to learn. One of the best study sessions I ever participated in took place the night before my Calculus II exam. A friend and I simply taught ourselves how to identify which method of integration to use based on what we saw in the problem.

My third review idea sort of comes from this. I think that many geometry students struggle on tests because they cannot figure out what in the long list of definitions, postulates, and theorems is needed to do each problem. Of course, I haven't tested this yet, but here's the idea.

Give each group a set of cards with each card containing a vocabulary term, a theorem name, a postulate name, or a problem. The goal is for the students to arrange the cards so that the vocab, theorem, and postulate cards "point to" the problems that use them. I would leave it up to the students to determine what is meant by "point to". When finished, the students could create a graphic organizer to display the information.

I might actually have to do this activity myself before presenting it to the students. This way I could predict potential trouble spots. I think my students might surprise me though. They have a tendency to be very creative when under the gun. The ultimate goal though? A deeper understanding of how the geometry machine works via a big picture view of the way the pieces fit together.

Expert Study Teams

This is part 2 of a 5-part series on review activities that could be useful for reviewing before exams and for teaching students test-taking skills.



Review Activities to Make Real Students
Predicting Exam Questions


Okay. I kind of stole this idea from a project that I did with my AVID freshmen last year. I thought I'd take advantage of the fact that my students are already organized into Survivor Geometry tribes. Each tribe member will be assigned a topic from the upcoming exam. Then students will separate into what I call "expert" groups by topic to review their topic and do some practice problems. After a predetermined amount of time students will return to their tribes. Each student will then serve as the specialist for his topic as the tribe works through a review assignment.

The goal here is to develop the idea of study groups. In class, I call them study teams to reinforce the concept of working together. It would be interesting to find a way to get the students to extend these study team sessions outside of the classroom. You may be scratching your head right now if your students already know this little trick, but at our school study is a 5-letter word. Who knows? Maybe this divide and conquer method is a way to get them to buy in.

Predicting Exam Questions

This is the first of a 5-part series on activities that could be used for review before an exam.




Review Activities To Make Real Students


As a high school student I worked through problems in the textbook to study for my math exams. As a teacher, however, I'm finding that my students don't seem to realize what the test problems will look like even though I tell them exactly what topics will be covered. Here is my solution.

• I put my students in groups of 4 and gave them the task of creating 3 problems that could be on our first exam. Each problem had to have 2 parts and each had to match one of the 3 concepts that were being tested.

• I only allowed the students to use their notes and their homework assignments in order to give them a feel for how notes, homework, and exams were all related. They couldn't use the actual problems from the assignments and examples, but they could emulate them.

• The groups used poster paper to put their problems up around the classroom.

• After we assessed that everything looked okay, I told the students that they now had a good selection of practice questions and instructed them to write them down. We did this in sort of a walk about fashion with each group starting at a different poster and working its way around the room.

• We ran out of time, but my next step was to have each group post the answers to their problems so their classmates would be able to check their work.

This little activity worked out a little better than I expected. Many of my students wanted to just start making up problems that were like those on the homework without regard to whether or not they covered the topics that would be on the test. I discovered that many of my students didn't relate inductive reasoning to the first lesson that we did. My goal was to help my students take the mystery out of what they'd see on the test. I believe that students who learn this test taking skill will have less anxiety and perform better. I guess I'll get to check this little conjecture when I grade their exams later today.