Saturday, September 29, 2007

Lesson Idea: Proportions and Ratios using Statues and Action Figures

My students had a lot of trouble with applying proportions and ratios to geometric figures and other problem situations, and I believed that the problem was in their inability to visualize the idea of scaling something up or down. I gave innumerable examples, of course, but being able to see in your mind what is described in a word problem is probably the most difficult skill needed to master Algebra I and pass the 9th grade math TAKS test (our state standardized test). They also had trouble doing measurement problems.

So I came up with a simple idea last year: why not have the students measure themselves and figure out the dimensions of a giant statue of themselves? They would have to make measurements, use measurements, and understand and solve proportions and ratios. Students would have to get up out of their chairs to make the measurements, do their own calculations with their own numbers, and would be forced to visualize a real life proportion problem.

After a successful trial during tutoring last year, I brought back the idea for this year's class. The only supply needed is yardsticks (ask the science teachers). Here's the plan:
  1. I introduced the activity by asking students to imagine that it's the far future, and they're all doctors, lawyers, engineers, scientists, and Presidents of the United States. They're so famous that their hometown wants to honor them with a giant statue in the middle of town. In order to make the statue lifelike, they need to use proportions to make sure that you don't look like a telephone pole or worse, Eric Cartman.
  2. Students make three measurements (in inches): height, shoulder width, and shoe length. They have to work together to get the measurements done quickly and easily.
  3. Optionally, they can measure a partner to give them something to compare their measurements to.
  4. Students return to their desks to make calculations; the teacher gives examples and then monitors independent work.
The questions are rather straightforward but require multiple calculations. I also included at this point in the lesson the idea of shrinking my students down to action figure size. Here are the questions:
  1. If we wanted to build a 50 ft tall statue, how wide and long would it be?
  2. If we decided the statue would be a ratio of 5:1 bigger than you, what would the dimensions be?
  3. If we wanted to make a 4 in tall action figure, how wide and long would it be?
  4. If we were making an action figure that was a ratio of 1:10 smaller than you, what would the dimensions be?
As an assessment you could give them standardized test-style questions with similar triangles (and other polygons) and word problems requiring application of proportions and ratios. I included a similar question on our weekly quiz which is linked in the resources at the end of this post.

Pitfalls and suggestions:
  • When I originally tried this activity, I displayed the questions via document camera (fancy replacement for an overhead projector) with the idea that I would write in examples and how to set up the proportions and ratios so we could do it together. I lost their attention after so effectively gaining it with the initial part of the activity. I corrected this in later classes by including a clear graphic organizer.
  • While getting them out of their desks once and a while is a good idea, you need to manage the activity effectively. Make sure you have enough yardsticks for pairs or groups of three. Give them a time limit and hold them to it. Most importantly, make sure their are no yardstick fights!
  • Many of my students had trouble setting up proportions themselves because they wanted to do something with all three dimensions at the same time. Thus, it might make sense to start with a two-dimensional idea (giant painting, miniature cut-outs) and then add the third after you are sure they have mastered it.
  • This activity is meant to be done after you have taught solving proportions, what ratios are and converting ratios to fractions.
  • This can be a very difficult concept to grasp, and thus this activity might be better suited for later in the year when you are targeting students to help them pass standardized and end-of-year exams.
Statue of Me documents available at The TeachForever Notebook:
  1. Statue of Me initial activity - introduction and questions for display on overhead
  2. Statue of Me Follow-Up Activity - Complete activity with graphic organizer that helps spell out what to do with their measurements
  3. Weekly Quiz - Covers proportions, ratios, rates and percents. Included is an example problem connected to the Statue of Me activity.
I think this idea could use a lot of work, so I appreciate any suggestions and ideas you have. Please post a comment or email me (remove NOSPAM)!

Thursday, September 27, 2007

Triumph at HESTEC Robotics Day

Today I was lucky enough to bring a group of 5 students to HESTEC Robotics Day at the University of Texas-Pan American in Edinburg, TX. HESTEC stands for the Hispanic Engineering, Science and Techonology Conference, which is now a week long event. This year's event was big enough to draw Speaker of the House Nancy Pelosi (D-CA), who spoke glowingly of the conference's accomplishments over the years and the beneficial work of local Congressman Ruben Hinojosa (D-TX). We saw some of her speech via video, but we were whisked away to our day-long project shortly after she began.

The students were given a huge 600+ piece K'NEX EDUCATION Solar Energy System. The goal was to build a working car that would be raced against teams from 40+ area schools later in the day. I was not allowed to help them--I was relegated to keeping time, offering words of encouragement and trying to keep the other teams from blatantly cheating. Instead, the students were aided by a university engineering student who worked well with them.

I saw immediately how excited and engaged these students were. As soon as we began they were talking about aerodynamics, how engines work, and how different weights and designs would effect the final product. After 2.5 hours of work inside a campus fine arts auditorium, however, our car was only partly finished. We headed out to the campus track to test and fix our car.

As per usual in south Texas, it was blistering in the midday sun (my face is an enchanting shade of red) and our car was not ready. The kids never gave up--there were plenty of teams that threw in the towel early, but these kids worked hard to figure out how to get it working.

The first of 3 trial runs was a disaster. The car didn't move an inch. When the trials started, the time in between to make adjustments was short, so much so that the kids were willing to skip their second trial to completely redo the car to make it work. They tore it all apart, moved the engine around and changed entirely the way it made the wheels spin.

But this time, it worked.

There was almost no time for testing--one dry run was it before it was time for our third and last trial. The rules stated that the top ten times of all trial runs would make it to the finals. I had been running back and forth between the other trials and their diligent work, and it became clear that very few of the cars were even reaching the finish line. This meant that with one good run we had as good a chance as anybody to make the top ten.

And so there I was, sweating and trying to calm my restless leg, feeling useless and helpless because I couldn't do anything to help them besides tell them that they still had an excellent chance.

Once the car started, it just kept going, reaching the finish line successfully in about 17.6 seconds. The kids were ecstatic for simply making a successful run, as they too had seen very few cars make it at all. When the results came in, we didn't just make it by a thread. We rocked the house: the 3rd fastest trial of the 40+ teams out there. I could barely contain myself that not only had they persevered and made the finals, but had a legitimate shot at placing and going home big winners.

Did I mention the prizes at stake?
  1. 1st Place: Laptops for every student
  2. 2nd Place: iPods
  3. 3rd Place: iPod Nanos
Although these had piqued their interest at the beginning of the day, it was clear this was the farthest thing from their minds. They wanted to win, but not as much as they wanted it to work as it had in that last miracle run. As the race began, our hearts collectively stopped, and almost as soon as they did they resumed again, for it was all over too soon.

I could rehash the griping about the inconsistent enforcement of the rules and the underhanded tactics of other teams that I made to the people in charge after our miracle run ended, but the truth remains: in what could have been their finest hour as would-be engineers, the car once again wouldn't work. Even if the team that went on to win first place had been dealt with appropriately, it wouldn't have changed our outcome, and that was the hardest thing to accept.

Except that it was only me who had trouble accepting it. My students were disappointed, but still riding the high of success in the face of failure, of triumph on what could have been dismissed as just another day off from school. They saw and heard my outrage, and they understood it, but their spirits were never crushed. I realized that they had accomplished everything I could have hoped for and more. In their words:
  • "At least we had fun!"
  • "I learned never to give up."
  • "We can come back next year, right?"
  • "When's the next competition?"
  • "Sir, are you going to have the kit? Because I want to build another one."
With our great success on Robotics Day, now my administration is suggesting I start some sort of engineering club. I hope I'm lucky enough to be able to.

Thursday, September 20, 2007

Basketball review game

I have always used games to review for tests and quizzes--they make the often painful work of reviewing fun, easy and memorable, they help break up a sometimes boring routine, and they can make your students excited about coming to class. Last year, I developed a version of the common basketball review game. The setup and rules are simple (see the picture below as well):
  1. The desks are arranged into two groups (3 desks deep) facing a wide center aisle. The hoop is at the end of the aisle.
  2. The class is split into two teams (one side vs. the other).
  3. One student from each team comes to the board to complete a question, whoever answers it correctly first gets a shot for their team.

The twist I added to the versions I've read about is that I thought it would be fun to use one of those giant inflatable basketball hoops, such as the Sportscraft Monster Basketball Set you see in this picture from last year. I can't stand the idea of using a garbage can as a "hoop" and wads of paper as a "ball" as this basketball review game (via About.com) calls for--my students would be insulted if I tried to pull that trick. I wanted it to be as authentic as possible without leaving the room.

I looked around at the local big-box retailer and saw many versions of giant outdoor hoops. The one I actually preferred, which looked like those round ones that you usually see floating in pools, was $60. I have been trying to cut back on the whole spend-thousands-out-of-pocket thing and this was simply too much for something I could only use sparingly. When I found the Monster Basketball Set for $20, I picked it up immediately. It's a little over 6' tall and the ball is 16" in diameter, big enough to make an impression but small enough to fit in the room.

Students took shots from the front of the room (near the first row of chairs), which made the shot difficult but not impossible (due to the ceiling, you had to throw it straight or underhand in order to make it). When we played last year, the games were always low scoring (2 or 3 points total) even when we plowed through a lot of questions and the students took a lot of shots.

I just ran this game again this year, and this is my advice for running it smoothly in your classroom:
  • Make sure that while the two (or more) students are competing for a shot up at the board that everyone else is doing the same work. The easiest way to do this is to inform your kids you'll be collecting all of the work on all of the problems we did a the end of class, and since you would review each answer there would be little excuse for students not having complete work and answers for each problem.
  • The game play allows consistent opportunities for the teacher to explain common mistakes and reteach difficult items by design. I usually confirm a winner, let them take their shot, and then discuss what the winner did right and what (if any) mistakes the other player had made.
  • This game is ideal for easier content that only requires memorization (the lower levels of Bloom's Taxonomy), although it can be used for concepts that require multiple steps and require higher order thinking (it just may take longer and you won't be able to complete as many questions).
  • Depending on your students' level of confidence on the topic being reviewed, you can choose to give them the problem first with a chance for them to work on it before coming to the board (which I did today for the challenging topic of solving two-step equations and inequalities) or keeping the questions a surprise until they are already waiting at the board (which I did last year when I was trying to get them to visualize and sketch linear equations without a calculator). The latter is better when you are focused on the type of easy material I described above.
  • As with any game, you need very good classroom management in order to keep everything under control. If you have problems with vandalism, or don't believe your students can handle this without hitting things or each other with the ball, don't even think about using this game.
The game keeps the kids engaged and while they can easily get overexcited, in a well-managed classroom you should be able to tell them the alternative will be the most boring thing you can think of, and the mere idea of that will keep them focused.

Unfortunately, my hoop did spring a leak after repeated uses last year and being stuffed into a box over the summer this year. I couldn't patch it (I didn't keep any of the patching material included with the game) even with a ton of duct tape and spent too much time inflating it repeatedly throughout the day. Alas, this game will have to go on hiatus until I can get another (or better) hoop.

I am extremely happy to report that the grades on today's weekly quiz, covering all the material reviewed yesterday in the game, are excellent. My students made a huge jump in comprehension and retention this week compared to how they did on similar quizzes the last 2 weeks.

[Update 4/21/10: This idea and many others are part of my recently updated book Ten Cheap Lessons: Second Edition ($9.95 paperback, $2.50 digital).]

Saturday, September 15, 2007

Inspiration from last year's students

Recently I wrote here that on the first day of school, I had read quotes from end-of-year surveys from last year to my new students. My students had answered the question: "If you knew someone in the 8th grade who was going to be in this class next year, what would you tell them?" I also left a space for them to write whatever they wanted, which also garnered interesting answers.

I think it's important for all teachers to ask these sorts of questions and to look back at student responses periodically to both inspire us to keep going and tell us what we need to do to do well this year. I wanted to share some of the responses that a question like this can get:
To not sit next to his friend and put attention when the teacher is talking and ask questions if you have problems.

To follow instructions and try the best they can do cause when I heard Algebra I said I think I am not going to pass that class, but I did.

To be very responsible for all the worksheets she does because they're all for a grade even when there is a substitute! ...It has been great as you know you helped me succeed to the next level 10th I passed my Math TAKS Thank you for teaching me for reaching my goal!

No, don't, you should consider flunking and staying in 8th grade another year LOL! JK!

Yes thank you for all the help you have given me. I really appreciate all the time you gave up for us. Seriously I would of probably failed if you showed us you didn't care. Cuz then I would not care either.

To pay attention and to do your work and take notes and you will pass the class with no problems... this year was good and I learned a lot and it was the first time I got commended on the math test.

I would tell him/her that you were a cool teacher, but not to joke around too much because there is a time & place for that. Also he/she would learn a lot from you.

I would tell them to do there work because the teacher is really badas* and you will learn a lot if you pay attention.

Always pay attention + please try real hard not to piss him off cuz then you + the sir will have a BAD DAY... thank you for always being there for me + actually caring for me + teaching me (not like the other math teachers I've had before)

I would tell him/her that its better if you pay attention since the beginning of the year because if you don't pay attention and don't respect the teacher with Mr. D you are not going to pass TAKS

Mr. D this year has been great as you as my math teacher becaus I asked my other friends what have they learned in there other math class and they said nothing at all!!!!!
This is the stuff that keeps me going. I see the same themes every year in their responses--thank you for caring, I learned a lot--and that all the hard work we did was appreciated and had a positive impact.

I'm not posting this to brag. In fact, after seeing some recent poor test results of my current group, I need to see this to build my confidence back up. While I was a Teach for America corps member, a common punchline to our jokes was "...and that's why I Teach for America!" But the truth is having an impact like I think I did last year is why I got involved in the first place, and why I will continue teaching. Nevertheless, though I may seem confident in my ideas I am constantly questioning my ability; I see myself making mistakes I shouldn't be making in my 5th year, and I wonder whether I'm doing a good job at all.

I do hope to give some inspiration to others that your hard work and dedication to your students is going to pay off, and that you continue in the noblest of fields.

Fantasy Football and Mathematics Draft Day

Friday was draft day for our Fantasy Football and Mathematics project. Unfortunately, drafting took far longer than I anticipated. We could have finished with the entire period devoted to drafting, but they were having trouble with the short weekly quiz we did beforehand and took far longer than expected.

After hinting about fantasy football since the first day of school, last Friday I formally announced our project and asked students to start gathering information. I provided a copy of the roster sheet they would need to fill out later so they could take notes during Week 1 of the NFL season. I listed the many ways they could find information about players without watching games (which, understandably, some students didn't want to do):
  • Watch highlight shows on local news, ESPN (NFL Live, NFL Primetime, Sunday NFL Countdown, Monday Night Countdown), and FSN
  • Go to ESPN.com, CBSSportsLine.com, NFL.com, SI.com for ideas
  • Type in "fantasy football" in any search engine
  • Ask a friend or family member who knows/watches a lot of football
  • Read one of the 9 different fantasy football magazines I had purchased
  • Alternatively, wait until Monday and Tuesday and read our local newspaper, The Monitor, in class (free copies are delivered daily through the Newspapers in Education program)
Most importantly, I emphasized that you don't need to know anything about football to play the game. The great equalizer is the $40 million salary cap. This means that even if you know all the best players in the league, you can't afford to have all of them on your team. Also, students are allowed to pick the same players if they want to, so the background knowledge necessary for your average online FF league isn't needed.

I had to guide many students past the frustration of not knowing anything about football by emphasizing that point--if all else fails, they could do just fine picking anyone that could fit under the cap. Even if you want to see pictures of players so you can fill your roster with the hottest guys (as some of my students are doing) you can. You'll probably have no more or less success than anyone else.

The other side is that even when they did excellent research, as one Pre-AP student did, they might come up with a roster no one (in fantasy or real life) could ever afford:
  1. QB - Peyton Manning, IND
  2. QB - Tom Brady, NE
  3. RB - LaDainian Tomlinson, SD
  4. RB - Steven Jackson, STL
  5. RB - Frank Gore, SF
  6. WR - Marvin Harrison, IND
  7. WR - Terrell Owens, DAL
  8. WR - Chad Johnson, CIN
  9. WR - Steve Smith, CAR
  10. K - Adam Vinatieri, IND
  11. K - Robbie Gould, CHI
  12. DEF - Chicago
  13. DEF - San Diego
I told her she had done an amazing job assembling a great team, but the salary cap was going to make her team a little less like a Pro Bowl roster and more like the Kansas City Chiefs. Based on Fantasy Football and Mathematics' player values, this team would probably cost 2 or 3 times the cap. For example, the 2 most expensive players, Tomlinson and Jackson, cost about $22 million together (and you'd still have to fill 11 other positions).

Even though no class finished filling out their rosters, this was a great start because now students have a jumping off point. Many were excited to go home and do "research" over the weekend. Some students told me they had a sibling or cousin who they would seek out this weekend to help fill out their rosters, and I'm glad to both get them excited about school and foster some family bonding.

They must have their roster set by next Friday, in time for Week 3. I expect that students will pick up on how good or bad their team is fairly quickly and be scrambling to make adjustments as the weeks go on. After Week 3, they will learn how to calculate their points. Later, I can incorporate several activities and ideas from the FSM curriculum to extend the project into other areas.

So here's my list of what's needed for draft day:
  1. Build pre-draft buzz - Start talking about it ASAP, discuss the information gathering suggestions above, start bringing in newspapers and magazines
  2. Player values printouts - Free with the FFM Teacher's Guide (if you have an older edition of the guide you can purchase this year's numbers for $4), or already included in the FFM Student Workbook
  3. Handout of FF Description and Rules/Fantasy Roster - Again, you can get this from the Teacher's Guide or Student Workbook. This describes the basics including the salary cap.
  4. FF related magazines - I found 9 different titles out there, but they are expensive (usually a $7+ cover price)
Optionally, Internet access would be helpful so that students could find up-to-the-minute information.

If anyone else reading the blog is using this system, I'd love to hear about it. Please leave feedback or email me!

Tuesday, September 11, 2007

Lesson Plan: Graphing on the Coordinate Plane using "Battleship" game

Yesterday in class we played SINK THE SIR! (a play both on what kids call male teachers in the RGV, "the Sir," and on the old movie Sink the Bismark!), a version of the game Battleship . The main objective is for students to know how to identify and graph points correctly and to learn the necessary vocabulary:
Last year, I found a lesson plan on Education World called Play Battleship on Graph Paper. The only real difference between the real game and the lesson was that the original's grid was replaced with a coordinate plane. I followed this lesson closely, having the students play against each other. The students certainly had a lot of fun, and got familiar with the coordinate plane, but the objectives were totally lost. I did a poor job of explaining the directions and making it easy to do; the result was that students were graphing points incorrectly and confusing each other. Some students were just fooling around because the student vs. student design made monitoring difficult. Later in the year, far too many students still had trouble graphing points accurately, which could be traced directly back to the game.

I was determined to fix the problems and make "Battleship" work for my classroom. The first thing I did was change the game to a whole-class activity: teacher vs. students, sink "The Sir" before he sinks you.

Each student had a graphic organizer with directions, a table for coordinates fired at me and fired at them, and a coordinate plane to keep track of their ships. On the whiteboard I had the plane where everyone could keep track of when they hit or missed "the Sir". After labeling parts of the graph (x and y axes, origin and quadrants), the rest of the game remained the same. The slightly tweaked lesson design allowed me to make sure the objective was covered thoroughly because I could come back to the key points easily:
  1. With each shot made, I could ask students to identify the quadrant or axis where the point was located.
  2. I could also give them multiple options for the location by pointing at my coordinate plane to check that they understand how to read ordered pairs, i.e. knowing the difference between (-2, 3) vs. (3, -2) vs. (2, -3)
  3. I focused on points on the x-axis and y-axis, which the students always mix up.
  4. I was able to give hints to check their understanding, i.e. "One of my ships is located along the y-axis" or "I have a ship in Quadrant II" and then see if the next student fired at the right area.
  5. I also connected the game to graphing linear equations by having my aircraft carrier located along the line y=x (a parent function), discussing how to figure out where that line would be and then aiming at points along it.
The possibilities are endless for how many directions and how much material you can cover in this activity. Since the teacher directs the activity and the students are engaged (because they love competition and love beating you even more), it's easy for you to steer them towards many different objectives. You could easily incorporate:
  • more linear equations
  • domain and range
  • linear inequalities (identifying points that satisfy a linear inequality is a common question on our state standardized math test, like #51 on this released test)
  • transformations
  • quadratic and absolute value equations
You could do this game for half of the class period (as I did due to time constraints), but you wouldn't need more than a regular 45-55 minute period to complete the game and have students complete follow-up practice questions. The students did excellent on practice problems today, so I think this year's version of the game was a great success (time will tell if these concepts remain with them throughout the year).

If you decide to use this lesson, I recommend you change the domain and range of the graph -4 to 4 instead of -5 to 5. The latter was a bit too big and made it take a little longer than necessary for us to sink each other's ships. You could also adapt this to return to the student vs. student format, but I think you then miss out on the possibilities I wrote about above.

It also helps to look the part; I wore a $7 captain's hat from the local costume shop and taped "CAPTAIN" on my school ID. You could also cue up some video or audio clips of torpedoes firing and ships exploding for dramatic effect. Have fun with it--then your students will too!



UPDATE: Check out the revised 2008 edition of this game!

Wednesday, September 5, 2007

Follow-Up: Combining like terms card game

I tested out the Like Terms card game in class today with fairly positive results. It took me a few periods to work out the best way to introduce the game and explain the rules, requiring a lot of adjustment on the fly, but by the end of the day things were going swimmingly.

I made a false assumption that many students had played a variation of rummy or any card games where you take a card, make a play, and discard. However, beyond Uno or poker, many students were unfamiliar with this style of game. Thus, I had students following the rules to make groups of 3 or 4 like terms (which is good) but through varying methods of obtaining cards.

As far as knowing which cards go together (and thus which terms can be combined), I think there was no problem--that part of the objective was clear even in classes where the rules of the game were confusing. What was lacking in the classes earlier in the day was a better explanation on how to score the game--taking the tally of each group of cards and turning it into a longer expression.

I realized that I needed to walk everyone through a turn or two to get things started. At first, I would explain the rules myself, showing examples from the decks and referring to the Like Terms rules and scoring guide I had written before arranging them into groups or having the cards dealt. This was a significant mistake on my part that gave some students in earlier classes quite a bit of confusion.

Later in the day, I made sure the groups were formed and cards were dealt before I explained anything. Then I had the first person in each group complete a turn along with me walking the whole group through it, so each group saw a clear example and knew how to proceed. I held off on the scoring until a few groups had ended the game, and using the score tracking sheet I had printed on the back of the directions, wrote out a full example to show them when and what to add or subtract.

To clear up the morning confusion and review for everyone who did get it, I filled out a score sheet with 2 sample scores, one from a winning hand and one from a losing one, and will ask them to total up the scores properly to start tomorrow's class. I told students all day that as long as they understood and remember the main idea of the game--which terms are like terms and how to simplify expressions containing them--it doesn't matter if the rules of the game themselves were confusing.

So if you plan on doing something like this, be sure to:
  1. Arrange students into groups and distribute cards first.
  2. Walk students through the first turn (or more if needed).
  3. Understand that it may take time for students to grasp the rules of the game (but probably not the concept).
  4. Constantly monitor and be prepared to walk groups through the game procedures to get them to the point where they can play on their own.
  5. I recommend having groups play through no more than 2 full games.
  6. Design a closing activity, even as simple as 1-5 sample questions on the overhead, to end the lesson.
  7. Follow up the next day with a filled out sample score sheet (you can borrow ones from students that are correct and cover the totals OR take one that is incorrect and have the students identify the mistakes) and related simplification activities (we will be doing the ever-present "Find the perimeter of the polygon" where the sides are labeled with algebraic expressions.