My CP Algebra 1 classes have started factoring trinomial today, where a = 1. I have always enjoyed factoring trinomials personally, however many of my students don't share my enthusiasm. It baffles me that they don't enjoy this puzzle of sorts. "Can you think of two numbers that add to this and multiply to that?" I believe they don't see it as a puzzle because I don't present it as a puzzle. I changed that this year.
I started class by giving each student an index card. I asked them to write their name on the lined side and two integers from -12 to 12 except 0. Like this:
Next I told them to flip the index card over to the blank side and write the sum and product of the two numbers like this:
Once they were all finished I took the time to walk around the each student and make sure he/she added and multiplied correctly. It only took a minute but I did find a few mistakes.
Then the fun begins. Each student was to hold his index card so that the Add/Multiply side was showing and the two original numbers couldn't be seen. All students were asked to stand up and go from person to person and try to figure out their puzzle. In other words, "What were their original two numbers?"
The students really seemed to enjoy trying to figure out each other's puzzles. They especially liked when they stumped someone.
Overall, I think the activity was a success. But I did find this stink-poop drawing on the board after class so I'm not so sure anymore.
Review linear equations: slope, intercepts, equations, graphs, and solution ordered pairs
I created this game a few years ago to help my students review linear equations. The students were doing fine with the topics when it was presented one at a time, but this game requires them to use all those topics at once. I remember one students saying, "I have never worked this hard in a math class!"
For the game, you will present the students will one graphed line at a time, they are required to match 5 attributes to that line as quickly and accurately as they can. To do this, the cards with the attributes are dealt to the teams randomly. The first team to identify a matching card will be rewarded with 5 points, the next correct team will receive 4 points, etc. until all 5 cards are matched.
If a team incorrectly identifies a card, they will lose 2 points from their score. Likewise, if a team has a matching card and doesn't recognize it, they will lose 2 points.
After all 10 lines have been displayed, the team with the highest score is the winner.
Print a copy of the answer key. Click here for the answer key. The answer key is the third page of that document. I laminated my copy of the answer key and use a dry erase marker to keep track of what cards have been matched during the game.
Beginning of Class:
Divide your class into five (5) teams and give each team ten (10) random game cards. Instruct them to look over the cards. Make sure each team member can see all the cards and the images being displayed.
Display the first line and remind the students that there are five cards out there that match the graphed line (slope and y-int, slope and point, equation, two ordered pairs, intercepts). Once a team believes they have a match, they tell you the code on the bottom of the card.
The first correct team is awarded 5 points
The second correct team is awarded 4 points
The third correct team is awarded 3 points
The fourth correct team is awarded 2 points
The fifth correct team is awarded 1 point
If a team is incorrect, their score is reduced by 2.
If a team has a matching card, but doesn't recognize it, their score is reduced by 2.
Note - In order to avoid having teams with negative scores, you might want to start each team with a certain amount of points. Perhaps each team could start with 10 points.
Make the students aware that since the cards were distributed randomly, a team may have more than one matching card on a line, or even no cards that match a particular line.
After each line, instruct the students that those five cards will not match anymore lines and they can set them to the side. After each line, I like to go over any incorrect matches that the students made (not that they listen, but I try).
Tips and Tricks:
I do not let the students know that there are 10 lines. I tell them that there are 11, that way once we reach the 10th line they will still look to see if cards match rather than automatically calling out the codes. This only works the first time we play the game.
Make sure all students can see the projection.
Make sure all team members agree on a card before checking your answer key.
Rules and Game Play Video:
I apologize for the volume of this video. I had to turn my speaker all the way up to hear it and I will invest in a microphone in the future :)
A few months ago I decided to give Adsense a try. Why not? It's free money. So, what to do with this free money? Well, a giveaway of course. The only reason I received any of this is because you are clicking on the ads on my blog page. So, keep clicking on those ads and I'll keep giving stuff away. Thank you!
From my first adsense income, I will send a copy of my game Absolutely Valuable to one of you. All you have to do is click on the link below and follow the directions (you will need a Twitter account). That's it. Don't forget to click on an ad for brownie points while you're here.
Now we tackle factoring trinomials that have minus or negative signs. This time the blue tiles are positive and the pink tiles are negative. Each student was given a set of blue and pink tiles, while I made large tiles to use on the class white board.
Here's what I told my students:
If the last sign in the expression is minus (negative), then the positive and negative x tiles must be kept separate. For instance, the negative Xs are built to the right while the positive Xs are built down (or vice versa).
In the example below, we are factoring x^2 - 2x - 8. We start with a blue x^2 tile, 2 pink x tiles, and 8 pink 1 tiles.
I place the x^2 tile in the upper left like I always do and the 2 pink x tiles to the right of it. As you can see, the 1 tiles are just sitting there not fitting in to the rectangle.
There is where things get interesting, I hold up one pink x tile and one blue x tile and ask the students what is the sum of those two tiles. Eventually, they say 0. Then I ask if I would change the value of the expression if I add zero to it. Most students tell me that's okay.
To keep building, I can place one pink and one blue x tile, then fill in as many of the 1 tiles to complete the rectangle. If there are 1 tiles remaining, repeat the process. Finally you can see that the answer is (x + 2)(x - 4)
This year I decided to teach factoring trinomials algebraically first, then with Algebra tiles. Today was their first day (ever) with the tiles. There is certainly a learning curve for students when working with Algebra tiles. My students claim they never saw such a thing....it's possible.
Today we only worked with x^2 + bx + c where b and c were positive numbers.
I gave some rules:
1) Begin building your rectangle with the x^2 square in the upper left of your work area.
2) Build off your x^2 with x rectangles to the right and down.
3) Fill in the bottom right of your rectangle with the 1 squares.
4) You must create a rectangle (no holes).
Before class started I downloaded this template for algebra tiles, copied them on different color paper, cut them out myself (because my students take forever to cut), and bagged them in Ziplock bags. In hindsight, I should have used red and green paper to use later with negative and positive.
Next, I needed to make sure that the students have enough tiles to create the rectangles.
Here are all the trinomials that will work this this tile template:
I've been in this funk lately, hence the lack of posts. It's not that I don't want to post, it's just that I have nothing interesting to post about.
They way I function is that I put all my effort and heart into a current project. When our department was involved with the PARLO study, it was all I thought about: formative assessment, interviews with students, high performance questions and activities, clear learning goals, etc. But it's been a few years since the study and now I'm focused on game design. I spend every free minute thinking about, working on, and talking about game design and that leaves my 45 minute prep to work on my school work. I'm not proud of this (actually I'm embarrassed by it), but most of my lessons are direct instruction and I'M BORED!!
The answer is clear; stop designing games. But that's not advice I want to follow because I really enjoy designing games. If I had to pick what I do in my evenings and my choices were to create dynamic lesson plans or design games, I pick design games.
This is why it bothers me so much. If I want to be a great teacher I have to forfeit my hobbies to do so. Or in other words, teaching has to be my hobby. However, the school district will provide me with enough time to be a mediocre teacher. Why can I be a great teacher on school time?