My new school is one-on-one instruction. Just a teacher and a student. In some ways this is AMAZING. We can cover so much material, I can gear my explanations specifically to that student and take their learning styles into account, I can really see if they get it or if they're just faking it so as not to stand out. It is not amazing in terms of games though. None of my old games will really work. A lot of them are team based, or competition based or communication/discussion based. I can play some of the competition games with the student, but any of the games that are based on knowledge or practice are not too much fun because I'll always either beat the student or the student will know I'm going easy on them. One of my boys got very upset with me when he realized I was "letting" him win. I don't enjoy games where winning is based on chance (i.e. board games where you roll a die and answer the problem you land on.) Or where math is just a hurdle to play the game, not the focus of it.
I've been writing a lesson plan on equations of horizontal, vertical, parallel and perpendicular lines and I came up with a game that I think will be good. Winning takes strategy combined with luck and the strategy is independent of, yet still related to knowledge of the material. This means that hopefully, the student will have a chance of beating me while still practicing equation writing skills. I have NO idea if this game will work, but I thought I'd share it.
Horizontal, Vertical, Parallel and Perpendicular Lines Game
Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts
Sunday, November 18, 2012
Wednesday, February 1, 2012
Absolute Value Warm-up
I always try to plan every lesson to death. I don't plan out minute by minute, but I do try to figure out exactly what I'm going to say, how I'm going to introduce an activity, exactly how the students will be organized for this or that problem, but sometimes I forget that the best activities or lessons can spring organically out of our collective energy. I had an idea for a warm-up problem today about 2 minutes before class was going to begin, and I decided to run with it.
Our school is in Sheridan- which is a very small town, so most of the teachers and the students live in McMinnville which is a much larger town 20 minutes away. The topic I was planning to introduce was graphing absolute value functions as the culmination of our algebra 1 unit on linear relationships.
When the students came in I asked who I should make part of the warm-up problem and everyone volunteered. I picked two students- one who is 15 and one who is 13. I said that the 15 year old just got his license but because he's so nervous, he drives to McMinnville at an agonizingly slow 10 mph. Sheridan and McMinnville are about 20 miles away from each other. At this point, my students- on their own I might add- started making x-y tables to figure out how far the two students are from McMinnville at any given time. We made a simple table on the board and realized that it took the two students two hours to get to McMinnville from Sheridan. At this point the students start poking fun at the 15 year old because he's driving so slowly, and he starts defending himself saying he doesn't want to kill anyone and however long it takes doesn't matter. I asked the students if this relationship is linear and if we can model it with the equation of a line and immediately they start finding the equation for the line. At this point I interjected with a new piece of information. The 13 year old navigator wasn't paying attention and forgot to tell the 15 year old to stop and that they made it to McMinnville safely. My 13 year old student says that actually, she fell asleep. So the 15 year old driver drives right on through McMinnville and out the other side. So we continue the table for distance vs. time, but now they're getting further and further away from McMinnville. So here's what our table looked like:
Hours driving 0 1 2 3 4
Distance from McMinnville 20 10 0 10 20
It made perfect sense to the students why we didn't go into the negatives, why the values started to "bounce" back up. The students were having a lot of fun poking fun at the 15 year old and the 13 year old for driving so slowly and for spacing out and missing McMinnville. One student even made his own table asserting that, since McMinnville is 4 miles across, the second half of the table should go 6, then 14 instead of 10 then 20.
After this warm up problem I had no trouble at all showing the students that an absolute value equation "bounces" but that on either side of the vertex, we have linear relationships. I had complete engagement with the rest of the lesson.
I think maybe why it worked so well was that the problem was almost a "make your own adventure". The students were able to add details for fun or change the numbers to fit in with their understandings of the real world. I always start lessons with a warm-up that tries to pull the material we're learning that day into a real-world context to see what kinds of intuition the students already have for the subject material, but rarely does it work so well. Sometimes no planning is the best planning- but I wish there were a linear relationship between how much time I spend on a lesson and how well it goes because then every day would be awesome.
Our school is in Sheridan- which is a very small town, so most of the teachers and the students live in McMinnville which is a much larger town 20 minutes away. The topic I was planning to introduce was graphing absolute value functions as the culmination of our algebra 1 unit on linear relationships.
When the students came in I asked who I should make part of the warm-up problem and everyone volunteered. I picked two students- one who is 15 and one who is 13. I said that the 15 year old just got his license but because he's so nervous, he drives to McMinnville at an agonizingly slow 10 mph. Sheridan and McMinnville are about 20 miles away from each other. At this point, my students- on their own I might add- started making x-y tables to figure out how far the two students are from McMinnville at any given time. We made a simple table on the board and realized that it took the two students two hours to get to McMinnville from Sheridan. At this point the students start poking fun at the 15 year old because he's driving so slowly, and he starts defending himself saying he doesn't want to kill anyone and however long it takes doesn't matter. I asked the students if this relationship is linear and if we can model it with the equation of a line and immediately they start finding the equation for the line. At this point I interjected with a new piece of information. The 13 year old navigator wasn't paying attention and forgot to tell the 15 year old to stop and that they made it to McMinnville safely. My 13 year old student says that actually, she fell asleep. So the 15 year old driver drives right on through McMinnville and out the other side. So we continue the table for distance vs. time, but now they're getting further and further away from McMinnville. So here's what our table looked like:
Hours driving 0 1 2 3 4
Distance from McMinnville 20 10 0 10 20
It made perfect sense to the students why we didn't go into the negatives, why the values started to "bounce" back up. The students were having a lot of fun poking fun at the 15 year old and the 13 year old for driving so slowly and for spacing out and missing McMinnville. One student even made his own table asserting that, since McMinnville is 4 miles across, the second half of the table should go 6, then 14 instead of 10 then 20.
After this warm up problem I had no trouble at all showing the students that an absolute value equation "bounces" but that on either side of the vertex, we have linear relationships. I had complete engagement with the rest of the lesson.
I think maybe why it worked so well was that the problem was almost a "make your own adventure". The students were able to add details for fun or change the numbers to fit in with their understandings of the real world. I always start lessons with a warm-up that tries to pull the material we're learning that day into a real-world context to see what kinds of intuition the students already have for the subject material, but rarely does it work so well. Sometimes no planning is the best planning- but I wish there were a linear relationship between how much time I spend on a lesson and how well it goes because then every day would be awesome.
Sunday, January 22, 2012
FOIL, Factoring and Quilting
I've spent my whole long weekend (Thursday, Friday, Sat and Sun. We got a day an a half off due to rain. I'm feeling guiltily giddy at having so much time to prep and to play) working on my next algebra 1 unit. I've specifically been thinking about how to introduce FOIL and factoring. I don't like the acronym FOIL very much either, but it is a better name than "multiplying binomials."
I've been trying to come up with a new way to introduce it. I've played with using algebra blocks and I like the connection to area, but I find them a bit unwieldy. The last two years I've just introduced it using this solid worksheet I found online somewhere (but I can't remember where.) Intro to FOIL Guided Notes I think working through this worksheet with my students has gotten the job done, but it's a little bit dull and unconnected to reality. Why would we be trying to find the area of random rectangles that we don't actually know the dimensions of so we have to write the dimensions as x+2 and x+3? I know it's just a way to introduce the logic behind FOIL, but I find it a bit unsatisfying. I do think it does a great job of showing how and why the process works and my students have enjoyed learning FOIL this way.
So I threw together some ridiculous replacement activities modeled on this worksheet and on algebra blocks. Mostly, I am just trying to give a tiny bit of context and some humor and silliness to this topic. I may, though, have just confused the point. The beauty of the above worksheet is its simplicity and what I've thrown together is much more complicated.
I thought I'd start with the following algebra blocks that I made myself: Algebra Tiles for Teaching FOIL V2 I'd let the kids cut them out and play with them a little, then I'd have them work through the following "quilting activity" in pairs.
Algebra Tiles for Teaching FOIL Quilting Ws I've already changed the third rule of quilting to "all quilts must be formed with exactly four rectangular pieces of cloth" because I realized that without this rule, the kids would probably get pretty confused.
The purpose of this is just to try to introduce them to the idea of having rectangles with dimensions that have variables and to see if they can intuit FOIL for themselves. I would follow this activity with a more conventional multiplying binomials lesson with some notes and some homework. I'm unsure about this lesson.
The advantage is though that I was able to make a follow up activity for when the students start factoring that follows the same pattern, so doing FOIL this way, then factoring this way may help students connect the two processes with one silly context problem. Here's the factoring worksheet: Algebra Tiles for Teaching FACTORING Quilting Ws I think I like this one a little bit more than the first one, but I'm still not sure if this is the best way to go about teaching these two topics. Oh no, and I just noticed on the last page I put it's, not its. I like to have correct grammar, I really do, but I can't hold good grammar and math together at the same time. I'll go fix it on my originals...
I've been trying to come up with a new way to introduce it. I've played with using algebra blocks and I like the connection to area, but I find them a bit unwieldy. The last two years I've just introduced it using this solid worksheet I found online somewhere (but I can't remember where.) Intro to FOIL Guided Notes I think working through this worksheet with my students has gotten the job done, but it's a little bit dull and unconnected to reality. Why would we be trying to find the area of random rectangles that we don't actually know the dimensions of so we have to write the dimensions as x+2 and x+3? I know it's just a way to introduce the logic behind FOIL, but I find it a bit unsatisfying. I do think it does a great job of showing how and why the process works and my students have enjoyed learning FOIL this way.
So I threw together some ridiculous replacement activities modeled on this worksheet and on algebra blocks. Mostly, I am just trying to give a tiny bit of context and some humor and silliness to this topic. I may, though, have just confused the point. The beauty of the above worksheet is its simplicity and what I've thrown together is much more complicated.
I thought I'd start with the following algebra blocks that I made myself: Algebra Tiles for Teaching FOIL V2 I'd let the kids cut them out and play with them a little, then I'd have them work through the following "quilting activity" in pairs.
Algebra Tiles for Teaching FOIL Quilting Ws I've already changed the third rule of quilting to "all quilts must be formed with exactly four rectangular pieces of cloth" because I realized that without this rule, the kids would probably get pretty confused.
The purpose of this is just to try to introduce them to the idea of having rectangles with dimensions that have variables and to see if they can intuit FOIL for themselves. I would follow this activity with a more conventional multiplying binomials lesson with some notes and some homework. I'm unsure about this lesson.
The advantage is though that I was able to make a follow up activity for when the students start factoring that follows the same pattern, so doing FOIL this way, then factoring this way may help students connect the two processes with one silly context problem. Here's the factoring worksheet: Algebra Tiles for Teaching FACTORING Quilting Ws I think I like this one a little bit more than the first one, but I'm still not sure if this is the best way to go about teaching these two topics. Oh no, and I just noticed on the last page I put it's, not its. I like to have correct grammar, I really do, but I can't hold good grammar and math together at the same time. I'll go fix it on my originals...
Friday, January 20, 2012
Adding Like Monomials
I just spent the last three hours working on one algebra 1 lesson plan even though I have about 20 lesson plans I'm supposed to write this weekend. Maybe not the most efficient use of my time, but I'm kind of excited about this one. The topic is: adding like monomials. Students understand pretty readily that they can't add expressions without variables to expressions with variables and they can't add two things that have different variables, but I've found they have a lot of trouble with understanding that they can't add an x expression to an x squared expression. They won't take my word for it and it takes a lot of work to stop them from writing 2x+4x^2 as 6x or 6x^2. Thinking about this, I threw together the following story worksheet/activity to see if it may help clarify the difference between an x and an x^2. Any feed back would be awesome. Adding Like Monomials
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