If any of you are reading this blog because you are teaching using the IMP books let me tell you about an awesome website that has great resources...The Greater Philadelphia Secondary Mathematics Project. Our trainer from It's About Time shared this website with us and it has some invaluable resources. I found some questions on there that I used for my quiz today on graphing. I only used two graphs but set up a rubric where they had a very good chance to pass (is that bad?) whether or not they could come up with the rule for the graph. I gave points for labeling the axes, scaling them correctly, plotting the points correctly, graphing the line of best fit, answering the question, and getting the rule. The 2nd problem gave the students a situation and they had to graph it, answer a question about it and give the rule.
I was really very pleased with the quizzes. Every student in the class can not get the rule for the graph yet, but they do SO much more with this word problem than I believe my previous students would ever have done. I hope to one day soon have the opportunity to find some multiple choice questions where students are given a graph and asked to find the equation that matches it and see how they do. We still have not "formally" learned slope-intercept form.
My 5th period did a Thanksgiving coordinate plane graphing activity today. It was the end of the day on Friday before Thanksgiving and I noticed as they worked on it that they NEEDED to review plotting points so I am glad we did it!
Showing posts with label lines of best fit. Show all posts
Showing posts with label lines of best fit. Show all posts
Friday, November 21, 2014
Tuesday, November 18, 2014
I'm Calling Bullcrap! - Adventures in teaching IMP
Sonya New is my hero! I'm just saying... If it were not for Sonya I would not be the teacher I am today. She makes me want to be a better teacher. She makes me think! UGH! AND...she cracks me up sometimes.
Yesterday we were looking over some of the Meaningful Math Algebra lessons that we were going to be teaching the next few days. She had her honors algebra students complete the Who Will Make It activity for homework and she told me that they had asked if they could use a "squiggly line" between zero and the first output value so they didn't have to label all of the values in between. She told them no. However, when we were discussing it she said she wished she had let some of them go ahead and do it so that they would be able to talk about the inaccurate conclusions that would be drawn. She decided to do a graph with the "squiggly" and talk to them about it. Her graph is below:
The context of the story is to see who will make it to Green River before the flood that is predicted (by the almanac) to happen in 30 days. The y-axis is distance to the river and as you can see all 3 of her families make it to the river (the x-axis) way before 30 days. After discussing the class's answers she put her answer under the document camera and told the class that she had all of her families to make it before the flood. She said at first they were starting to erase their answers...they assumed she was right and they were wrong. However, she had one girl yell out, "I'm calling bullcrap!" and run up to the board to point at her "squiggly line" to say that Sonya's answer was wrong. I loved this story. I have told Sonya over and over again I wish she would blog about her personal "imp adventure" so that I could read all about it. We talk almost every day but we don't always have alot of time to go into detail. I told her I just had to tell this story. I loved that a student ran from the back of the room to prove that Sonya was wrong and she was right.
P.S. - I hope nobody is offended by the title...it is a renaming of a popular card game that has to do with calling someone's bluff when you think they are not telling the truth about their cards.
Yesterday we were looking over some of the Meaningful Math Algebra lessons that we were going to be teaching the next few days. She had her honors algebra students complete the Who Will Make It activity for homework and she told me that they had asked if they could use a "squiggly line" between zero and the first output value so they didn't have to label all of the values in between. She told them no. However, when we were discussing it she said she wished she had let some of them go ahead and do it so that they would be able to talk about the inaccurate conclusions that would be drawn. She decided to do a graph with the "squiggly" and talk to them about it. Her graph is below:
P.S. - I hope nobody is offended by the title...it is a renaming of a popular card game that has to do with calling someone's bluff when you think they are not telling the truth about their cards.
Friday, November 14, 2014
My apologies to AMSTI...I just didn't get it
The last few weeks I have really come to appreciate more and more what the AMSTI program has done for math teachers. If you happen to not be from the state of Alabama AMSTI is the Alabama Math Science and Technology Initiative. Participating schools send their math and science teachers for 2 weeks of training in the Summer (and the teachers get paid) and the teachers receive AMSTI kits with the materials needed to do the activities in their classrooms. My first Summer of AMSTI training I totally didn't get it. The math training consists of going through some of the activities from the IMP units (All About Alice, Cookies, the Pit and the Pendulum, Fireworks, etc...). The teachers usually receive two drop-in units (classroom sets). As a participant in the training I sat there and thought, "I don't have enough time to do these activities in the classroom! I don't even have time to cover the material I am supposed to cover WITHOUT all these activities!" I also thought that the activities were too difficult. However, I did leave AMSTI training with a determination to put my students in groups the following school year and stick with it for a year no matter what.
The following school year a colleague (Sonya New) and I really started looking for discovery or inquiry-based activities to use in our algebra classes. We took "baby steps" and really only used a handful that year but we really started seeing the value in them. Then I attended year 2 of AMSTI algebra training and was blown away! I had 100 light bulbs go off as I realized that our "AMSTI books" did have the discovery/inquiry-based type activities that we had been scouring the Internet to find. Tanya Barnes and Melanie Griffis encouraged me to just try the activities with my students (even though I was still afraid some of them were "over their heads"). They told me that I would be pleasantly surprised. I left training that year just thinking that we really needed to dig into our IMP units and see which units covered which standards. Following this revelation I had the "chance meeting" of the president of It's About Time (the company that publishes the IMP books) Tom Laster, in Atlanta at the ISTE conference. And now our algebra teachers are piloting the new Meaningful Math Algebra textbooks that take the traditional approach BUT use the IMP units that we had been receiving training on at AMSTI. Those "AMSTI units" are not just activities to "drop in."
I would like to publicly (or not so publicly since most of them will not read this blog post) apologize to the AMSTI trainers and organizers for being so slow to "get it." Now that I have been teaching the curriculum I realize that doing an activity here or there just does not do it justice. When you go from the beginning to the end of the unit and see the way concepts are developed and revisited the brilliance of the curriculum can be seen. I am learning so many things about developing a concept. For instance, I have always thought that the "line of best fit" was to be taught when I am covering the statistics section and scatterplots. I have never thought to use real data and graph it, find the line of best fit, and have the students discover the rule for the line. We have been doing this without the help from graphing calculators. My students have "had their hands" on so much graphing already and we have not formally talked about slope-intercept form one time. However, they can find a rule or equation for a graph and they can find the "rate of change" within a context. When we talk formally about slope-intercept form they are going to have such a firm foundation on which to understand the concept. I can't wait to go completely through the book and see all the other ways the mathematical concepts are developed. THANK YOU AMSTI AND IT'S ABOUT TIME!
The following school year a colleague (Sonya New) and I really started looking for discovery or inquiry-based activities to use in our algebra classes. We took "baby steps" and really only used a handful that year but we really started seeing the value in them. Then I attended year 2 of AMSTI algebra training and was blown away! I had 100 light bulbs go off as I realized that our "AMSTI books" did have the discovery/inquiry-based type activities that we had been scouring the Internet to find. Tanya Barnes and Melanie Griffis encouraged me to just try the activities with my students (even though I was still afraid some of them were "over their heads"). They told me that I would be pleasantly surprised. I left training that year just thinking that we really needed to dig into our IMP units and see which units covered which standards. Following this revelation I had the "chance meeting" of the president of It's About Time (the company that publishes the IMP books) Tom Laster, in Atlanta at the ISTE conference. And now our algebra teachers are piloting the new Meaningful Math Algebra textbooks that take the traditional approach BUT use the IMP units that we had been receiving training on at AMSTI. Those "AMSTI units" are not just activities to "drop in."
I would like to publicly (or not so publicly since most of them will not read this blog post) apologize to the AMSTI trainers and organizers for being so slow to "get it." Now that I have been teaching the curriculum I realize that doing an activity here or there just does not do it justice. When you go from the beginning to the end of the unit and see the way concepts are developed and revisited the brilliance of the curriculum can be seen. I am learning so many things about developing a concept. For instance, I have always thought that the "line of best fit" was to be taught when I am covering the statistics section and scatterplots. I have never thought to use real data and graph it, find the line of best fit, and have the students discover the rule for the line. We have been doing this without the help from graphing calculators. My students have "had their hands" on so much graphing already and we have not formally talked about slope-intercept form one time. However, they can find a rule or equation for a graph and they can find the "rate of change" within a context. When we talk formally about slope-intercept form they are going to have such a firm foundation on which to understand the concept. I can't wait to go completely through the book and see all the other ways the mathematical concepts are developed. THANK YOU AMSTI AND IT'S ABOUT TIME!
IMP Day 34 - variety day!
My 2nd block class had to finish the Sublette's Cutoff/Who Will Make It activity today and then we discussed it. I had a class discussion yesterday with my 3rd block about these activities so I should have been better the 2nd time around. I felt that I was worse! I randomly called on a few students (using the dice) and their graphs needed a little work and then I got the information backwards as we were discussing it and then the whole thing was crazy. I hope by the end we learned a little bit about what is going on at the intercepts and how to use the "line of best fit" to predict!
My 3rd block was a little ahead so we got out the graphing calculators and did the "Graphing Calculator In-Outs" activity. This was a very good introductory activity with the calculators. I did lose a few students along the way and finally just told them to write down the correct answers when I told them to. HAHA! I am pretty sure I could have facilitated this better. Maybe I should have paused and allowed them time to get help from their group members. I tried to walk around and help everyone at the beginning but we would NEVER have gotten finished. I know...I was too impatient. My goal will be to pause and allow students to help each other more in the future. I didn't tell them not to help each other...but I didn't encourage it either.
My 5th block did "To Kearney by Equation" today. Today I lead them to the "new equation" for profit per trip AFTER they discovered that they are not given the captain's pay per minute and they are given round trips in minutes. They did fairly well. I still have a few that seem to sit and wait until they are told what the answer. I randomly call on people and sometimes I end up having to "help" a student find the answers from the beginning to the end because they haven't put much thought into it during the time they were supposed to be working!
My 3rd block was a little ahead so we got out the graphing calculators and did the "Graphing Calculator In-Outs" activity. This was a very good introductory activity with the calculators. I did lose a few students along the way and finally just told them to write down the correct answers when I told them to. HAHA! I am pretty sure I could have facilitated this better. Maybe I should have paused and allowed them time to get help from their group members. I tried to walk around and help everyone at the beginning but we would NEVER have gotten finished. I know...I was too impatient. My goal will be to pause and allow students to help each other more in the future. I didn't tell them not to help each other...but I didn't encourage it either.
My 5th block did "To Kearney by Equation" today. Today I lead them to the "new equation" for profit per trip AFTER they discovered that they are not given the captain's pay per minute and they are given round trips in minutes. They did fairly well. I still have a few that seem to sit and wait until they are told what the answer. I randomly call on people and sometimes I end up having to "help" a student find the answers from the beginning to the end because they haven't put much thought into it during the time they were supposed to be working!
Thursday, November 13, 2014
IMP Day 33 - Sublette's Cutoff or Who Will Make It? (5th period - Laced Travelers) - They don't need me!!!
Today I took the suggestion from Mr. Webb and Ms. Whitt and divided Sublette's Cutoff and Who Will Make It between the groups in my classes. In other words some groups did Sublette's Cutoff and some did Who Will Make It. The 2 activities were similar enough that I was able to introduce the activities pretty easily. They are asked to plot data for 3 different families and then draw 3 different lines of best fit. Then they are asked to answer questions and make estimations with the lines. I think that even I have a better understanding of why we do lines of best fit after teaching these last few activities. I know that I "knew" what it is for but I do not think that I have applied it within a context very many times. Over the course of this week my students will have used lines of best fit within at least 3 or 4 different contexts. The discussions about what the x and y intercepts were so meaningful and productive! We are really talking about slope and the y-intercepts without formally introducing the equation. It is so cool to see how the authors develop each of the concepts. I think it is hard to appreciate until you teach an entire unit.
Today after we finished graphing and "sharing out" the answers I asked the students to share with me the meaning for the x-intercept and the y-intercept. I had one student say, "The y-intercept is the starting point and the x-intercept is the ending point," and the BELL RUNG!!! UGH! I was very excited that she said that and I wanted to discuss it with the class...there is always tomorrow.
In 5th period today I did something different. I wrote the assignment on the board and referred the students to the assignment as they walked in the door. All I did was tell them to read over and it and put the "entry" into their notebooks. Dude! They got on it! I had one student figure out the answer to #1 (which deals with multiple constraints) by the time I had answered roll! AMAZING! As a whole they worked harder today than I have ever seen them work. Once the one student got the answer he walked around and helped other groups. I would ask them to explain how they got their answer and wouldn't give them candy (the great motivator) unless their explanations made sense. They don't need me! Well...not as much as I think they do. HAHA!
Today after we finished graphing and "sharing out" the answers I asked the students to share with me the meaning for the x-intercept and the y-intercept. I had one student say, "The y-intercept is the starting point and the x-intercept is the ending point," and the BELL RUNG!!! UGH! I was very excited that she said that and I wanted to discuss it with the class...there is always tomorrow.
In 5th period today I did something different. I wrote the assignment on the board and referred the students to the assignment as they walked in the door. All I did was tell them to read over and it and put the "entry" into their notebooks. Dude! They got on it! I had one student figure out the answer to #1 (which deals with multiple constraints) by the time I had answered roll! AMAZING! As a whole they worked harder today than I have ever seen them work. Once the one student got the answer he walked around and helped other groups. I would ask them to explain how they got their answer and wouldn't give them candy (the great motivator) unless their explanations made sense. They don't need me! Well...not as much as I think they do. HAHA!
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