We started class today with another warmup on solving systems of equations. My students will have their 3rd and final opportunity to retake the quiz in order to improve their grade for this 9 weeks.
Once we went over the warmup I assigned A Wonderland Lost. We read it together and discussed it some first. I love the question the teacher's guide advises you to ask about how long it will take the rain forest to be completely gone. Several students think it is 10 years. I did an example at the board using a beginning amount of 100 and worked through decreasing by 10 percent per year. I led them to the "shortcut" of taking 90% of the previous (or beginning) amount each time. I am learning to be more comfortable writing exponential equations within the contexts we've used so far. I don't know if my students are going to retain these lessons but I'm quite sure I will. This was a time when the teacher's guide gives you the rule. I had to stop and think about it to be able to explain it. AND relating back to the walk thru we did for the Alice problem certainly made it easier for me to understand and explain! After today's lesson I took a few minutes to give notes on the differences between exponential, quadratic, and linear functions. I also made sure they heard me use the vocabulary terms of exponential growth and decay.
My 5th period finished the Scrambling Equations activity from Overland Trail. I invested a little more time in this activity this time through and I think it went better. I found many mistakes in the students' work and tried to clarify some misconceptions. I had my students write their "complicated equations" on notecards. I also provided a problem I made up and wrote on the board for students to use if they didn't feel certain of their problem. After they worked each other's problems I asked them to write down a brief description of the process they used to solve the equation. They used phrases like "canceling out" and "did the opposite." We also emphasized that looking on the side with the variable tells you what to do. After the activity I passed out a worksheet for them to practice 1-step equations. We didn't have much time to work on them today. We will build up in difficulty and have a quiz by the end of the week.
Monday, March 9, 2015
Friday, March 6, 2015
Quiz retakes and Mystery Bags
Today my Algebra IB students retook their quiz on systems of equations. The majority of my students improved their grade. This semester I have taken two concepts so far and worked hard to try to ensure that my students have mastered them. (This statement actually has me shaking my head...I promise I hope that all my students master all of the topics...but in my experience with struggling math students that doesn't happen.) One of them was graphing lines. We gave them a quiz and then gave the students individual feedback on what they missed. Then we gave a retake for all students who did not ace the first quiz. We did the same thing with systems of equations (substitution and elimination). This topic seems to really get the better of my students every year.
I have been "transforming my teaching" for a couple of years now. For years I taught a topic and then tested it and moved on. There would be some times that I could tell that the students were struggling with a topic and I would reteach it or spend extra days practicing. However, once I taught it and tested I moved on. Well...I still think that you can't sit a topic until every student gets it. I wish I could. However, we would never cover the required objectives if we do that. Sometimes my students either don't care enough to get it or do not come to school enough to get it. So...I have tried to do a better job of giving smaller quizzes on a few topics and then giving the students individual feedback. After the feedback they are given at least one opportunity to retake the quiz (possibly more). I wish we had the time and opportunity to do this with every topic. I truly believe if my students would pay attention in class, do all of their work, and ask questions when they don't understand so that I can help them at their points of confusion they would ALL PASS. However, I do not teach in a perfect world. I do not have perfect students who come to class prepared and ready to learn each day. Also...my students do not have a perfect teacher. So...until these things change I am going to continue to take a few topics each 9 weeks and give students individual feedback with the opportunity to retake. If any of you reading this blog (all 2 of you - haha!) have any ideas that might help this process to be less painful please shoot me an email at towens@attalla.k12.al.us. I thought I would ask...just in case...
Today my 5th period continued working on the 2nd mystery bags activity in Overland Trail. This is definitely a place where we will need to pull extra practice on solving equations. I think that if your students come to your algebra class and they can already solve one and two-step equations successfully then you won't have to supplement as much. However, many of my students still struggle solving basic equations. Therefore, after the More Scrambled Equations and Mystery Bags activity I think I am going to do a quick quiz to assess their fluency on one and two-step equations. The Mystery Bags activities have actually taken them through working on equations with variables on both sides. However, students will need more practice on equations that involve subtraction (integer coefficients). I really believe that referring back to the Mystery Bags context will help. We will see!
I have been "transforming my teaching" for a couple of years now. For years I taught a topic and then tested it and moved on. There would be some times that I could tell that the students were struggling with a topic and I would reteach it or spend extra days practicing. However, once I taught it and tested I moved on. Well...I still think that you can't sit a topic until every student gets it. I wish I could. However, we would never cover the required objectives if we do that. Sometimes my students either don't care enough to get it or do not come to school enough to get it. So...I have tried to do a better job of giving smaller quizzes on a few topics and then giving the students individual feedback. After the feedback they are given at least one opportunity to retake the quiz (possibly more). I wish we had the time and opportunity to do this with every topic. I truly believe if my students would pay attention in class, do all of their work, and ask questions when they don't understand so that I can help them at their points of confusion they would ALL PASS. However, I do not teach in a perfect world. I do not have perfect students who come to class prepared and ready to learn each day. Also...my students do not have a perfect teacher. So...until these things change I am going to continue to take a few topics each 9 weeks and give students individual feedback with the opportunity to retake. If any of you reading this blog (all 2 of you - haha!) have any ideas that might help this process to be less painful please shoot me an email at towens@attalla.k12.al.us. I thought I would ask...just in case...
Today my 5th period continued working on the 2nd mystery bags activity in Overland Trail. This is definitely a place where we will need to pull extra practice on solving equations. I think that if your students come to your algebra class and they can already solve one and two-step equations successfully then you won't have to supplement as much. However, many of my students still struggle solving basic equations. Therefore, after the More Scrambled Equations and Mystery Bags activity I think I am going to do a quick quiz to assess their fluency on one and two-step equations. The Mystery Bags activities have actually taken them through working on equations with variables on both sides. However, students will need more practice on equations that involve subtraction (integer coefficients). I really believe that referring back to the Mystery Bags context will help. We will see!
Wednesday, March 4, 2015
IMP Alice Day 3 - Logic POW and Mystery Bags revisited
Today my Algebra IB students took a short quiz on systems of equations. The grades were not all that great but Ms. Whitt (my incredible coteacher) and I did our best to talk to each of the students about what they missed. The students will be given the opportunity to retake the quiz within the next week.
After the students turned in the quiz they were instructed to start working on the Logic POW. This is a very different POW than any that we have done before. It gives the students several pairs of statements and asks them to figure out if there is a logical conclusion that can be made. Some of the pairs do not have logical conclusions. I think this is a great way to introduce them to the type of thinking and reasoning that is required in geometry!
My 5th period Algebra IA class started Mystery Bags this week. Today we did the More Mystery Bags activity. I appreciated the context the first time I went through this last semester. I went back and read the blog I wrote after that day. The first time through most of my students seemed to have a pretty firm grasp of solving basic equations. However, my 5th period class needed more prompting. When the students had a problem like 5M +3 = 2M + 15 the context gives me such an easy way to explain why you would first want to take 2 Ms (or mystery bags) from each side of the equation (balance). In the mystery bag activity the constants are referred to as the weights that are on the balances. Therefore it once again makes logical sense that the next step is to take 3 ounces of weight from each side. We want to get mystery bags only on one side and weights only on the other side. Almost every student then understands to divide the amount of weight by the number of bags. (They are told that each mystery bag has the same amount of weight in it.)
Tomorrow they will be thrown some problems with some negative numbers. I explained to them today that the concept of getting all the mystery bags (variables) on one side and all the constants (weights) on the other will still work.
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| Ms. Whitt tutoring a student one-on-one on solving systems of equations. |
After the students turned in the quiz they were instructed to start working on the Logic POW. This is a very different POW than any that we have done before. It gives the students several pairs of statements and asks them to figure out if there is a logical conclusion that can be made. Some of the pairs do not have logical conclusions. I think this is a great way to introduce them to the type of thinking and reasoning that is required in geometry!
My 5th period Algebra IA class started Mystery Bags this week. Today we did the More Mystery Bags activity. I appreciated the context the first time I went through this last semester. I went back and read the blog I wrote after that day. The first time through most of my students seemed to have a pretty firm grasp of solving basic equations. However, my 5th period class needed more prompting. When the students had a problem like 5M +3 = 2M + 15 the context gives me such an easy way to explain why you would first want to take 2 Ms (or mystery bags) from each side of the equation (balance). In the mystery bag activity the constants are referred to as the weights that are on the balances. Therefore it once again makes logical sense that the next step is to take 3 ounces of weight from each side. We want to get mystery bags only on one side and weights only on the other side. Almost every student then understands to divide the amount of weight by the number of bags. (They are told that each mystery bag has the same amount of weight in it.)
Tomorrow they will be thrown some problems with some negative numbers. I explained to them today that the concept of getting all the mystery bags (variables) on one side and all the constants (weights) on the other will still work.
Tuesday, March 3, 2015
IMP Alice Day 2 - Graphing Alice - raising to the zero power
I remember Sonya New telling me how much she loved Alice because it gives a context for any number raised to the zero power equaling one. Now I have taught it with the Alice context and it is so exciting! For years I have just told my students to memorize it as a fact. Today I got to use the Alice context... Just in case you might be reading this and you don't know what I'm talking about let me share.
As I'm sure you know Alice (in Alice in Wonderland) shrinks when she drinks the beverage and grows when she eats the cake. The first activity in the unit tells the students to imagine that Alice's height doubles for every ounce of cake she eats and is cut in half for every ounce of beverage she drinks. In graphing Alice they are asked to graph the two situations for 1-6 ounces. For the cake situaion you are graphing y=2^x and the beverage situation is y=.5^x. The outputs (y values) are actually giving you what you will be multiplying Alice's original height by. The x values represent the number of ounces eaten or drank. The teacher's guide advises you to talk about what happens when she eats zero ounces. This would mean you are raising 2 to the zero power. It was so awesome to have the context to explain that when she eats zero ounces of cake her multiplier (y value) is 1 because multiplying by 1 doesn't change Alice's height!! My students can't appreciate how exciting it is to be able to explain the why. I told them today that I have never been able to explain why anything to the zero power equals one and I just got blank stares. Haha! Some of you may be looking at the computer screen like...
It doesn't matter. I know I am a math nerd but today's lesson made me HAPPY! And I felt the need to write about it even though I am sure it is hard to follow.
As I'm sure you know Alice (in Alice in Wonderland) shrinks when she drinks the beverage and grows when she eats the cake. The first activity in the unit tells the students to imagine that Alice's height doubles for every ounce of cake she eats and is cut in half for every ounce of beverage she drinks. In graphing Alice they are asked to graph the two situations for 1-6 ounces. For the cake situaion you are graphing y=2^x and the beverage situation is y=.5^x. The outputs (y values) are actually giving you what you will be multiplying Alice's original height by. The x values represent the number of ounces eaten or drank. The teacher's guide advises you to talk about what happens when she eats zero ounces. This would mean you are raising 2 to the zero power. It was so awesome to have the context to explain that when she eats zero ounces of cake her multiplier (y value) is 1 because multiplying by 1 doesn't change Alice's height!! My students can't appreciate how exciting it is to be able to explain the why. I told them today that I have never been able to explain why anything to the zero power equals one and I just got blank stares. Haha! Some of you may be looking at the computer screen like...
It doesn't matter. I know I am a math nerd but today's lesson made me HAPPY! And I felt the need to write about it even though I am sure it is hard to follow.
Monday, March 2, 2015
IMP All About Alice Day 1 - Alice in Wonderland
We have had multiple delays and missed school days in the past few weeks. Therefore I have decided to skip the last portion of the Cookies unit and start Alice. I'm going to try to make up for it by using systems of equations problems as my warm-ups for the next several days.
Today we read the intro and then watched a film clip from the movie. Thank you to Lori White for providing the film clip this past Summer at AMSTI training. After giving the students about 10 minutes to work on the 4 questions in the Alice in Wonderland activity I had them to write their answers on 2' by 2' marker boards. It has been a while since we have used them. I like placing all of their boards at the front of the class and comparing/critiquing the answers with the class. I rolled my 8-sided dice and called on a group to explain the answer to each question. After the explanation we compared the answers on all the other boards. It was interesting to see the different ways the students worded their answers. For the first part of #1 some students said Alice height doubled twice, some said multiplied by 4, and some said quadrupled. A common mistake made for the 2nd part of #1 was students thought they should multiply by 10 for 5 ounces. Some students did say that Alice's height was doubled 5 times. I did have one student to say her height was multiplied by 32 when she ate 5 ounces. He is such a good math thinker. It was sad to me that none of the groups created a table to answer the questions. I showed them how we could use a table to help us to recognize the patterns which helped us to write the rules.
Today we read the intro and then watched a film clip from the movie. Thank you to Lori White for providing the film clip this past Summer at AMSTI training. After giving the students about 10 minutes to work on the 4 questions in the Alice in Wonderland activity I had them to write their answers on 2' by 2' marker boards. It has been a while since we have used them. I like placing all of their boards at the front of the class and comparing/critiquing the answers with the class. I rolled my 8-sided dice and called on a group to explain the answer to each question. After the explanation we compared the answers on all the other boards. It was interesting to see the different ways the students worded their answers. For the first part of #1 some students said Alice height doubled twice, some said multiplied by 4, and some said quadrupled. A common mistake made for the 2nd part of #1 was students thought they should multiply by 10 for 5 ounces. Some students did say that Alice's height was doubled 5 times. I did have one student to say her height was multiplied by 32 when she ate 5 ounces. He is such a good math thinker. It was sad to me that none of the groups created a table to answer the questions. I showed them how we could use a table to help us to recognize the patterns which helped us to write the rules.
Wednesday, February 25, 2015
Reflections after 4 months of IMP Meaningful Math
I am totally sold on the idea that anyone who is purchasing math textbooks should take a hard look at the IMP curriculum - whether your district uses the integrated or the traditional approach. I feel like using this curriculum has made me become a better teacher. I know that I am doing more with my students than I have ever done before.
When I first started working through the book (and I still feel like I am a newbie for sure!) I tried to be so literal. It is recommended for you to go through the curriculum without supplementing (especially the first time through). Because I have not been through the book before I had moments where I was unsure whether or not I should introduce a concept - especially technical vocabulary or formulas - because I didn't want to mess up a future lesson where the students would have the opportunity to approach problems with a more intuitive, context-driven method. For instance, in Overland Trail when students are asked to write the rules for the graphs I had several students (even after being introduced to slope-intercept form) who used a table and worked the pattern back to the point where x=0 in order to find the y-intercept or starting point. Teaching them this curriculum has shown me what it really means to allow students to use different approaches for solving problems. I do not think I understood what that meant prior to teaching this curriculum. I allowed students to "approach" solving equations from different ways - if they wanted to solve an equation by getting the variable on the right side instead of the left I allowed them to do that. HAHA! I have now seen what different approaches look like in a classroom. I truly have some students using formulas, others using tables or graphs, and others writing a paragraph which just explains how they reasoned through the problem. What an education I have had!
Another thing I am realizing is that BALANCE is a key. There are going to be times that we need to stop and give notes in which we make the connections to the "naked math" (my AMSTI buddy Melanie Griffis calls it that!) like they will see on state exams or the ACT. I can remember when Jim Delawder made the comment in our training session that what we will do with the curriculum is so much harder than the way they are tested. Now that I have taught it a little while I totally understand his comment. However, if the students don't make the connections between the IMP-style problems and the standardized test style problems then their math ability will not be reflected in their test scores or future math courses. I also remember Jim telling us in our training that he usually pulls sample questions to practice with the students to show them how questions covering those concepts will appear on standardized tests. We just want to create a system that works for us. Sonya New (my often-mentioned algebra teaching buddy) and I have a goal of identifying places in the curriculum where we take a pause and teach the "naked math" version and practice the standardized-test version.
Lately I have been thinking about how I have always found the need to find materials to supplement the textbook we were using. The difference now is that it is so much easier to find some practice worksheets instead of trying to find or create activities that build concepts around a context. Most of the textbooks I have used in the past were mainly a collection of "naked math" worksheets with a few application problems that were stand alone. In the past I rarely ever assigned those application problems. My students seemed to struggle with the basic problems so I rarely ever went to the "next step." Now that I am teaching with the problem-based curriculum that teaches everything within a context things are so different. The students engage with the problems because of the context.
I am going to publish this post because...I just am. However, I have so many thoughts swirling around in my head that I would like to express but I am at a loss right now. I may add more later:)
When I first started working through the book (and I still feel like I am a newbie for sure!) I tried to be so literal. It is recommended for you to go through the curriculum without supplementing (especially the first time through). Because I have not been through the book before I had moments where I was unsure whether or not I should introduce a concept - especially technical vocabulary or formulas - because I didn't want to mess up a future lesson where the students would have the opportunity to approach problems with a more intuitive, context-driven method. For instance, in Overland Trail when students are asked to write the rules for the graphs I had several students (even after being introduced to slope-intercept form) who used a table and worked the pattern back to the point where x=0 in order to find the y-intercept or starting point. Teaching them this curriculum has shown me what it really means to allow students to use different approaches for solving problems. I do not think I understood what that meant prior to teaching this curriculum. I allowed students to "approach" solving equations from different ways - if they wanted to solve an equation by getting the variable on the right side instead of the left I allowed them to do that. HAHA! I have now seen what different approaches look like in a classroom. I truly have some students using formulas, others using tables or graphs, and others writing a paragraph which just explains how they reasoned through the problem. What an education I have had!
Another thing I am realizing is that BALANCE is a key. There are going to be times that we need to stop and give notes in which we make the connections to the "naked math" (my AMSTI buddy Melanie Griffis calls it that!) like they will see on state exams or the ACT. I can remember when Jim Delawder made the comment in our training session that what we will do with the curriculum is so much harder than the way they are tested. Now that I have taught it a little while I totally understand his comment. However, if the students don't make the connections between the IMP-style problems and the standardized test style problems then their math ability will not be reflected in their test scores or future math courses. I also remember Jim telling us in our training that he usually pulls sample questions to practice with the students to show them how questions covering those concepts will appear on standardized tests. We just want to create a system that works for us. Sonya New (my often-mentioned algebra teaching buddy) and I have a goal of identifying places in the curriculum where we take a pause and teach the "naked math" version and practice the standardized-test version.
Lately I have been thinking about how I have always found the need to find materials to supplement the textbook we were using. The difference now is that it is so much easier to find some practice worksheets instead of trying to find or create activities that build concepts around a context. Most of the textbooks I have used in the past were mainly a collection of "naked math" worksheets with a few application problems that were stand alone. In the past I rarely ever assigned those application problems. My students seemed to struggle with the basic problems so I rarely ever went to the "next step." Now that I am teaching with the problem-based curriculum that teaches everything within a context things are so different. The students engage with the problems because of the context.
I am going to publish this post because...I just am. However, I have so many thoughts swirling around in my head that I would like to express but I am at a loss right now. I may add more later:)
Tuesday, February 24, 2015
Kahoot! - educational and fun - especially for reviewing
Today we were delayed for 3 hours so there were several students who were absent. Also, we did not meet with all of our classes and I like to keep my classes together (for my sanity!) so I did not want to move forward with the next lesson. I was thinking about pulling some standardized-test style questions and reviewing. I was just going to project them on the board and have them work on them using the ipads (educreations app) or the small whiteboards. BUT then I remembered how much fun my students from last year had playing Kahoot! for reviewing.
Fortunately I ran across a wonderful Kahoot when I did a "public search" for graphing equations. It had 16 questions that reviewed finding slope, graphing, finding intercepts, and evaluating functions. I was able to use it with my Algebra IB for review and in my Algebra IA to reinforce concepts we are currently working on.
I realized last year that when we worked through Kahoots which makes the review feel like a game the students invested in trying to learn how to get the correct answer so they can get the points for the next question. After each question the game shows who the leader is and you also have the opportunity to stop and go over the question. Today I gave the winning player 2 pieces of candy and all the other players on the "leader board" 1 piece of candy. It was a fun and productive day.
If you have never used Kahoot! it is great for all subjects and grade levels. You can create your own reviews or you can do a public search for ones that have already been created. There are sometimes mistakes in the public reviews but I just use them and then address any mistakes as they come. My husband showed me last year where the writers of the Kahoot! website even recommend you have students to create their own reviews for the class to play. That is also a great way to see if your students have a clear understanding of the material. Last year I had the students to use their own smartphones. There is a code that they use to log into the game - they do not have to have an account to play. I let students share if they needed to. Today I had 9 ipads for the students who didn't have smartphones so it went great!
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| Coach Whitt explaining a problem from a Kahoot! |
Fortunately I ran across a wonderful Kahoot when I did a "public search" for graphing equations. It had 16 questions that reviewed finding slope, graphing, finding intercepts, and evaluating functions. I was able to use it with my Algebra IB for review and in my Algebra IA to reinforce concepts we are currently working on.
 |
| These 2 guys were working together:) |
I realized last year that when we worked through Kahoots which makes the review feel like a game the students invested in trying to learn how to get the correct answer so they can get the points for the next question. After each question the game shows who the leader is and you also have the opportunity to stop and go over the question. Today I gave the winning player 2 pieces of candy and all the other players on the "leader board" 1 piece of candy. It was a fun and productive day.
If you have never used Kahoot! it is great for all subjects and grade levels. You can create your own reviews or you can do a public search for ones that have already been created. There are sometimes mistakes in the public reviews but I just use them and then address any mistakes as they come. My husband showed me last year where the writers of the Kahoot! website even recommend you have students to create their own reviews for the class to play. That is also a great way to see if your students have a clear understanding of the material. Last year I had the students to use their own smartphones. There is a code that they use to log into the game - they do not have to have an account to play. I let students share if they needed to. Today I had 9 ipads for the students who didn't have smartphones so it went great!
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