IMP Overland Trail - solving equations using mystery bags - 5th period

I really enjoyed using Mystery Bags and Scrambled Equations. However, when I gave my students some "naked math" one-step equations they have really struggled. I have one class that is taking all year to work through the 1st half of algebra. They were identified to possibly have a struggle in algebra. I have several incredibly bright students in there. I have often thought - why was this student put in this class...   I had an eye-opening experience today. There were a few of my students who excel when we work in our IMP books who really struggled with today's work. I mean...the ones who are always "piping up" to answer the questions and seem to just "get" the big picture. One student even started the age-old, "When am I ever going to use this? This is stupid!" It took hearing him say that for me to realize that I have not heard that near as often since we started using our IMP Meaningful Math Algebra I books.

Ok...I am rambling a bit in this post so I am going to resort to using bullet points to make sure I get the main ideas that I am trying to convey:

• If I am teaching students who are struggling math students I am going to have to supplement material to help them learn to solve 1 and 2 step equations ...for sure. When integers were thrown in (after mystery bags) it has totally blown their minds. I think I am going to go "old-school" tomorrow and just teach the process in steps.
• After today I have a greater appreciation for how the context and story lines in the books give the algebra more meaning. I think it helps all students but I think it makes an even bigger difference in struggling students who don't usually do well in math.

IMP Alice Day 5 - Here Goes Nothing

Today we spent the first part of class taking our 3rd version of the systems of equations quiz. I had 9 students in each class to improve so I think it was worth it. Overall I am disappointed because I still have many students who just still don't get it. UGH!

Here Goes Nothing is an activity that the students can do pretty quickly. It helps the students to further analyze the nature of 2 to the zero power. I am glad that we did the Graphing Alice activity on chart paper so we had them hanging in the room to help us. I also wish that I had at least done one graph on chart paper of A Wonderland Lost - just for discussion purposes. The teacher's guide really adds to this activity so make sure you read through it before you teach it.

Since we did Here Goes Nothing quicker than I expected I had my students to graph #5 from A New Kind of Cake on chart paper. This is a comparison of y=2^x and y=x^2 and I really like it. We will discuss it tomorrow.

IMP Alice Day 4 - A Wonderland Lost and Scrambling Equations (Overland Trail)

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.

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!

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.

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.

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.

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.