IMP Overland Trail - Getting the Gold

I skipped Getting the Gold when I taught Overland Trail last year. I am so sad that I did! This is such a cool activity because it has such real-world applications. In this activity the students are asked to compare the profits of 2 different ways to gather gold. While discussing this activity it is fun to bring up discussions about making business decisions.

The discussion points that are a part of this activity include:

1. Business start up costs
2. Profit
3. Breaking even
4. BONUS...This is the first activity where the starting point is negative so it is fun to watch the students say..."the starting point is negative this time!" 

**I still catch myself wanting to give the student too many hints. I am sometimes excited about how the activities bring in different aspects and I just want to point them out! HAHA!

This activity and Water Conservation are fun "wrap-up" activities that have the students once more create graphs and answer questions. I love to ask questions like:

How do you know how much profit they had on Day 7 according to the graph?

Now, how can you answer that same question using the rule we created?

Could you use a table to answer that same question? 

 

Going from the "Context" to the "Abstract"

I have been mulling over the advice of a veteran IMP teacher (Michael Reitemeyer). He mentioned in an email how he tries to use the context of the lessons to introduce topics but then moves as quickly as possible to the abstract. Sonya and I were discussing today how we would like to develop around 8-10 "homework/classwork" problems that reiterate the concept of the day/lesson. This is not appropriate for every lesson but there are several that it would work well with. For instance, each time we develop/investigate a new exponent law in Alice we could assign 8-10 practice problems. There is a point in Overland Trail where I wish I had given them more problems in which they practiced graphing lines without a context.  The problems they will see on standardized tests won't always have a story to go with them.

Now...having said all of the above...I have been practicing solving equations with my 5th period.  We have been working through a packet together of different types of equations. Today I once again heard some grumblings. I told them that they didn't realize how much they liked the textbook we were using (IMP Meaningful Math Algebra). They were talking about LOVING the textbook. They enjoy the math so much more when there is a story/context to help make sense of it all. I have especially found this to be true with my students who struggle with the math.

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 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!