SREB - Another new journey in math curriculum for seniors

I had the opportunity to attend SREB Math Ready training for 3 days recently. I am excited to be piloting this course at Etowah High School this coming school year. It is another problem-based curriculum so I am looking forward to teaching it. I hope to have time to write blog posts about it like I did when I got to pilot the IMP Meaningful Math curriculum (which I am still teaching!!).

Here are the points of interest for the course that were sent to us to share with parents:

Alabama’s Southern Regional Education Board (SREB) Readiness Course Pilot Initiative

(Points of Interest)

• In order to decrease the percentage of students entering community college requiring developmental courses, the Alabama Community College System (ACCS), the Alabama State Department of Education (ALSDE), and the Southern Regional Education Board (SREB) have partnered together to offer two senior-level, ready-for-college courses: The Essentials of College English and The Essentials of College Mathematics.
• The courses are designed for students scoring below college-and-career-readiness benchmarks. These courses are not dual-enrollment courses.
• To be eligible for the courses, rising seniors must score within the following ACT score range: Math ACT 16-19, English ACT 14-19, Reading ACT 15-19.
• Students who successfully complete the course or courses with a B or above are exempt from taking the highest level of corresponding developmental courses (Math 098, RDG 085 & English 093 or ENR 094) at participating two year community colleges.
• Currently, the following community colleges are participating in the partnership: Wallace (Selma), Wallace State (Hanceville), Wallace (Dothan), Jefferson State, Calhoun, Gadsden State, Northwest Shoals, Lawson State, Snead, Bevill State
• The long-term goal is for all Alabama community colleges to become part of the partnership.
• The Essentials of College English and The Essentials of College Mathematics can replace the fourth year of English Language Arts (ELA) which is English 12 and the fourth year of mathematics.
• Please be aware that this is only a partnership with the two year community colleges, not four-year institutions. Because of the entrance requirements for four year institutions, students planning to attend a four-year institution should not be enrolled in these courses.
• Four year institutions require Algebra II for freshman college entrance and will not accept The Essentials of College Mathematics course as a replacement for Algebra II. However, if a student has 30 plus hours in a community college, then most four-year institutions do not require the Algebra II for admission.
• The Essentials of College English and The Essentials of College Mathematics currently will not meet the requirements of the National Collegiate Athletic Association Clearinghouse (NCAAC). School systems may apply to the NCAAC for acceptance but there is no guarantee that they will approve the courses.
• Although The Essentials of College English can count for English 12, it will not meet the requirements of admission for four year institutions.
• The Essentials of College Mathematics course emphasizes an understanding of math concepts, as opposed to memorizing facts. Students learn the context behind procedures and come to understand the “whys” of using certain formulas or methods to solve a problem. By engaging students in real-world applications, this course develops critical-thinking skills that students will use in college and careers.
• The Essentials of College English course utilizes a disciplinary literacy approach that teaches students strategies for reading and understanding complex texts in different subject areas. Students learn to develop and defend ideas from textbooks and write about them in college-level formats for English, history, and biology.
• Teachers selected to teach The Essentials of College English and The Essentials of College Mathematics were required to attend training specific to the implementation of the courses.
• Successful completion of the The Essentials of College English and/or The Essentials of College Mathematics courses has the potential to save your child time and money at his/her local community college. (Hint: Parents successful completion of the Essentials courses mean you will not have to pay for costly developmental courses that do not count toward a student’s

program of study)

• Students completing The Essentials of College English and/or The Essentials of College Mathematics courses will complete an exemption request form. The form should be submitted to the community colleges registrars’ office.

STUDENT End-of-Year Reflections on IMP Meaningful Math Algebra

Wow! What a year it has been! It has been a while since I have written a blog post due to the craziness of the end of the school year. I have so much that I would like to share.

Here are the student responses I got from the end-of-year review questions in the Fireworks portfolio. We did not have time to do the complete portfolio so I just had them answer the questions on pg. 421 in the book. I feel like what they have to say is more important than anything I could add. I only had one student to just absolutely say that he wishes he was taught out of the "old" type of textbook. Of course the responses I am sharing below are the "fun" ones for me to read as a teacher. There were some students that talked about how they didn't like that the book was so "wordy" but those same students later admitted to growing more confident and learning how to work in groups. I also had a few students to tell me that they still preferred to work alone but the overwhelming majority had positive things to say about group work. I told my students to be honest with their responses and give good explanations to support their comments. I told them I really wanted to know what they thought.

The first question set included the following:

How was this experience different from your previous work in mathematics? Did you learn the mathematics differently? How was the math itself different? 

Here are some of the responses: (I really wanted to fix all the grammatical errors...but I didn't because I didn't want to put my "spin" on what they said.)

• The books we used this year was all word problems and that will help me during high school and college. 
• Working in a group helped me understand better cause some of them understand better than I did and they helped me understand it better. 
• It was more fun with the activities and been taught different.
• ...the mathematics itself was longer and a bit harder also
• My past experiences I didn't understand anything but now everything seems a lot easier. (this is a repeat algebra student)
• This book is also different because it never (is) just straight on work it always has a fun story. Also it helps you a lot more than any other math book.
• We actually learned about real work stuff. We did a POW about having a house, paying bills, etc...

The second question set included the following questions:

How have you changed personally as a result of your experience? Has your confidence in your own ability grown? How has your experience of working with others changed?

Student responses:

• Working with others - I've started talking about it more than just trying to work on it.
• I'm more conficent in math now than I ever was. (this comment was repeated by several students)
• All year I've had a group to work and to collaborate with so I do believe I have gotten better working with others.
• My confidence in math has grown a lot because at first I never answered out loud, but now I know that I can do it.
• I don't hate math as much. It's not as hard as it was. My experience of working with others has grown alot and I can talk better with other people. (this student is a very quiet and shy young lady) 
• I like working with other people. You get to see what everybody thinks and their ideas. My personality has grown to like math a little bit more. I still kinda don't like it, but I like it more than I did.
• I think I have become more confident. I think I have learned to work with people that I normally don't talk to.
• It's changed (experience working with other) cause if I need help then I can ask my group members.
• It has helped me change by helping me with the word problems to look for clues through the paragraph. I myself had a hard time on word problems till this book helped me out.
• Personally I changed mathematically. My math skills have grown and so has my confidence in my own ability. My experience of working with others has changed like now I can work better with others. I can cooperate with others better. (This student stated in his answers to the first question set that he didn't like the book. I sure did like the results he got though!!)
• Yes my confidence has grown going into ninth grade. I never like working in groups but now I do.
• From a special education student: My confidence grown alot since last semester. It change because I use to just copy people because I didn't know how to do it but now I work together to figure out the answer.
• Working with others gave me more confidence and helped me understand something I didn't know and I could just tell my group and see if they know so we could help each other out.

The last question set had these questions:

What are your mathematics goals for the rest of your high school years? How have those goals changed over the past year and why?

Student responses:

• I also would want to keep learning more math cuase it can actually be fun to do.... But this year in math it has been easier for me and I'm getting higher grades.
• My goals have changed because I feel like I'm trying in my math classes and not just copying.
• I wanna keep improving my math skills for the rest of my high school years and beyond that. My goals have changed over the past year because I learned that I can keep improving my math skills. 

IMP Fireworks - A Lot of Changing Sides

I really enjoyed doing this activity with my students. It starts with a background story of a housing developer wanting to change the lot sizes for a new housing development. Instead of all the lots being square the city planner wants some of other types of rectangles. The questions tell the students exactly how to change the dimensions of the lots. The first 4 are situations where they increase the size of the lots and the last 2 involve a decrease in the length of at least one side.

Mrs. New had already taught this lesson and showed me the way the teacher's guide recommended the sketch of the lots be drawn. These diagrams will look like "the box method" that they will use to multiply and factor polynomials. The activity asks the students to express the area as the product of the length and the width (which will be binomials) or as a sum of smaller areas. Since the 2 areas are equivalent the students are led to realize that the 2 expressions are equal. I aksed them to look for connections between the sum and the product and a few of them saw it.  I love that the authors have once again provided a context for the formal math to make sense to them!

I led the students through #1 so I could model how to sketch the diagram with the original side length of X. In #5 and #6 I let them come up with their own diagrams to represent the situation. Also, just for the sake of organizing, I labeled the bullets as A, B, and C so that it would be a little easier to organize and discuss.

IMP Fireworks - Using Vertex Form, Crossing the Axis, and Is It a Homer?

In Using Vertex Form, the students have another picture to create with their graphing calculators. Then they are given equations in vertex form and asked to give the vertex. Most of the students could do this without using the graphing calculators but a few still depended on them. I advised them to use the "Trace" feature of the calculator to find the coordinates of the highest point and then compare the coordinates to the equation. This improved their confidence in finding the vertex.

I gave my students a quiz where they had 6 questions in which they matched quadratic equations to their graphs. Then they had a couple where they had the equation and had to list 3 things they know about the equation. The last 2 questions had them describe how to flip a graph so that it was concave down and then sketch a graph with 3 different parabolas and give their equations. I was so excited about the quiz results. I wish I could say that all my students aced it but that is so not true! However, the large majority of my students passed the quiz and many made As and Bs. I have never expected my students to be able to do so much with graphing quadratic equations. The way the activities led the students through the process was so thorough it made the quiz seem easy.

The Crossing the Axis lesson gets students to start thinking about how many x-intercepts the graph of each quadratic equation will have based on the phase shifts. The activity also has students to write the equation given the vertex and another point on the parabola. They have to use the information to solve for the value of a. Numbers 5 and 6 are very important to complete because they give the students the tools they will need to complete the Is It a Homer activity.

Is It a Homer is an awesome activity to me as a former softball player and coach. It was also fun to the students. Mr. Webb shared a link with me of a Youtube video of a "dramatic reading" of a poem about the "Mighty Casey." We watched it before we read the activity. They are challenged to figure out if the ball clears the fence and they must prove it mathematically. I had the students sketch the graph with height on the y-axis and distance from home plate on the x-axis (which was advised in the teacher's guide). I gave the students the hint that they will be using the same process they did on 5 and 6 of the previous activity. After giving the students some time to think I went to the board and sketched the graph and labeled the vertex. I asked the students if there was another time when we knew what the height of the ball was. My 2nd block students chose to use (0,0) and but my 4th block students pointed out that the ball was not hit off the ground so they used (0,3). They struggled some with the computation of this problem but a few students in each class got the answer correct based on the height of the ball at contact. I had one student who told me that he estimated that the ball would fly 400 feet because the maximum height was after the ball flew 200 feet. Even though we have not yet talked about the symmetry of the graphs he had recognized it and used it for his reasoning. Unfortunately he didn't tell me his thoughts until AFTER class. I will be sharing it with my classes tomorrow.

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.

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.

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:)

IMP Overland Trail - Water Conservation and stopping to find balance...

My 5th period class is Algebra IA year-round. They should be covering Overland Trail and Cookies before the end of the year. I just realized that they are at a point of Overland Trail where I had to skip some of the activities with my Algebra IA Fall Block classes. I was determined to finish Overland Trail by Christmas in order to start Cookies in January.

The Water Conservation activity is another good one to put on chart paper. Most students will generate a chart in order to answer questions 1 and 2. However, I had some students who graphed the lines first and then tried to go back and answer how many gallons each family had left after a given number of days. This did give us the opportunity to discuss how it is easier to be exact when you use a table instead of the graph due to the estimation that is required when looking at the graphs.

I loved that the group that generated the work shown above included the table and the graph along with their answers to the questions. One of the questions that this group did not address is how to find how much water each family has after x amount of days. This forces them to think about the starting point and rate of change. They know to muliply the amount of water used per day times the number of days but then they have to consider that they are trying to give an expression for the amount of water LEFT not the amount of water consumed.

After covering this lesson I pulled some practice problems where graphs were given and we were asked to find equations. I also talked about the slope formula and had them find the slope given 2 points. I know that I need to take time to stop and explicitly teach topics that we have covered but they may not know the "math vocabulary" so I am going to list them here:

• graphing from slope-intercept form
• writing the equation of a line when given a graph
• finding the slope of a line given 2 points
• finding the slope of a line given a graph

Our students have done so much more with this curriculum and creating graphs given real-world circumstances. However, when they take the end-of-course exam and the ACT they are going to need to be familiar with how to do these problems when there is NOT a context. After having taught through this unit (Overland Trail) the first time I realized that there are times I needed to stop and teach the students what types of "traditional algebra" problems they might see from the content we have been covering. The problem was that having never been through the curriculum before I did not want to "steal the thunder" of a lesson that we were going to cover in the future. I feel that to teach using the "exploration/inquiry/problem-based" method you have to also find a balance with showing students what the "traditional/worksheet/drill and practice" version of the algebra looks like. I KNOW that I can do a better job of finding a balance between the two. 

IMP Cookies - Solving Systems of Equations (Only One Variable and The Classic Way to Get the Point)

I love the way the Cookies unit starts with solving systems of inequalities and then works into solving systems of equations. In the Cookies and Inequalities portion of the unit the students are introduced to "real-world" problems where systems of inequalities can be used for solving them. The students practice writing constraints and then graphing the inequalities that go with them. In the real world problems often have more than one possible answer - much like is true of the feasible regions you get when graphing systems of inequalities.

Then, as you try to solve the Cookies unit problem or other problems in the unit involving minimums and maximums you discover that you need to find the "corners" where the lines intersect. We had our students just estimate using their graphs in order to find the points of intersection. However, it is neat to be able to introduce the topic of solving systems of equations by talking about how we really need to be more precise when we find the "corners" of the graph. For a couple of days this week our classes worked on an additional activity that helped them to explore the elimination method.

Today I first had my students do the Only One Variable activity. We had alot of fun with it because we integrated some technology too. Each group had an Ipad and they were projecting their screens using air server/airplay. I gave the group 3 minutes to work on the problem and then after the time was up they had to put something on their screen (they were using the Educreations app). It is so cool to be able to see several samples of student work on the board at the same time. We can critique the work without the class knowing whose work it is. We are able to celebrate different approaches for solving the problem. Also, we are able to talk about common mistakes. They love when they are working on a problem and I point out their work. I can say, "Hey, this person is really moving in the right direction."

Each group's problems projected simultaneously! Cool stuff!

Next we worked on The Classic Way to Get the Point which introduces the substitution method. Mrs. New and I had looked through the rest of this unit and we saw so many activities that give the students the opportunity to practice solving systems again and again. I used to teach these two methods of solving systems of equations separately. Then after covering each method I gave them some "mixed practice" where they had to choose the method to use.  However, I now like the idea of giving them some time to practice a few of each type and then let them decide which method to use as we go. The ACT and other tests are not going to tell them which method to use so they need to learn how to choose which method works better for each type of problem. There are several activities in this portion of the Cookies unit that give them a few more systems of equations to practice solving so hopefully by the time we revisit the topic several times my students will retain the information.

IMP Cookies unit problem with a "New" twist

The unit problem in IMP Cookies has to do with finding the maximum profit for a bakery when they meet constraints pertaining to oven space, preparation time, amount of dough and amount of icing. Throughout the unit the students do activities that give them all the information and tools they need in order to answer the unit problem. My often-mentioned teaching buddy Mrs. New has done a couple of really cool things with this unit problem. She is having the students to present their findings to a panel of administrators, our instructional partner and another math teacher. They are going to have to tell them what amount of iced and plain cookies will give them the highest profit and prove to them why.

The BEST part is the idea that Sonya had of telling the students that they could change ONE and ONLY ONE constraint. She has told the students to make a proposal to the panel of which item they should increase. Should they buy another stove, hire another person, or buy more dough or icing? There are some constraints that even if their limits are increased they will not increase the profit. I LOVED this idea. I am doing the "lazy version" of Sonya's activity and just having the groups present to the class. I have tried to encourage the groups to be creative as to why they chose the constraint to increase. I told them they could make up a story to go along with it in order to convince us that it is the best thing to do. However, they are also supposed to have a new graph that reflects the changes in the constraint. I had students to realize today as they were preparing that they chose to increase an item that did not improve their profit. Their feasible region was still the same.

I love teaching with creative people! Sonya is ALWAYS coming up with really cool ideas and activities. I will update this post after her groups have done their presentations...I'm sure she will have some awesome things to share.

UPDATE after presentations:
Things we like:

• We love the problem...especially having the students change one constraint and then explain if it improves the profit!
• Mrs. New loved having the students present in front of a panel
• Mrs. New's students loved that they went in a separate room to present...no other students were present during their presentations
• Mrs. New required them to have a digital presentation - most used Prezi or Powerpoint

Improvements:

• The students didn't seem to fully understand what we wanted from them. We need to somehow do a better job of explaining the purpose.
• To address the above bullet...Ms. Whitt mentioned she wished we could model a presentation for the students...maybe use the Picturing Pictures activity to model a presentation, then let them practice presentations in the classroom using Rock 'n' Rap
• Remind the students to explain the problem like nobody has a clue what they are talking about...give some background info...

The students presented in this small "conference" room

IMP Day 46 - Fair Share for Hired Hands

Today we finished discussing Fair Share on Chores. Then we worked on Fair Share for Hired Hands. Both of these activities start with a situation where the students will write an equation that starts in standard form due to the way the problem is read. Then they are asked to describe in words how to find one of the "unknowns" if you know the other. The cool thing is that the next question asks them to then write it in equation form. It is a neat approach because the context helps the students to identify mistakes.

At the beginning of the activity the students are asked to explore the problem numerically. One strategy I have encouraged my students to do is to brainstorm WITHOUT erasing. I want them to write down things they try or ideas they have and just put a line through them if they decide they are incorrect. This helps them to keep track of what they tried. When they are working on their POWs they are asked to explain their process and write about what they have tried. I loved the work of the student whose paper is pictured below because she did keep track of her brainstorming.

Mr. Webb gave me an idea today. One of the issues I am having with using our new textbooks is the amount of time it takes to do each activity. You can really go in depth and spend some time exploring and discussing these activities. He said that when there are 2 lessons that are similar he pretty much  walks them through the first one as a class activity and then assigns the 2nd one for them to work on in their groups. I feel like this is a great idea especially since we started the book 7 weeks into the year so we are already trying to find activities that we can skip in order to cover.

AP Teachers - IMP Curriculum might help you!!

For some reason today I was thinking about how the problems in our Meaningful Math Algebra books remind me of the tasks that students have to do on AP exams. I taught AP Calculus for several years and always felt like I had to cover the topics before I could have the students "tackle" the free response style questions. I came to realize that I really needed to practice those free response style questions throughout the year instead of waiting until the end. This reminds me of going to AMSTI training and feeling like I would have to teach the algebra topics before my students could do the activities in the IMP books. I often tell the other teachers at our school that I hope that they will see that our students leaving our algebra classes will be better students in general... More willing to tackle tough tasks... More practiced in explaining their reasoning.

I also think that these students will be much more prepared to tackle the multi-step, multi-concept AP questions they will encounter on AP exams. Many of the activities we are doing in our books combine several of the concepts that have been covered to date. Several of them require students to examine a word problem and then create a table and a graph. Then they are asked to answer questions about the situation AND write the rule or equation AND explain their reasoning. Because the majority of the assignments our algebra students are doing now require them to read a word problem and think through the problem. They have very few tasks where there are multiple problems of the same type that they just "run through." I can tell that many of my students have really grown in their confidence and willingness to tackle word problems. I know that I have never seen a textbook that I would favor as an AP teacher until now.

IMP Day 30 - You're the Storyteller and POW writeups

Today I had some fun with my classes. We made a "contest" out of beating Mr. Webb's class on making creative stories for the equations in You're the Storyteller: From Rules to Situations. I had one group do a rap and another do a video depicting a bank robbery. They were really entertaining and the students who were brave enough to do them had fun and were proud! The other groups just wrote the stories on chart paper. The "stories" on the chart paper below were the ones who also did the rap and the skit! It was loud and rowdy in my room today but it was alot of fun!

**My 2nd block class didn't get as much time to "have fun" because they had to finish up the quadratic graphs for From Rules to Graphs. Only a few students completed their homework (which was to graph (Out=In^2). None of them had the "u-shape." I decided to do a graph on chart paper on the board. I only had room to go up to 25 on the y-axis so they they were limited to x-values between -5 and 5. This was an interesting activity. I asked each student (28 total) to share an ordered pair that they got on their homework. It didn't take long for us to use up all the integers. I did have one student who used a decimal even before the integers were taken up so I made the remark that he sure was thinking "outside the box." I also told them numerous times that there were an infinite number of possibilities. When the students started getting the hang of it and we got all 28 points on the chart paper the u-shape was evident. We then discussed the difference in the equation for this u-shaped graph compared to the other equations and they came to realize it was the "squared part." I thought this was a very good investigation and we were able to explore the ideas of continuity and "infinite possibilities."

The most impressive part of my day was when I read the Haybaler POW writeup written by one of my 5th period students. It was AMAZING! Talking about understanding the whole point of a write up in the first place! I was inspired and amused throughout her writing! Here is a piece of her write-up. The sentence on the previous page discussed how she must first make sure she completely understands what the problem is asking.

I have come to the point where the POW write-ups are my favorite part of the IMP book (at least for today!). When reading them it is extremely easy to realize who is comprehending the math and the problem-solving process. Some of them (unfortunately) are so far out in left field I can not figure out why they would write such stuff. However, there are many who are increasing their math and problem-solving fluency just by doing the write-ups and having to think and reflect about their work. The ones who are in left field will hopefully start getting closer as the year goes on!

IMP Day 29 - From Rules to Graphs and Instagram

Today I took a breath (I haven't slowed down and done this in a while) and allowed my class to use chart paper to share their graphs for  From Rules to Graphs. We had some good discussions about the graphs and whether or not they should have been continuous or discrete. My first class didn't get the u-shape of the quadratic graphs so I assigned the two quadratics again for homework (#2 and # 4b).

My second class happened to have 2 groups that graphed number 2 and when we combined the points from the 2 groups we "saw" the u shape of the graph. Both blocks were told to start thinking about stories that they could use for the equations in "You're the Storyteller." I had one student start rapping and I so wish I could get someone to do a rap or a song but I am afraid they won't follow through. We will see!

On a side note...some of my students have been trying to get me to get an Instagram account and use it instead of Twitter for posting "pictures of success" or other pics from class. I set one up last night and it was so funny how they reacted to me having an Instagram. I post pics to Twitter pretty often and we have started the hashtag #WeAreEtowah for sharing positive things going on at EHS. I had a "younger" teacher explain to me yesterday that Instagram, like Twitter, is set up where people can follow you and you don't have to follow them back. Also, you can post pictures to both Instagram and Twitter using Instagram. I am excited because I can post as many pics of my students on Instagram as I want now and they don't fill up the feeds of other teachers who follow me on Twitter (who may get tired of all the EHS pics!). BUT, when I do have some pics I want to share with my principal or other teachers on Twitter I can post both places when I want. Also, you can use hashtags in Instagram too! I'm sure that there are many people that already know all of this but I just thought I would "share." I would like to start using Instagram as a way for students to share their work with me on occasion.

IMP Day 27 - More Graphing Sketches, Notebook Check, Out Numbered and...Searching for Dry Trails

Progress reports are being printed next week. Therefore I needed to do a notebook check with my classes. I gave them pg. 117 as a quiz and graded their notebooks while they were taking the "quiz." When they completed the quiz they started working on Out Numbered from pg. 49.

Funny thing...many of my students with the best "math minds" HATE estimating. They didn't like assigning a coordinate to the points that didn't go "through the crosshairs." One student in particular is extremely bright but doesn't realize how smart he is! Several of my students, when assigning themselves grades for their POWs, underestimate their work.

Sonya New, Gary Webb, and I had a brief discussion after school today about how things are going. Gary and Sonya don't seem as worried about time and grades. I need them to "rub off" on me. Gary's students were displaying their stories from "You're the Storyteller: From Rules to Situations" today. Our senior counselor, Kali Brand, walked by and said that those students looked like they were having fun. I was secretly (or not so secretly) jealous. I am going to have to take a deep breath and just enjoy where we are. We are piloting a new curriculum. We have made a change because we did not believe what we were doing was effective. We hope to see improvement. We started 7 weeks late. Relax! Roll with it! I am trying to convince myself:)

I almost forgot to mention something awesome! My 5th block finished Family Constraints and started The Search for Dry Trails today. They cracked me up arguing (justifying) about which trials they would choose and why. They did a great job today. Several of them have some great thoughts...I just tried to help them "tie" some math vocabulary to those thoughts today. I had 2 or 3 of them up at the board at the end of class still arguing their points. It was super!

Reflections after 5 weeks of IMP Meaningful Math Algebra

1.  I can no longer walk in and wing it...effectively. To get everything out of a lesson  (that the authors intend) one must study over the teacher's guide first. The guides are so much different than the typical teacher's edition!
   **Later revision - this sounds bad, I know. I also know that "on the real" I am not the only teacher that hits "spells" where my life (at school and with my family) gets so crazy and busy that I can not put the planning time into my school lessons that I would like. This past week has been that way for me. 
2.  I am not going to be able to get the "big picture" until I have taught through the book once. 
3. Grading is so strange. I haven't quite figured out how to grade effectively using this curriculum.  I know I can still give "normal" quizzes but... it is harder to identify good places for quizzes...and they aren't really recommended...
4. Since almost every activity has a context you can spend forever on them if you want to...
5. It is easy to get frustrated when things are so unfamiliar.
6. Referencing back to #3...because the way grading is done so differently I feel unsure about where my students stand.  I ask them to explain a lot...I think I know where they stand...I think they are learning...look at the picture of an excerpt from a POW write-up 

Things I know I'm doing better than before IMP...

1. Addressing literacy standards
2. Teaching how to solve word problems
3. Stretching the students (especially with POWs)
4. Questioning...there are always suggested questions in the teacher's guide. 
5. Making real-world applications
6. Celebrating various approaches to problems...I find that since there really isn't a mathematical title to the lesson (i.e. Percent Increase or Systems of Equations, etc...) that students tend to take more varying approaches to problems.  Also...I don't say to students as a form of a hint..."Hey guys. ..look at the title of the section!" (I really used to do that sometimes.) 

**I love #6 because no problem we face in the real world comes with a title that gives you a hint on how to solve it:)

IMP Day 24 - Real-world percent increase/decrease

Today we had a morning assembly that went over into our time for our 2nd block class. Dr. Montgomery gave me the idea of doing a formative assessment to see if they got percent increase. I made up the following problem...

The students had to show their work and write an explanation. Some of the students had to clarify and/or rework but overall I felt very good about their comprehension of the work!

IMP Day 23 - If I Could See This Thing

Today was a frustrating day. We worked on If I Could See This Thing all block (1 hour and 25 minutes!!) and didn't finish! The "time allowed" in the pacing guide is like 25 minutes. So...I did try several different strategies today. The first thing we did was to allow them time to read the intro and excerpt silently then "notice and wonder" with a partner. We have never done the Noticing and Wondering strategy before. Afterwards I rolled my 8-sided dice to choose groups to share their findings and I recorded them on the board. I told the students that if they would research any of the "wonderings" and type up a summary that they could earn bonus points which are rare in my class. Then we used the same noticing and wondering strategy for #1. They did not notice and wonder the things I was hoping for. In my 2nd go around (with my 3rd block class) we popcorn read instead of reading silently. Also when we got to number 1 I did a better job of encouraging them to notice and wonder about the math part of the problem too!

We started number 2 but will have to finish tomorrow. Dr. Montgomery has made tombstones and death certificates for the students to use for their family members who "didn't make it."

Day 21 IMP - Kearney and Vermillion

Today I had my students finish To Kearney By Equation. We completed numbers 1 and 2 on Friday so they just needed to do numbers 3 and 4. I helped each class come up with an alternative formula where we used round trips for the profit equation instead of hours. This would have been a GREAT extension of the problem but I just kind of "happened" across it when I was trying to keep them from dealing with a fractional amount of time in hours. (That scares them!)

I almost led my 2nd block class astray because I asked them to compare which river crossing was cheaper between Kearney and Vermillion. THANKFULLY I caught onto the fact that in Kearney you are finding the amount of PROFIT for the Pappan Bros. and in Vermillion you are finding the amount it costs to cross the river. I was able to use this as a teaching point in both classes. We also defined formula and added it to the vocab list. I assigned Ox Expressions for homework and offered bonus points to the student who finds the most meaningful expressions...

**Hints for the future - I use what I have previously called Interactive Notebooks but since I have been using our new textbooks I have not been "giving notes" like I used to. We have not any more foldables...  However, the notebooks have come in handy because we create an entry for each activity in the table of contents and I hope it makes it easier for my students when it comes time to do their portfolios. In the future I would like to make a vocabulary entry at the beginning of each unit and leave enough room for them to go back and add vocab terms as we go through the lesson. Right now I have them listed and defined on chart paper in my room. However, when the unit is over I will take them down. I would like them to be able to have something to go back and review all vocab at once.

I have done ALOT of guiding (talking too much!) the last couple of class periods. My students still demonstrate their lack of number sense on a daily basis! I definitely need to work on my reactions so that I don't make crazy faces when they say something crazy! For some of the harder ideas I have a class discussion and the brightest 2 or 3 students end up answer the questions and "leading us home" to whatever idea I am looking for. I feel a little guilty about this but I am looking at it right now as an opportunity for my stronger math students to stretch. Once I guide them through questioning to whatever concept I am trying to reach I try to re-explain it to everyone. I am specifically referring to the "new formula" we developed for profit in Kearney which was profit = 2W-0.10T where T equals round trip. I thought this formula was easier to use but I tried to not just GIVE them the formula...