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.

MTBoS Blogging Initiative - Better Questions

Boy...when I look at the prompt for this blog post my mind goes in so many different directions. I wrote this post in which I discussed trying to use "quality questioning" in my classroom. I was not really talking about questions to put on an assignment, quiz, or test. I was thinking about questions used to do the following:

• guide students to think deeper during discussions
• guide a struggling student toward understanding a concept 
• scaffold and access prior knowledge
• defend and/or explain answers or reasoning

The prompt seemed to be more along the lines of writing questions for assignments or quizzes. I happened to attend a PD today on Webb's Depth of Knowledge (DOK) in which we discussed asking more level 2 and 3 questions when we assess our students. Of the 4 levels of questioning we were told that the ACT and the ASPIRE assessments have very few questions that are level 1 (basic recall or computation) and the majority of questions are levels 2-3 (harder stuff...HAHA!). Anyway, the majority of textbooks are filled with level 1 questions but not many that are levels 2 and 3. 

For those of you who want to know here is a VERY brief description of Webb's DOK:

Level 1 - Recall and Reproduction - "Right there" questions where you can look it up in a book or follow steps from an example
Level 2 - Skills and Concepts - "think and search" questions where you have to put information together or categorize - these may be open to using different approaches and explanations are often required
Level 3 - Strategic Thinking and Reasoning - More than one way to approach and more than one possible answer - non-routine problems are often used here - often asked to state and support with evidence
Level 4 - Extended Thinking - Extended thinking that takes more time - possible products would be films, plays, research reports (with multiple sources), video games, documentaries, newspaper articles, etc...

(source: A Guide for Using Webb's Depth of Knowledge with Common Core Standards by Karin Hess, E.D - copyright 2013 Common Core Institute)

We were given some strategies on things to do in order to use our textbooks and resources that we have and take the questioning up a notch. One example of moving into the Level 2 questioning is to ask for "non-examples." We often ask our students to give an example of a _________ but they can demonstrate an even greater understanding of concepts if they can also give a non-example.

I had the pleasure of using two non-routine tasks with my algebra classes this week. Both of the tasks seemed impossible at first but when we continued to work toward the solutions we found that there were ways to arrive at a solution.

The first task was the Shuttling Around Problem of the Week #13 in my IMP Meaningful Math Algebra book. It is actually a puzzle where you really have to get out manipulatives to work through it. On the day we introduced the problem only one student found a solution. It took him a while but he finally videoed it so that he could email it to me as part of his POW write-up. The funny thing is that even though I stood there and watched in order to verify that he had a valid solution...I could not do it myself. So, today I allowed another class some time to work on the task and I was going to sit down and figure it out myself so they would see that it was possible...but I couldn't. I called down to the classroom where the guy who found the solution was and he came to my class and showed us the solution again. After watching him do it I had several students go back and work to figure it out themselves...he and I went around the room trying to help and I FINALLY got to where I could do it. The task asks them to investigate other problems too so we weren't taking away all of their fun. It was a great way to end the week! The coolest part of this is that the student who really excelled is not an A/B student. He is rarely ever one who aces a quiz or test. He has an incredible work ethic and tries to do every thing that I ask of him. It was so rewarding for him to have an opportunity to shine!!

The other task was A Mini-POW About Mini-Camel again from our text. One of the great things about our text is the "key questions" in the teacher resources which helps you have ways to guide the students. In this one all I had to say was, "Who says you have to go straight there?" and I had students to begin to find possible solutions. I even had multiple students to go to the board to try to prove to everyone else that their answer was correct. (Here is a link to my Instagram where I posted a video of them.)

I had one student ask me why we had to do these types of problems and I told him that it is important for him to realize that just because something seems impossible at first glance it does not mean that a solution can not be found. I even told them that I may be helping to save their future marriages (haha!) because they may think one day that the only solution is to give up but remember that one time in algebra class they kept on trying and working at a task that seemed impossible only to find that there was a solution!! I know that is goofy but I got some giggles and I do hope that these problem solving skills stick with them after they leave my class.

I love that I have these tasks included in our textbooks! I wrote my last MTBoS blog about how my textbooks are my favorite tool that I use in my classroom here.

Students teach the class - IMP Mini POW About Mini Camel

Today I decided to do the Mini POW About Mini Camel activity from The Pit and the Pendulum. We decided to skip Corey Camel POW and do this one first. I had not worked through the problem myself prior to doing it with my Algebra IB class today. Please don't judge me on this. Haha! I find that I do not lead the students quite as much when I don't know the answer myself. Actually, the teacher's guide does give you the highest possible answer but doesn't tell you how to arrive there. It does give you the hint to ask the students if the camel has to go straight to the market. (In other words...can he go part of the way and put a portion of his bananas down?)

I knew that the camel had to have some "pitstops" along the way but I had not sat down myself and figured out the problem. I gave the students some manipulatives and gave them approximately 20 minutes to work. I walked around and helped them to model their ideas with the counters. When I had one of  the boys in my class tell me he figured it out I was skeptical and made him show me. He and his partner talked me through the situation (which involves the camel only traveling distances of 1 mile at a time - and is pretty cool!!) I was amazed. I often find that my students are better than me at logic problems. I told the student that he had taught me something today and he was so proud.

Typically if my students do not come up with and defend a solution I will work through the problem with the entire class. If no one had come up with a valid solution I would have done that today. Also, if I model the problem solving process with the entire class and we don't come to a solution right away I just tell the class to help me think about the problem and let's see if we can work on it again the next day. It is so exciting to me when my students do it on their own.

IMP Problems of the Week and Rubrics

For some reason today I have been thinking about how much I enjoyed doing the Problems of the Week (POWs) with my algebra students. (Disclaimer: We did not do them every week...we did about 2 or 3 each 9 weeks). Here is a post with a picture of part of a POW writeup that was good. And this post (toward the bottom) has a portion of one of my favorite write ups from this year. One of my favorite quotes from a POW was "every time we use this I go deeper into thinking than I ever have in math."

When I attempted to grade the first POW writeups I was so disappointed. I had a rubric that I used to grade it that I found at gphillymath.org and it was so helpful. Our Instructional Partner, Dr. Shelley Montgomery (@DrSMontgomery), came by and I was talking to her about my students' writeups. She asked me if I had given my students the rubric when I gave them the assignment. I didn't even find the rubric until I got ready to grade the assignment. I went over each of the categories for the POW Write-up and gave examples...but I did not give them the rubric ahead of time. Don't judge me! HAHA! Please remember I am a math teacher and I was not accustomed to grading writing assignments. I ended up giving the writeups back to the students WITH my grading rubric. The 2nd attempt at the POW writeup was much better. As the year went by my students really improved in this area. It was frustrating how many of them just did not pay attention to details. I am hoping that the experiences they had using rubrics in my class will serve them well as they use them in their future English classes - I know that their 10th grade English teacher uses them often.

If you are teaching using the IMP curriculum please go to the gphilly website. There are many awesome resources which will make your life easier. AND...give the grading rubric to the students on the first day that you go over the POW in class.

As a math teacher I feel that there are 2 different ways to use rubrics. The POW writeups are similar to the types that English teachers use. However, before this year I had mostly used rubrics to help me to grade my tests consistently. Awarding partial credit can get confusing when you can't remember how many points you gave for portions of the answers being correct. I have not included these "rubrics" on the quizzes or put them on the board for my students to look at while they are taking the quizzes but I feel that it would be a good thing to do. Maybe if the students saw the ways in which you were going to award credit they will be more willing to try problems that seem difficult at first.

Even the teachers had to PERSEVERE in problem solving to figure out the POWs - Coach Whitt was cracking me up on this day!

I love that the students learned how to ask for help and find other ways to help themselves via the Internet or asking for help from their parents or friends. I allowed that for POWs as long as they included how they received help in their writeups.

The Four 4s - an activity from Jo Boaler's book

Today I spent most of my day in the computer lab where my Algebra IB students took a "mock" end-of-course exam. Those days are so draining for some reason! I am happy that it gave me the opportunity to finish reading Jo Boaler's What's Math Got To Do With It? which I believe every math teacher should read! Thankfully one of the last chapters discusses some puzzles and number talk activities that are good for students. I was so tired I could not imagine having a "normal" class with my 5th period today. Instead I gave them The Four 4s to do as an activity. The task asks them to try to make every number between 0 and 20 using only four 4s and any mathematical operation. The directions for the task gives one example and then asks them how many of the numbers between 0 and 20 they can find.

At first my students wanted me to give them more examples but I refused by telling them I didn't want to rob them of the opportunity to get them on their own (haha!). I finally got a few of them moving by telling them to just write four 4s on their papers and then put some operation signs in between them. Once they did this I told them to evaluate the expression making sure they used the order of operations correctly. This really got them rolling. A cool thing about this task was that everyone worked on it. At the beginning I had to seperate a few that were totally off task but once they saw that they could get some of the numbers they worked on their own.

I think that you need to have variety in your classes. I have many students who do not enjoy an activity when they view it as purely mathematical but when you give them a puzzle to solve they engage. I intend to use activities like this more often. One of the discussions on Boaler's website (youcubed.org) talked about how they just listed the numbers 0 thru 20 on a board in the back of the room and allowed students to write their expressions and put their name beside it. That way all of the classes throughout the day could contribute until all of the numbers are found. This task will engage some students that are bored with the normal daily routine!

Just in case you read this blog because you are using the IMP Meaningful Math textbooks, Jo Boaler has a list of 3 curricula that she recommends for use in 9-12 and the Interactive Mathematics Program from It's About Time is on that list. After I started reading her book I realized that she was one of the keynote speakers at NCTM this year. I learned so much about what the research says about the best ways to teach math for student success!

IMP Alice Day 8 - Having Your Cake and Drinking Too

When I saw that the teacher's guide allowed 60 minutes for this activity I thought there was no way. I thought we would get through it quicker...haha! We didn't even finish and we had OVER an hour. This activity helps the students to explore and HOPEFULLY discover the rule for dividing powers with the same base. I love it! It is really revealing the lack of number sense that my students have. The questions are not really that difficult...that is why I thought we would breeze right through.

I have allowed myself to "sit" on this activity and not rush it because I really believe it might help to cement the concept. I am going to be absent tomorrow from my classes and I have some good exploration worksheets on exponents to leave for my students. However, it has reminded me how blessed we are to have found a book that combines the exploration with the context. Someone had a wonderful imagination!

**Update 3/7/15** Original post was made 3/16/15
This year when I taught this lesson I took the time to help the students to explore #2. I did not let anyone blurt out an answer when we first started looking at it. I have been using the random integer generator on the TI-83 (which is awesome but I just now figured out how to do it!!) to call on students. In my classes I just happened to call on students who were unsure of what to do so I just asked them to start by making a guess. I told them to tell me a number of ounces of cake and a number of ounces of beverage and then I showed them how to "test" their answer to see if this would give an answer where Alice's height was multiplied by 8. Then I randomly called on more students. The first 3 students guessed more beverage than cake (ugh!) so I asked the next student to make a "conjecture" on whether or not more beverage than cake would EVER allow Alice's height to be multiplied by 8. My 2nd class arrived at the correct number of ounces much faster than my 1st one did but I feel that modeling to the students how to "guess and check" was valuable. I am always telling them not to ever erase their guesses. I want them to learn to look back over the ideas that didn't work in order to help them to identify new theories that might work!! Anyway...the day I taught this lesson this year I felt really good about what we had accomplished:)

Coteaching with my principal?

Yesterday my 5th period students were working on the Fort Hall Businesses activity from the IMP Meaningful Math Algebra books. Some of the groups in the class had #1 and some had #2. Each of the problems asked students to find the "starting point" for a situation. Anyway, I had "helped" the groups who had #2 first because it was a little more difficult.  I had guided the students through how to take the two sets of data points and think through how to find the "starting point" which was the amount of money that a movie theater had started with in their cash register. We had "deduced" that they started with $10. What I didn't realize is that when I wrote down the two data points out of the problem I had written one of them incorrectly. Therefore although the students' reasoning in how they found the answer to be $10 was correct I had "led them astray" by writing down the wrong value.

So, my principal walks in and sits down for a minute. When he comes in I am working with the students who are doing #1 and writing on the back board. The problem that is still projecting on the front board is problem #2 so he finally asks me if we are doing different problems. He then goes and talks to a couple of the groups doing #2 and starts working on the problem. When I walk back to the front of the room he is telling the students that the starting amount of money in the cash register is $25. In my mind I am thinking, "O bless his heart! He is wrong and he is going to be embarrassed in front of all these students." Thankfully I didn't claim that he was wrong. I just asked him to explain his reasoning. He did a wonderful job explaining his reasoning and he was RIGHT - not bad for a former history teacher. My brain literally had a cramp in it because I was so confused why we had gotten $10 earlier. I KNEW we had used the right reasoning. After a couple of minutes looking back at the values I had written on the board we found the mistake. Needless to say my principal now thinks that he is a math expert!

I had a couple of students to throw their papers away because we had made a mistake. I tell them to never erase or throw away papers because I want to see their thinking on paper. I even had one student who graphed the 2 data points and extended the graph back to the y-axis in order to find the starting amount in the cash register. He had the correct points graphed and had $25 as the starting point until I went and "corrected" him because he hadn't graphed the points I had written down. I felt so bad! I told them to just write down "Owens was wrong" on that page in their notebooks instead of starting all over. I knew that they understood what was going on with the problem. I also used the situation as an "object lesson" about working in groups. I told them that this was an example of why you can't just accept everything that the "smart kid" in the group says. When you have different answers or ideas in the group you need to take time to explain and listen to each other's reasoning. Today they saw the mathematical practice standard #3 (construct viable arguments and critique the reasoning of others) acted out by me and my principal.

My principal and I are both former coaches and highly competitive individuals. I am sure he will never let me forget about the day he had to "set me straight" in my own algebra class.

IMP Day 42 - Moving Along - making connections!

The teacher's guide for Moving Along says that all algebra teachers love it because it has types of  problems that we are used to seeing. The students are given two points and asked to write the equation of the line. The interesting part of this assignment is seeing the different approaches that the students will take to solving it since we have not discussed the slope formula or the point-slope form of an equation.We have explored graphing through starting points, rate of change, and in-out tables. We have used slope-intercept form (without calling it that) by discussing that when the equation is y=ax + b that b is the starting point and a is the rate of change. The majority of my students write their equations in the form y=b + ax which seems more logical when we talk about b as the starting point.

I started class by assigning each group 2 of the 4 problems (everyone did #4). I gave them 10 minutes to brainstorm on how to approach the problem. The first group who got their equation explored the problem by using a table and finding the rate of change. The two points given in this problem were (0, 36) and (6, 24) so they remembered that the starting point had to be 36 because we had discussed for several days that the x-coordinate of the starting point is always 0. They realized the values for y went down by 2 each time and wrote the equation. One of the girls actually said, "I am getting good at this!" Here are their In-Out tables:

After the first 10 minutes I had the girls share with the class how they came to find their equation for #2. I took a graph from one of the students in a group that was working on #3 where the 2 points given were (2, 300) and (10, 196). He had graphed the 2 points and drawn a line through it which touched both the x and y axes. By looking at the graph the starting point was estimated to be 325. I gave the groups another 10 minutes to work. There was another group working on #3 and they were trying to build a table that worked with a starting point of 325. One of the students at that group blurted out, "I got the rate of change. It's 13." I directed the students to try that rate of change and adjust the starting point as needed and they found an equation that worked! I was surprised that the student's rate of change was correct. I went to the boy's side and asked how he found it. He had subtracted the y values and then divided the answer by the difference of the x values!!! Shazam! He used the slope formula and didn't even know it! The slope was actually -13 instead of 13 but he figured that out when he wrote his equation because the y values were getting smaller. I had him share with the class how he found the slope and then I went to the board and wrote the slope formula there. I asked them if they knew what it was and none of them remembered it from last year. I showed them how my students from previous years found the slope using the formula. I also showed them that if they "plug into" the formula correctly they would get the correct sign for the slope of the line. I was so excited at the connections that we were making to the "traditional" algebra. The majority of the groups came up with the correct equations...on the first day that we wrote equations given 2 points!!! I was amazed!

This is Hunter sharing how he found the rate of change using 2 points. He did an incredible job of figuring it out AND explaining it!

Lastly, #4 in this activity was the first situation/problem that we have encountered where the starting point is negative. The 2 points given were (3, 12) and (7,32). I had 2 different students to use a table to find that the rate of change is positive 5. I had to give them a prompt to help them to find the starting point. The students who figured out the rate of change had created tables that started with an input value of 3 and went up to 7. All I had to do was put a 2, 1, and 0 in the input column (I put them above the 3 to help them see the pattern) and asked them if they could continue the pattern to find the starting point. It ended up being -3. 

Now, my teaching buddy, Mrs. New, and I have been talking about whether or not teaching the formulas is important. AND...we still think that students need to be exposed to the "old-school" formulas and even practice some problems using the formulas. However...I think I had more students to get their equations correct given 2 points (on the 1st day!!!) than I ever have. The exploration and work that we have been doing over the last several weeks gives them such a firm conceptual understanding of writing equations by finding the starting point and rate of change that I believe the "old-school" work will have more meaning!!!  Mrs. New keeps asking me to consider whether or not the majority of our students remember how to use the formulas when they see these problems on standardized tests and my answer is NO... the majority do not remember! Now our students have a "hook" (as our instructional partner, Dr. Montgomery calls it) on which to hang that concept so that they will hopefully retain the information. They have also been shown how to use various approaches to examine and solve these problems.

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 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:)

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...

IMP Day 19 - Wow! Laced Travelers

Today I took entirely too long on Laced Travelers. However, I am beginning to realize how this curriculum gives me so many opportunities to identify my students' misconceptions. I have never really realized this before. They may be able to tell you their numerical answer. BUT they may have just gotten lucky because they just randomly added or multiplied or etc... When you ask them what that number really means is when the real meat of a discussion happens. In my other textbooks and tasks I often didn't have a meaning to refer back to. WOW! So many of my students were SO FAR OFF in the Laced Travelers activity. They just multiplied a couple of numbers and got an answer. There were multiple approaches that worked so I would ask them what that answer meant. I would also ask them if the answer was significant to the task. THEY DIDN'T KNOW... I did ALOT of talking today once we identified that their number sense was so far off on these problems. Maybe I talked too much...but I think they really learned something...I HOPE!

This activity probably took twice as long as it should but if felt meaningful...

I wrote the above paragraph after my 2ndd block class. Many of the same things occurred during my 3rd block class. They made up some great problems for #2. When we started creating variables they did things a little differently than my 2nd block. This led into a realization (by me) of how dimensional analysis can help a little with making sense of the algebraic expressions. We had covered dimensional analysis earlier in the year but it was a struggle for my students.

Reflections on Week 1 of IMP curriculum

The activities that I have done this week with my students were designed to get them used to the new curriculum and improve their confidence.  I think that more than that I have been able to ease into the curriculum as a teacher. I see that I have already done more of these things in one week than I did in the previous 7 combined:

• Teach problem solving skills but NOT by telling them how to problem solve! The students were given a task and then as they figured out how to get closer to a solution I had them share with the class. I asked them to explain how they came up with the idea. I did often repeat  them and use more technical  math vocab but this was exciting to see them generate their own ways to approach tasks.
• Have students think about the process of solving a problem and write in complete  sentences. They were asked to explain the process and write the solution in a complete sentence. This also helps me to cover literacy standards. 
• Help students realize that math is not just about finding an answer and moving to the next problem. The way the curriculum presents the activities the idea that there can often be more than one valid answer is driven home, especially when the students can explain their reasoning. (We have been working on patterns and finding rules for function tables.)