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.

Reviewing Exponent Rules with "The Zombie Game" and the Alice Portfolio

I was looking for some ideas over the weekend and ran across this blog post by Sarah Hagan (Math=Love). The post includes alot of great ideas but the one that I borrowed came from yet another blog post by Nathan Kraft. I have really gotten so many great ideas from the teachers I follow on Twitter and through my Feedly blog reader! I am so thankful for teachers who are so willing to share their resources and ideas with others.

So, today was the first day back after Spring Break and I wanted to review problems using exponent rules. I borrowed some individual white boards from Ms. Whitt and gave one to each student. I had my students go write their names on my board and put 4 x's under each name. The last student with an x under his/her name wins. I gave the class a problem to work and had them put their markers down after a certain period of time. Any student who gets an answer correct gets to go erase an 'x' from any person's name. The "zombie" part comes when students have all 4 of their x's erased. Even though they can no longer win the game, they can still erase x's from others.  I will give the winners 5 bonus points on the next quiz grade. Ms. Whitt and I did go over how to work each problem afterwards.

I altered what my students will be doing for the Alice portfolio. Due to time constraints we chose to skip some of the activities that were mentioned in the portfolio list in the book. I created my own Alice Portfolio assignment. I borrowed some items from the Meaningful Math version of the portfolio. I do not necessarily think that mine is better; it just was a better fit for me this year since we had to cut some of the activities.

Reflections after 8 weeks of IMP

Areas for improvement:

• Getting students to present their work
• Getting through the lessons on time
• Managing vocabulary - stopping and explicitly teaching vocab after we have "had our hands" on a concept or idea
• Getting students to do their homework
• Ensuring all group members are working when given time to work individually or with their group
• Telling them too early whether or not they are correct
• Letting the students correct/critique each other

Areas I am making improvements:

• I'm taking students' pencils out of their hands much less
• I am recognizing that it is okay to let them put incorrect work on chart paper (this is hard for me) -  however, when I do this and I allow the students to discuss their "findings" the STUDENTS can critique and learn to analyze and discuss their ideas
• I am beginning to allow myself to divide assignments up where I assign a few problems to each group instead of having everyone do every problem. Picking and choosing the assignments is hard though. There are some that I want each student to have at least read and "struggled with"  before anyone starts sharing their solutions.
• Celebrating different approaches
• Giving a quiz that has depth but using a rubric so that success on the quiz is easier to achieve. I used to be scared to put too many "hard ones" on a quiz or test for fear that I would set the students up for failure. However, with our new curriculum every activity we do is based off a word problem within the context of the unit. I have found that my students are much more willing to attempt word problems now. The quiz I gave Friday had 2 multi-step word problems on it. That was it. These are types of problems that the students would skip if it were a 20 problem test and the other 18 were just computational. I made a rubric for the 2 problems and gave 5 points for each item (labeling axes, scaling axes, plotting points correctly, drawing the line of best fit correctly, generating the rule for the line, etc...).
• Trusting the curriculum...I must admit that this is more of a "forced" thing right now due to time. There are times I think about stopping and pulling out old tests or other standardized-test-like questions to see how the students will do on them. However, I don't have time since we started using the Meaningful Math books 7 weeks into the year. I do believe in the curriculum - more and more every day. I do think that my students have really engaged with the content and will have a much better shot at retaining the information because of the way it has been presented within the context and revisited several times. 
• I remember our Instructional Partner, Dr. Montgomery, telling me a few times in the past to create a project that covers several standards at once (when I was stressing about covering everything in the COS). Well, most of the activities in this book do that. Therefore, even though the activities are in depth and at first difficult to the students, they will have the opportunity to become "fluent" in them because they get opportunities to do the same type of activity multiple times. There may be a few tweaks to the activity but the topics are usually revisited. Especially the big ones. 
• I have often said that the 2 most important concepts I want my algebra students to be able to understand (and retain) is graphing and solving all types of equations. Well, as far as I can tell in our new standards these 2 topics should technically be mastered prior to entering algebra. My interpretation of the standards is that once in 9th grade they must learn to APPLY their knowledge of graphing and equations. WOW is that covered in these books! The majority of my students are not proficient at solving equations and graphing when they come to me but hopefully they will be stronger every year.

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 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.)

IMP Day 3 - POW write up discussion, Who's Who, Inside Out

Today I started class by going over the 5 parts of the POW write up. I enjoyed being able to talk about the real world connections to scientists,  chemists,  teachers, managers,  inventors, etc... I'm loving how this curriculum is definitely helping us to address literacy standards!  After the POW discussion they did the Who's Who activity.  They did very well with this and I had someone come to the board and draw their diagram as I read the description.  I also questioned them as if I didn't understand.  We talked about the different approaches they took...some just recorded their thoughts in sentences but most drew a diagram.

Presenting her diagram and solution for Who's Who

The last activity we did today was Inside Out. I loved how the teacher's guide suggested you start with a mystery function.  I had fun with that! I also like the way the activity asks the students to describe the function in words.  I probably would have jumped ahead to writing an expression.

The thing I am most excited about is that my colleagues are getting excited about the new books and curriculum.  My previously unnamed teacher buddy who has always made me want to be a better teacher...Sonya New... (I asked her permission to use her name...lol) says that the IMP curriculum is like riding a roller coaster.  She has some challenging classes behavior wise and she was ready to throw in the towel yesterday but today was terrific.  Mr. Webb...the other teacher I "coerced" into this new adventure was telling us today how his student engagement is much better. AND Ms. Whitt said she didn't think she would like the curriculum when she first looked at it but she really likes it. What a good day!

I just hope the students are really learning something! Will they remember these problem solving skills and use them later? Will they make higher test scores due to this new way of teaching? Will they learn algebra? Really learn it???? Time will tell.