Survival Mode...perfect for December!

I don't know if anyone else does this but there are times that I have to enter full blown "survival mode." This is when I am on overload either personally, professionally or BOTH and I have to take my foot off the gas pedal for a while. I know in the first line I said that I don't know if anyone else does this...but in my heart I believe that everyone does this (or at least needs to) from time to time. If you have never given yourself permission to do so and you are feeling overwhelmed heading into Christmas break now is a perfect time to try it.

Another way that one of my teacher friends describe this time is a "mental health day." This is a good one when you are in the middle of the semester and so far behind on grading that you can't even see the top of your desk anymore. This is where you take a day and actually give your students work that they can do without you...even if it is the dreaded review worksheet. Then you take that day to catch up. Sometimes your family life and/or coaching responsibilities make it impossible for you to spend extra time working on your school work in the afternoons or evenings. If you find yourself in a season like that give yourself permission to pause, take a breath, and catch up. If your administration is as awesome as mine they will understand!

I must confess that if anyone comes in my room when I am in this mode I feel the necessity to explain what is going on...LOL.

IMP Days 48-49 Finishing Overland Trail

The last 2 class days we have been trying to finish Overland Trail. I will start Cookies after Christmas! I have had to skip a few activities here toward the end which hurts my feelings! I did the in-class and take home assessments that come with the book. I will let you know how they went.  My semester exams are going to be their portfolios.

IMP Day 47 - The Mystery Bags Game and More Mystery Bags

Today my students completed 2 "mystery bag" activities. These activities are designed to provide a contextual understanding of solving equations. I have used an activity that used the idea of using a balance before but there wasn't a story to go with it. Once again I believe the context helped my students to grasp hold of the concept. Supposedly my students learned how to solve all types of equations last year. I could definitely tell that they were better at solving equations than previous years. However, I retaught solving equations before we started our new books.

The IMP Mystery Bag activities assumes that students have already been exposed to solving equations. Doing this activity makes me wonder how many times it takes our students to see a topic for them to retain it.

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.

IMP Day 45 - Fair Share on Chores

Today we started the last section in Overland Trail.  The activity was Fair Share on Chores. This activity builds on the creating equations concepts that we have already done in this unit.  However it looks like the authors are beginning to develop the concept of solving literal equations.

My classes were given 30 minutes to finish their POW #4 at the beginning of class.

My #KidsEnjoyingMath post

My math teacher "twitter friend" Justin Aion has challenged math teachers to post pictures of students enjoying math in this blog post. Here are some pictures of my students having math fun.

Well, I take alot of pictures of my students! I better stop here! This year I have started using Twitter and Instagram to post pictures of things going on in my classroom and school. I started with Twitter but some of my students talked me into getting an Instagram because they used it more. I love that you can set up an account on both of these and people can "follow" you and you don't have to follow them back. It seems more appropriate for teachers and students. I sometimes have the students to ask me to take their picture when they are proud of what they have accomplished! I am their proud math mom! We also started a school hashtag. Anyway...that is why I had so many pictures for this #KidsEnjoyingMath post. I think this is a wonderful idea! Thank you Justin!

IMP Day 44 - Quiz on writing equations given 2 points

Today I gave my algebra students 30 minutes to work on POW 4 - On Your Own. This is a great POW that makes the students create do some research on the types of jobs they could get right out of high school. It also has them to find out how much living expenses would be and create a budget for living on their own. They also have to decide whether or not they will need a roommate in order to pay their bills. This is a research POW instead of a math or logic problem.

I gave the students a quiz on writing the equation given 2 points. One of the points was negative and one was positive. For this first quiz both slopes were integers. Out of 50 students who took the quiz 16 students aced it. another 3 students made between a 35 and a 39. 14 students made between a 24 and a 24 (a 24 is passing with a 60%). 17 made less than a 24. There were only 5 students who were absolutely clueless. So...67 % of my students passed the quiz. Now I have always said that having making a 60 in algebra does NOT mean that you are proficient. However, 38% of my students did extremely well on the quiz after working on this for 2 days. I wish I had this type of data for the first time I covered this topic in previous years. All I can do is tell you that my algebra grades in general were declining over the last 3 years (with the exception of last year when I started trying to find new teaching methods...even before the new IMP books). It was not unusual for my average quiz or test scores to be in the 40s or 50s. (My average score for this one was around 63.) I also feel like my students have a much better conceptual understanding of what we are doing. Several of the students who didn't perform well filled in their tables correctly and found the correct slope and had the coordinates for the y-intercept they just haven't gotten everything to connect just yet. However, I really think I can help them to get there! I intend to give them the opportunities to correct their quizzes so that they can see how close they are!

IMP Day 43 - Making "formal" connections

I have thoroughly enjoyed the Moving Along activity and decided to "sit down" here and make some formal connections to the slope formula and slope-intercept form. However, we first did the activity without using either formulas and it was AMAZING! We actually have been using slope-intercept form but they just didn't know it as y=mx+b. The IMP book uses y=ax+b and calls b the "starting point" and a the "rate of change."

Today I gave the class a "warm-up" where they were asked to find the slope of a line and write the equation of the line given 2 points. There was no context given and they did great! There were no formulas on the board but most of the students proceeded to put the 2 points in a table and then fill in the x-values from 0 to the highest x-value given. They go back to 0 for x because we have drilled the fact that x-coordinate of the starting point is always 0. We have also tried to drill that the starting point is always on the y-axis but they seem to forget that sometimes...

After the warm-up, which most of them got with a table, I had them add the slope formula and slope-intercept formula to their notes. I told them that they would receive a reference page on their end-of-course (EOC) algebra exam and that I wanted them to be familiar with the formulas. We went over how we could have used the formulas for the warm-up and then I gave them another problem.

I used this weird effect on my picture to make it a little more readable. 

He writes so light I know it is a little difficult to read. However, Raul (whose paper is above) was the first student finished finding the slope and equation of the line! Then I gave the class a problem where the slope was a fraction thinking that they would resort to using the formula (and most of them did). However, Raul and one other student STILL used the table to get the equation. Their "number sense" is very good and thinking in fractions (or decimals) did not bother those 2 a bit! We have only been writing equations of lines given 2 points for 2 days and there are many more students who do it correctly than I have seen in the past.

It is exciting to realize that there are students who really benefit from their exposure to the different methods that can be used to write equations. I guess that since I am so accustomed to using the formulas I thought they would automatically start using them. However, the majority of my students are still using tables! I don't think I have ever used a table to find the slope or y-intercept so I am getting an education too!

Math teachers are "Formula Babies" - we need to be more natural!!

My teaching buddy, Sonya New, and I are writing this post together! We have learned this week that we are FORMULA BABIES!! We ran across some problems where students need to write equations given 2 points and thought the students would just HAVE to have slope and point-slope formulas because that is how we learned to do it ourselves. BAHAHAHAHAHAHA!!

What an education we have received! I was so concerned about how they would find the "starting point" or y-intercept without formulas! Earlier this week Sonya's honors algebra realized that once they found the rate of change (slope) they could multiply the x coordinate by the slope and find the b (or starting point) by figuring out what to add or subtract to get y. I know that makes no sense when you read it! However, it took me and Sonya 2 WHOLE DAYS to realize that what they are doing is using the slope-intercept formula to solve for b. We felt STUPID!

ALSO, I had students to use tables to find rate of change and then extend the table "back" to zero to find the starting point or y-intercept. I had one student who hated the formulas yet got EVERY SINGLE PROBLEM correct using tables. Even problems with fractional slopes!! IT WAS AMAZING AND EYE-OPENING!!

Then we laughed about the fact that we are "formula babies" and have come to the conclusion that we need to understand that the logical (or NATURAL instead of FORMULA) way to write equations makes more sense to our students.

P.S. - Sonya is a new mother and I have had 3 breast-fed babies myself...so we couldn't resist the analogy.

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.

IMP Day 41 - Travel on the Trail and Wagon Train Sketches

Yesterday Mrs. New informed me that I skipped a couple of activities in the book! I claim that it was "turkey-induced" mental lapse! I didn't realize that All Four, One had 2 parts in the book. I was about to skip 2 great activities so I'm glad she helped me realize!

Today I started class by having them read "About James Beckwourth." Once again I am reminded how this course is truly written to be cross-curricular. This unit really crosses more with history but I know that future units will cross with physics and English also! Today I gave them time to do do #1 and #2 in class with their groups. Then I had them to put the 2 graphs on chart paper. One thing I did that I liked was take 2 people out of each of the groups of 4 and let them work on answering #3 instead of standing and watching the others write on the chart paper. I always struggle with using the chart paper because 4 people can't really be working on it at the same time. Those who are idle often get in trouble. I liked giving them the idea of answering the next question. The downfall to this idea is that all of the students in the group don't get a chance to "struggle" with the problem before they see the solution explained. I ended up explaining how to do #3 anyway so I don't know that it was much of a loss. I led a student in the class through the discussion of #3 and I think it went well.

5th period -

Sometimes getting students to have meaningful conversations about an assignment is difficult!! Today my 5th period discussed the Wagon Train Sketches and Situations activity (that they had completed a while back when I was absent one day). Sometimes getting students to engage in the math feels like roping the wind!  (venting over!) Then, on the most difficult situation that they were asked to graph one of my most talkative students blows me away by just blurting out the correct answer. He is the only one in 3 classes to get that graph correct:) We do have some break through moments!!

IMP Day 40 - All Four, One and Straight-Line Reflections

Today we were trying to "get back into the swing of things" in algebra. The All Four, One activity asks students to consider the 4 representations of a linear function (situations, graphs, tables, and rules) and create a report on how to convert between one to the other. In the instructions the text gives a "common form" for writing a linear equation as f(x) = ax + b where a is the rate of change and b is the starting point. This description fits nicely with the way graphing has been introduced and developed over the past few weeks. I "borrowed" a worksheet from another IMP teacher that already had the scenarios written out (i.e. From situations to graph, from graphs to rules, etc...). I gave my students 35 minutes to work on the task. I had to help them do a couple before they were able to work in their groups.

I am trying to improve my students' presentation skills. Therefore today I told them that I was going to "roll the dice" to randomly call on at least one person in each group. That is nothing new. However, I made each student come to the document camera and show his/her answer instead of allowing them to talk from their desks. Then I talked them through correcting the answer if it didn't fully explain how to do the conversion. I told my classes that we were going to work on giving better presentations. I tried to move toward the back of the room so that students would at least appear to be addressing the class (Jim Delawder tip!). I did have a couple of students in my 3rd Block class laugh at other students. It worked out well because their groups hadn't gone yet and the boys who were laughing had to present instead of the random "roll of the dice." I hope this helps to get them to quit teasing each other during presentations.

The main thing I liked about this assignment was that students talked over and over about the importance of finding the starting point (which was always on the y-axis) and the rate of change. Today was another day that I loved that I had all kinds of graphs on chart paper hanging around the room to refer to.

I did not spend much time on Straight-Line Reflections. However, I did use Desmos on my Ipad and project the graph for #3. It is really cool how you can just pinch or expand the graph in Desmos so that it is easier to identify the y-intercept and the rate of change. As of right now we find rate of change by discussing the change in the graph over 1 x value. I am going to assign #4 from Straight-Line Reflections as a warm-up tomorrow.

My 5th period completed the If I Could See This Thing activity. It is interesting to see how many students could figure out the correct population (after the 90% decrease) but their explanations on paper were "train wrecks." Writing mathematical expressions correctly is a topic that is difficult for that class. I was excited because some students found the 90% and then subtracted from the original population and some found 10% of the original. It is cool when students come up with the different ways to complete the same task.

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.

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...the math teacher in me makes me do this...39 - Quiz day

If any of you are reading this blog because you are teaching using the IMP books let me tell you about an awesome website that has great resources...The Greater Philadelphia Secondary Mathematics Project. Our trainer from It's About Time shared this website with us and it has some invaluable resources. I found some questions on there that I used for my quiz today on graphing. I only used two graphs but set up a rubric where they had a very good chance to pass (is that bad?) whether or not they could come up with the rule for the graph. I gave points for labeling the axes, scaling them correctly, plotting the points correctly, graphing the line of best fit, answering the question, and getting the rule. The 2nd problem gave the students a situation and they had to graph it, answer a question about it and give the rule.

I was really very pleased with the quizzes. Every student in the class can not get the rule for the graph yet, but they do SO much more with this word problem than I believe my previous students would ever have done. I hope to one day soon have the opportunity to find some multiple choice questions where students are given a graph and asked to find the equation that matches it and see how they do. We still have not "formally" learned slope-intercept form.

My 5th period did a Thanksgiving coordinate plane graphing activity today. It was the end of the day on Friday before Thanksgiving and I noticed as they worked on it that they NEEDED to review plotting points so I am glad we did it!

IMP Math Day 38 - Finishing Fort Hall Businesses and POW Write-up

Today my 2nd and 3rd blocks finished up Fort Hall Businesses. The neat thing about these questions was that the starting points were not given. The students are given a couple of data points in the situation itself and one of the problems gives the rate of change but the second one doesn't. It is so rewarding to see the students work through these problems and figure them out. The odd thing is that my 2nd block class solved the problems using graphs and my 3rd block class mainly used In-Out tables or just reasoned through them.

#2 had to do with a movie theater selling tickets and it gave the amount in the cash register after 20 tickets were sold and then after 60 tickets were sold. This one gave my 2nd block alot of trouble (they didn't have as much time to work on it either) so I asked them how many points does it take to draw a line. I then had a coordinate plane that one of the groups had labeled but hadn't put a scale to it yet or graphed any points...they were frozen. I had talked with all of the groups doing #2 and we pulled out 2 ordered pairs from the information that was given so during the class discussion I showed them that one method of solving the problem would be to simply graph the ordered pairs and draw the line containing them. From this info we could answer the question of how much money was in the cash register to begin with. Then I guided them to find the amount of each ticket (slope) and we were able to write the rule for the graph. They are taking a quiz tomorrow on graphing and I can't wait to see how they do. I am anxious yet optimistic!

My 5th block took a quiz yesterday and I gave them feedback on their papers without assigning grades. Today I went over a similar assignment from the book (again) and then gave them their quizzes (with the feedback) back and told them to make corrections based on the feedback. Understanding variables is a difficult concept for 9th graders for some reason. I expect to have to offer a quiz retake but maybe I won't!

I read another encouraging POW Write-up today. An excerpt is below:

IMP Day 37 - Following Families and Fort Hall Businesses

Today we finished Following Families by answering questions 3 and 4 and finding the rules. We defined slope (informally) and parallel lines. It was fun to see them realize that #3 had a point where the families were the same distance from the river because the lines intersected. Also, in #4 some of the students' explanations included comments about the starting points for the amount of coffee being different and then they consumed the coffee at the same rate. This opened us up to talking about rate of change being the slope. Today we also got to discuss that the "starting point" on the graph is where it crosses the y-axis and that value needs to be written down first when writing the rule. I hope they became better rule writers today!

My 5th period was supposed to go over Ox Expressions at Home and then take a quiz today. They were not quiet while we were going over Ox Expressions so I decided to cut the discussion short and make them start the quiz. However, I am going to give them written feedback on the quiz and give them the opportunity to address the feedback. I will not assign them grades until they turn them in the 2nd time. I actually used pg. 110 as the quiz. I read the intro on pg. 109 and discussed subscripts with them before they started the quiz so that wouldn't throw them off.

I'm Calling Bullcrap! - Adventures in teaching IMP

Sonya New is my hero! I'm just saying... If it were not for Sonya I would not be the teacher I am today. She makes me want to be a better teacher. She makes me think! UGH! AND...she cracks me up sometimes.

Yesterday we were looking over some of the Meaningful Math Algebra lessons that we were going to be teaching the next few days. She had her honors algebra students complete the Who Will Make It activity for homework and she told me that they had asked if they could use a "squiggly line" between zero and the first output value so they didn't have to label all of the values in between. She told them no. However, when we were discussing it she said she wished she had let some of them go ahead and do it so that they would be able to talk about the inaccurate conclusions that would be drawn. She decided to do a graph with the "squiggly" and talk to them about it. Her graph is below:

The context of the story is to see who will make it to Green River before the flood that is predicted (by the almanac) to happen in 30 days. The y-axis is distance to the river and as you can see all 3 of her families make it to the river (the x-axis) way before 30 days. After discussing the class's answers she put her answer under the document camera and told the class that she had all of her families to make it before the flood. She said at first they were starting to erase their answers...they assumed she was right and they were wrong. However, she had one girl yell out, "I'm calling bullcrap!" and run up to the board to point at her "squiggly line" to say that Sonya's answer was wrong. I loved this story. I have told Sonya over and over again I wish she would blog about her personal "imp adventure" so that I could read all about it. We talk almost every day but we don't always have alot of time to go into detail. I told her I just had to tell this story. I loved that a student ran from the back of the room to prove that Sonya was wrong and she was right.

P.S. - I hope nobody is offended by the title...it is a renaming of a popular card game that has to do with calling someone's bluff when you think they are not telling the truth about their cards.

IMP Day 36 - Following Families on the Trail

With today's activity we venture from using discrete (nonlinear) data and finding the line of best fit to being given a starting point and a constant rate (average miles traveled per day or amount of coffee drank per day). The students were asked to graph the information and then answer some questions about the graphs. Lastly they were asked to write the rule for the graph.

These pictures are in reverse order to what they needed to be. We started the activity with "noticing and wondering" about the problem. I am trying to teach the students to "notice and wonder" about the parts of the problem that help them perform the mathematical task...we sometimes get sidetracked!

I was so excited to hear one of my students say, "I'm going to make me an In-Out table!" so I had to take a picture of her paper! The teaching guide for this lesson tells you to go ahead and tell the students to let July 12th as Day 0. I still have students that use the x-axis as a "data point" instead of letting it be zero. Many of them counted by 25s or 50s today and wrote 25 or 50 at the origin. Also I still had some students that didn't use consistent spacing. I sometimes wonder how many times we have to practice something for it to sink in! I am giving a quiz on Friday so I hope my students remember by then!

My 5th period students finished Ox Expressions and started Ox Expressions at Home. All of my classes were given an assignment to complete for homework and I am assigning a grade for it tomorrow. Lately I have only had 1 or 2 per class (of 20-28) attempt to complete any homework tasks. And I am not asking for them to do something that should take more than 15-20 minutes! I hope the grade motivates them to actually attempt the work. We shall see.

IMP Day 35 - The Basic Student Budget

Today was a neat lesson because the students were asked to "break away" from the Overland Trail theme and consider using lines of best fit to analyze data considering the budgets of 3 college students who share an apartment.

Common mistakes today:
1. "connecting the dots" instead of drawing a line of best fit
2. not extending the lines of best fit to touch the x and y axes...even though one of their data points was (0, $ that each student had at the beginning of the month)!!
3. Scaling their axes incorrectly - by this I mean one "box" was 100 and then later on they spread 100 over 2 boxes
4. When answering #3 several of the students looked at how much money the guys were projected to have on April 21st instead of how much extra they had on April 30th.
5. One student started all of her lines at some random starting point on the y-axis because her group had Who Will Make It last week and all of the families started 330 miles away from the Green River...

I got frustrated today because I expected a higher percentage of the students to "get it" since we have been working on similar types of problems for 2 or 3 days now. I was disappointed to see students connecting the dots and not extending their lines to the axes. I felt like I had done such a better job covering this because of the experiences they have already had with "lines of best fit." I also need help on reacting better when my students are way off the mark. I am so good sometimes...and then other times I know they can see it all over my face and hear it in my voice that I am frustrated... This is my confession day I guess!

On a positive note...I had some students that flew through the activity and had a very good conceptual understanding of what was going on! The rules were difficult for everyone but we went over them today and I know that we will continue to work on writing rules and equations as we go.

**It is good to use chart paper and leave some of the graphs hanging up in the room. I still had several graphs from Previous Travelers hanging up in the room so we used them to compare the graphs that start from the origin with those that don't (like in The Basic Student Budget).

My 5th period today did Vermillion Crossing in class and I introduced Ox Expressions and assigned it as a bonus for the student with the most meaningful algebraic expressions.

My apologies to AMSTI...I just didn't get it

The last few weeks I have really come to appreciate more and more what the AMSTI program has done for math teachers. If you happen to not be from the state of Alabama AMSTI is the Alabama Math Science and Technology Initiative. Participating schools send their math and science teachers for 2 weeks of training in the Summer (and the teachers get paid) and the teachers receive AMSTI kits with the materials needed to do the activities in their classrooms. My first Summer of AMSTI training I totally didn't get it. The math training consists of going through some of the activities from the IMP units (All About Alice, Cookies, the Pit and the Pendulum, Fireworks, etc...). The teachers usually receive two drop-in units (classroom sets). As a participant in the training I sat there and thought, "I don't have enough time to do these activities in the classroom! I don't even have time to cover the material I am supposed to cover WITHOUT all these activities!" I also thought that the activities were too difficult. However, I did leave AMSTI training with a determination to put my students in groups the following school year and stick with it for a year no matter what.

The following school year a colleague (Sonya New) and I really started looking for discovery or inquiry-based activities to use in our algebra classes. We took "baby steps" and really only used a handful that year but we really started seeing the value in them. Then I attended year 2 of AMSTI algebra training and was blown away! I had 100 light bulbs go off as I realized that our "AMSTI books" did have the discovery/inquiry-based type activities that we had been scouring the Internet to find. Tanya Barnes and Melanie Griffis encouraged me to just try the activities with my students (even though I was still afraid some of them were "over their heads"). They told me that I would be pleasantly surprised. I left training that year just thinking that we really needed to dig into our IMP units and see which units covered which standards. Following this revelation I had the "chance meeting" of the president of It's About Time (the company that publishes the IMP books) Tom Laster, in Atlanta at the ISTE conference. And now our algebra teachers are piloting the new Meaningful Math Algebra textbooks that take the traditional approach BUT use the IMP units that we had been receiving training on at AMSTI. Those "AMSTI units" are not just activities to "drop in."

I would like to publicly (or not so publicly since most of them will not read this blog post) apologize to the AMSTI trainers and organizers for being so slow to "get it." Now that I have been teaching the curriculum I realize that doing an activity here or there just does not do it justice. When you go from the beginning to the end of the unit and see the way concepts are developed and revisited the brilliance of the curriculum can be seen. I am learning so many things about developing a concept. For instance, I have always thought that the "line of best fit" was to be taught when I am covering the statistics section and scatterplots. I have never thought to use real data and graph it, find the line of best fit, and have the students discover the rule for the line. We have been doing this without the help from graphing calculators. My students have "had their hands" on so much graphing already and we have not formally talked about slope-intercept form one time. However, they can find a rule or equation for a graph and they can find the "rate of change" within a context. When we talk formally about slope-intercept form they are going to have such a firm foundation on which to understand the concept. I can't wait to go completely through the book and see all the other ways the mathematical concepts are developed. THANK YOU AMSTI AND IT'S ABOUT TIME!

IMP Day 34 - variety day!

My 2nd block class had to finish the Sublette's Cutoff/Who Will Make It activity today and then we discussed it. I had a class discussion yesterday with my 3rd block about these activities so I should have been better the 2nd time around. I felt that I was worse! I randomly called on a few students (using the dice) and their graphs needed a little work and then I got the information backwards as we were discussing it and then the whole thing was crazy. I hope by the end we learned a little bit about what is going on at the intercepts and how to use the "line of best fit" to predict!

My 3rd block was a little ahead so we got out the graphing calculators and did the "Graphing Calculator In-Outs" activity. This was a very good introductory activity with the calculators. I did lose a few students along the way and finally just told them to write down the correct answers when I told them to. HAHA! I am pretty sure I could have facilitated this better. Maybe I should have paused and allowed them time to get help from their group members. I tried to walk around and help everyone at the beginning but we would NEVER have gotten finished. I know...I was too impatient. My goal will be to pause and allow students to help each other more in the future. I didn't tell them not to help each other...but I didn't encourage it either.

My 5th block did "To Kearney by Equation" today. Today I lead them to the "new equation" for profit per trip AFTER they discovered that they are not given the captain's pay per minute and they are given round trips in minutes. They did fairly well. I still have a few that seem to sit and wait until they are told what the answer. I randomly call on people and sometimes I end up having to "help" a student find the answers from the beginning to the end because they haven't put much thought into it during the time they were supposed to be working!

IMP Day 33 - Sublette's Cutoff or Who Will Make It? (5th period - Laced Travelers) - They don't need me!!!

Today I took the suggestion from Mr. Webb and Ms. Whitt and divided Sublette's Cutoff and Who Will Make It between the groups in my classes. In other words some groups did Sublette's Cutoff and some did Who Will Make It. The 2 activities were similar enough that I was able to introduce the activities pretty easily. They are asked to plot data for 3 different families and then draw 3 different lines of best fit. Then they are asked to answer questions and make estimations with the lines. I think that even I have a better understanding of why we do lines of best fit after teaching these last few activities. I know that I "knew" what it is for but I do not think that I have applied it within a context very many times. Over the course of this week my students will have used lines of best fit within at least 3 or 4 different contexts. The discussions about what the x and y intercepts were so meaningful and productive! We are really talking about slope and the y-intercepts without formally introducing the equation. It is so cool to see how the authors develop each of the concepts. I think it is hard to appreciate until you teach an entire unit.

Today after we finished graphing and "sharing out" the answers I asked the students to share with me the meaning for the x-intercept and the y-intercept. I had one student say, "The y-intercept is the starting point and the x-intercept is the ending point," and the BELL RUNG!!! UGH! I was very excited that she said that and I wanted to discuss it with the class...there is always tomorrow.

In 5th period today I did something different. I wrote the assignment on the board and referred the students to the assignment as they walked in the door. All I did was tell them to read over and it and put the "entry" into their notebooks. Dude! They got on it! I had one student figure out the answer to #1 (which deals with multiple constraints) by the time I had answered roll! AMAZING! As a whole they worked harder today than I have ever seen them work. Once the one student got the answer he walked around and helped other groups. I would ask them to explain how they got their answer and wouldn't give them candy (the great motivator) unless their explanations made sense. They don't need me! Well...not as much as I think they do. HAHA!

IMP Day 32 - Previous Travelers (and Shoelaces with my 5th pd)

Today my 3rd block finished Previous Travelers. The last two class days my 2nd block class was cut for different reasons. Therefore they are behind! Anyway, in Previous Travelers the students plot some data points and then draw the line of best fit. Then there are instructed to find the equation for the line and lastly they have to predict the amount of supplies they need for their Overland Trail families. I only gave each group one of the 3 supply items to graph. That made it where each item had at least 2 groups graphing the data. The neat thing about that was that the two groups could compare information AND when I had that one group that was behind everyone else because they wouldn't get on task in a timely manner I just had them to sit down and we still had another group that finished. I had the students write the rule for their supply on their chart paper and pointed the information out to the class. Then I let them use the rules to predict the supplies for their families. I was proud of myself for "shortening" the assignment by not making each group do all three of the supplies. We "divided and conquered" but I still think that they got enough experience with the activity to get a feel for using the line of best fit. I had some time to get my 3rd block to reflect on what they had learned so far about graphing. A couple of them really impressed me by saying something about how we took discrete data and learned how to create an equation using the line of best fit. I didn't even mention the fact that the data was discrete so they made me proud!

Another "victory" today was that I completely finished Shoelaces (from beginning to end) in my 5th period class which is 55 minutes. I used the tips of some experienced IMP teachers and did not wait for each group to get every part of each question correct. I allowed time for "productive struggle" but then had a student to share their findings on the board. I think I am more relaxed about not waiting for each group to "get it" because I am more familiar with the way the book "circles around" on most of the important topics. We will have another activity (or sometimes several more) that will reinforce what we covered today. Shoelaces uses constraints again and introduces the students to using algebraic expressions in the place of more complicated verbal explanations.

IMP Day 31 - Previous Travelers and the progression for teaching students to graph

Today we started the "Traveling at a Constant Rate" portion of the Overland Trail unit. For Previous Travelers I gave each group one supply to graph. They were provided a table with 4 columns where the 1st one was the number of people and the other 3 told how much of each supply they used. I had them to write their In-Out tables for the supply they were graphing (beans, sugar, or gunpowder) and then graph the points on graph paper. A few things stood out to me:

1. I had several students put the number of people (the input) on the y-axis instead of the x-axis so we had a productive discussion about independent and dependent variables again.
2. I had one student want to have fewer points to graph so she added some of them together and graphed the sums instead...whoa!
3. We still had some people who did not scale their axes appropriately or didn't start with the origin as (0,0) so I got to address that.
4. It REALLY bothered them to have an input to repeat. There were multiple families where the inputs repeated and that threw them for a loop!
5. I discussed the fact (before they started graphing) that the data was discrete instead of continuous since you can't have fractional parts of a person. I wish I would have waited to see what they did with their graphs and let them answer that question for themselves!

We had a Veteran's Day assembly today so 2nd block didn't get to graph their points on chart paper but my 3rd block did. I am excited about doing the line of best fit tomorrow. I don't know if I have ever been "excited" about it before...having the students work within a context makes so much more sense! The way the book develops the idea of using approximations with the data since one rule won't perfectly match all data points is really neat.

Progression for teaching students to graph - We started with "graphing stories" where we interpreted graphs of situations and created graphs for certain situations. Then the book led the students to a discussion about scaling your axes correctly and when to use continuous or discrete points (The Issues Involved). Then the students were given graphs and asked to create tables and then rules for the graphs (Out Numbered). Then the students were given some rules (using In and Out instead of x and y first) and asked to graph them (From Rules to Graphs). Now, with this lesson (Previous Travelers) the authors point out that all "real" data doesn't fit nicely into a rule so approximation must be used. However, with a line of best fit we can still develop a "rule" for the data. There are so many real-life applications to this concept I don't know where to start. The one that comes to mind first is calculating insurance rates. But how about the first time the medical world found "normal" heart rates for certain ages?

My 5th period worked on the More Graphing Sketches activity. We will be finishing it tomorrow.

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 28 - Algebraic Expressions quiz retake, Out Numbered and From Rules to Graphs

Today I decided I would go over the Ox Expressions at Home assignment (which I gave as a quiz) in class and then give them a quiz retake. I had a different version of the quiz and let them take it. The majority of the class improved.  We then finished Out Numbered and started From Rules to Graphs.  I love the way this unit develops writing function rules and graphing!

You have to like them to teach them

I am amazed at the turn around in one of my classes. At the beginning of the year I really struggled with this class. They were full of rowdy boys and I had a difficult time connecting with them. Honestly they got on my nerves! I have them at the end of the day and I had to find the most patience at the time that I am worn out from my day.

I displayed my frustration and annoyance on a daily basis. And then I realized I needed to hit the reset button. I needed to learn to like those students. I take pride in being able to see the positive in most circumstances but I had not applied that "talent" to that class. One day I announced to the class that I did not like the ways things were going and that we were going to change it. I started trying to enjoy the students. Miracle of all miracles it worked! I know that "they don't care how much you know until they know how much you care" but I don't know that I have ever seen it so clearly. Yesterday I had to leave that class a little early and several of the students made the remark that my class was their favorite. The funny thing is that class has my heart now. They make me laugh on a daily basis.

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!

IMP Day 26 - Graphing intro activities and The Issues Involved

I had started to skip pages 40-47 in the book because I spent a good amount of time on graphing stories at the beginning of the year (before we received our new books). However, there was some things brought out in the activities in Meaningful Math that I did not talk about before. I actually had assigned these pages several weeks ago when we had PD for our books. Therefore I just gave them a completion grade and handed it back out.

We went through and discussed some vocabulary like constant, linear, discrete and continuous. We went over #7 on page 44 in class because it was a commonly missed graph. I love the tie in to the absolute value graph.

We wrapped up the day with The Issues Involved. Once again...I feel like I am moving too slow. Will I ever shake that feeling?

IMP Day 25 - Categorical Data on the Wagon Trian

This was a good activity for apply percent questions and logical reasoning. It was like putting a puzzle together. The students were using number of people as the percentage of people. I had one student who did an awesome job of using the idea of percent as per 100 and he took the 17/25 and instead of dividing the fraction to get the percentage he multiplied top and bottom by 4. I was excited about his prior knowledge because that is something we have not discussed this year. RETENTION STILL EXISTS!!  I HAVE SEEN PROOF!

I think this assignment could be assigned as a homework activity although we did it in class.

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 22 IMP - Ox Expressions and Ox Expressions at Home

Today I started class by having each group compare to see who came up with the most meaningful algebraic expressions using the Ox Expressions chart. It was a sad comparison because the vast majority of my students did not do their homework. I had told them that the winner would receive bonus points to try to motivate them.

After they had time to compare, I took up each of the "winning" papers from each group and gave a piece of candy to each of those students (candy always motivates!). Then I put their papers under the document camera and we assessed each expression to see if it was meaningful. This was a tedious process but I am not sure how else to get them to go through and determine meaningful expressions! Unit analysis really helps! Again...we did unit analysis before we started the Meaningful Math books. I do not know if they REALLY understood it then and I am not sure how many students REALLY understand it now, but for the few that do it seems to help to verify whether or not expressions have useful meaning. Also...I talked about "like terms." For example, it means nothing to add the number of wagons plus the number of gallons of water a person drinks per day. I point out that adding wagons to gallons doesn't mean much. However, if you add the number of men plus the number of women plus the number of children it is MEANINGFUL because they are all the same unit - people!

After we trudged through determining whether or not the expressions were meaningful and found a winner for each class (one girl had 14!), I made them do the Ox Expressions at Home activity as a quiz. I look forward to seeing how well they did. These concepts seem to be difficult to "drive home."

Lastly, Dr. Montgomery, our instructional partner and former human anatomy and physiology teacher, came in and discussed the diseases in "If I Could See This Thing." She also has created death certificates and tombstones for me and Mrs. New to use with our classes. I have to prepare for tomorrow's lesson but I think a certain percentage of the people in our wagon trains have to die due to these diseases. More tomorrow...

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 20 - 4 weeks... - To Kearney by Equation & Meaningful Conversations

It doesn't seem like we have been at this a month! I have had the books for 20 school days and the pacing chart says I should have finished in 14 days. UGH! I did miss 3 days for professional development so I am only 3 days behind. I also have not assigned much for homework. I will eventually...maybe...my students just don't do their homework much. I am working on it.

This curriculum gives you so many opportunities to have meaningful conversations. I can understand why the title of the book is Meaningful Math! I love the tie in to the Westward Expansion because it has been a LONG time since I have had history. I am relearning too!

To Kearney by Equation once again took much longer than expected...and we aren't finished! It is very neat how the real-world equation is given within a context and then the students analyze what each part means. I took a good bit of time teaching the students how to take notes while they are reading a passage. Reading for information is a skill! Also, I love the tip from Jim Delawder about having a student to restate a passage in his own words. Today I did that after we read aloud in class and it is amazing how many people didn't have a clue. Hopefully I can help them to improve their listening and retention skills.

Trying to get students to work together and write their findings on 2x2 whiteboard can be like ROPING THE WIND!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! This is my reflection from today's 5th period class today. Last class on a Friday afternoon...

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.

IMP Day 18 - Laced Travelers, etc...

Today I started class by giving the students time to continue working on their Haybaler POW write-ups. I am finding it hard allowing students to struggle without telling them the answer. There comes a point with almost all of the more difficult problems where I just want to say, "Okay, now everyone watch me so I can tell you how to do this." It feels like I don't get "closure" on some of the problems. Is that a real thing? Teacher closure? I could define it by saying that it is when a teacher feels that he or she has sufficiently told the students what they need to know.

I try to have the students to share but I don't think I do a great job of that yet. I tend to allow them to share a little bit and then I repeat and extend. Repeating and extending is okay...I think. However, my students need more guidance in presenting their findings and I am not yet sure how to direct them. I am going to have to go search some of the resources that Jim shared with us last week.

After the time for writing the POW, I discussed the Diagonals Illuminated activity. Thing is...very few of my students spent any time finishing the activity for homework. That is so frustrating! Anyway, I had one student out of 60 who did come up with the function rule for the activity. He is such a good thinker! He gave me the pattern verbally and I wrote it as he was saying it. Then I gave him a few hints and he told me how to write the algebraic expression. I asked him if he wanted to share it with the class and he didn't want to. Therefore I shared his findings for him.

The last activity we did today was the Laced Travelers activity. It is neat how the authors used a similar situation but changed the way they gave the numbers. There is not an "algorithm" that is reapplied. They have to think through the information that is given and arrive at their answers. I had a few students to do this activity VERY quickly. I started giving candy to the ones who figured out how many men, women, and children went through Westport.

My 5th period class finished their Creating Families activity today. Some of them still didn't get their families correct according to the constraints. This is definitely a case where I really wanted to take their pencils out of there hands and just do it for them! I decided to just give them a grade today (everyone passed but the I deducted points for incorrect families) and then tomorrow I am going to do the kind of just go through creating each type of family with the students and give an example of each of the 4 types of families. While the information for the families is still on the board I am going to have them do the Hats activity. I hope this goes well. We will see...

IMP Day 17 - Shoelaces and Diagonals Illuminated and Creating Families (5th period)

Today I handed out my rubric for the Haybaler POW and then gave (through questioning and getting really excited when someone got close) them the hint that two of the bales are 39 and 41. HINT HINT HINT! Some of my students still didn't take the hint!

Then we read the intro to Setting Out with Variables and did the Shoelaces activity. I really liked this activity! Jim had warned us in training that many of the students were going to forget to calculate for 2 shoes in each pair and he was right! Reading the teacher's guide is VERY IMPORTANT for this activity because it has you lead the students through assigning variables and coming up with an algebraic expression for the amount of shoelaces each family needs to buy. *Family folders are needed for this activity because they figure how much they need for their own family first.* Then we talked about substitution...  Having not taught out of this book before I keep being anxious to see when the topic is going to be revisited. I know that the topics spiral but I wish I had time to investigate and see how they deepen as they go. Ain't nobody got time for that!!  (not right now anyway)

The next activity we did was Diagonals Illuminated. This activity revisits In-Out tables and creating a rule.

My 5th period started Creating Families today. I used Jim's method of grouping them randomly using playing cards and then assigning the type of family by suits. They relocated and worked on their families in the "new" groups so that they were working with the same constraints. I liked this much better than the way I did it with my 2nd and 3rd blocks.

I have also taken some advice from Theodora Psitos (a trainer with It's About Time) and started posting the definitions from the unit on chart paper. Today I would pause every time I came to one of the vocabulary words and point to the definition for them to read to me. I hope it helps!

Popcorn reading seems to work even though they groan a little when we start using it. I also find myself getting impatient and just reading it myself...ALOT. I noticed when we were in training and I was in "student mode" it took me several reads for the info to sink in. I figure that they don't pay great attention to detail the first time through anyway so I speed read to hurry up the process. #trueconfessions    I do read slower on the most important parts. Wow...today I really rambled!

O yea!! We received the teaching kits from It's About Time last week for the PD. In the kit there were 2 books about the Oregon Trail and I read excerpts to my classes today. I didn't read long but it was fun. The book I read from has a collection of journals from the perspective a 15-year-old boy. I plan to read a little every day.

IMP Days 14-16 - Graphing Stories, Haybaler, and The Search for Dry Trails

Last week during our PD my students worked on graphing stories on pg. 42-47. I really had fun teaching graphing stories earlier in the year. After going over a few of the videos on graphingstories.com I had my students complete some graphing stories worksheets that Lori White shared with me at AMSTI training this year. The graphs were the same as some I have used previous years but she had places for them to explain why one choice was correct and the other 3 were wrong. This approach gave us the opportunity to discuss the details of every single graph. THEN (my favorite part) we checked out the Ipads and we went outside to let them film their own graphing stories. The majority of them did some kind of flip or cartwheel. In those cases I had them to graph the relationship between the distance of their feet off the ground and time. The coolest one was one where 3 students were standing on a 2 foot wall and one student stayed on the wall and the other 2 flipped at different times. Then one jumped back on the wall and then back down to the ground. We graphed all three on the same coordinate plane in different colors. I think the students had almost as much fun as I did. I wish I would have made some of them bounce a ball and film it. One group did drop a pencil. This was a VERY fun activity. When the students finished graphing I played the video and we critiqued the graph as a class. This activity helped us to set the tone of "Mistakes are okay in here. Let's just learn how to correct them!"

Okay...back to the IMP curriculum...I made the graphing stories assignment for them to do while I was in PD because they should have been able to understand how to do them after the extensive time I have already spent teaching it (prior to using our new books).

Today I gave my students close to 30 minutes to continue working on the Haybaler POW. The one question I have kept asking my students is whether or not any 2 bales can have the same weight. Today, after encouraging them to just start testing values, I had one person in each of my 2 classes to realize that none of the hay bales could have the same weight because there are no 2 sums that are the same. I thought they would NEVER come to that on their own! I have also now had a couple of groups to come up with a solution.

The Search for Dry Trails really does not take long to go over. The students came up with their answers fairly quickly and we had a discussion and went over the definitions for mean and median. I ended up giving them additional time on Haybaler because we finished "The Search" so quickly.