Monday, December 15, 2014

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.

Saturday, December 13, 2014

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.

Wednesday, December 10, 2014

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.

Tuesday, December 9, 2014

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.

Monday, December 8, 2014

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.

Saturday, December 6, 2014

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!

Friday, December 5, 2014

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!

Thursday, December 4, 2014

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 we couldn't resist the analogy.

Wednesday, December 3, 2014

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.

Tuesday, December 2, 2014

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!!

Monday, December 1, 2014

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.