My Calculus Class's Final Published Work: Rate of Change of the the Sun Setting Throughout the Year.

We studied the sunsets for the years 2012 and 2013. We graphed two dates, the 1st and the 15th, from each month for the two years. This is what we found:

x=0 represents Jan. 1st 2012

x=1 represents Jan. 15th 2012

x=2 represents Feb. 1st 2012

.........

x=48 represents Dec. 15th 2013

Then we looked at the graph and came up with an equation:

f(x)= 1.5sin(π/12(x-66/π))+7

or 

f(x)= 1.5cos(π/12*x)+7

To find the rate of change we derived the equation and got:

f '(x)=.3927sin (π/12*x)

  

So the rate of chance of the sunsets on May 15th 2014 is:

x=58 y=0.19635 min/day 

Pre-Algebra UbD Proportions/Percents Unit Student Work

So, how did writing argument papers go in my Pre-Algebra class? I think I can say it went just okay. There are still a lot of gaps that are disheartening that I mention in the reflections below. The students are presenting on Monday... I will post the video of the debates. Today was supposed to be peer reviews of almost accomplished papers.

Let me include that this is an improvement from the last time I tried debates", which let's just say, my students did poor because I did poor. Writing was something I thought they could do, and I looked past trying to address the modeling, guidelines or organization for writing. I assumed my students could write. The ability to write surely was not an obstacle besides the fact that they all were in the mind set that "This is a math class. We should not have to write!" :( Do not even get me started on this comment... Back to my assumption that literacy is high and totally strong in all Freshmen... Sarcasm can be so painful sometimes. They were in a way being assessed on their ability to write and their ability to analyze proportions, ratios, and percentages. If they did not have a paper, was it because they just did not have the skills of writing their thoughts, or was it because they did not know how to analyze percents?

Last year I had to accept it as a learning experience,  sadly mainly just for me, that I would just have to provide more literacy pointers towards thinking how to write successfully. This year, I have taken on literacy which only affirmed the reflections from last year. Now that I have hopefully addressed the literacy demands more by creating the phases, practice in argument writing, and an outline- the obstacle of writing is addressed, and the analysis and critical thinking about ratios and proportions can come out.

To try to establish a way of deciphering understandings, I do have a formative assessment, and also a project to end most of the UbD units I have created (I do have two more that I will posting soon). The projects of course are meant to engage and provide a student-run, critical thinking environment without walls and limitations. I try to align my other, old test as best I can to the project assessment, but let's face it, it is just a paper test with time and space limitations. Am I too scared to move away from tests? No, I do not think so... The project and thoughtfully aligned paper tests together, I believe, can both serve as a way to see if students can transfer the knowledge and understanding of the unit in any situation. I will post the assessments next week as well.

Reflections on the Pre-Algebra UbD Unit for Proportions:

I will post the video presentations of the students down below. You can view and see for yourself and notice and wonder about the shortcomings, but also some definite successes. So far these are my pre-reflections of how this has gone so far.

This debate still becomes more of a writing project... Is that good? I suppose, but I wish they would start making the percentages more real and focusing on that. In the 1:1 conferences I tried to make the point of, yes you can say that 1 in 4 families have burdensome health care bills, so what does that mean for this classroom. We made a point to look at the classroom, and say, according to this statistic there are about 5 students, FIVE, out of the 19 students that sit in this classroom that go home to families who have heavy doctor bills hanging over them... Do I need to call that something, like make a statistic personal to the classroom or something, and have that in the rubric? Maybe... because what they tend to do is just highlight a statistic, and quote it in there paper. They absolutely do not see a need for proportions to help them convince in their papers. In this regard, my project failed.

As stated, today, when they were supposed to do peer reviews, only 5 out of the 19 students had a functioning paper for a peer to review and grade. I need to add that these students are not the motivated type. I yelled at them- it went something like this -"I gave you a weekend and a whole week of in class time to work on this. We have tried hard to help you organize your pace. YOU KNEW WELL YOU WERE TO COME TO CLASS, SO SOMEONE COULD EDIT YOUR PAPER AND FILL IN YOUR GAPS. YOU KNOW I WILL NOT ACCEPT LOW QUALITY WORK ON THIS. THIS NEEDS TO BE QUALITY!!" ... In motivation, this project failed.

Now, despite the two major failures, I do believe my students get me and know that the problems we do as practice are not for nothing. As I came around and gave pointers, a lot of them did see proportions at work. They did see how percentages are sometimes better to use rather than just numbers. Some are really excited that normally would not be. They are thinking... We will see I guess on Monday.

Pre-Algebra Percentage UbD Unit

Here is my almost finished Pre-Algebra UbD unit plan. The overall goals are for students to be able to justify decisions and choices with reason and facts. This includes a range from choosing the best deals on a shopping spree to winning a debate/argument. My students will be active in both of these things. At the end of the unit, they will be writing an argument paper and presenting it to the class in an informal debate.

If you have any questions about Understanding by Design UbD, I would go to http://grantwiggins.wordpress.com/2013/08/24/some-resources-for-math-teachers-in-need-of-a-little-nudge-and-some-re-direction/.  Grant Wiggins is at the forefront of research about UbD. We use a lot of our PD days to continue on with developing and executing UbD units successfully in our school. It is all about execution. You really have to know the big concepts you want your students to walk away with and keep that in the CENTER of your and the student's path. That is what implementing UbD really allows- direction, even for more chaotic looking types of lessons.


Here is one of my plans I started in the last PD day we had... I am working on attaching the worksheets below.

Unit Plan: Ratios and Percents

Stage 1 –Desired Results
Established Goals (Standards) Ratios and Proportional Relationships 6.RP Understand ratio concepts and use ratio reasoning to solve problems. (6.RP.A) 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." (6.RP.A.1) 2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."1 (6.RP.A.2) 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (6.RP.A.3)	Transfer Goals
	Students will be able to independently use their learning to… What kinds of long-term independent accomplishments are desired? 1.)  Form reasonable decisions (opinions, arguments) based off of factual information and evidence and then be able to justify their decisions 2.)  Analyze proportional relationships and statistics and use to solve real world and mathematical problems. 3.)  Set up proportions and decide from a variety of processes to solve for real world problems 4.)  Use 21st century skills concerning responsibly research to expand knowledge and understanding of points of interest
	Meaning-Making
	Understandings Students will understand that… Facts and evidence make an argument strong and trustworthy. Porportional relationships and statistics relate smaller groups to bigger groups and can make an argument or fact more personal and easier to visualize. Research expands knowledge and helps a person gather evidence and facts needed to form an opinion or take a stance.	Essential Questions (F=Factual; C=Conceptual; P= Provocative) Students will keep considering How can I support my argument to convince others? Do I have an argument worth fighting for that can be backed with fact and evidence? What am I trying to find, or solve in this situation? What do I need to know to find that out, and what do I know that will help me? Is this a fact or an opinion? Can you fight for your answer?
	Acquisition of Knowledge and Skill
	Students will know… What facts and basic concepts should students know and be able to recall? ·      Solving proportions ·      Ratios ·      Percentage conversions ·      “of” means multiply ·      Calculate percentage of amounts ·	Students will be skilled at… What discrete skills and processes should students be able to use? ·      Setting up proportions ·      Identifying relationships that are proportional ·      Take percentages of wholes or figure out percentages of parts of wholes ·      Create a problem solving strategy ·      Take surveys ·      Form hypothesis/ideas based on statistics ·

Stage 2-Evidence of Understanding

Students will show their understanding by…

Performance Task(s): How will students demonstrate their understanding (meaning-making and transfer) through complex performance?

Other Evidence: Students will show they have achieved Stage 1 goals by ... What other evidence will you collect to determine whether Stage 1 goals were achieved? Assessment Task #1- 1:1 Conference about argument analysis “Argument Analysis WS”  I will marking them as mastering the content so far based on 1.) Are they able to set up proportions given certain information, 2.) Are they able to solve proportions once set up, 3.) Do they know that percentages are just another ratio out of 100%, and 4.) Are they beginning to question information and statistics given to them. 5 will be mastery meaning I can say yes for all of these and there is little teacher prompting are guidance. Assessment Task #2- Ch 7 Percents Quiz 1: Students will be assessed on their ability to… 1.)    analyze situations where relations are proportional; 2.) set up proportions and recognize knowns and unknowns that will lead to the ability to solve; 3.) Analyze and draw meaning out of ratios/statistics Assessment Task #3- 1.1 Conference about Percent Change and “Making an Argument WS” I will be marking them as mastering the contest so fare based on 1.) Do they identify the knowns and unkowns of the situation successfully organize this information?  2.) Can the use the percent change formula successfully? 3.) Do they know order of operations and solving equations? Are they beginning to question information and statistics given to them. 5 will be mastery meaning I can say yes for all of these and there is little teacher prompting are guidance. Assessment Task #4- Argument Paper:  Students will be part of brainstorming some controversial topics that can be argued using data, reasoning, and research. Students will make a decision about where they stand (some may have to be on the other side, but still make the effort of walking on the other side of the line). Students will be writing an argument paper for their particular topic given the side that they chose/ended up with. Students will have prompts and requirements that make them critically think in making statistics more real to themselves and their audience of peers. They will read out their papers in a sort of “debate” and winners will be decided. Assessment Task #5: Formative Test: Chapter 7 test that should be easier compared to their argument paper. Tests on skills and ability to transfer those skills to various situations.

I

Stage 3- Learning Plan

Summary of Pre-Assessment, Progress Monitoring, and Key Learning Events

Pre-Assessment KWL Progress Monitoring • How will you monitor students’ progress toward acquisition, meaning, and transfer, during lesson events? I will be checking to make sure they are organizing their notes and their homework, so that they can use their own work as a resource in their learning- they should be able to look back and find organized set up examples of solving proportions or be able to look through their practice problems and see that they have practiced processes that they can transfer to various other problems in this unit. • What are potential rough spots and student misunderstandings? There are a lot of various set ups for solving and the students will have to choose which set up they want or which method they want to go with. Multiple ways of solving can occur, and we should all arrive at same answer. Students will just need to be able to JUSTIFY there process. This reasoning and justification, whether it is writing it out or talking it out to explain their process is the observed HARDEST thing for these students to do. • How will students get the feedback they need? We will have conference and quizzes along the way where we can both see, as a student and as a teacher, where there are misunderstanding and understanding. Students will be having 1:1 conferences with me. If they do not have the assignments done, they will need to schedule an appointment outside of school time… Hopefully this will push to get them to do their assignments on time, so they can conference with me during class. Learning Events Student success at transfer, meaning, and acquisition depends upon ... Day 1: Introduction to percents answering essential question “How are rates, ratios, and percentages being used?” Students will do a KWL on percentages and Health Care in America.  They will break into groups to read an article and have a discussion in groups about the strength of the arguments for and against. Fill out WS #1 “Ch 7 Intro KWL and Percents Discussion” Homework: Finish “KWL and Percents Discussion” Day 2: (Skip 7.1) Lesson over 7.2 “ Percents and Proportions” Homework: Chapter 7.2 pg. pg. 337: 1-8, 10-16 even, 24, 25 Day 2: ”Lesson over 7.3 “Percents and Decimals” Homework: Chapter 7.3 Pg. 342 #s 13-16; 21-24; 25-28; 33; 36 Day 3: Students will have a workday over reading an article and applying their skills of 7.2 and 7.3 to answering prompts about making statistics more real and personal in WS #2 “Argument Analysis”  I will be conferencing with them Day 4 as part of ASSESSMENT TASK #1 1:1 CONFERENCE Homework: FINISH “Argument Analysis WS” Day 4:While I am conferencing with students about their WS#2, students will be working on the practice quiz on Pg. 350 #2-16(ev); 17-22. Homework: Finish Practice quiz and look over Argument Analysis. If did not go because you were not done, finish and will conference Day 5. If did go, look over and make any necessary changes. ORGANIZE BINDERS. There will also be a binder check for a chapter 7 homework and note section. Day 5:  Finish conferencing and have Mrs. Lowe help in review activity “Silent Library Review” working through some of the practice quiz problems. Day 6: ASSESSMENT TASK #2: CH 7 QUIZ (Refer to WS #3 Ch 7 Percents Quiz) Day 7: Go over quizzes and Lesson over 7.4 Using Dan Meyer’s Three Act “Which Deal” at http://threeacts.mrmeyer.com/duelingdiscounts/  and WS #4 Deals WS (this ws will be done with computers) Homework: Finish Deals WS Day  8: Lesson over “7.5 Rates of Change” Homework: 7.5 Pg 354 #1-9; 14-16; 21-22 Day 9: Workday on WS #5 Percent Change Argument WS  Homework: Finish WS #5 Day 10: ASSESSMENT TASK #3: 1:1 CONFERENCE- RATES OF CHANGE ARGUMENT WS; other students will be working on brainstorming controversial/debatable topics with Mrs. Lowe. Day 11: 1:1 Conferencing while students begin WS#6 Phase 1 of "OutlineRubric of Argument Paper Day 12:  Finish Survey/Data Collection and start transitioning into Phase 2 of   Day 13- 14: Work on WS #6 Argument Paper Research/Outline Phase 2/3 (1:1 conferencing on outline must be completed in these two days) Day 15-17: Typing of Argument Paper WS #6 Argument Paper Outline Phase 4 Day 18: Peer Reviews Worksheets WS #1 Ch 7 Intro KWL and Percents Discussion: WS #2 Argument Analysis Practice: WS #3 Ch 7 Percents Quiz WS #4 Deals WS - This I have students do on the computers (we are going 1:1 next year) **Dan Meyer** WS #5 Percent Change Argument WS WS #6  OutlineRubric for Argument Paper I do have this template that you can print out at http://www.scribd.com/doc/217761861/Chapter-7-Ratios-and-Percents .

OutlineRubric for Argument Paper

Angry and Unproductive Blog

I wrote this last Saturday morning and was not sure if I wanted to post it since as I warn in the next paragraph, I was speaking out of a rush of anger that came up in me. As, I read over it, I decided I should share… So, here it is. I will post a more productive and useful blog this weekend. I already failed posting twice in February. I will make up for it. I have three days left, and I will add a couple more blogs in that time.

Warning: This blog is angry. I will also preempt this with saying I do not classify all parents like this, but I do feel a need to address the loud ones that ARE classifying all teachers and are willing to cruelly insult and  discredit an entire school family on the grounds of exceptions. We do get praise, but unfortunately it is not nearly as loud and as obnoxious as the insults and complaint. I address the parents and media that do not get addressed anymore because everyone knows they tend to not know how to listen or are just in it for big head liners. I do not know if this means anything to those parents and their consciences, but it makes teachers like me, new and close to burn out as it is , want to walk away.

As I was doing my laundry today (very excited I might add since I’ve got myself a PILE”, I had overwhelming sweeps of desire to finish my list of things to do between today and tomorrow:  finish laundry, organize my lesson plans ( 5 preps for dare I say it, only four days this week), finish creating my Pre-Algebra Understanding by Design (UbD) unit, complete my paperwork for finding my birth family, help my foreign exchange daughter dress up her prom dress, make bread, make a couple videos for my flipped classroom,  make my grandma’s birthday present (I am making a pop-up card stationary set for her that a colleague showed me how to do:) , sweep and clean the floors that are covered in spring dog prints, and complete the transfer of files and programs to my Mac that I will start to use this week.   I also will take some time to do my hobby of cooking and sitting down to a nice dinner with my family. On top of this list running through my mind as I was folding shirts, I also had waves of anger that started taking hold. I did not attend, but I heard that a small crowd of parents who came to the most recent school board meeting began using insults and criticism towards the teachers at our school in order to make arguments against a 4-day week that was not even the topic of the agenda.  I realize this may be a small group, but I am tired of the ignorant voices being the ones that are the loudest. I wanted to respond to a couple of comments that just drove me nuts.

A comment that all we do at school is watch movies and a four-day week of longer days would just be more time for children to watch movies. I will not even respond to this because that is just a really stupid comment. Don’t even waste my time with gross untruths, but if you are saying we provide a study hall…

For those of you that dare to criticize a teacher having a day where the students are given a study hall because the teacher felt he/she could afford to give that to the students. Heaven knows the students get behind, and heaven knows we, teachers, also could use the period to catch up on grading and planning. I tell you it may happen once in a while that life beyond school does happen once a teacher goes home. Do parents forget that? Do they think it is okay for a teacher to go home and do things for his or her family? For me, EVERY DAY there is a list of things that need to get done for school. Some days, that list does get put aside because I have promised my family I will do something fun with them, rather than hole myself up in my room and work on school for the night like I do pretty much every night. Some days at school will be catch up days.

A comment that anyone can teach. Also not true.

For those of you that dare say “anyone can teach”, I will only quote my friend’s response that “anyone can become a parent.” All children are brought before us. We also become parents, and I will tell you, we do a better job than some of you. Yet, you do not see us walking into your domain pointing out your weaknesses in an I-know-all, arrogant manner. There are a lot of home issues these students are bringing into the school, and there are a lot of changes the school is attempting to do to try to reform education so we are creating innovative, critical thinking, competitive students, so please!!! stop acting like there is a quick fix for all of this.

I would love to have discussion with parents who are willing to talk about ideas for lessons and integrating real world experiences into my math classes. Please, come collaborate with me in building lessons, rather than building extravagant headliners that do nothing productive in your “quest for better education” if that is indeed your quest. Please do not fool yourself in thinking anyone can teach.

I know I am a good teacher. I work hard for it. That does not mean I deliver perfect lessons, am always on top of it, or know exactly how to fix the things that are going wrong in my classroom. In fact, I end up questioning every lesson I give because there are always these contradicting desires:

I want to create more structure and scaffolding to bring all students into the same playing/learning field, but I want students to have the ability to be creative and innovative.  I want them to face challenges where they go beyond the structure and expectations I hold.

 I want students to have the math skills concretely down and I want them to adopt my algorithms and my logic, but I also want them to be creative and form methods that work for them.

 I want to teach them perfectly, but I would rather they are able to teach me.

I want my students to THINK , not about a grade, but about expansion of knowledge and creation and productivity that follows from knowledge.

I want them to dive deep into exploring the patterns, processes, connections, and possibilities of my subject, but I have 45 minutes in a day, and students have sports, activities, and jobs that they are too tired for homework.

I am always trying to find the perfect lessons that will meet these things and it haunts my mind constantly when I wish it would not- not to mention I also have some very low motivated students that always haunt me.  I go to bed late, and I wake up early to do my work. My husband actually expects not seeing me very much during the school year. We try to establish a date night weekly so that at least one night a week we can spend time with each other, no distractions and no work. This does not always happen, and you can bet as I sit at a movie, I am dreading the fact that I could have corrected so many papers or created this/that activity in that amount of time.

As you read this, you may think this teacher is crazy. I am. I am crazy about trying to be the best teacher I can be.  I am a bit more crazy in the amount of time I section off for dedicating myself to this goal. I am well aware that I pay and my family pays dearly for this, but I am not alone. I work with another family, of teachers, who most I admire and I am so glad to teach among. Sometimes we will just stare at each other and ask why are we doing this. For those of you that dare say we are not trying at our school, I dare you to find someone to replace us since anyone can teach. I dare you to instead of complain about us not helping to grow and better your children, to be PRODUCTIVE and contribute ideas of lessons that will be helpful. I dare you to try to step down from the high podium you hold yourself on in knowing what it is like to teach. I dare you to contribute and be productive in helping to build up a school that teaches worthy knowledge and truth.

It has been 45 minutes of typing this venting letter.  I will spend no more time on it because I need to go be productive….

mumble… was it worth trying to address those that do not listen?

 

Restart and plans

So, I just got really, really angry. I am correcting my Pre-Algebra Fraction Operation Test in my comfy bed with 4 comforter layers on it because our heat bill was ridiculous these last two winter months and we have now opted to live in very cold conditions in our house. I have lost the ruler I need to correct my tests 2 times in the last 45 minutes. It keeps getting lost in my layer of sheets. I then lost my pen as I tried to search for the ruler only to find it tucked behind my ear where I thought I thoughtfully put it. As I looked for my pen, I lost my ruler again. So, I decided to blog.

It has been on my mind that I failed once again to keep up. I blog hibernated during the fall, and I have awakened lately, rejuvenated and blog awake this cold, cold winter.

I will need to share some things that I have gotten myself into this 2013-2014 year.
1.) I took on coaching the robotics club again this year participating in the First Technology Challenge (FTC). I had two teams this year, and we saw so much improvement in both teams. We will work on documenting our progress and showing the process of designing, building, programming, and getting out in our community with robotics.

2.) I became a Professional Learning Communities (PLC) coach. This has been a bit chaotic, but we are developing PLC's at our school district using Daniel Venables Authentic PLC's. We have steered our professional development in the direction of literacy. One of the English teachers who also is a coach just presented an awesome perspective of literacy. As an math teacher I had a warped understanding of what literacy entailed. I have found that literacy is the ability to read, write, and discuss. Under all three of these skills lies the ability to critically think. As we approach literacy, we have now discovered we are really tackling the question of how to get students to critically think in all subjects they find themselves in. @MelissaSalgado3, my friend, and literacy guru drew a wonderful analogy for me. Teaching our students to read will look different in various classes: In English, she is teaching the students to read for comprehension using the mood, settings, and style in the writings; in PE, a teacher will teach students how to read an opponent's body language or the strategies of the game; in math, the students needs to read into the known's and unknowns's, the math symbols, and operation requirements. I noticed in each of the settings, the students needs to visualize the situations. The ability to visualize is soooo important in math, and I have not been emphasizing.

3.) I have slowly started to track my units in the UbD format after having taken some credits this last summer dealing with UbD

4.) I jumped into parenting a 16 year old (:. The husband and I, having been married 2 years, decided to host a foreign exchange student with the EF Foundation. Honestly, we will probably look for other options in terms of the organization, but our student is awesome. We have learned a lot. It has been good practice for parenting.


So... I sit here promising to start my blogging up again. I will be making it a goal to do at least two blogs a month (two a month- I am pathetic for having to make that measly amount a goal). I will be focusing my blogs on the following:
1.) Fixing my file cabinet lessons and adding more lessons
2.) Posting my UbD templates and organizing those
3.) Developing my math literacy strategies of visualizations and think alouds.
4.) Researching CGI's

I should probably stop because I still remember I need to complete one thing at a time, so I see success to keep moving. I fell in the trap of spreading myself too thin this fall, and not feeling satisfied with my results and accomplishments. One... thing... at... a... time.  Maybe 2. Or, 3. Apparently it is 4. Four.... things... I shall get them done.