Desk Dilemma

Desks--ugh. Most classrooms at my high school come equally equipped with them. Perfect for making those nice, straight, make-me-want-to-to-snore rows. I miss my tables. The first school I ever worked at had tables in all the classrooms. Each table was able to seat 4 students. It was so wonderful for student discussion and collaboration. The desks just make me want to cry--or be boring. But I prefer to not be boring if I can help it.

Recently I decided to make the best out of my desk dilemma. I put them in facing pairs and then put two pairs relatively close together. So if I squint my eyes and turn my head sideways then it almost looks like tables. It will do for now. For the most part it accomplishes the same goal.

How do you arrange your desks the facilitate discussion and collaboration?

Vocabulary-->Taboo!

Last Saturday I planned my week out in detail, as usual. It is highly unlikely that my week will go exactly as planned. However, I like having at least a framework for my week early on. It saves me time in the long run. Anyway, that is only partially the point. Yesterday afternoon I was reminded about a short assembly that was set to happen during one of my classes. Well, call me crazy, but I teach the same thing all day long. Yes, that's right. Four times a day I teach the exact same lesson. Soooo, with the assembly taking up only one of the four classes, I had to make a quick decision: go with the plan and get my classes off schedule or improvise!

Enter: Math Vocabulary Taboo! I had heard about this before but I wasn't exactly sure how to play or what to do. So here is how it went in my room. I quickly made 10 sets of index cards (enough for 10 pairs). The index card had the vocabulary word and then three words/phrases that were not allowed to be used a.k.a. the "taboo" phrases. (They also couldn't use the actual vocabulary word or spell or say "starts with" or "rhymes with"...that all made it too easy.) For example:

Slope

• slanted
• steepness
• skiing

 I moved the desks into pairs (similar to speed dating). I gave one partner the cards they were the "clue giver" and the other partner was the "detective". For the first two rounds of the game they were allowed to use their vocabulary squares to help. I put four minutes on the timer and let them go. After the timer went off I had the "clue giver" hand the cards to the "detective". The "clue giver" switched partners and then we played another round. After two rounds they had to put their vocabulary squares away and then we played a few rounds without the crutch. I had 10 total vocabulary words and it took the students 3-4 minutes each round. I imagine the more "common" the taboo words are the harder this game is to play. My goal was to take out all the obvious/common words so that they really had to think about the word and its meaning.

It was AWESOME! I'm not even kinda kidding. I loved this activity and I plan to do it again for the next unit. This was higher order thinking if I have ever seen it. The kids were all engaged and having a great time trying to come up with clever ways to describe the words. I had students coming up with sports illustrations, music, kinesthetic...you name it. The kids were so very creative.

I would definitely recommend this to anyone that is struggling with finding interesting ways to talk about and teach content vocabulary.

ELL - Independent vs. Dependent Variables

In my last post I included some samples of student work (mini-posters). I decided to make a separate post to highlight the two mini-posters from my ELL students. These two students started out the semester and I was super worried about having them in my class. As best as I could tell, they weren't able to speak any English. I'm glad I was semi-wrong. Some of it was just shyness. They are learning very fast and I am quite proud of their final products for this mini-poster project.

Independent vs. Dependent Variables

My class recently learned about independent and dependent variables. I found this great idea right in time. It turned out fabulously and it didn't take much time to prepare up front. I just needed some drawing paper and markers--the kids did the rest. I highly suggest you read the original post (because this wasn't my idea). However, the short version: the students came up with their own example of independent and dependent variables and then put them on a mini-poster. Below are some pictures of the final product:

That's A Bunch of Crap! --math activity

Recently I blogged about my love for YummyMath. I downloaded and tweaked this activity and then used it in my classroom about a week ago. Basically, I changed the names of the couple, changed the title, and added new captions for the graphic to make it more interesting to my students (things like "dude" and "you trippin"...they thought it was funny.) I changed the title to "That's a Bunch of Crap!" because we aren't really close to either mother's or father's day at this point in the year. The kids instantly loved the title and so I had at least a little bit of their attention from the start of the activity.

Just as a note, we have not talked about graphing linear equations and certainly haven't talked about solving a system of equations yet at this point. We have (in the form of games) taken information from tables and put it into an equation. So I was extremely pleased to see how this turned out (even though not every poster is perfect--trust me, I do notice some mathematical/grammatical errors in some of the posters). Enjoy!

YummyMath

So I have recently discovered (or rediscovered, I'm not sure...) YummyMath. I L.O.V.E. this website. So here is my attempt at a review:

Overview: The website contains activities arranged by math subject (geometry, algebra I, etc...). The activities are all relevant and pretty current. For example, the first posting today is about the wall street protests.

Pros: Just about every time I have searched for a particular topic, I have found something usable. The activities are easy to download/edit/print. The students have loved every activity I have used so far from YummyMath. The hard work is already done. Most lessons come ready to print and implement.

Cons: Other than the major subject (geometry, algebra I, etc...) there isn't much organization as far as topic is concerned. As best I can tell it is arranged by date posted. Therefore, in order to find something you want to use it can take a while sometimes.

Overall: The good far outweighs the bad. I will continue to use YummyMath to make math relevant to my students. I would gladly recommend this to a friend.

Standards Quiz #2

Today I finished grading my second round of standards quizzes. We just finished standard #9: The student will be able to describe and/or order a given set of real numbers (rationals & irrationals). This quiz was much easier to grade than the first one. It only had 9 questions (3 easy, 3 medium, 3 hard) and it was all multiple choice. I made the students show work anyway. However, this saved me a lot of time. I was able to quickly skim the multiple choice responses for right/wrong and then any questions I wanted further clarification on I could just look at their work. I finished grading all four classes worth of quizzes before the day was over. I had just as much information as I did from the previous quiz and I was able to spend more time providing written feedback.

I will probably do the majority of my quizzes this way from now on. The state test is multiple choice anyway, so they might as well get used to it.

As a side note, I used a web-based program called Discovery Ed to make the quiz. It is a service my district has subscribed to. You are able to select the course and then drill down to the individual standard. It provides a whole back on easy/medium/hard questions. The questions are remarkably similar to the state test my kids will take at the end of the year. This has saved me a TON of time this year. I can pick through my choices and have a beautiful standards quiz in a short amount of time. So thankful for Discovery Ed.

First Stadards Quiz - Grading

My students took their first big standards quiz on Wednesday. I had no idea what to expect about grading. I didn't know how long it would take or how difficult it might be to score it correctly. So far I have finished two out of four classes and it is taking about twice as long to grade as it would have last year under the old system. However, last year I only used multiple choice tests. I could easily go through and mark off a, b, c, d, etc... This first standards quiz was strictly free response and essay. Therefore, I am not basing my "time it takes to grade" on this one assessment.

Overall, I like this system a lot better so far. The usual points or percentage systems never really made me too happy. Even though I have only graded two classes, I am pleased with the results. The kids who are currently failing are the kids who don't know what they are doing and that is a small percentage. I have one in each class right now that is failing. The rest are spread out As through Ds. The quiz scores match up perfectly, I feel, to what the students actually know.

Tomorrow I will be handing the quizzes back. The students are going to chart their own progress. They all have a "standards" tab in their binder (go me!). I will work on giving some valuable feedback to each student. I want them to know exactly what they should work on in order to improve their score.

I'm excited to give the quizzes back. I'm interested to know how long it will take for the students to really catch on to the grading system. I am sure once they fully understand it, they will appreciate it.

I'll keep you updated! As always, feedback is welcome.

ELL Students

For the first time in my teaching career I have several ELL students in my classroom. I'll admit that I really have no idea what to do for them. Two know how to speak English fairly well (enough to "get by"), but the rest only know a couple phrases. The phrases include "I don't speak English" and "I know little English". Comforting! Not.

I've been doing some research as I have been able to, but I haven't found anything that is really satisfying. Most places say to give visual vocabulary: word, picture, definition. This is something I already do, and it doesn't strike me as much "good ELL teaching" as it does just "good teaching". Other resources say to model everything. Uh, duh. And then other resources say to shorten the assignments and requirements for the ELL students. I'm not sure how that is helpful, but maybe?

The thing that really bothers me is that several times I've been told "they won't count against your AYP scores". Well, that's great...but it doesn't change the fact that I want these kids to learn Algebra I.

So for now, I am spending time translating my vocabulary into several different languages thanks to Google Translate. I am making the students write the English version, but they have their own language side-by-side so they at least know what they are writing. I think that will serve two purposes. One, they will grow their technical English vocabulary. Two, they will be able to answer the problems I give them in class because they will know words like "simplify", "evaluate", "sum", "subtract", etc... For now, I am not doing anything with the assignments. They are staying 100% English. The only work I am translating is the vocabulary.

I really wish there was some more helpful information out there about teaching ELL students. At the end of the day, they are still students in my classroom and I still want them to learn Algebra I. Even if they don't count against my AYP.

1/3 Scale - SBG % Translation

I officially decided to use the 1/3 scale. I think it will better represent what the kids know and are able to do. I will be able to more accurately pinpoint their proficiency level for each standard. Here it is:

4.0 – 100% A

3.67 – 97% A

3.33 – 92% B

3.0 – 90% B

2.67 – 83% C

2.33 – 77% C

2.0 – 70% D

1.67 – 67% F

1.33 – 63% F

1.0 – 60% F

<1.0 – 50% F

I chose not to divide the 4.0 to 3.0 range evenly because it left 3 opportunities for an A and only 1 opportunity for a B. If a student gets a 3.33 that means they are proficient and low-partially proficient at advanced content. To me, that represents B work, not A work. 

Just so you know, in my district this is the grading scale we are given:

93-100 A

85-92 B

75-84 C

70-74 D

0-69 F

Algebra I Standards List for SBG

So after many months of planning for standards-based grading in my classroom this year, I have finally written out the standards. These are the standards provided by the state.  I am considering merging and/or splitting a few of them. I have seen several lists that are simply “topics” and I know I do not want to do that with mine. However, the problem is that I don’t want them to be so specific that I have boxed myself into one type of problem. I also don’t want it to be so broad that I have trouble testing it all or assigning a mastery grade. If anyone has any suggestions for my list, I’d love to hear them! Also, I should mention this is for Algebra I only.

THE STUDENT WILL BE ABLE TO….

Mathematical Processes

1.       Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.

2.       Write an equation symbolically to express a contextual problem.

3.       Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.

4.       Translate between representations of functions that depict real-world situations.

5.       Recognize and express the effect of changing constants and/or coefficients in problem solving.

6.       Determine and interpret slope in multiple contexts including rate of change in real-world problems.

Numbers & Operations

7.       Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

8.       Multiply, divide, and square numbers expressed in scientific notation.

9.       Describe and/or order a given set of real numbers including both rational and irrational numbers.

Algebra

10.   Express a generalization of a pattern in various representations including algebraic and function notation.

11.   Operate with polynomials and simplify results.

12.   Factor polynomials.

13.   Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

14.   Write and/or solve linear equations inequalities, and compound inequalities including those containing absolute value.

15.   Interpret various relations in multiple representations.

16.   Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

17.   Determine the equation of a line and/or graph a linear equation.

18.   Solve systems of linear equation/inequalities in two variables.

19.   Find the solution of a quadratic equation and/or zeros of a quadratic function.

20.   Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

Geometry & Measurement

21.   Develop and apply strategies to estimate the area of any shape on a plane grid.

22.   Solve contextual problems using the Pythagorean Theorem.

23.   Solve problems involving the distance between points or midpoint of a segment.

24.   Convert rates and measurements.

Data Analysis, Statistics, & Probability

25.   Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

26.   Identify the effect on mean, median, mode, and range when values in the data set are changed.

27.   Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.

28.   Generate the equation of a line that fits linear data and use it to make a prediction.

29.   Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.

SBG - first opinions from admin

I had a meeting with my administrator sometime mid-spring semester and asked her if she would support me through implementing standards-based grading in my classroom. She gave the approval for me to go forward with planning based on what she knew of it. The plan that I posted here was the first write up of what I informally presented to her two days ago. I added a few details but the bulk of what I wrote stayed the same. She did not require that I keep her updated, but I have found over my years that it makes life much easier if you keep your administrator in the loop.

Anyway, so I unveiled the plan and I got three questions in return:
1. How do you plan to communicate the plan and its benefits to parents and students?
2. What do you expect will happen to the distribution of grades? More As, Fs? Stay the same?
3. How can you make re-assessment more mandatory and less invitational?

I had a response for the first two, but the third one threw me for a loop. I don't have anything in place to make sure the students reassess. At this point, it is up to the student to reassess if they want to. They don't have to. Aside from staying after school (which isn't an option because I am coaching fall and springs sports) or coming in early (which very few students are willing to do)...I don't know what to do.

So that is where I am at with the process right now. I am thinking about how to make the process less-invitational. I hope to come up with a plan (or "acquire" a plan hehe) that doesn't require me to spend countless more hours at the school building. Maybe an in-class arrangement? I dunno...

Visual - Objectives

Here is a picture of the sentence starters I use in my classroom. See my last post for the full explanation of how I use them. I made these with my Cricut because I got tired of re-writing this part every single day. I put magnets on the back so they stick to the whiteboard. Now I don't have to write as much each day. I just use bullet points for the rest of the information each day. This makes the task a little less time consuming each morning.

Objectives

At my school (and I assume many many other schools around the nation), we have to post our standards every day for each class. For several years I posted the exact standard--number and all. I got the box checked off on my observations but that is about it. It wasn't useful. This past year I used the following format and I found it to actually be useful. I was able to refer to it often. The students got used to coming in and reading it. It gave them a good idea of what to expect for the day. It was a tool that was actually used instead of just "checked off". Anyway...here it is:

Today I will learn...
To do this I will...
My teacher will know I learned it because...

Simple but effective. After the first sentence starter I would put the objective in student-friendly terms. For example, "Today I will learn...how to solve equations with variables on both sides." The second sentence starter would be the actual agenda. It would list any learning activities that would be taking place during that lesson. For example, "To do this I will...take notes and then get with a partner to solve problems." The last sentence starter would be the day's assessment. This could range from "she will check my homework" to "she will grade my quiz and provide feedback" or even "she will ask for thumbs up/thumbs down responses" possibly "she will check our whiteboards"....you get the idea. It was the way students would know what the assessment of the day's work would be.

Now that I am working on SBG, I think I like this even more. I will continue to use the three sentence starters with "kid friendly" language. However, I will add somewhere in there the learning goal number because they will have a numbered sheet of learning goals handed to them at the beginning of the year. That will make it easier for them to keep track of what they are working on.

SBG - Initial Plan

Here is what my "basic" SBG plan is after putting together four+ years of reading and research. I am finally ready to implement this in my classroom. I think... :)

I plan to have a general 4 point rubric:
4- Advanced, learning exceeds goal
3- Proficient, learning meets goal
2- Basic, learning below goal
1- Below Basic, student needs help to reach basic level
0- Student isn't successful even with help

This rubric I got primarily from Marzano's Formative Assessment & Standard-Based Grading. However, I do not plan to make a specific rubric per learning goal. I will only have the one generic rubric and just make my learning goals descriptive.

I will be working on a scale to convert my 4-pt rubric into 100% scores because that is the constraint I work within for my district. For instance a 4 would be 100%, a 2 would be a 70%...etc I haven't worked out those details yet because I am not sure if I am going to make my scale increment in .5 or .33 points yet. More to follow on that in a later posting...

Record Keeping:
In my "official" gradebook that gets entered electronically, I will only have one grade per learning goal and then the final exam. This grade will represent the summative score for that learning goal. So after I have written out all my learning goals for the year, it is possible that students will only have about 50 or so grades for the entire year. Each score will go into the gradebook out of 100%. So even though the students will have fewer grades than in the past, the "total points" will be about the same.

I will also keep a paper record of all formative (graded) assessments that I give the students. That could be homework, bell ringers, quizzes, mini-tests, ...anything that will inform me and the student of progress towards the learning goal. These formative assessments will be crucial to the student's progress in my class. I will have to find an efficient way to provide timely feedback to each student, otherwise I think my plan is going to flop. I haven't come up with the "efficient" part yet, so that will be reserved for a later post.

I really like this because it is going to completely remove "missing work" and "late work" and "zeroes" from the equation. I absolutely HATED giving a student a zero simply because they didn't turn something in...or worse yet, they turned it in but it was late. I want the grade to represent how much they LEARNED, not that they are responsible...or whatever.

Reassessment:
The other key point that I want to include in the system is the ability for students to re-assess. I don't want their grade to represent what they knew in August. I want it to be (as close as possible) representative of what they currently know or learned.

That being said, I realistically I do not have time to constantly re-assess every learning goal. This part the students are going to have to take some ownership. I will have two days a week that I will be available for re-assessing. The students will only have the re-assess the goals that they are wanting to improve. They will need to give me at least a school day's notice so that I can prepare an alternate assessment for them. They will need to sign in with the reassessment log so I can keep track of who has come in, etc... I may limit the number of students that can sign up per day. That may prevent the "mad dash" at the end of the grading period. I'll have to think that through a bit more before I decide.

I do not plan to put a time limit on the reassessments. If they want to re-assess a skill in April that they learned in August, that is fine with me. The only time limits I will put on them will be at the very end of the semester...I'll have to make some type of a cutoff date so I am not grading down to the last second.

Other thoughts:
I really like this because if a student's grade is crappy then all they need to do is learn the material. They do not have to do hours of makeup work. They are not ever "hopeless". They just need to study up and re-assess. As for now, I do not have a way that I am going to require them to study or prove they studied. I also do not have a limit on the number of times they can reassess a certain learning goal. Both of those things may change.

Anyway, so that is what I have so far. Questions, comments, and concerns are always welcome. Stay tuned...because I'm sure it will change before August arrives.

SBG - In the Works

So I have been researching SBG since I was in college getting my BA. However, I haven't had the guts to really jump in...until now. In college I read through "Classroom Grading that Works" by Marzano and that really got me thinking about what I wanted my grades to represent. I decided to research the topic a bit further and I ended up writing a million page paper on it (okay maybe more like 20 page, but it was still torture).

Then I got my first job and they already had everything laid out for how I was supposed to grade and SBG didn't really fit the formula. So I put it on the back burner for a while. Then when I moved to Tennessee, I started thinking about it again. I really wanted my grades to represent what the students actually KNEW. I didn't want any type of "responsibility" or "work ethic" or "late points" or ... anything other than content knowledge to be represented in my grade. So I kept researching and a friend pointed me in the direction of the blogging world.

If you know me, I am the type of person that would rather do something "right" than just halfway. So, I read everything I could about SBG and just kept learning. This past school year I was teaching six sections of geometry. Geometry is a math topic that I was not completely comfortable with just yet. Instead of jumping in with relatively new content and a new grading system I decided to just learn the content well and then do SBG the next year.

So that is where I am at now. I have been reading books, skyping, reading blogs, tweeting, ... anything I can think of to prepare for the implementation of SBG in my classroom. Next school year 2011-2012 I will be teaching only Algebra I. Not only that, but I will have freshmen. And not only that, but my school "loops" so the freshmen I have next year will be with me again as sophomores for geometry. I can't think of a better time to start up this system of grading in my classroom. New subject (one I know!!), new students, and new grading.

In the next post I will outline the skeleton of what I plan to do. I am sure it will change a million times before now and school starting. Comments are welcome. :)

Next year

There are a few things that I want for my classroom next year, but they seem to conflict with each other. I haven’t really figured out how to merge the two in such a way that satisfies each expectation individually. I hope by next school year I have it figured out a little bit more…but for now, here are my hopes for next year:

1. I want my grades to reflect ONLY what the students know. Whenever I see an 80% in my gradebook that should mean the student truly knows 80% of the material. It won’t indicate anything about his/her ability to turn in assignments on time (or at all). It won’t indicate how well a student can furiously copy down answers to last night’s homework before class. It will only describe what the student actually knows. Standards based grading anyone?

a. Fear #1: I will have a lot of students fail because they no longer have the cushion of “classwork” and “homework” to absorb the shock of poor test grades.

b. Fear #2: My administration will not back a system that has such a small amount of grades. I say “small” because under my school’s current policy we are required to enter a minimum of 2 new grades each week of the school year.

2. I want my students to learn responsibility. This means: I want them to be able to appreciate and follow deadlines. I want them to be able to advocate for themselves. I want them to see the value in homework and working hard (even if it isn’t going in the grade book).

a. Fear #1: Without an actual grade in the grade book my students won’t complete my assignments.

b. Fear #2: They won’t be able to learn lessons in responsibility without learning them the hard way.

3. I want to be ahead on all the “paperwork”. I want to have my syllabus done and copies made before the day-before school. I want to have at least a basic “plan” for my first semester.

_______________

So those are just a few things that I want for next year. We will see what happens over the summer. :)

Workshop Experiences

Okay finally time to write my workshop experience down. Overall, I think it went well. I think that most of the people that attended the workshop got something out of it that they could immediately use in their classroom. A few things that I walked away with:

1.       My limited experience really humbles me when I’m speaking in front of a room full of people that all have been around longer than me. By this I mean, I have only been teaching for 3 years (4 if you count student teaching…but we won’t go there). Most, if not all, of the people that attended this workshop have been teaching well beyond my 3 years. So even though I know what I’m doing is good for my students, it was still incredibly difficult to share. I felt like what I had to say was inadequate or boring or “fill in the blank”… I was worried about what all my colleagues would think. They are math teachers. They are also experts on math content. I wasn’t just presenting an idea in front of someone who didn’t know any better. I was presenting ideas to people who were very capable of picking every inch of my ideas apart. That was scary.

2.       My feelings were confirmed from previous posts. A lot of people had never used “discovery” or “inquiry” in a math classroom as a tool to teach new content. I took a quick poll and out of 18 people, only 2 had ever dabbled in this method. Those two had only done it “unofficially”. So I knew the information was new to most.

3.       I need to work on my presentation skills if I plan to do this again. My face was red the entire time. So it was very obvious that I was nervous and there was absolutely nothing I could do about it. The second I saw my face getting red…it just kept getting worse. Because then I was nervous and then even more nervous because of the redness…and it was just a vicious cycle.

I want to keep presenting. I enjoy sharing my ideas with others. I also want to get better at presenting. My goal is not to get so nervous next time. They are just big kids, right? …big mean kids! We will see. Pretty soon my survey results will be returned to me. That way I will have some data to show how I actually did…instead of just how I thought I did.

Group Work vs Cooperative Learning

All too often the phrases “group work” and “cooperative learning” are used interchangeably. This, in a word, is—incorrect. To me the distinction comes from what the students are actually doing while they are in the group.

Group work means that the students are probably sitting together with their desks all facing each other. They are likely discussing the math, but they are using each other more as confirmation. They work independently and then “check” with the others to see if they are on the right track. Group work can also include working on some type of larger activity. This larger activity would more than likely be a display of knowledge. For example, they might be making a poster or a presentation about a topic they just finished in class. Most often, group work does not involve the students learning something new (BEFORE the teacher has “taught” it).

Cooperative learning, on the other hand, means that the students are relying on each other to actually learn something. They are engaging in academic discussion to figure something out. Most often what they are learning is new material that the teacher hasn’t explicitly stated or an extension of a basic idea that was presented in class. In cooperative learning, students are in charge of their own learning (with a watchful teacher eye, of course). The students ask the questions to each other first. Only after they have exhausted their resources do they ask the teacher. It is critical thinking and problem solving at its best.


In my classroom, I use both. However, cooperative learning is my favorite. Please do not make the mistake of thinking they are the same! You should always ask yourself, “Would I be able to do this lesson without the students in the room?” If the answer is yes, then it certainly isn’t cooperative learning and perhaps you shouldn’t be doing it at all!

Unwitting Collaboration

I read a lot of blogs. And by read, I really mean skim. And by skim, I really mean I only read stuff if the title looks interesting or if it has pictures or if it has been specifically recommended to me by a friend. However, there is a particular blog that I actually read almost every time a new post is made. This "Mrs. H" is a fabulous and creative person. One post in particular (linked here: Mrs. H's Star Chains) I tried in my classroom. We had just finished working on properties of various quadrilaterals. Each card led to the next and when the students were done they had a full self-checked chain of math problems. It was a beautiful thing. Below are a few pictures of the finished product.