Sally Byrd’s Final Project EDET 637 UBD Lesson Reflection


My linchpin is the “Rules” for Order of Operations. Students must follow the rules to the order of mathematical operations in order to come to the same conclusion as the mathematical world set forth.

My evidence is student work. I gave a pretest that showed the students knew more than I expected. It was too easy and pointless to give it as a post-test. I will make this modification in my lesson plan to make a test that has more challenging problems.   After their first book assignment I modified my unit to a higher level (Algebra). The unit was limited to simple grouping symbols and so I added solving expressions through substitution that used exponents and grouping symbols.

This is the assignment out of their book. You can see the Pre-algebra is a pretty simple “Order of Operations”. This is a typical result of the students’ work from this assignment. It was the first assignment of the unit after the pre-test. The red check marks are made when the student graded their paper. I also corrected the paper and made the green marks. I want the students to see how they did and I wanted to know how they did. I also pay attention to how they grade their paper. Are they doing it correctly or not. This helps me understand the student better.

At this is when I decided that I needed to take the students to a higher level to challenge them. The most incorrect on this assignment that was turned in was three problems.

First trouble I have

You can see they needed to subtract before they add (marked in green), because addition and subtraction are equivalent operations with an addition rule of left to right when you have more than one. The subtraction is to the left of the addition sign.

The next three assignments were from Pizzazz so they have the answers with a pun joke. It is harder to catch the individual errors to make the corrections. I didn’t like how the students were writing notes around the problem. I did appreciate that they took the time to write down a portion of their answer and not trying to remember everything.   These worksheets are great for immediate feedback. The students are trained to look for their answer to make sure they are on track.


The students love these worksheets. They don’t always ask for help when they need it. They just keep trying. I grade these papers too so I can see where they can use assistance with the rules of order.

I realized that I wasn’t getting the full picture of how the students were doing, due to them not writing in the mathematical language. So I switched to creating my own worksheets that provided room to write in the mathematical language. To keep the confidence in the students I provided the answers on the paper where they can be assured of doing the work correctly.


Again, I felt that the students could go a little higher. I decided the answers were now hindering my evaluation of their work. It wasn’t allowing me to see the mistakes that I could discuss with the students.

Up to this point all the students were only missing a problem here or there. Students asked for help when there was an exponent outside the parenthesis and a number in front of the parentheses. For example, 3(4)2, some of the students multiplied 3×4 before using the exponent. I had to show them that the exponent only had the 4 inside and the 3 was a separate entity then the exponent. This was very appropriate for this lesson. The little errors that they are making are different with each student and we need to sort out the errors and correct them. The next time I teach this unit I will be sure to point this out and emphasize that it is a common error that needs to be corrected.

I made the switch to no answer on the worksheets and created a worksheet that gradually move to a higher level of challenge. As a class the students did well on the first six problems and made similar errors on the next set of problems. With the next set of worksheets I did the grading and returned the worksheet back to the students to make corrections. I would use two different color markers to show where the students made their error and a second mark to show if they fixed it or not. My first student that I will follow had made tremendous gains. She took advantage of the individual instructions and corrected the errors.

correct errors

So, here in the picture the first six problems were pretty easy for most of the students.

As we get into the grouping symbols the students weren’t sure what to do with the fractions (#24). After a couple of days of practice and instructions they understood to simplify the fraction before applying the exponent. The students wanted to divide and leave a decimal for an answer. This is an application of learning the fraction bar is a division sign.

This student had shown great growth in her learning. She did a great job writing in the mathematical language, this helped her stay on the right track.

After an assignment I tallied the problems that students were having trouble with. This helped me to see who was having trouble with which problems. I could see how well a student was doing by looking at their graded assignment, but I wanted see which problems were giving them trouble.

evaluation of Order

After I finish grading their papers I write their initials by the problem so I know which ones we can focus on.

On the next assignment, I graded and immediately returned their work to them for corrections. The students were happy to see their own progress and that I had pointed out to them the step that they missed.

corrected errors after evaluation

You can see I graded with blue first and this student had subtracted before dividing. With the mark on the paper she knew she had to divide before subtracting. On the last problem she had to correct she didn’t take care of the parenthesis first.


On the last assignment before our final assessment we focused on simplifying fractions before using the exponents. The two different types confused the students. The first one #11, the fractions can divide down to a 3 and that is cubed and the second one doesn’t come out of the fraction and both numbers have to have the power of 4 applied to it and is left as a fraction.

You can see on her final assessment she was able to do the first one with out assistance. I had graded their paper and either marked it correct or wrong without instructions. The students were allowed to make any corrections they needed to. Most of the students took advantage of this opportunity.

test corrections

When I had returned the test for corrections I did announce for them to remember to simplify your fractions before using your exponents. Several students understood and made the corrections.


The first student had done exceptionally well on her final assessment. She had only missed one problem and was only able to redo the problem half way through before making an error.  She received almost full credit for this work.

When she did her correction she just didn’t simplify her fraction before using the exponent. This is her only error on the final assessment. SUCCESS!

This is the same error as the others. This is an algebra problem and it seems to be the concept that is a bit of a stretch for these students. This reminds me that it is a sign of being in the right place. The students are still challenged and are rising to meet the challenge.

Overall, I am very proud how hard the students worked at conquering this concept.  The start of the unit they weren’t writing in the mathematical language and by the end of the unit they were not just writing in the language, but the 80-95% of the answer were correct at the algebra level.  They rose above the level expected of them and yet when I raise the standard they almost conquered it. In my lesson plans I will expand the lesson to algebra standards and will emphasize simplifying fractions that don’t divide out. I will have more instruction and practice on switching between the two different types of fractions (one simplifies and the other divides out). The Math Antic videos do a great job with pre-algebra order of operations these videos gave us a great launch into the unit.

In the beginning of the unit I had the students play “Rags to Riches” (Who wants to be a millionaire?) game show where they had to complete Order of Operation problems correctly and try to win a million dollars. The students loved trying to win the money. They worked hard to win and were very proud when they did. One of the girls said she went home and played until she won. This game provided great extra practice. This worked well the first three days then I didn’t have time to create new games to coincide with their work for the next days to come. The assessing their work had taken more time than I expected. Time well spent on analysis so I will slowly add to “Rags to Riches” games at a higher level as I teach this unit next time.

At the first part of the unit the students were in groups to help each other with the problems. I eventually was able to stagger their work where they sat in groups but they were busy making their own corrections which made them work at their own pace. This gave me time to work with each student individually, where I could analyze their work and discuss it with them.

The extent of assessing the data of the students’ work and test is not normally done in my classroom practices. I do this normally with the assessments to see what I need to continue to teach, but to do it with the assignments help to bring more students to a higher level of success. I will have to shorten assignments in my classes to make this possible. I am impressed with the success of the students and I believe they are too. This lesson, with all the modifications, has been very successful.


Week 12 Reflection

The students seem so mature this time of year and they walk in and are ready to deal with whatever task is put before them. I know they don’t always understand and need more help then they ask so I have to pry my way in. Overall they are doing well for pre-algebra. The are touching just enough algebra to make next year easier.

My linchpin for my unit was students’ writing in the mathematical language. They seem to have embraced the idea and used it for their benefit. I had two students that continued to struggle with writing and it would mess up their work. I had another student that does well at “Order of operations” and yet does a careless version of the language. They don’t carry everything to the next line and yet remembers what was left behind and comes to the right answer. Yet, I had two students that I was very concerned about in the beginning of the unit and they have conquered writing in the mathematical language with minimal error. I believe the “Math Hygiene” video made a huge impact in their thinking and it cleaned up their mathematical thinking. It made it easier to read the next step in the problem and they were almost flawless.

Twitter was interesting. I like leading with the questions.  It requires me to focus early on the essential questions.  With three of us asking questions made it a little bit challenging to come up with unique questions.

Sara, too, is having trouble with attendance. It seems that it is always a hold up on education. I see the purpose of extracurricular activities, but education sure pays a toll for the events. I’m amazed at the journaling that Amy does. My journaling is a little different. I wrote on the students worksheet and stapled their work together so I can see individual progress.

Essential question: What evidence am I collecting for my final project – and for what purpose?

Week Twelve 


My evidence that I am collecting for my final project is the work of the students. I have collected them and kept them in order so I can see the progress of the students. I can evaluate their work and pick out the errors that I need to correct and watch for those errors to be corrected. I had noticed that the students were correcting their errors before I could catch them due to the Pizzazz assignment have the answers on the paper. I realized that I needed to allow the students to make the errors so I can see them. I created worksheets with the answers and it provided work space for the students to write in the language to reduce errors.  When I would grade their papers I would use it as a teaching point to help them to write in the mathematical language so they wouldn’t make errors or I would help them to see the error they needed to correct. If time didn’t allow me to have individually talk with the student they would have to read their mathematical writing and recognize the colored marker emphasizing the step that needed to be done, that wasn’t done in the correct order. The assignments were collected daily and immediately graded by me and returned to the student for corrections. This was exhausting to me, but it allowed more individual mentoring. Most of the students embraced the change and appreciated the insight to the “Order of Operations”. I did have two students that resented receiving their work back. They just wanted the task done. Due to the quick turn around of the assignment for immediate feedback most of the assignments were turned in daily.

On Monday, we reviewed the higher-level problems. This allowed me to give instructions again that pertained to grouping symbols and exponents. We continued our pattern of turning in the work to be graded and returned for corrections. Students did well at working through the problems that were difficult.

On Tuesday, we took our final assessment. Students we spread out to their own table with binders up to block the view among students. They work diligently and turned in their work. After grading their assignments I only marked c for correct and / for incorrect. I gave no hint to how to correct their error.  This final assessment was not the same as the pre-test.  The students had exceeded my expectations and so I moved to a high level of performance.  These are pre-algebra students and I moved on to algebra level work for them.

On Wednesday, I returned their assessment for any corrections that needed to be made. I enjoyed watching the student strut back to my desk after making a couple of corrections. You could see how proud they were of how well they performed. I had one student fear his test and was quite pleased that he didn’t do as bad as he thought. I had another boy refuse to make any corrections. He didn’t like his papers returned either. We offer him help, but he gets in a mood that requires time to accept the task he doesn’t want to do. To my dismay he didn’t make any corrections on his final assessment.  He did exceed the pre-algebra level of work, but did struggle some with the algebra level of work.  This will be taken into consideration in their grades.

Reflection Week 11

On day four of my lesson I had to add a scaffolding strategy of grading the students papers for immediate feedback. This was a little stressful, but I learned a lot more of their struggles and how to help them. (My struggle this week was being homesick with a headache.) I couldn’t be there for the lesson and implemented my grading their papers when I returned. It helped me to catch up with where the students were at in their progress of Order of Operations. This scaffolding helped me to see where each student was at and gave me a moment with each student for individualized instruction. I also received feedback from the students. They appreciated the individual feedback that emphasized the language and required the students to read their answer, see where they went wrong (marked in color by me) and they could continue the problem to the end. This worked great with most students. I had one student refuse to correct some of the problems that they needed to fix. I know to watch for this from her and we will sit and walk through the problems on our next round. Overall, or the majority of the class the extra scaffolding worked wonders for both the students and I.

The twitter session always awaken our focus of the week. This makes writing easier when the twitter session breaks down points and I get to hear what others are experiencing. I do struggle with the limitation of characters that we get to write with, so I spend too much time trying to limit my words to get my point across.

I suggested to Sara that a pre-test might have caught the lack of knowledge on the students’ part.   I suggested videos from Math Antics to Amy. I think Amy is doing a great job and I just shared a strategy that works well for me. I loved Larissa’s honesty in recognizing that her students needed to know ahead of time what to focus on.

Essential question: What are my challenges and successes in implementing my unit?

Week 11

I started my lesson late last week and we worked through this week. We will finish the middle of next week. We started with Pizzazz worksheet that provide the answer for immediate feedback. If the students can’t find their answer they know something went wrong somewhere. This made it hard to find errors made by the students. They would erase and fix their error before I could see what the error was. This isn’t a bad-thing it just made me work harder in trying to evaluate their work.

The students have been troopers. They show interest in the videos on how to do “order of operations” and “math hygiene”.   These videos were entertaining and repeat the concepts in a way that kept you focused. The students love the immediate feedback. It encouraged them to continue and finish their work. The students transitioned to the computer game as if on a mission. They seemed to like the variety of learning that was offered to them.

In the middle of the week I had one of the assignment done on their own without help from their peers or teacher. It was still a Pizzaz worksheet that had the answers on the paper that answered a pun joke. The students had almost perfect papers. I didn’t see much on the written language and this persuaded me to move to no answers on the papers. We had not covered exponents yet and I wanted to check on them before implementing the exponents into our “order”.

I had to change my worksheets to where the students didn’t have the answers and had to  complete the assignment and I would immediately grade it, evaluate the errors that were made. I would put a large C on the correct ones and use a marker to show the Order of Operation that needed to be done and wasn’t in the proper order. I would return the paper and give the student an opportunity to correct their error. This made it easier to catch errors, emphasize the purpose of the written language and see if they could read the language by fixing the error. I will continue to assess the errors to see if there is consistently the same error among the students or individual student. Let the fun begin. Data time.


Marcy, S., Marcy, J., (1996) Algebra Pizzazz. Wright GroupIMcGraw-Hill One Prudential Plaza

WEEK Ten Reflection

I think this was the scariest week for writing. This week was fun to read through the lessons that were written by my peers. It was very enlightening to see the different approaches to teaching/learning.

I really liked Sara’s idea of calculating the cost of material in her lesson (day 4). This I could use in my units that I create. I would change it a little and have them purchase a box, because the store doesn’t sell one at a time and see how much excess that companies have to purchase in order to build in Alaska. Just a different twist for a higher-level class.

The next lesson that I read through was Amy’s on fractions. I like how she implemented journaling through out the lesson. She did well on add a variety of opportunities for students to respond to the concept. She had them writing, talking and working through the concept. I thought she did well in keeping the student moving through a variety of ways of thinking and implementing their thoughts. Amy had connected her technology standards to her lesson, I didn’t remember to add this to mine.

I found Larissa’s lesson the ecosystems fascinating. I liked the variety of technology and opportunities that she offered for her students to grasp the concept. She also add in technology to her standards, I’ll have to add that to mine.

Twitter chats have been helpful by hearing how other people interpret what things mean. Life got the best of me this week and to top it off it was parent/teacher conference week. It was a great to read the lessons; it took some time due to the variety types of lessons written and trying to analyze the lesson (and sharing with my peers). Therefore, I spaced the reflection blog this week.   I was confused with the writing with the unit and the reflection.