Clearing Fractions from Equations Notes

When I jumped into blogging and the world of Twitter at the beginning of this school year, I couldn't imagine how much these two outlets would help me grow.  I love learning from other teachers' experiences, and I love being able to share my resources with other teachers as well.  As I find myself feeling too busy to blog some days (or, let's be real, some weeks...okay, maybe months...), #teach180 reminds me that while reflecting on lessons and my teaching practices is helpful for me, sometimes simply sharing my daily resources (and using resources and activities that other teachers have shared) can be even more beneficial to the community as a whole.

With that said, today I am sharing notes that I used with my students in our multi-step equations unit.  I don't have much to say about these notes other than feel free to use them if you teach students how to solve equations containing fractions by clearing the fractions and solving an equivalent equation with integers.  The notes are available to download as a PDF or an editable Publisher file.

Additionally, I'm sharing this homework assignment that I used with students before we completed the notes above.  This assignment was used to prepare them for clearing fractions from equations.  It gives students a chance to find the LCM and LCD, multiply fractions by whole numbers, and use the distributive property with fractions.

View/Download: Clearing Fractions from Equations Notes and Preparing for Clearing Fractions Assignment

First 1000 Digits of Pi Posters

Earlier this month I put up these digits of pi posters in the hallway outside my classroom.

They sparked a lot of great questions and conversations with my students, other students, and other teachers in the building.  I blogged about some of these conversations here.

In case anyone may be interested, I thought I'd share the file I used.  To create the posters, all I did was google the first 1,000 digits of pi, which I copied and pasted into a Word document.  I enlarged them until each digit filled a page and I added the ellipsis at the end of the document.

After determining that I could fit a 7 by 14 array of digits on the wall, I needed to print the first 97 pages of the document, plus page 1,003 for the ellipsis.  I knew that I wanted each digit to be a different color, so I arranged my colored paper on the floor like this.

I used my Word document of poster pages to determine the pattern of numbers where I would stop - so I looked at pages 93-97 to know that I was ending with the digits 3, 4, 2, 1, 1.  Then I went back to the webpage showing the digits of pi (rather than clicking through each page of my document) to start arranging the colored papers in order.  I inserted white pages for the decimal point and the ellipsis.  By having the colored paper in order of the digits of pi, I was able to simply put that stack of paper in the printer and print pages 1-97 and page 1,003 of my document.

Here are a few more printing tips:

• Make sure you're set to print single-sided.
• Print a custom selection of pages using the hyphen to include the pages of digits you want to print and a comma to also list the ellipsis page (p. 1003).
• Be sure that you know if your printer starts printing with the first page of a selection and prints forward through the selection or if your printer starts with the last page of a selection and moves backward through the selection (if you don't know, print a short selection on scrap paper to find out).

You'll need the free font Comic Zine for the Word document to display correctly (or feel free to change the font to something else - you may also have to adjust the page margins and font size if you do that).

View/Download: First 1000 Digits of Pi Posters

Good Things

I feel like I've had a lot of negative posts lately.  And if I haven't, that's just because I wrote them and didn't publish them.  Maybe it's just that time of year, but I'm ready for a change!

This was our first week back after February vacation.  I was feeling very refreshed after the week off and I made a few changes to the room, including putting up these digits of pi posters in the hall outside my classroom.  And the comments I've been hearing from students this week really just bring a smile to my face each day.

The first day the posters went up, a lot of students just mentioned how colorful it was.  A few wondered how many numbers were up there and I listened as one student said she would count them all and another said he was going to count "across and down, then multiply."  That was a conversation I didn't expect to hear as it was not related to pi itself, but it was neat to hear their different strategies.

Then I had seven or eight students standing outside my room after school when I came back up to my classroom from outside duty.  Some of the students I didn't even know because they aren't on my team, but they were all talking about the numbers.  And they had so many questions for me when I got there!

They knew the numbers were the digits of pi, but that was about it.  They asked what pi is, how and why it never ends, if there are other numbers like pi that never end, how pi was discovered, if pi ever repeats.  We talked about how pi might be a "long" number, but it's not really a big number - it's only between 3 and 4.  It was so cool to have those conversations with some of my students, but also with students I don't even know (and some of whom I only know of because they're in trouble a lot, but here they were after school, talking about math with me and other kids!).

Feeling so refreshed helped me to pick out the positive in some of the other things that happened this week.  We had one and a half snow days.  I am so sick of snow and at this point we've had so many that we have to make them up at the end of the year, but it makes that transition back to work from a vacation week a little bit easier when it's not a full week.

I had my formal observation this week.  Every year I've finished my formal observation feeling like it went well.  This year I really didn't have that feeling, but I realized after some reflection that I think it was the type of lesson that I picked this year.  Students were engaged and working hard all class.  It was a productive struggle, but it wasn't resolved until the next day in class, which my principal did not get to see.  So while I'm not sure how my observation went, the full lesson itself over the course of two and half days did feel worthwhile and really challenged my students.

I also got news this week that my principal is thinking of moving me to a sixth grade team next year when one of our teachers retires.  I have such mixed feelings about this because while change excites me, I really love where I am.  I love my team, I love my students at this age, I love the eighth grade curriculum.  And I always figured if I was going to teach, it would be high school.  I started out in a 7th/8th grade split position and have moved my way up to full eighth grade.  I want to keep moving up to high school, not down to sixth grade!  But the idea of catching kids earlier, when they're still more curious and hopefully don't hate math yet, is intriguing.  Nothing's been decided and I don't know that I have much say in the matter, but if anyone has feedback on teaching sixth grade, I'd love to hear it!

Teacher Report Card Part 3 - Analysis & Interpretation

Yesterday I blogged about the results of the Teacher Report Card survey (modeled after this one from Mr. Vaudrey) I gave my students.  You can view the results here and the original blog post here.  Now I want to dig deeper into some of the trends I noticed.

But first I want to say that I know this survey is not the end-all be-all.  I like assigning numbers to things and comparing them and so I've spent a bit of time analyzing my students' responses.  But I know that some students gave me high ratings just because they like me, the same as how some students may have given me low ratings just because they always get in trouble in my class and they don't like me.  Only about half of all my students chose to participate in this survey, so we could also be talking about participation bias here.  I am attempting to quantify things that are, to some extent, subjective.  How do my students perceive me?

AREAS OF STRENGTH:

I dress professionally.

Ms. Ess...

Period C

Period FG

Period J

Average

... dresses professionally.

94.67%

95.00%

86.67%

92.11%

I'm not sure what happens at the end of the day here!  I kind of wonder if it's just student opinion or if maybe by the end of the day my hair is sloppier and my clothes appear wrinkled and more worn.  I'm not really concerned, just amused!

I respect each student.

Ms. Ess...

Period C

Period FG

Period J

Average

...respects each student.

91.25%

95.00%

86.67%

90.97%

I needed this confirmation from students.  I do feel as though I respect each student.  I try to model this respect for others so that my students will also treat each other with respect.  My toughest class gave me the lowest rating.  I need to stop thinking of them and referring to them as my "toughest class."  Whether or not I am actually treating them differently than other classes, they perceive it that way.

AREAS OF WEAKNESS:

I need to keep the class under control without being too tough.

Ms. Ess...

Period C

Period FG

Period J

Average

... keeps the class under control without being too tough.

69.33%

53.75%

72.73%

65.27%

The fact that this is an area in need of improvement is no shock to me.  What does surprise me is that the class that feels most out of control to me gave me the highest rating.  As I try to make sense of this, I am realizing that behaviors in that class are usually so extreme that I need to send students to the office.  In other classes, I tend to tolerate minor behaviors for too long.  Disruptive behaviors are disruptive no matter how minor or major they are.  I need to stop tolerating behaviors that impede learning.

THINGS THAT IMPROVE AS THE DAY GOES ON:

I encourage more questions.

Ms. Ess...

Period C

Period FG

Period J

Average

...encourages questions.

85.33%

88.75%

90.00%

88.03%

This makes sense to me because I have heard the questions and comments made by students in earlier classes and I take more time to encourage discussion.

I listen to students' ideas more often.

Ms. Ess...

Period C

Period FG

Period J

Average

...listens to our ideas.

85.33%

87.50%

90.00%

87.61%

I think at the start of the day I am more focused on pushing through the lesson, and as the day goes on I lay off that a little and I do take more time to listen to my students.  I rarely have a class not get through a lesson and fall behind, and when it happens I have never attributed that to "wasting time entertaining students' ideas."  It is important to me that students feel as though I really listen to them.

I use language students can understand and I say my words more clearly.

Ms. Ess...

Period C

Period FG

Period J

Average

... uses language that we can understand.

81.25%

84.00%

91.67%

85.64%

...says her words clearly.

76.25%

80.00%

91.67%

82.64%

This makes sense to me.  After presenting the same information three times, I should hope that I've figured out a better way to say it!  Also, that seems to be a pretty significant difference between my first class of the day and my last.  I know what I'm talking about, but I should really start practicing how I'm going to say it to better communicate with my first class.

I praise good behavior more often.

Ms. Ess...

Period C

Period FG

Period J

Average

...praises good behavior.

78.75%

82.67%

95.00%

85.47%

The last class of the day is my toughest behavior-wise, and I do make a conscious effort to tell students in that class when I'm proud of how they're acting.  I should really make that a conscious effort in every class.

I give fair punishments.

Ms. Ess...

Period C

Period FG

Period J

Average

... gives fair punishments.

73.33%

75.00%

76.67%

75%

This is an area I need to work on across the board.  I tend to have more behavior issues in my last class and so, more consequences, and I wonder if my students interpreted this question as rating the fairness of my punishments or the giving of punishments at all.

THINGS THAT DECLINE AS THE DAY GOES ON:

I seem to enjoy teaching less.

Ms. Ess...

Period C

Period FG

Period J

Average

... seems to enjoy teaching.

92.00%

88.00%

81.67%

87.22%

I get tired as the day goes on, just like my students.  I need to do a better job of not carrying over the frustrations from previous classes into the next ones.  I need to find a way to still feel fresh at the start of each class.

I answer questions less completely.

Ms. Ess...

Period C

Period FG

Period J

Average

...answers questions completely.

82.50%

80.00%

76.67%

79.72%

I do feel like I struggle with this.  Sometimes I forget that a question sounds familiar because I answered it in the last class.  The students in my current class still need a complete explanation.

I tell students their learning goals less often.

Ms. Ess...

Period C

Period FG

Period J

Average

... tells us our learning goals.

77.33%

75.00%

71.67%

74.67%

Overall this is another area in which I could definitely grow.  In fact, I was surprised that my students didn't all give me 1s and 2s here.  I guess they really do read the agenda on the board, even when I don't talk about it!

THE MOST CONSISTENT THINGS AMONG ALL CLASSES:

I give quizzes/tests that reflect the material in the unit.

Ms. Ess...

Period C

Period FG

Period J

Average

...gives quizzes/tests that reflect the material in the unit.

90.67%

90.00%

91.67%

90.78%

I would expect to see consistency here as all classes take the same quizzes/tests.  We no longer have common assessments among all the middle schools in the district which means I write my own quizzes and tests.  

I treat students as individuals.

Ms. Ess...

Period C

Period FG

Period J

Average

... treats me as an individual.

82.50%

83.75%

81.67%

82.64%

This is another one where I would hope to see consistency among all classes.  It is so important to find the balance between treating students the same while also recognizing their individuality.

My students also answered some open response questions.  Full responses can be viewed here, but common themes included:

• needing to be more strict/being too nice - one student even referred to her class as "a zoo"
• students recognizing my stress - when I freak out, stutter, or "have moments"
• seating - wanting to choose their own seats and rearrange the room
• gratitude - for listening to them and being involved in their lives

One of my biggest takeaways from all this is that when I make a conscious effort to do something, I'm usually pretty successful.  When I really focused on praising good behavior in one class, my students recognized that.  When I model good behavior and respect for everyone, my students feel respected.  When I work hard to write fair assessments, my students find them to be reflective of the unit.  I need to make a conscious, full-hearted effort to be more consistent with behavioral expectations in my classroom.  But that is a post for another day!

Teacher Report Card Part 2 - Results

Earlier this year I blogged about the Teacher Report Card I gave my students and some of the preliminary feedback.  Here are the final results from my eighth grade math students.  I did not use the teacher report card with my functional math students.

Participation:

This survey was sent to students as a Google form.  Students were told that the survey was anonymous (unless of course they wrote their name in one of the responses - I was surprised that several students did that).  I knew how many students in each class period took the survey, but not which students.  About half of all my students participated.

Period C: 16/28 students

Period FG: 16/29 students

Period J: 12/28 students 

The first part of the report card survey asked students to rate the truth about statements related to my teaching.  Students used ratings from 1 to 5: 1 being Not At All True and 5 being Definitely True.  Statements included things like, "I think Ms. Ess encourages questions" or "I think Ms. Ess gives quizzes/tests that reflect the material in the unit" or "I think Ms. Ess cares about me."  I used and modified the Teacher Report Card that Mr. Vaudrey tweeted about here.  For the full list of statements I used, keep scrolling to the table below.

Overall, about 75% of each class gave me 4s and 5s (those are the good ones!).  The next graph breaks down student responses by statement, rather than overall class summaries.

The table below shows the ratings as percentages.  Now these are a tiny bit inflated because I can't actually earn 0% with this scale (5/5 is 100% and 1/5 is 20%).  Nevertheless, it is fairly representative of the actual results and much easier than trying to modify the scale now that responses are in.  In the future, I might change the rating scale to 0 to 4.  Or maybe even use the SBG scale we use for grading quizzes...!  In which case I probably would not display the results as percentages.  I'm turning into my students who desperately want the percentage written at the top of their quiz!  Old habits die hard, right?  I digress...

Ms. Ess...	Period C	Period FG	Period J	Average
... dresses professionally.	94.67%	95.00%	86.67%	92.11%
...respects each student.	91.25%	95.00%	86.67%	90.97%
...gives quizzes/tests that reflect the material in the unit.	90.67%	90.00%	91.67%	90.78%
...encourages questions.	85.33%	88.75%	90.00%	88.03%
...listens to our ideas.	85.33%	87.50%	90.00%	87.61%
... seems to enjoy teaching.	92.00%	88.00%	81.67%	87.22%
... uses language that we can understand.	81.25%	84.00%	91.67%	85.64%
...praises good behavior.	78.75%	82.67%	95.00%	85.47%
... provides time for review of material.	86.67%	81.25%	88.33%	85.42%
... tries to see the student's point of view.	87.50%	87.50%	78.33%	84.44%
...praises good work.	82.67%	81.25%	86.67%	83.53%
... treats me as an individual.	82.50%	83.75%	81.67%	82.64%
...says her words clearly.	76.25%	80.00%	91.67%	82.64%
...grades fairly.	85.33%	73.75%	88.33%	82.47%
... gives good, fair assignments.	81.43%	76.25%	89.09%	82.26%
...leads good class discussions.	81.33%	85.33%	80.00%	82.22%
...encourages me to be responsible.	76.25%	85.00%	83.33%	81.53%
... tries new teaching methods.	86.67%	73.75%	81.67%	80.70%
...gives enough time for assignments.	81.33%	76.25%	83.33%	80.30%
...answers questions completely.	82.50%	80.00%	76.67%	79.72%
... makes me feel important.	75.00%	83.75%	80.00%	79.58%
...encourages different opinions.	81.33%	76.25%	78.33%	78.64%
... does a good job of treating all students the same.	86.25%	72.50%	75.00%	77.92%
...has interesting lessons.	76.00%	72.50%	81.67%	76.72%
... has a great sense of humor.	66.25%	85.00%	78.33%	76.53%
... cares about me.	76.25%	80.00%	73.33%	76.53%
...has a good pace (not too fast or too slow).	78.67%	68.75%	81.67%	76.36%
... explains topics clearly.	73.75%	77.50%	76.67%	75.97%
... gives fair punishments.	73.33%	75.00%	76.67%	75%
... tells us our learning goals.	77.33%	75.00%	71.67%	74.67%
... keeps the class under control without being too tough.	69.33%	53.75%	72.73%	65.27%

The second part of the report card survey was open response.  Here are the questions.  Again, I added to Mr. Vaudrey's original Teacher Report Card and included the Keep, Change, Start, Stop reflection questions from Sarah Carter.

If you're interested, you can view a table of all student responses here.

This post has been rather long and it took a lot of formatting for me to show responses here.  With that said, I'll save my analysis and interpretation of these results for another day when my mind is fresher.  Stay tuned!