There Are Those Days…

There are those days, that no matter what attitude you have, what you have tried, or what skills you employ- that as a teacher you do this.


There are days where I really hate the challenges that come with my particular job.  To get students to believe in themselves and their abilities in math, you have to create a strong rapport with them.  These relationships can’t be built in a day, it takes time- and I am one to support that and typically I use the first two to three weeks for it.  My current position doesn’t provide me with that time, I don’t have a consistent group for a year, a quarter, a month, a week or in some cases a day.

I believe in positive student struggle, and it is weird that @veganmathbeagle made this post- Watching Solitaire in Silence.  Students always tell me I’m a “hard” teacher for the first few weeks.  It is because instead of providing them answers to problems, I ask more questions.  I tell them to try their ideas to see where it takes them, something they do not want to do because they feel it is a waste of time to do something wrong.  They love talking, but hate trying to explain what their thinking is.  These outlooks always change over the course of the year- and I have many students who have told me that math classes after mine were easier.  When I ask them why they tell me it’s because I got them to step outside their comfort zone in math, and that it made them more confident in what they could do.  My high school colleagues told me how much of a difference it made when I was moved to the middle school, and thanked me often for my work.  Those types of compliments are ones I take great pride in.

The problem lies within my current setting.  Every day I could gain or lose 0-6 students.  One Monday when I entered my building, we had 10 new students enrolled.  The time to create strong rapports is strained here, and it took me to the test yesterday.  I have a student who I really enjoy in class.  She has been with me for 3 days now, and although she has been guarded she has done very well in my class.  That came to a head yesterday when she encountered reflections- something that she considers hard.  We talked through an example as a class, where students were describing and presenting to the class what to do when we reflect polygons along the line y=x.  This student understood what to do when we reflect over the X or Y axis but became totally lost with the diagonal reflection.  I didn’t have time to talk with this student at all before the explosion happened.  I am used to outbursts- and typically I have a good feel when they will occur and what I can do to prevent or deescalate them.  The paper was crumpled up, thrown across the room and “I HATE MATH” was screamed.  A body slammed back in a chair, head slammed on her arms on the table.  I had a class of shocked faces looking at me, and I’m sure I had the same startled stare back.

There are options for students who have outbursts, the one our center prefers is the time out room.  This is a small room at the end of the hall where students can go to get themselves back in control.  While I agree that there are situations where this is needed, it typically is because of a different degree of behavioral problem that I implement this option.  This wasn’t that degree, this was frustration of not knowing a concept and being afraid to accept it.  The problem was, the time to build a positive relationship with this student wasn’t there yet, and as such I was ignored and rebuffed when I tried to approach her individually to talk.  Should I have sent her out?  Perhaps.  At the time, other than being a physical distraction with her head on the desk, she was not disrupting learning for my other students.  She was still in the room, listening to the conversations- and ultimately learning.  I will choose this option every time (even though my Administrator disagrees).

She came up to me the next day and talked with me.  She apologized about what happened and confirmed my suspicions about what was going on.  She also thanked me for not taking her out of class- even though she was trying to get booted at the time.  Out of the bad comes good.  That day is the day I made a positive connection with her.  Now I can start to build her confidence in herself and change the way she approaches math class.  If only I could show these kids the end of the tunnel first so they didn’t feel they had to react in the ways they do- if only there weren’t these days.

The Guitar Class: MAPs Activity- Cutting out what you don’t need

Once again I am using the Shell Center resources for class, this time looking at Modeling Situations with Linear Equations.  Once again, I am looking at the student handout and although it is designed as a pre-assessment, I am wondering why they are supplying students with so much information- time to get the scissors out….

The Guitar Class:

To be totally honest here, I’m scrapping pretty much the whole handout and start from scratch, here is what I will show students.

Guitar Student Handout

Students should come up with ideas about rent, how many students are in the class, and how much each student should pay for the class.  They should also sketch a graph starting at a negative balance (showing the rent for the space) and increasing with each student enrolled.  I will then ask them to write down answers to the following questions on their paper:

Teacher Questions:

What values for each factor did you assign?

How did that determine where to start your graph?

How did that effect your Axes? How did it effect your scale?

What do you notice about your graph?  (hopefully they say 2 things, it’s increasing at a steady rate per student, and that is crosses the X axis)

Students will have a varied set of values for each factor, and that is OK, their graphs will all have the same general look, and they should recognize that where it crosses the X axis is where the music teacher breaks even for cost.  I don’t want to give away anything with this question, it provides a great platform for students to provide ideas and values, as well as creating their own ideas on how to graph the scenario.  Looking at each individual’s work will give me instant information on how much the student comprehends the material and what I need to address.

As students are done with their graphs and our group discussion is when I would put back in the original scenario from their handout:

Guitar Class

I do not think I will ask students to write an equation right away, giving students the proposed values instead. I would then ask these questions for students to answer on their paper:

Teacher Questions:

What is the situation the music teacher faces? (using these values)

What is the teacher’s balance at the beginning of the class?

How does each student effects that balance?

Write an equation representing this situation.

I also would not show them questions 3 or 4, I would instead ask verbally these questions, have students record their thoughts and discuss each one as a whole class at the end of the hour:

Teacher Questions:

How can we determine the teacher’s total cost.  Write that as an equation.

How can we determine the teacher’s total profit?  Write that as an equation.

What factors do we need to consider to determine the cost for each student?  Write that as an equation.

Are there values that are unreasonable to charge students for taking his class?  Explain.

I will be trying this out with my groups tomorrow.  I plan on engaging their creativity and mind- which will produce great ideas to discuss.  I realize that this is a pre-assessment for their unit, but students will provide me with enough information on where their skills lie with my student handout and follow up questions.  I will write a follow-up to see if I “Cut too Much.”

Linear Art Project

This is a fun project that I started doing to support my Art teacher and show students that Algebra can make the most amazing things.

Step 1:

Have students pick out a picture.  This is a great sell to students since they have control over what type of picture, icon, avatar, etc that they use for the project.

This was the example I used, the logo from my college, the Bemidji State University Beaver.

IMAG0600_BURST001Step 2:

Have student create a free hand drawing of the picture.  This allows them to adjust the picture, editing lines and shading that they may not want to show.  It allows them to be creative and adapt the picture for the project.

Here was my free-hand drawing of the Beaver.

IMAG0601Step 3:

Students recreate their free hand sketch on graph paper and using only lines.  They should try to make shapes end on grid points of the paper.  This part can take a while, if students created a large enough free hand sketch, you could allow window tracing to help transfer the image to graph paper.  I have students make 2 copies of the graph image, one they can decorate and one for the next step.

Here is my colored graph paper image.


Step 4:

Have students create an X&Y Axis on their picture.  I allow them to create them wherever they want, and usually they have them right in the center of their drawing.  Depending on the patience level of the students, I have them label points that create their drawing.  There are times I only have them do a set amount (20 or so) and times I have them label each line segment ending.  This is totally up to you.

My XY Axis image:


Step 5:

DESMOS!  Need I say anything more.  I used to have students write the equations of the lines that create their image, but with the totally awesome program DESMOS, I now have students create their image with it.  DESMOS has helped students understand how changing the slope or intercept effects the line, and with the instant drawing of the line when they enter the equation, it allows them to visually see where their line is.  This is a great error check for students, and they accept mistakes more readily than if they are writing equations on paper.

My DESMOS image.

BSU BeaverStep 6: The Finalé

To complete this project, I have students create a collage of their sketches, and a printout of the equations from DESMOS.  I then hang these posters out in the hallway for everyone to enjoy.  This attracts students from all over the building to come check out what kind of cool activities we do in 8th grade.  I am even getting new 8th grade students asking me when we will start this project!

What Matters in My Math Class

1. Be there: I really enjoy all of my students in class (yes, every one).  These past 11 years have really impacted me on the importance of being in class.  I know I plan for every student all the time, and it makes it better if everyone is there, it’s not about me.  Students can’t expect to understand content if they miss too many class periods.  Missing students also impacts the learning of the rest of the class.  Students drive my classes, and having multiple ideas and approaches are critical to class.  I need them there.


It reminds me of an anthropology class I took in college.  I did not show up for class after the first day.  I got the syllabus and went home.  I only showed up for test days.  I ended up getting a B for the class, but to this day I can’t not tell you much about the class.  I filled my short-term memory for the test, but that’s it- it’s short term.  I regret that and sometimes consider retaking the class or at least buying the text again and actually studying the material

2. TRY: I start every year out with this word on my board.  I want students to try.  I tell them some things will be easy, and some hard.  The most important thing is to try something, anything in fact.  The only way to learn is to engage your mind.

7N 3

This is my #1 check-in with students, if they ask for help but have not tried then one of two things happen.  The first is that they report out on the problem to me (which many students do not like to do), the second is that they agree that they will reread the problem and determine what they need to do.  If they get stuck after they have attempted some work, they can ask for help again.  This normally takes students a month to understand and attempt, after that they can explain the problem and what they have attempted before asking for help on the next step.

3. Talk in Class: I expect students to talk.  I expect them to talk a lot.  In order to have rich discussions that will engage their minds, I need to have students communicate mathematics to each other as well as me.  The format of the talking is varied: partner work, small group, large group, presentations and individual check-ins.  This is the one area I push my students the most.


When I tell them I expect them to talk in class, I get a very wild reaction.  Then, when they understand what I mean- the reaction normally shifts 180*.  I do tell them I understand that they will get off task at times, and when I first introduce this type of behavior in my class I tell them that they need to live by the 90% rule.  90% Mathematics, 10% other.  I know conversations will drift, they are only 13, but in the initial weeks I just ask “Are you keeping with the 90 rule?” and they know exactly what I mean and expect.  After the first month the types of conversations they have is truly awesome.  I wish I would take my own advice and start to tape them, I barely keep up with all the great ideas.

4.  Show your work (to help ME understand): I have always said: “Math is Messy!”  I HATE erasers, and regularly stop my students from using them.  I want to see work shown, and it’s not just to make homework longer or to torture them.  Drawing diagrams, taking notes, underlining, sketches, anything and everything is useful.


I was having a conversation with one of my students about a problem (I have conversations, not help sessions or answer confirmations) when I noticed she started to erase her work.  I took the pencil out of her hand (one of the good times teachers take the pencil away) and asked her what she was doing.  She seem surprised but said she had some wrong thinking down and wanted to start over.  I took her paper away, wrote only the problem and asked her what her incorrect thinking was.  She was unable to remember what she had done or what she needed to correct.  I told her that is why I don’t want to see her erase work.  It is the “notes” of solving math, it gives her the outline of what she has done and what she needs to do.  I asked her to show me where she thought she went wrong.  I then asked her to start her new work beside that point but to leave it.  As she started working, she realized that her initial work was right, she just solved the problem in a different way.  Having both solution paths side by side allowed her to compare her methods where she would not have been able to before.

5. Understand you work: “Rules vs Understanding” is my class motto.  I want students to make deep connections to the mathematics they do so they can replicate and refine it.  I want things to make sense so they can tackle problem solving outside of the classroom in everyday situations.  I want students to have such confidence in their knowledge that they can argue with me about problems, that they will take the marker out of my hand, march up to the board and teach- helping the class find a solution.


I had another conversation about a problem with a student and they found an answer, then reflected on that answer and determined it was correct (and could defend that stance).  When I asked them who did the problem, they said that they started it, but needed my help to finish.  I asked them what part of the problem I did, the answer was none.  I asked what answers I gave them, the answer was none again.  I asked them who solved the problem, the answer was that they did it themselves.  The pride in their eyes and tone of voice tell you how powerful that is to students- they start to believe that they can be independent learners.

6. Get a correct answer: Do not get me wrong, having a correct answer IS important in mathematics, it is just not the end-all-be-all of their evaluation and grade.  The process is important, but so is the answer.  I am trying to prepare my students to become responsible adults after school, and if they can’t produce the correct answer then I have failed in that.  How long with they last at a job where they give incorrect change?  How can they be successful small business owners if they do not evaluate sales trends?  How can I expect them to work in research labs if they are not accurate, knowing that the slightest error will nullify their research?


There have been many pushes to just focus on the process and not worry about the outcome.  Let me tell you the secret of that.  If you are REALLY focusing on the process, communicating with students and giving them proper intervention- the correct answers take care of themselves.  Don’t make either part more important, but stress they are equally important.  Reflecting on your work and deciding if you answer is correct only strengthens their understanding.

My plan for next year….

Sorry for the reblogged posts of late.  I am researching what kind of practices I want to incorporate into my classroom for next year and am “compiling” blogs about the pieces I need. 

As I work more and more with my 8th graders, I am of the same mind as Jim Scammell.  The students who are taking homework home and bringing it completed the next day are the ones who are good students and driven by grades.  Those students who truly need the practice leave their materials at school because they either go out and hang with their friends all night, or go home and take care of their siblings because their parents are going out and hanging with their friends all night.  Our district uses a Developmental Design behavioral strategy, and with that is a lesson plan layout of Spark/Lesson/Reflect- which is similar to Jim’s model of class.  I have 60 minute classes so my breakdown is normally 15/30/15 (For 3Acts, my time is typically 15 Act1, 30 Act2, 15 Act3).  During this time, I try to allow for as much in-class work as possible.

With that, formal Direct Instruction has gone out the door for me.  Typically I present student with some type of problem, or more recently a picture or video (in a 3Acts format).  I allow students to work on the problem, walk around and check in on students, and offer quick help.  One thing that my students are not used to when they first enter my class is the type of help I provide them.  I ask questions (normally those I listed in my previous blog), I never give answers and that throws students for a loop.  After a few minutes of good student struggle, I discuss things about the problem as a class.  We list strategies to try, and work through them.  One thing I don’t do during this is erase any strategy, just because it didn’t work the way the class is progressing through this problem doesn’t mean it won’t be helpful in future problems.  We get a problem done, and they are given another that becomes student led.


When that problem is finished, we hit the 30 minutes of practice and this is where I would look at splitting students into either similar solver or mixed skill level groups- depending on what activity I had planned for the day.  This is my time to give differentiated instruction to my similar solver students, and to support student discourse in the mixed level groups, similar to what was posted on the Life of Mrs. Rilley.  Which group students would be placed in would depend on whether it was a discovery day or practice/application day.  I really want to be careful of creating a “tracked” theme with myself or the students as evidenced by Fawn Nguyen.  There will be days where I will utilize both groupings.  When students are discovering or applying mathematical skills I want a mixed group so students approach the problem from all angles.  This also provides the opportunity for a lot of mathematical conversations about what method students should implement and whether their answer is correct.  During practice time I want to correct student mistakes or misconceptions and would provide work appropriate to their challenges with the mathematical concept (group students with a similar misconception, group by a missing skill, group students who have a great handle of the topic and provide them with enrichment activities).  With Ashli’s approach to grading, students would not see this as any type of leveling of “smartness”- and would realize the grouping as a result of need.

After we have the problem worked out, students would get either the big reveal or an exit pass.  When students receive the big reveal they would be expected to discuss the similarities or differences in their work and answer.  Students would show their work (via a doc-cam) and work through how they solved it and what troubles they encountered (if any).  Since I would have them in groups, there would be 4-5 presentations and students would share out reporting duties.  Before students left class in this scenario, they would be expected to complete an exit reflection form- giving me information on how they perceived the activity, what things were good/bad about it, and what they now know and still need help with.  This will help me “tweak” the activity to my student’s needs.

Reflection form

If my class is comprised of practice/application then all I really want to do is give them an Exit Pass that has problems from the practice on it, as well as 3 Reflection questions so that I can better address these problems for the next class period.  The problems on the Exit Pass/Reflection form would be graded in my gradebook, but not for students.  Instead, questions about their work will greet students to create conversations about what they need to correct.

Exit Pass

Using these forms will allow me to differentiate instruction for the next day, which will improve student performance in class.  I am still thinking out formal end-of-unit assessment, but this plan is really taking shape in my mind and I am excited to implement it for the upcoming year.


What is 3/5 Follow Up

One great thing about blogs, you can reflect on what you have done in class, and remind you when you haven’t done a follow up you intended to do.


So, I needed to go back to What is 3/5.  My students had made some good connections during that week and I wanted to see how much of it was retained.  I went with a basic warmup today.


I decided on this because I really want students to expand their thinking past one basic shape for fraction representation.  As I expected however, the first two diagrams students drew were circles and rectangles.  I was pleasantly surprised when one student drew a pentagon.


At first I was worried when I was walking around the room, typical comments on why their figure was 3/5 included “3 out of 5 are shaded.”  I am thinking, WHAT? We covered that fully just a month ago, how could they backtrack again?  My worries were unfounded when for the last explanation students showed me they were indeed thinking of EQUAL parts, not just 3 parts out of 5.  In the first responses it is easier to “explain” that way without fully relating everything.  When I asked students to revise it so that I would know exactly what they were thinking, they came up with what a few students already had (as you can see in the student work photo):

3 out of 5 equal pieces are shaded

I am proud of them for remembering the concept and how to explain it so I could understand their thinking, and told them so.



How many options do I have?

Chris says the following problem has a limited number of solutions:

Directions: Fill in the empty spaces so that you create two distinct parallel lines.  You can use whole numbers 1 through 6, but can only use a number once.

___ x + ___ y = ___

___ x + ___ y = ___

How many solutions does it have?  Provide evidence for your answer.

Is there another way to represent the number of solutions for this problem?

What is a linear function?

So today we are reviewing Linear Functions; and when asked what those are, I get a textbook-like explanation.

“It is where each x only corresponds to one y and graphs a straight line.”  Another student asks, “What does that really mean?  How does it even relate to what I would do when I’m done with school?”

I will post later on how my conversation went, but I’d like to hear your ideas before I give away any secrets.  (For reference, I teach 8th grade students in a public school on the reservation with high poverty rates.)

Conference Seating -3Act Math

ACT 1:

Recently I had to go to a conference and when I walked in, this is what I saw


What questions do you have when you look at this picture?

Ask students to write down their questions, I normally ask students to find at least 3.  When I observe that most students have questions written, I ask them to share those questions with their neighbor.  I then throw up a Microsoft Word document and start typing down questions students supply.  Students from my classroom came up with all sorts of different questions, some we can easily answer and others that we can’t.  I am looking for a key question or questions to start this lesson.  If students do not ask one of these questions, I tell them that I hope I can answer most of the questions provided, but that I need them to consider one of these questions first.

  • How many tables are there?
  • How many people are there?
  • How many people are in a row?
  • How many people can sit at a table?

Any of these type of questions will lead students down the inquiry I hope to explore with them.

There are 512 attendees at this conference, how many tables are needed to seat them all?

How would this change if I needed to seat 900 attendees?


ACT 2:

Linear Equations is the topic I wish to address with my students.  Students will need to think of counting strategies needed to determine the number of people at the conference.  There are many different combinations of ways to figure this number out, but here are the stats:

There are 8 people seated at the head table, but they needed to use 6 tables (extra space was used for the podiums). Otherwise there are 4 sections of tables, 9 rows of tables to a section, 14 people to a row, and the table size is 6′. 

These are hard to identify by the picture so the students really work on the following pieces of information: 6′ tables, 9 rows and 512 attendees.

I also ask students to create an equation for the number of tables that are needed.


ACT 3:

For comfort reasons, 2 people are seated per table.

You will need 7 tables per row.

4 x 9 x 7+ 6 = 258 tables.

Students will typically write this type of equation based on attendees:

512 = 2x + 8

504 = 2x

252 = x

Then I typically ask them how many tables per row, and what type of configurations makes sense for the conference (does one LONG row really work?).



After we decide the general equation for the conference, I then ask the students how many tables are needed for varying amounts of attendees: 200, 900, 1200, 2500.  What type of configurations would work for these new conventions?