What about those SMPs?

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About a month ago my teaching team was asked by administration to map out our new sixth grade unit assessments.  By mapping, I mean that we had to review the questions on the tests and determine if the question was was multiple choice, short answer, essay or a performance assessment.  We then wrote what type of objective was present, the domain for learning, and the DOK level.

This mapping took a long time and the entire team was knee-deep in our teacher guides. It was a productive session, but we all needed some more caffeine afterwards.  While reviewing the assessments, we noticed how the guides emphasized the standards and the Standards for Mathematical Practices.  Both were given somewhat equal allocated text boxes in the guides.  Both seemed to be highly valued by the publisher and our district math coaches.  While the team was matching up questions and standards, I noticed that the SMPs weren’t getting any love.  They sat there unhighlighted and under appreciated. This had me internally asking questions about how teachers actually incorporate and communicate the SMPs.  So I went to visit the #Mtbos community and came across a Tweet by @cmmteach.

I completely understand that the standards are important, but what about the SMPs?  These practices are part of our lessons, but I’m wondering how teachers address that importance.  I asked a bunch of teachers this same question (I think they’re tired of me talking about it) and I generally get the same generic response.  That response generally is, “I know what they are and they are part of the lessons” or “I sometimes mention them when moments come up to use them.”  I see the SMPs briefly reviewed during math pd opportunities.  I also observe posters of the practices hanging in the classrooms around schools.  I even think there’s a Jedi one roaming the Internet as I’m writing this.  I wonder how often they’re referred to and what students think of them.  A few years ago I even had my students personalize the SMPs, but haven’t revisited them in as much detail since them.  Are they really engrained as part of the daily math lessons or do they need to be outright communicated.  Maybe there isn’t a right answer here.

I’m curious to how other educators communicate the SMPs.  What’s your favorite strategy or technique?

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Reflection and Math Goals

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Two of my classes took assessments this week.  These are considered unit assessments and are related to math skills that the class has been working on over the past 1-2 months.  My fourth grade class just finished up a fraction unit, while fifth graders ended a unit on equations. I tend to grade the tests and then pass them back in the next day or two.  Seeing that it takes so much class time to give these tests (and the grading) I want students to be able to use these assessments.  By using them, I mean that students should be able to look at them with formative lens and purposefully reflect on the results.  Usually the assessment process looks like this:

Stage 1

  • Assessments are passed back to students
  • Students review their score and are excited or disappointed
  • Students try to figure out how everyone else did

Stage 2

  • Teacher reviews the assessment solutions with the class
  • Students ask questions about why or maybe how they can get additional credit
  • Students see where fixable mistakes exist

Stage 3

  • Students receive their math journals
  • Students fill out a reflection sheet looking at skill strengths and areas to improve
  • Students indicate the most memorable activity and why
  • The teacher and student meet and sign-off on the test analysis and reflection portion

 

Okay, so stages 1-3 have been happening in my classroom for the past seven or so years.  It’s become part of my classroom’s math routine.  I see benefits in having students reflect on their progress on assessments, but I also want students to look at an assessment beyond the grade itself.  I’ve blogged about this evolution before. I stopped putting actual letter grades on assessments because of this.  I also considered taking off the point totals as well, but ended up keeping them since it was on the grade report anyway.

I see value in the student reflection component.  I believe students feel empowered when they’re given more control, choice, and access in the classroom.  This year I’ve added my own stage 4.  I’ve added this for a couple different reasons.  One, I’ve noticed that students that don’t necessarily meet their own expectations are really hard on themselves.  They often react negatively on the reflection component and I don’t want students to feel worse after reflecting on their performance.  I want this to be a valuable experience and growth opportunity.  Two, my students have kept their math journal for multiple years.  Some of them are jam packed with notes, reflections, and foldables.  You’d be surprised at how much is in some of these journals.  One thing that students continually tell me is that they love going back in their journal and looking at what they completed over the past few years.  They see that their mathematical writing has changed as well as the concepts that they’ve encountered.  It’s similar to a math yearbook to many of my students.  My third reason is that I’ve always been interested in how students perceive themselves as math students.  Over the years, I’ve emphasized that creating an individual math identity is important. I emphasize this at my school’s back to school session. This math identity shouldn’t come from a parent, but instilled within.  Being able to see students for multiple years allows me more of an opportunity to do this.  Also,  I’m excited to share this at NCTM and learn with other educators about the goal setting and monitoring process. This has been an area of growth for me as I’m continually refining the student math reflection process.

So, here’s stage four:

Stage 4

  • Students review and rate their perceived effort level and attention to detail
  • Students provide an example of where their effort level increased
  • Students create a math goal that will be achieved by the end of the year
  • Student indicate how they know that the goal will be met
  • The teacher and student sign-off on the reflection sheet

 


 

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Don’t get me wrong, this type of reflection is time consuming.  Whenever I discuss this process with other teachers I get quite a few questions about how to find the time.   Meeting 1:1 with kids to discuss their goal takes time and usually the other students are in stations or working on something independently. I can usually finish up meeting with the kids over 1-2 classes.  Instruction still occurs during this time, it’s just not a whole-group model.

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I’ve attempted many strategies to move kids away from comparing their score with others.  One strategy that seemed to work well was to have students go to stations and then I passed out the assessments.  I realized later that they just compared the results when they left the classroom.  I want to shift the paradigm to more of an individual growth model.  It’s a challenge.  Through the years, I believe progress has been made in this, but more needs to be done.

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The student math goals are interesting.  I had to have a brief mini lesson on the topic of math goal setting as many students wanted to initially make a goal of “getting everything right on the next test.”  I think many students were more interested in thinking of what their parents wanted and not necessarily a specific goal for themselves. Keep in mind these are 3-5th graders.  After a few different attempts, students started to make goals that were more skill focused.  Some students are now writing goals about “becoming better a dividing fractions”, “divide decimals accurately”, “become better at solving for x with one-step equations.”  While conferring with the kids I’m reminding them that the goals need to be measurable.

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After the assessment students review their math journals and monitor whether they’ve met their goal or not.  If not, they write down why or possibly change their goal.  I’ll then meet with the student and sign-off on the goal.  My next step is to involve parents in the goal and have a more frequent monitoring process.

Investigating Inequalities

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This week one of my classes spent a good amount of time investigating inequalities and absolute value.  Both topics were brand new to students.  I looked around in my math files and decided that there might be a better way to introduce inequalities.  Students are familiar with number lines, math symbols and plotting points.  They weren’t familiar with extending points and graphing inequalities. So, while jumping around Twitter I came across a Tweet talking about a Desmos lesson related to this particular topic.

Desmos

I took a leap and decided to check it out.  You see, I’m a Desmos newbie.  I’ve heard many people within the #msmathchat and #mtbos talk about how it’s such an amazing tool.  I haven’t had a chance to try it out until this week. My school isn’t 1:1 and technology is used from time to time, but less frequently in math classes.  After reviewing the lesson and playing around I dived in and made a commitment to use the activity.  I borrowed Chromebooks from a couple other teachers and had a sample run before starting it up on Tuesday.

Students started off by plotting points on number lines.  They also made predictions of what their peers would place.  During the first day, students made it through almost all of the activity.  Students still had questions and they were answered as I paused the slides (I definitely like the pause function).  Near the end of the lesson I thought students were becoming better at being able to identify inequalities and match them to graphs.

The following day students finished up the activity with a WODB digital board.  It was interesting to hear their responses and reasoning behind them.

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On Thursday, students took their inequalities journey a step forward.  They were asked to complete an Illustrative Mathematics inequality task.  Students were given a situation where they needed to write two inequalities, graph them on separate number lines, and create a description.

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Students worked in stations, but completed each sheet on their own.  The students had some productive discussions during this time.  I have to remember to discuss the positive elements of this with the class after the weekend.  Students had to create a number line and then plot points where necessary.  They had to figure out if a close or open circle was needed and where the overlaps occur.  The only hiccup occurred when discussing the word between.

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Does the word between in this context include 37 and 61, or does it mean that it omits those numbers.  Students went back and forth on this issue and we had a class conversation about that particular topic.  Eventually, the class decided that 37 and 61 were included.  Students turned in the task on Thursday and I returned them back today.  Just a handful of students needed to retake the task, but it was mainly because the directions weren’t fully read or labels were missing.

Today the class explored absolute value and coordinate grids.  A test is scheduled for next Wednesday, but I could probably spend a lot more time on this topic.  The class will briefly investigate absolute deviation on Monday and complete a study guide on Tuesday.

I’ll end this post with a Tweet that made me think a bit about math instruction.

I believe “instructional agility” is necessary and teachers become more aware of this through experience.  Instructional agility can also lend itself to the resources and tools that are used in the classroom.


 

Equations and Rules

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My fifth grade crew is making progress.  Last week we explored equations and learned about the distributive property.  My district has an institute day and MLK day, so it ended up being a three day week for the students.  Over the weekend I came across Greta’s amazing blog and found some great ideas that I could use immediately.  If you haven’t had a chance to check out her blog, stop, and get over there.  I actually used her Desmos activity this morning.

Today was our first day back and equations was on the agenda.  The day started off with a brief review of the distributive property and equations.  We then dove into a different activity related to creating rules for situations.

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The students understood the question and the situation.  A few even commented that this could happen outside of school.  You think?  So, after reading about the situation students moved to the questioning portion.

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From here, students wanted to put together 19 hexagonal tables and count them all up.  Some students started to think out-loud about creating some type of rule so the class didn’t have to connect all of the hexagons together.  After more discussion and many, I mean MANY attempts at creating a rule, we moved back to the drawing board.  Shortly after the attempt session, I brought the class to looking at different strategies.

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I brought out the hexagon pattern blocks and put them together.  The class then filled out the table and graph.  We noticed and wondered about why the graph went up the exact same amount every time, except for the first n.  The class knew that four was an important number as that’s how much the # of guests went up each time.  The trouble came when solving for just n on the table as the rule couldn’t be n + 4.

Students met in groups and discussed the topic of creating a rule for this situation.  They needed the rule for the next groups of questions.

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Some students were successful and came up with a rule that worked.  Many students started to notice that their rules were different.

A few arguments came around this, but what was interesting was that the rules worked.  Students observed that the rules could look different, but simplified, they were the same.

The last part of this task asked students to create an expression to represent the number of tables needed.

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This was more challenging.  Even if students were able to create a rule for the first part, this caused headaches.  Students had to look at the rule that they created and find a way to rearrange it to match a different expression.  Some students were successful with this, others not.  I had all the students turn this sheet in and briefly looked over the results.  I was excited to see that about a quarter of the class had everything correct the first time.  This means that the class will be exploring this topic further as students get a second attempt tomorrow.

A Week of Equation Exploration

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My fifth graders started to explore equations this week.  They’ve created number models and solved for the unknown, but most of their experience has been using one method.  They tend to substitute a number in for x and then check their answers.  If it doesn’t work then they guess a different number.  This guess-and-check type of of strategy has worked well in the past with 1-2 operations and with x on one side of the equation, but this unit that I’m teaching starts moving students towards using a more formal substitution method.

So, in an effort to improve students awareness of equations I decided to use a few specific activities.  My intention was to give students an opportunity to see equations in many different settings.  I started off the week with a few Nearpod review questions related to order of operations.  The class worked in groups of 2-3 to solve the problems.  Students definitely needed a review on this topic because it seems like forever since they’ve completed problems like this.

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The next day students used SolveMe mobiles.  I drew a balance on the board and the class completed a few different examples.   Students worked in groups to find out what each shape represents.  This class used these types of mobiles earlier in the year with a certain degree of success.  This particular math unit will put the reasoning behind these mobiles into a better context.

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How much is the triangle worth?

Students were given homework that night related to equations.  After checking it over I noticed that students needed additional practice with the properties of numbers.  Specifically, students were struggling a bit to identify the correct property.  Students completed a few different problems involved with properties the next morning.

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I reviewed the terms with the class and connected them to what happens when a variable is substituted for a number.  Students were making progress.  They were continuing to use the guess-and-check substitution method and checking their work to see if they’re correct.

Next week, students will start to investigate inequalities.  This is one of my favorite lessons as students observe that there can be multiple answers for an equation.  While some students are  stoked to learn about this, others get confused.  At this point, many students have been conditioned to look at equations as problems that have one solution.  Having multiples solutions, or solutions with a specific range of numbers isn’t usually the norm at the fifth grade level.

While looking for a few new ideas I came across Always, Sometimes, Never.

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I’ve heard of ASN, but haven’t had a chance to try it out in the classroom.  I paired up students and modeled one of the solutions.  Students were off to the races to think about statements and label them as always, sometimes, or never true.  The discussions about numbers were fantastic.  I went to each group and asked questions to help direct students towards possible solutions.  While this was going on I could tell that students continued to have questions.  These questions impacted whether a statement was sometimes, always, or never true.

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The discussion that stemmed from the above questions provided an opportunity for students to discuss their understanding of numbers.  Overall, this discussion, along with the previous activities will help set the stage for students as we continue to discover and solve equations.

Next week, students will  use the distributive property to solve equations.  They will also delve deeper into a study on inequalities and how they’re represented outside of the classroom.

Moving Towards 2018

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It’s the last day of 2017 and I’m in reflection mode.  It’s around two degrees outside right now and I’m planning on staying inside with a warm cup of coffee.  By the time I’m done with this coffee, I’m hoping to have finished up this post.  This is allowing me some time to look at what I can change and keep the same for next year.  It’s been a year of ups and downs and many different commitments along the way.  I’ll be splitting up this post into ideas that I’d like to continue and some possible additions for the new year.

Continue

  • I’d like to keep my arrival and flow chart process in place.  I’ve been using this process with K-5 this year and so far it has been working fairly well.  Over the years I’ve noticed that the first five minutes of class are golden.  Getting the students thinking about math quickly after they enter the room is an important piece and is also helps get the class moving in the right direction from the get-go.
  • Using WODB, Estimation180 and Scholastic math magazines for my bell-ringer work.  I believe these daily tasks are beneficial to students and gets them thinking about math in different ways
  • I’ve used a daily agenda this year.  It’s visible to students as they enter the classroom.  I’ve used a slide made in PowerPoint or Keynote and it includes all the daily activities for the class.  I believe it has eliminated a lot of the “what are we doing today” questions that I’ve heard before.  It doesn’t eliminate all of them, but I’ve noticed a huge reduction. Students can take a brief look and get a general idea of the tasks that are planned out.  I’d say that the class rarely makes it through everything on the agenda, but it helps keep the students (and teacher!) aware of today’s happenings.
  • I want to continue to have a balanced instructional approach in the math classroom.  I tend to use bell-ringers and have certain math routines that stay the same, but changing up the lessons and tasks has benefits.  Designing lessons throughout the week that has students working with partners, group conversations, including technology components, and having whole-class conversations tends to help students encounter math in different ways.  It also adds an unexpected element that students sometimes need at this level.
  • I’ve been using a digital planbook this year.  It’s been a great way to plan out lessons  away from school.  Also, it has helped me leave school at a decent time this year – a struggle many teachers have.  Being able to create the lessons and then copy and paste the lesson into my agenda slides have been an efficient process year.

Changes/Additions

  • I’d like to be more intentional in planning out my math questions during lessons.  Creating questions that are open-ended, yet give students time to truly think about mathematics in multi-faceted ways can be challenging.  Depositing a question in a specific place within a lesson can yield dividends later on in the lesson and throughout the year.
  • I’d like to actually use my planning time for planning purposes.  That sounds odd while I’m writing this down.  Like most teachers, I have a certain amount of time that is deemed for “planning”, but I tend to not use it for that purpose.  Generally I use it to check emails, copy, call parents, or check-in with other teachers.  Ideally, I’d like to use it for planning out or modify my upcoming lessons.  I think this is more of an effort on my part to use this time for actual planning.
  • When planning out my lessons I’d like to add more of a cyclical design.  Lessons are usually designed to meet one specific mastery objective.  This is often required at certain schools/districts and is part of the evaluation. The assessments and tasks are related to that one objective.  I’d like to include more opportunities for students to review past concepts.  This also moves students away from thinking that “fractions are done” since we finished a unit on that particular topic.  Having a revision review is such an important topic and I feel like I could write an entire post on just that topic.   I’m continuing to look for ways to make a 2-3 times a week commitment for this purpose.
  • I’d like to commit to being more aware of what is being taught to students after they move on from my classroom.  It shouldn’t be a mystery to what I’m preparing students for, although there’s sometimes a disconnect between what happens at a 5th grade level and in middle school classrooms.  I’d like to check out how the standards that I teach connect to what students will experience in 7th and 8th grade classrooms.

Side Notes:

  • I’m currently in the process of getting through module 3 of my NBCT certification. Watching yourself teach is a bit cringeworthy, but I’m making progress with the editing.  If everything goes well, I should be getting my credentials next December.  This seems like a long way off and I know that there’s a lot of work that needs to be done before then.  Also, I’m hoping to connect, learn and share with my PLN during the NCTM conference in April.

I’m looking forward to 2018.  See you next year!

Coordinate Grids and Houses

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My fourth graders just ended a unit on decimals and coordinate grids.  The unit lasted about a month and a test is scheduled for next week.  This unit was packed with quite a bit of review, decimal computation and coordinate grids.  Students were able to play Hidden Treasures, use a 1,000 base-ten block (first time they’ve seen this), and create polygons using points.  One of the tasks that stands out to me for this unit involved a coordinate grid problem.  The problem caused the majority of my class to struggle. It was a great learning experience.  Many students thought they knew the answer initially, but then had to retrace their steps.  I modified the questions a bit from the resource that I used in the classroom. Here are the directions:

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So, many students read this and thought twice as wide meaning they’d have to multiple the width by two.  Even without looking at the diagram they assumed that this was going to be a multiplication problem involving two numbers.  Below the directions came the house and grid

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Even after seeing the diagram, students were fairly sure that they just needed to multiply the width (4) by two.  When digging a bit deeper into what they were thinking I found that students were looking at the height where the roof started (0,4).  Many were absolutely certain that 8 was the correct answer.  I had the students think about the direction and discuss in their table groups what strategy and solution makes sense.  Students had about 3-5 minutes to discuss their idea.  Students reread the directions and then started to gravitate their attention to “as it is” high and then started the problem over again.

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As I walked around the room I heard students say:

What is the actual height?

Does the original width matter?

You have to multiply it by three?

What do you have to multiply?

This is confusing.

I’m not sure about this.

Is this a trick question?

I’ve got it!

How do you know?

I thought the conversation that students had was worthwhile.  I probably could’ve spent a good 15-20 minutes on just the conversation. Fortunately, at least one person at each table starting to think that multiplying the x-coordinate by two wouldn’t work.  When I brought the class back together, I started to ask individual students how their thinking has changed.  Some students were still unsure of what to do.  I brought the class back to the directions and then more students started to make connections.  Eventually, one students mentioned that because the height is six, the width has to be double that, which is 12.  Another student mentioned that the x-coordinate needs to be multiplied by three to equal 12.  More students started to nod their heads in agreement.  The class then moved to the next part of the task.

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Students said that we should write down “multiply the width by three.”  I wanted students to be more specific with this, so I asked the students if that meant that you could multiply and part of the width by three.  The students disagreed.  A few students mentioned that you need to multiply four by three and that could be the rule.  Again, I went back to the directions, which asked students to create a rule.  After more discussion, the class decided that you needed to multiply the x-coordinate by 3.   Students were then asked to fill out a table to show what the new drawing would look like.

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Students were drawn to complete the third row above.  That made the most sense to them since the first two started with zero.  Multiplying the x-coordinate by three would create (12,0).  Most kids were on a roll then and were able to fill out the rest of the table.

On Monday the class has a test on this unit.  Even after the test I’m thinking of spending some time reviewing coordinates and having students actually re-create this house on a grid.  I believe it’ll be useful as later in the year students will start to look at transformations.  This may be a good entry point to that topic.

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