Transparent and Organized Math Instruction

A puzzle for my math teaching this year was how to make our learning goals transparent and how to organize class work so that it could be easily coalated into a portfolio at the end of the year.  Then I learned about a resource called Betterlesson.com.  They hire master teachers to submit lessons in a variety of topics.  I liked one teacher’s work in particular, especially the way her lessons featured student notes.

I appreciated the way she focused on her learning goals, both questions and mandated standards.  The “I will be able to” statements allowed students to understand what they were responsible for learning. The “Do Now” offered a way to kick off activities or to do mini-assessments.  The notes can contain information, activities, links, or resources.  It is easy to attach class or homework to them.  
I adapted this model for my own class and felt much more organized this year.  It was easy to integrate essential questions into our every day lessons.  It is also a useful system for differentiation as each student can get an individualized set of activities attached to the notes.   Students continued to need reminders to keep up with the notes and to use the notes to study for tests, but the system was in place for them to do so.  It was also useful during conversations with parents, as my expectations were clearly articulated in the student materials.  Here are some samples:

Cooling It Down

My students would like me to:


For eight weeks we have been having a grand time exploring ancient civilizations, E.B. White, Geography, paragraph writing, sensory details, Chinese language and characters, factors, multiples, variables, and equations.  Specials classes in science, Spanish, art, PE, music, and chorus have been incredibly exciting and wonderful. We just had conferences and many parents talked about how their students are feeling engaged, challenged and resilient.

Which is exactly where we want them.   
But now that they are there, we need to slow down a bit.  
There are a few signs indicating this.  The first is an unfinished project that several children need more time on to finish.  Many children were finished two weeks ago, but a few want to do their most careful and thoughtful work, and we have not had time for them to be as deliberate as they would like.  School should have time for careful work.  
Another sign is a geography writing project that now needs a consistent amount of time allowing for individual conferences and writing instruction.   The part where we teach them all together is ending and the most important part, where students receive assistance and feedback designed just for them, is beginning.  School should have time for differentiation and individual instruction and feedback.  
School should have time and sometimes it feel like there just isn’t time.  But we teachers sometimes make the beds we lie in.  When the signs start appearing, it is time to pull back, stop planning for the “next” thing, and support the thing that is happening right now.  It’s too easy to get caught up in all that is to come, all that we have to do before the end of the year or the start of the break or the date of the test.  The children would like to live in the moment a little to enjoy and remember their work.  It will be nice for us to do that too.  

Reflection: Order of Operations and Geography Stories

So one of the deals with this reflective blog business is that I want to make my practice visible and vulnerable.  Best to start with today.  Beware, extremely detailed lesson talk ahead.

Over the weekend I replanned our geography unit and set up another round of Algebra week for our fourth graders.  These are both units that I have loved teaching because the ideas are accessible at many different levels allowing for much differentiation and the information is useful for a variety of tasks in and out of school. There are a lot of fun activities and what we do now will be helpful later on in their studies.

Today I taught a lesson on the order of operations.  Now this is truly an idea they will explore extensively in 5th and 6th grade so why bother in 4th?  We have a pretty wide range of mathematical abilities, but these beginning algebra lessons have a little something for everyone.  They are learning to reason algebraically, recognize and construct equations,  and apply basic principles such as balancing values and using inverse operations fluidly, while practicing all sorts of basic operations and reviewing their facts.  We talk about working systematically and efficiently.  We talk about challenge as a good thing.  We are previewing material many students find scary in a fun way with little risk.   I don’t expect them to master this material.  We are just playing around with numbers.

Meanwhile we are asking some deep questions such as:

We will try and keep these lines of inquiry open and reflect on them as we review a variety of topics throughout the year.

The goals for the lesson were:

  • To introduce the order of operations
  • To practice writing equations that reflect our thought processes
  • To apply memorized math facts in a novel situation
We started with the equation 18 + 6/3 x 2 and asked them to provide an answer they thought would work.  We received mostly 4 and 16 from the students.  Teachers then threw out 40, 19, and 22.  We discussed why this was happening, tossing around the idea that everyone was starting in their own place and following their own path.  I presented the idea of an order of operations that mathematicians had agreed upon.  Then we played hopscotch and learned a rhyme to go with how we might solve an equation: Parentheses, Exponents, Multiplication or Division Left to Right, Addition or Subtraction Left to Right.

Students then practiced on 3 more equations with partners, looking for the most accurate answer.  They encountered parentheses and exponents and I explained how those worked.  They had questions about how the order of operations might work within a pair of parentheses.  They wondered about whether to do multiplication or division first and I reinforced the idea of them being equal so we just go left to right.  We found instances where the answer wasn’t dependent on the order of operations, but recognized it was important to not assume that would always be the case.  I am leaving the PEMDAS vs. GEMS debate to the middle school and did not introduce those terms at all.

Then I gave students the four 5’s problem. I had made cards with the 4 operation symbols,  a pair of paratheses, four 5s, and an equal sign (which I had forgotten but they asked for).

I asked them to make as many equations as they could and find out how many different answers they could get.  I had found two versions of this activity and was trying to simplify one and make another more open ended.  I realized from their questions that I had taken away some of the structures that made the problem particularly challenging and interesting.  I had also not predicted and prepared contingencies for some of the directions they would go.    Were they allowed to make numbers like 55?  Did the answer have to be 5?  Did they have to use all of the cards?  What if they wanted to repeat an operation, but didn’t have another card with that sign?  Could they make exponents?  Now I am pretty flexible and was mostly interested in watching them work it out:

It all went fine.  There were some thoughtful equations and some ripe for refinement.  Overall, I could see the benefit in going back to the original problems the way that they were presented, which should probably be the next step.  Instead of exploring the open range of equations (with no self checking mechanism) we can move towards puzzler models, uncovering equations that will allow us to get to 10 or 125 or 24.   

My writing lesson got smooshed between an art project and lunch.  As part of our geography unit we are going to write geography stories about places and geographical features that are meaningful to us.  I had prepared a pre writing activity, but after a vibrant work period involving watercolors, interspersed with PE and an emergency drill, I was left with only enough time to present the idea and then give it out for homework. Ideally we could have brainstormed in class, began the pre-writing activity, and shared our work.  This didn’t happen. We will see the consequences of this on Thursday.

It may be that I get away with it, or that we will need to compensate with more coaching on the back end.  It’s something I know I could have taught better and will teach better next time.  I am comforted by the fact that I am not the first teacher to run out of time or to sacrifice a darling for a greater cause. Nor am I the last.  It’s an occupational hazard.  Luckily, we all come back tomorrow and the project will live to see another day.

Winter Is Coming…

nd soon it will be time to stay inside, bundled up in sweats with cups of cocoa.  What will I do as the cold months descend upon us?

A) Reread the entire Song of Fire of Ice series.

B) Cook my husband dinner every night.
C) Start a new, more comprehensive, more reflective blog

If you guessed A, you are tripping.  I finished those books last winter and I am not reading them again. I am saving my energy for the 6th book or the devastating news that George R.R. Martin has died without finishing this story and we will never know who ascends the Iron Throne.


If you guessed B, you are either my husband, a friend of my husband, or someone else’s hungry husband.


If you guessed C, you are right and very perceptive as you happen to be reading said blog right now.


This is not my first blog.  No, I’ve been around the blogging block.  I blog here about our 1:1 iPad program.  I blog here about my trips to China.  Here you can find my amateur poems.  I kind of blog a lot, but I have become convinced I should blog even MORE.  By whom?  Steve Wheeler.  He gives seven reasons teachers should blog.  And it’s all about reflecting on our practice in order to better serve our students.


That gets me every time.


This month is Connected Educator Month and there are lots of events both live and online to help teachers use technology for good.  But Justin Baeder made a great point that if your connectedness isn’t helping your students, who cares.  Your students don’t need you to be a Twitter star.  Get back in the classroom and teach. Or plan. Or assess. Or blog.  Because apparently by blogging, I can become a better teacher.  Or so I hope.


Our technology coordinator keeps quoting John Dewey:


We do not learn from experience…we learn from reflecting on experience.”


Guess it’s time to dive in.



However, this blog isn’t for you.  It’s not even for me.  It’s for my students.  And if being connected is all it’s cracked up to be, it’ll be for your students too.