Recipes From Home – An Invitation

Recently, I had an aha moment.   It really should not have been one, but it was.    I was talking to someone about different spice blends, when I realized that I could ask my students for family recipes of spice blends (or other things).    I could then take these family recipes and use them to create some different tasks/questions to practice using models for division  and for ratio tasks  (This was not the aha moment).

I brought up the idea with some of my classes.    I offered 5 points of extra credit (which is nothing since my students earn over a thousand points in a marking period).   The room was suddenly abuzz.   Can I bring a recipe for scones?   My family has a bunch of different spice recipes.   I can bring something from Croatia.   Can I bring a recipe for something besides spices but that is a family recipe?   I can bring something from Argentina.   Everyone was so excited.   My aha moment was a realization that by doing something as small as asking them for recipes that we could turn into math problems, I was giving them a little more ownership of our class.  I was welcoming their families and their cultures into our world.

Here are the task cards I have created thus far for modeling mixed number division.


Modeling Division Problems


It’s not so elementary, my dear Watson

Sometimes, I imagine myself as the offspring of Meryl Streep and Sherlock Holmes.   It’s a strange combination, but a good teacher has to be able to do a lot of different things.

It’s the Theater!

A good lesson is embedded in a larger story, it doesn’t stand alone.   It draws you in, enticing you to turn the next page, to see where the story goes.   It makes you feel something – excitement, curiosity, outrage, wonder.  It engages your mind, stretching you, making you consider things you’d never thought of before.   It leaves you asking for more.

A good lesson is also a little bit of theater.   The rise and fall of voices, the pregnant pause, the excited exclamation – they all are part of the tale.

While I can tell a reasonably good story, creating theater is not my natural bent.   I have to work at the drama that Ms Streep creates so effortlessly.

Elementary, my dear Watson

While Sherlock Holmes  found everything to be elementary, I have found the detective work necessary to figure out how my students learn to be anything but elementary.   Figuring out how my students think is hard.   Figuring out why they aren’t learning despite my best efforts is hard work.   One of the best resources I have found is Twice-Exceptional Gifted Children by Beverly A. Trail, EdD.   It is a book about twice-exceptional children, but is a great resource for any teacher trying to understand how a student thinks and the strategies that may help them to be more successful.

The book has an easy-to-use assessment that helps teachers to see discrepancies that might indicate a student is twice exceptional.   It also has a great chapter on supporting cognitive styles.   It outlines characteristics and strategies for the auditory/visual dimension, sequential/conceptual dimension, and convergent/divergent dimension.   (I have found figuring out where a student falls on the conceptual/sequential spectrum helps me a lot in teaching math.)   It also has information to help support students with executive functioning difficulties (including organizational/planning handouts), students with attention issues, and students with sensory integration challenges.  It is my go-to when I feel like I have hit a wall in terms of meeting a student’s needs.





A 3-2-1 Formative Assessment on Ratios With a Side of Surprise

A few years ago, I started trying out some new formative assessment techniques.    It has been a journey full of surprises.   I’ve learned a lot about what my students think along the way.    One of the big surprises was during a unit introducing ratios.   I gave my students this  exit ticket.


When I made it, I was just trying out the structure and thought it was a little bit of fluff.    Then, I saw the results.   I gave the assessment about a week into a unit introducing ratio reasoning to my sixth grade class.   We had completed lessons on tape diagrams, ratio tables, and double number lines.   I expected students to just plop those three representations into the exit ticket without much thought.   Instead, I got 3:2, 3 to 2, and 3/2.

I’ve given a lot of thought to why I got these responses.   Did the students just key in on the “3” part of the question and not really read the prompt carefully?   Did I fail to draw out  the connections between tape diagrams, ratio tables, and double number lines enough?   I don’t know why I got the responses that I did, but pondering the question of why was important.   I started working harder at drawing out the connections between the different representations the next year and the next.

I gave this assessment a few days ago.   As I walked around the room, I marked each response with either a green or a pink highlighter.   Most of the responses were correct.  Those students who got a pink mark, went back through their interactive notebook to find their mistakes and correct them.

I still wonder why some of my students are making this mistake, but feel a little closer to the answer.


A Tour of our Room – A Work in Progress

Welcome to our room.   It is a work in progress and filled with imperfections.   We are learning together and building it as we go.

We are working on being kind and brave.

We believe that making mistakes is part of learning.   We believe that everyone is good at something and no one is good at everything.   We believe that we can all be successful if we work at it together.


We believe in making sense of problems.

We believe that seeing is believing, so we have pictures of people who look like us doing amazing work in STEM.  We also believe that experiences change lives so we code all manner of things (video games, apps, robots, 3D printers)

We believe math should be collaborative and fun, so we have a lot of card sorts and games.    We also have a poster of Lure of the Labyrinth that was signed by the artists and developers of the game because we love Lure of the Labyrinth.


We believe learning happens over time, so we keep portfolios.


We believe life should have a little silliness.   We put elephants on our heads when we take a test and get a shower of wisdom by pouring the elephants on our heads on birthdays.


Our room is a work in progress, just like we are.



Be Brave – A Work in Progress

This afternoon, as I scanned the room, I was pretty sure that a good 2/3 of the students were confused by something.   I asked them if they understood what we had just been discussing.   I was met with a chorus of “yes”.   I looked at them and said something to the effect that I wasn’t really confident of that.   I stood in the echo chamber of “all is well” until suddenly one girl spoke up.   She said, “I don’t really understand.”    I looked at her and said, “I’m so glad that you were brave enough to ask for help.”   Then, I told her to go get a piece of candy from the candy jar.    After she sat back down, we returned to the problem and talked about it a different way.   Then, I heard a chorus of “Oh! I get it.”

We are still working on our quest to be brave.   Today, I hope we took another step forward.

Random (and not so random) Acts

Last week, as I was walking down an aisle in the grocery store, I had a sudden flashback to my childhood.   A little girl was hopping down the aisle, making sure to only land on the white tiles.   I smiled as I remembered doing the exact same thing, selecting a color at random and then looking for the pattern in the tiles to navigate my way.   Seeking patterns and building structure has always been the way that my brain works.

Given my penchant for structure, it’s no big shock that my daily classroom routine follows a regular pattern and has a definite structure.   (I do all kinds of different things within that structure, but I stick pretty closely to the overall structure.)     I close each lesson with a summary and then take the last five to ten minutes of class to revisit material that we have already covered.   It is a chance to force delayed recall and to try to find new ways to address something when the first time didn’t work well enough for some kids.   This is where I differentiate instruction most days.

My Favorite Thing – Random Acts

Every once in a while, I step out of my box.    Yesterday, after our exit card,  I gave students a different kind of task.   They had to select a random act of kindness.     They must do the random act of kindness sometime in the next week.   I had my student aides create the set of tasks.   My only direction to my aides as they created the tasks was that the tasks had to be free and they had to be something that kids could actually do with relative ease by themselves.    These are some of the tasks they created.

  • Hold a door open for someone.
  • Help someone who needs help with a problem (math).
  • Smile at someone.
  • Give someone a compliment.
  • Do an extra chore for your parents (without being asked and without drawing attention to it).
  • Help a teacher clean up the room (and doing it for someone who gives you a reward doesn’t count)
  • Save pop tabs for the Ronald McDonald House (our Builder’s Club collects them)
  • Make someone laugh.
  • Share paper or a pencil with someone who forgot theirs.
  • Save Box Tops for Education (our SPSO collects them)
  • Compliment your parent’s cooking

The ground rules are that the act must be done without seeking reward/attention and that it should be a small thing to make someone else’s day a little bit brighter.

This was a follow-up to two other closing activities.   First, I had students share one brave thing on a post-it.   About a week later, I had them share one kind thing.    These small acts of bravery and kindness that they have done or witnessed at school fill a space on our classroom wall.

I have a plan in mind for my next step on the “brave” front.   I don’t know how well it will work, but I am trying really hard to bring “Be Kind and Be Brave” to life.

Not So Random Acts – Only if you want a “math”y answer

After each quiz or test, I track each student’s mastery of the different skills/concepts in a spreadsheet.   I use this information to form intentional groupings for different activities.  Sometimes, the groupings match skill levels.   Sometimes, the groupings pair someone with mastery with someone who is still working on putting a concept together.    The only thing that is consistent is that the groups are constantly changing and that everyone is an expert at something and no one is an expert at everything.

Tiered Grouping

I use tiered groupings early in the year as students work on number operations.   Students  play Jenga to practice decimal division.   I have three versions of the game with three levels of difficulty (dividing a decimal by a whole number for students who don’t know the standard division algorithm and need some 1:1 or small group instruction, dividing a decimal by a decimal for students who are learning how to manage the decimal point, dividing a decimal by a decimal with a zero in the quotient for everyone else).  Students are assigned to a version of the game using a color coding system.   As students progress, versions of the game are retired.

Skill Grouping  

I use skill groupings for number operations  in addition to tiered grouping.    Students are assigned to play a game to practice a targeted skill.   Students play Don’t Get Zapped to practice decimal multiplication, rational number addition and subtraction, and rational number multiplication and division,   They use Fraction Fortune Tellers to practice mixed number addition and subtraction.   They use Fraction Flip It (a game with cards) to practice mixed number multiplication and division.   I set these games up as stations and I circulate, working with students as they play different games.  The games don’t have a high DOK, but they aren’t intended to do so.   They are fun ways to squeeze a little bit of practice into a routine on a regular basis.   I try to make my lessons higher DOK, so I don’t worry too much if the last few minutes are just fun.

Mixed-ability Grouping

I use mixed ability groupings most often.

Oftentimes,  I pair a student who has mastered a concept with a student who has not (none of them know this – I am just intentional in forming the grouping).

  • I do this with task cards where students practice making double number lines and tape diagrams.      (For some reason, some of my students really struggle with these models.    A lot of these kids seem to view math as algorithmic.   Pairing them with a kid who is more of a “sense-maker” seems to help them make sense of the model.   The combination of the kid talk and the “this is not going away – you have to learn it” seems to help bridge the gap better than anything else I have found.)
  • I  do this with “find the error in the graph”
  • I do this with card sort activities for all kinds of concepts
  • I do this with manipulatives that build 3-D shapes.   Students create the net, find the surface area, and/or find the volume.
  • I do this with exit cards using green/red marking.   I send a kid with a green mark to work with a red mark.   (I can’t have a 1:1 conversation with every student who needs help in a couple of minute span, but someone can. )

I do this with the whole class with Quiz/Quiz/Trade card sets or Give One/Get One card sets.   Right now, I am collecting spice mixture recipes from my students (trying to reflect their cultural experiences in some of our problems) to create a set of cards to practice modeling mixed number division.   (Too many of my students didn’t do well enough with this skill on our last test, so we are going to keep working on it.)

What Does Division Really Mean

Fraction division is a messy business.   Now that we have Common Core State Standards, students must be able to model fraction division in addition to performing the task algorithmically.   This is no simple task for many of them, because it forces them to grapple with the question of what it means to divide.   In order to do it successfully, they must really understand that division represents one of two things.   It can be dividing something into a specified group size to find the number of groups. (I have twenty four cookies and I want to make packages of 2 cookies, how many packages can I make?)  It can also be dividing something into a specified number of groups to find the group size.  (I have twenty four cookies and I want to serve 12 kids, how many cookies can they each have?)  They have to be able to read a problem and figure out which of those two types of problems it is and then form groups accordingly.     Making sense of these ideas and constructing a real understanding of fraction division is hard, even for a lot of adults.

As we were wrapping up our work with these ideas this week, I wanted to do a quick formative assessment to see where everyone was on these ideas.   I took two of the ACE  questions (this is the set of problems from which we draw homework assignments)  from the Connected Math textbook that I use.   Instead of using them as part of a homework assignment, I turned them into a Vote With Your Feet activity.

Vote With Your Feet is a Marzano high engagement strategy that incorporates movement into a lesson. In the activity, students are presented with a multiple choice item.   They move to different locations in the room based on their chosen response to the question (e.g., north wall for A, east wall for B, south wall for C, west wall for D).  The activity gives students a chance to get up and still stay focused on the task at hand.   It also is a really quick formative assessment, taking only a minute or two to see what each student thinks and where their misconceptions are (if the question is well-designed).

Here are the two questions that I posed.


I had students vote on each of the two items without commenting on their choices.    Afterwards, we debriefed both questions by discussing what problems each model might represent.   Kids talked to partners and in table groups.   The class talked about it together.    As we talked, I asked students to give me two division problems for each model.   What is the problem if you are dividing by a specific group size?   What is the problem if you are dividing by a certain number of groups.

These are two of my favorite problems for a formative assessment on fraction division.   This year, I used them as a Vote With Your Feet activity.   Next year, I might take the four options and make them Quiz/Quiz/Trade cards.   I might take them and just use the model and present it as a “here is the answer, what is the question” formative assessment.   In the meantime, I will probably go ahead and make Quiz/Quiz/Trade cards with problems like this to use as a quick review of fraction division from time to time later in the year.