Inquiry Based Math Strategies

During our half day of Personalized Professional Learning, I hosted a workshop on inquiry-based math strategies, but not everyone who wanted to attend could attend… so I thought I’d recap the workshop here for those of you who could not make it – and for those of you at different schools who might be interested in this topic as well.

The structure of the workshop was very hands on, so in the absence of you being able to actually engage with the materials and manipulatives, I will provide a combination of notes, photos, questions and reflections that will hopefully allow you to engage in some of the same ideas, just in a different way.

Tuning in – What do already know?

Think about or jot down your current understanding of each of the inquiry-based math strategies listed below:

  • math time capsule
  • open ended centers
  • magic question
  • open-ended questions
  • number talks
  • math congress
  • visible thinking routines
  • inquiry cycle

If you have a thorough understanding of each of these strategies, you probably do not need to read on. If you think your current understanding has room to grow, read on!

Open-Ended Centers

I’ve already written a post about open-ended math centers and how they work in our early years classrooms. During the workshop today, each group had a bin with the three essential ingredients of an open-ended math center: manipulatives, writing utensils, and a placemat/whiteboard.

Here are some pictures of how teachers tested out a few open-ended math centers:

math workshop 3 math workshop 2 math workshop 1

The Magic Question

I’ve also written about my favourite inquiry questionWhat do you notice? In the workshop we looked at how this question can be used for math specifically.

Take a look at this multiplication chart. What do YOU notice?

Open-Ended Questions

Answer this question: Compare the following fractions using < > or =

1/4   ____  1/2

Now answer this question:

What is the same as a half?

Reflect on the difference between answering the first and second question. What are the benefits of asking open-questions in math?

Number Talk

Take a look at the following image. How many dots are there?

How did YOU figure it out? Here is a picture of all the different ways the participants of the workshop figured it out.

math workshop 8

Math Congress

Step 1 – Present the problem: A sports store has a number of bicycles and tricycles. There are 60 wheels in total. How many of each kind of bike could there be?

Step 2 – Work towards solving the problem. Markers and chart paper work best!

math workshop 6 math workshop 5 math workshop 4

Step 3 – Share discoveries and strategies with fellow mathematicians. Make sure fellow mathematicians are invited to ask questions, make connections, comments and conjectures!

Visible Thinking Routines:

Use the Visible Thinking Routine “Claim, Support, Question” to share some of your thinking about decimals.


There are also many other Visible Thinking Routines that are helpful in approaching math in an inquiry based way!

Inquiry Cycle:

Kath Murdoch’s inquiry cycle is a great way to make any math more inquiry-based.

A CCSS math standard: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

What do YOU already know about this?

What do YOU need to find out about this?

How could YOU find out about this?

Math Time Capsule:

Now, think about or jot down your understanding of each of the inquiry-based math strategies listed below. A math time capsule is a great way to show growth and progress in math – whether it’s over the course of a unit, a year… or even of the course of a workshop!

  • math time capsule
  • open ended centers
  • magic question
  • open-ended questions
  • number talks
  • math congress
  • visible thinking routines
  • inquiry cycle

How did your understanding of these strategies grow and change?

In the actual workshop, after each strategy, we took some time to discuss how the strategy could be applied/adapted to different content and different age levels. Too often when we are looking at strategies we are focused on the actual strategy within to confines of the example that is used. This leads to the conclusion that “That doesn’t work for the grade/content that I teach”. Instead, I challenged the participants in the workshop – and I challenge you in the same way – to focus on the essence of each strategy and how that same approach can be used in different ways, for different ages and for different strands of math.

Here are a few examples of how the same strategy can be adapted for different content and different ages:

Math time capsules – In Grade 5 you might give students the summative task on the first day and then again on the last day to show all of the growth and progress they experienced. But in KG, you may conference with a student and voice/video record everything they know about shapes, and then record them again at the end of a unit to capture growth in their understanding.

Magic question –  In KG you might show a ten frame and ask “What do you notice?”. In Grade 2 you might show a hundreds chart and ask “What do you notice?”. In Grade 4 you might show a multiplication chart and ask “What do you notice?”.

Inquiry cycle – In Grade 1 you may use the inquiry cycle to structure a whole class inquiry into measurement. What do we know about measuring objects? What do we want to know about measuring objects? How can we find out more about measuring objects? In Grade 6 you might use the inquiry cycle to structure self-directed, personal inquiries towards calculating volume of 3-d shapes. What do I already know about finding volume of 3-D shapes? What do I still need to find out? How can go about that?

The possibilities are endless. If you focus on the “why” a strategy is effective and “how” a strategy helps foster thinking and exploration… then the “whats” become infinite! I also shared this google doc with some of my favourite inquiry-based math resources (books, blogs and Tweeters!) Feel free to have a look!

What are your favourite inquiry-based math strategies?

An Inquiry into the Inquiry Cycle


When teachers are transitioning into the PYP-ways of collaboratively planning a Unit of Inquiry, it is not uncommon to receive requests to spend time “coming up with activities for the unit“. Such was true last week, when I received this request from our wonderful Grade 3 team. I have recently shared my perspective of the role of activities in the PYP, so I had to be careful to make sure that I resisted the urge to give them my meaning and instead provided them with an opportunity to construct their own meaning. In short, I wanted to take an inquiry-based approach!

Here is how it went:

Tuning in – Each teacher brainstormed 2-3 activities for their upcoming unit and wrote them on half-sheets of paper. I collected these so we could use them later. This also gave me a great insight into their understanding of what an activity is and their approach to inquiry-based planning.

Provocation – To provoke their thinking about activities and inquiry-based planning, I showed them the following excerpts from a collection of blog posts and encouraged them to share their reactions, connections, tensions and questions.

IC provocation 1

What inquiry teachers are saying…

IC provocation 2 IC provocation 3 IC Provocation 4 IC Provocation 5 Sorting Out – First, the teachers spread the stages of the Kath Murdoch inquiry cycle around our multipurpose room floor.


Then, they took all the questions from this version of the inquiry cycle and placed them beside the stage of inquiry they felt the questions supported.



Next, they took a collection of Visible Thinking Routines and matched them to the specific questions they felt the VTR could help explore.



After that, they took 20 printed out Tweets from #pypchat of actual PYP classroom examples and matched them the stages of inquiry or the respective question.


Finally, they took their own activities from the beginning of our time together and placed them around the inquiry cycle.


After much discussion, collaboration, disagreement, debate and deep thinking, the final result was a collection of questions, VTRs and classrooms examples that they could walk away with for their upcoming unit, that would hopefully help satiate their need for “activities” without stealing too much thinking from their students.


I also hope this inquiry helped to challenge their understanding of what planning looks like in the PYP, as well as to continue to experience what learning through inquiry feels like.

I haven’t had a chance yet to debrief and reflect with the whole team, but I did receive an email from one of the teachers  saying:

“Thank you so much for today. The activity really provoked me and it really got me thinking. It was great!”

I look forward to hearing the rest of the team’s reflections and what action they have taken since this inquiry!


PYP New Staff Induction as a Unit of Inquiry

This year we had 25 wonderful new staff join our Primary Years Program. As PYP Coordinator, myself and my trusty partner are charged with the privilege of training them in all things PYP. We decided this was a great chance for us – as coordinators- to participate in a process of collaborative planning and design our own Unit of Inquiry to structure our 9 one-hour sessions with our new staff. Here are the big pieces of our UOI:

staff induction UOI

We had 3 overarching goals:

  1. Have our new-to-PYP learn about the PYP, by learning through the PYP
  2. Model inquiry based, concept-driven teaching and learning practices they could take back and use in their own teaching
  3. Stay connected to the process of unit planning, unit delivery and unit reflection from a teaching perspective

Here is a brief (not so brief!) summary of what we did each week to hopefully accomplish these goals!

Week 1 – General overview

Diagnostic Assessment: What do you know, or think you know about the PYP?

Teachers sketched their own model of the elements of the PYP and how they work together.

Staff Induction 11

Tuning in: How do you feel about your current understanding of the PYP?

Teachers wrote their name or a symbol on a post-it and stuck it to a reflection spectrum that ranged from “I don’t even know what PYP stands for” all the way to “I should take over the PYP Coordinator’s job”

Staff Induction 5

Tuning in: Introducing the Unit of Inquiry

We shared the central idea, key concepts and lines of inquiry with the teachers.

Tuning in: Q&A

We facilitated an informal question and answer session and made sure to take note of questions that could guide our planning for future sessions.

Week 2 – International Mindedness

Tuning in: What is international mindedness?(Form)  How does it work in the PYP?(Function)

Teachers jotted down what they think they know about the form and function of international mindedness into their “Inquiry Notebooks”.

Staff Induction 12

Finding Out & Sorting Out: Resource Exploration & Visible Thinking Routine – Connect, Extend, Challenge


Teachers explored a variety of resources we provided about international mindedness and organized their ideas based on the Connect-Extend-Challenge Visible Thinking Routine.

Staff Induction 14

Making Conclusions: Reflection – How might I develop IM in the grade/subject I teach?

Teachers sat with colleagues who teach the same grade or subject to chat about and brainstorm ways to put their learning about IM into action.

Week 3 – Transdisciplinary Learning

Taking Action : Reflecting on international mindedness

Teachers discussed how they had put their learning about IM into action in their own teaching and how it went.

Tuning in: Visible Thinking Routine – 3,2,1 Bridge


Teachers completed the first part of the Visible Thinking Routine “3,2,1 Bridge” about transdisciplinary learning.

Provocation: Decomposition Lab

Teachers watched this YouTube video that shows a Grade 4 transdisciplinary unit in action and discussed what they noticed.

Sorting Out: Transdisciplinary Theme Visible Thinking Routine: Chalk Talk


Teachers completed a chalk talk for each of the 6 TD themes in the PYP, brainstorming what topics or specific areas of study could be explored in that theme.

Staff Induction 2

Making Conclusions & Reflection: 3,2,1, Bridge

Teachers completed the second part of the VTR “3,2,1 Bridge” and reflected on how their understanding about transdisciplinary learning had shifted and changed.

Staff Induction 15

Week 4 – Concept-Based Teaching and Learning

Taking Action: Reflecting on transdisciplinary learning

Teachers chatted about how the attempted TD learning in their own teaching practice based on what they had learned the week before.

Tuning in: +1 Routine

Teachers brainstormed a list of all the pieces of information they knew about concept-based learning.

Staff Induction 16

Provocation: Dr. David Perkins

Teachers read this startling statement “90%  of what we teach in schools is a waste of time… it just doesn’t matter” and then watched this YouTube video of Dr. David Perkins to provoke their thinking about “what’s worth knowing?”

Finding Out & Sorting Out: Resource Exploration & Visible Thinking Routine +1

Teachers explored resources that we provided and added relevant ideas and information to their +1 routine.

Going Further: Key Concept Questions

Teachers brainstormed questions about the Kuwait Towers from each key concept lens.

Staff Induction 6

Making Conclusions: Visible Thinking Routine- Headlines


Teachers wrote a “headline” that summarized their current understanding of concept-based teaching and learning

Staff Induction 1

Reflection: Stop, Start, Continue

Teachers reflected on their learning so far and provided us with feedback about what we could “stop, start and continue” to better impact their learning about the PYP.

Week 5 – Attitudes and Skills

Taking Action: Reflecting on Concept-Based Learning

Teachers discussed how they had used the key concepts with their students.

Staff Induction 20

Tuning in: Skills and Attitudes as Learning Targets

Teachers experienced what it is like to have learning goals/targets structured through PYP attitudes and skills

Staff induction targets

Finding out: Making the PYP Happen Jigsaw

Teachers worked in partners to research either attitudes or skills in order to share their learning with their partner. Teachers inquired into the form and function of the attitudes and skills as described by the IB in Making the PYP Happen.

Going Further: Resource Exploration & Visible Thinking Routine- See, Think, Wonder


Teachers explored provided resources and organized relevant discoveries through the VTR “See, Think, Wonder”

Staff Induction 17

Reflection: Attitude Reflection

Teachers reflected and posted which PYP attitudes they used the most throughout their learning activities.

Staff Induction 4

Week 6 – Action 

Tuning in: Quick Write about action

Teachers took 3 minutes to write everything and anything about action in the PYP.

Staff Induction 19

Finding Out & Sorting Out: Making the PYP Happen & Visible Thinking Routine- 4Cs


Teachers read the section about action in MTPYPH and pulled out “connections, challenges, concepts and changes” based on the Visible Thinking Routine.

Staff Induction 18

Making Conclusions” Visible Thinking Routine- Colour, Symbol, Image


Teachers choose a colour, symbol and image to represent their understanding of action in the PYP.

Staff Induction 7

Week 7 – The Role of subjects in the PYP

Taking Action: Reflecting on action

Teachers discuss how they have supported student-initiated action in their teaching recently.

Tuning in: Teachers jotted down what subjects they think make up the PYP.

Finding out: Teachers split up into groups and each group inquired into the role of different subjects in the PYP.

staff induction subjects

Making Conclusions: Teachers presented their findings to each other.

Staff Induction 9 Staff Induction 8

Week 8 – Summative Sharing

Check out this post to see a full recap of the provocative “PYP test” and real PYP summative!

Week 9 – Personalized Learning Plan

Even though our new-to-PYP staff training was coming to an end we did not want the learning or support to stop. We helped our new-to-PYP staff develop Personalized Learning Plans for the remainder of their first year in the PYP.

Tuning in: Teachers reflected on their current learning about the PYP and identified areas they wanted to pursue further. They set their own “learning objectives” based on what they want to learn more about.

Finding Out & Sorting Out: Teachers explored the OCC and this google doc to find resources that would support each of their learning objectives. Teachers browsed, skimmed, bookmarked, printed, and copied links that would be of interest later on when they had time to dive in. The idea is to invest all the time it takes to find, vet and organize resources so that for the remainder of the year, if there is a pocket of time to learn you already have everything you need!

Staff Induction 21


After our last session, we knew what we had to do… REFLECT! So, true to our goal of treating this like a Unit of Inquiry, my partner and I sat down together and collaboratively completed the PYP unit reflections.

Staff Induction 23

We also completed an inquiry self-reflection to help us identify how many ‘signals of inquiry’ were present in our adult learning community and if there we any ‘warning bells’.

Staff Induction 22

We discovered that next year we need to work on noticing, honouring and using our learners’ questions more to drive the inquiry and better build an environment filled with wonder and curiosity. We also noticed that after 9 weeks our new-to-PYP teachers learned so much about the PYP yet we never “taught” them anything, in the traditional sense. There were no Powerpoints filled with information. There were no lectures. There was no standing and delivering. That felt good!

What a great experience it was to plan, deliver, assess and reflect on our new-to-PYP staff training as a PYP Unit of Inquiry! We can’t wait to have a second chance next year to put our reflections and new goals into action!

We would love your feedback about our Unit of Inquiry! Please share your questions, comments, connections and suggestions with us. 

How Children Learn Math: Bringing it Altogether

Last year I wrote a post about what the PYP believes about how children learn math:

  1. Students construct their own meaning about math
  2. Students transfer their meaning into conventional symbols (vocabulary, notations, algorithms)
  3. Students apply their understanding to problems and real world contexts

I also shared some examples of how teachers at our school have been helping students to construct their own meaning about mathematical ideas and concepts. A lot of the teachers I work with are feeling confident about that first stage in the math cycle! However, they are still wondering how to bring all 3 of the stages together.

In an attempt to step back and see the big picture of how the stages fit together, our teaching teams generated a list of all the math strategies they use in their math programme.


Once the list was compiled, they asked these three questions:

What strategies give students the opportunity to construct their own meaning?

What strategies help students to transfer meaning into symbols?

What strategies provide students the chance to apply their understanding?

Then, they sorted each strategy into each phase of the math cycle. (Along with some amazing debates, disagreements, discoveries and many references to the PYP Math Scope and Sequence document!) We discovered that many strategies fit multiple stages in the math cycle depending on the question you ask or how you present it. We also spent a good chunk of time discussing how many of the strategies that allow students to construct their own meaning at the beginning of a new unit or new concept, would also be good at the end of the unit to allow students to apply their understanding using conventional symbolic representations.

It is interesting to note that no two teaching team’s chart looked the same. Another point for acknowledging that all learners construct their own meaning in their own way!

Here is the chart our Grade 3 team developed:

Math Strategy Sort

Now when we are planning a stand-alone math unit, we have an anchor chart that will help us purposefully select math strategies to support students as they to move through all three stages of the math cycle.

How do you bring the three stages of how children learn math together?

We tuned in!

Before our Units of Inquiry started, grade-level teams inquired into “tuning in” (with the help of  this post from Kath Murdoch). Many teachers walked away with a new, or deeper, understanding of the purpose behind the “tuning in” phase of inquiry. Teachers were excited to put their new learning into practice… here is how it turned out in our Grade 1 to 5 classes:

Grade 1: Peaceful relationships are created through mutual understanding and respect.

Students tuned in to problems and solutions:


Students tuned in to the concept of numbers:



Grade 2: Citizens build communities.

Students tuned in to the concepts of “community” and “citizenship”:



Grade 3: Decisions impact conseqeunces.

Students tuned in to “decisions” and “consequences”:


Students shared important decisions they made in their life:


Students tuned in to decisions made by readers:


Students tuned in to the decisions they make as mathematicians:


Students tuned in to the number of decisions they make:


Teachers tuned in to the type of decisions they make:


Grade 4: Relationships are affected by learning about people’s perspectives and communicating our own. 

Students tuned in to the concepts of perspective and relationships:



Students tuned in to different representations of numbers:



Grade 5: Relationships among human body systems contribute to health and survival. 

Students (and teachers) tuned in to the concept of systems:



Students tuned in to what they think they know about body systems:



I love that the students’ thinking is front and centre!

I love that the students’ thinking is visible!

I love that students were able to demonstrate their thinking in a variety of ways!

I love that teachers tuned into conceptual understandings, not just topic knowledge! 

I love that transdisciplinarity is evident!

I love that teachers were acting as inquiries themselves… doing reconnaissance to find out about what their students bring to a Unit of Inquiry!

The feedback from teachers about “tuning in” has been great! Teachers are excited because they have learned about their students’ prior knowledge, their misconceptions, their interests and their questions. It has not only provided them with diagnostic assessment data, but also a road map that illuminates “where to next?” based on students’ needs and interests! I can’t wait to see where these inquires lead!

How do you “tune in” to your students’ thinking?

What does an inquiry-based, first week of school look like?

During this year’s staff orientation, we used inspiration from two blog posts (sowing the seeds of inquiry & 10 things to do on the first day of school) to move towards a more inquiry-based, first week with students.

Here is a glimpse into what it looked like in classrooms from KG to Grade 5…

Students helped set up their learning environment:

IMG_0021 IMG_0115 IMG_0040 IMG_0086

Students helped choose what to do for the first week:

IMG_0014 IMG_0144

Students explored the school:


Students’ questions were honoured:

IMG_0106 IMG_0078

Students and teachers learned about and connected with one another:

IMG_0034 IMG_0026 IMG_0041 IMG_0049 IMG_0127 IMG_0139

Students and teachers discussed what it means to be ‘students’ and ‘teachers’:

IMG_0074 IMG_0048

Students shared what they want to learn about in the coming year:

IMG_0075 IMG_0032 IMG_0080

Students thought about and shared their learning preferences:

IMG_0130 IMG_0129

Students explored the learner profile, PYP attitudes, key concepts and action:

IMG_0147 IMG_0134 IMG_0105 IMG_0101 IMG_0100 IMG_0091  IMG_0045 IMG_0019

Student constructed essential agreements:

IMG_0143 IMG_0133  IMG_0104  IMG_0072  IMG_0155IMG_0145

Students reflected:

IMG_0137 IMG_0095

Students played:


The week was a success! The feedback from teachers and students was overwhelmingly positive. Students loved being included in the planning and set-up for a new school year and teachers felt the more ownership they handed over to students the more positive and enjoyable the learning community became.

There is a definite buzz around our elementary school. Enthusiasm… fresh ideas… confidence… inquiry… I can’t wait to see where all this amazing energy takes us this year!

What does your inquiry-based first week of school look like?



Inquiry-Based Staff Orientation

Warning: This is a long post! My partner and I wanted to be risk-takers and, as much as possible, run an inquiry-based orientation for our new and returning PYP staff. Here is a sneak peak into how it went.

Our leadership team had four main goals to guide our staff orientation this year:

essential agreements

So first we set-up our inquiry-based professional learning environment…


  • collaborative, flexible groupings
  • learning materials on each table (blank paper, markers, recipe cards, post-its etc.)
  • blank walls to display learners’ questions and thinking
  • resource wall to post strategies and visible thinking routines we use
  • wonder wall for questions

Day 1: An inquiry into learning spaces…

We did a Think, Write, Sort to open up a discussion around classroom set-up.

Think: What are the usual tasks of setting up a classroom?

Write: Write each classroom set-up task on a separate post-it note and place it in the middle of your group.


Sort: Organize all post-it notes into 3 categories. 1 – Tasks to do with students, 2 – Tasks to do before students arrive, 3 – Tasks that don’t belong in a PYP classroom. (Get rid of duplicates!)


Walk: Walk around and see what other groups think.


Post: Display teachers’ thinking in the learning space.


Day 2: An inquiry into learning communities…

We brainstormed the ways we, as staff, demonstrate the attributes of the learner profile in our professional learning community.

IMG_4970 IMG_5049

Then we took a break to play together. We played rock, paper, scissor entourage and it was AWESOME!

Everyone faces off against a colleague for a one-stop shot of rock, paper, scissor.


The winner goes on to face another winner, and the loser becomes the winner’s entourage who then cheers on the winner!


Then the loser and his or her entourage join the entourage of the winner, as the winner faces off with another winner. And do the pattern continues until there are only 2 winners left with HUGE entourages, cheering loudly!


Then we got back to work learning, using a Growing Definition to draft our staff essential agreements.

First in partners,


Then in groups,


Finally, as a whole staff (or in our case with a staff of 120, with a collection of representatives from each group!)


Now, we are ready to post our essential agreements. We plan to “live ’em, not laminate ’em” and continually reflect on them throughout the year as needed.


Last but not least, a reflection! Not about what we learned, but instead about how we learned.


Day 3: An inquiry into inquiry…

We mixed and mingled our PYP, MYP and DP teachers to learn and share about inquiry across the continuum. Inspired by this post by What Ed Said.

PYP MYP DP staff

We used the Kath Murdoch inquiry cycle and this prezi to structure our inquiry.

Provocation: What ideas about teacher and learning does this video portray?

Tuning In: What is your experience with inquiry?

Finding Out: Based on your current understanding, what are you questions about inquiry?

Sorting Out: Using the resources provided, self-select some blog posts, videos, twitter hashtags, pictures etc. that are relevant to your questions.

If you are beginning your understanding of inquiry:

 Blog Posts:

Strategies for Inquiry Based Learning

What do you notice? A first step down the path towards inquiry

Introduction to Inquiry Based Learning

Inquiry Cycle: Why, what and how

What does inquiry look like?

Planning and Inquiry Based Start to the Year


An inquiry approach

Inquiry based learning – developing student questions

If you are developing your understanding of inquiry:

 Blog Posts:

Developing independence and inquiry

Inquiry, inquiry, inquiry… but how do I do it?

What does inquiry learning look like?

Said no true inquiry teacher ever

Different models of inquiry

Inquiry and the specialist teacher

Moving on from the KWL chart

Is inquiry a struggle for you?

If you are extending your understanding of inquiry:

Blog Posts:

Letting inquiry unravel naturally

What inquiry isn’t

Busting some myths about the inquiry cycle

Minding our language: teaching in the inquiry classroom

This is how inquiry teachers teach

Inquiry and the art of listening

Inquiry and the culture of permission

Effects of Inquiry-based Learning on Students’ Science Literacy Skills and Confidence

Classroom Set-up: How much should we be doing without students?

Twitter Hashtags:








Going Further: Using what you’ve learned, create a Frayer model that demonstrates your current understanding of inquiry.

frayer inquiry

Making Conclusions: Based on what you discovered, what are you new questions?

Taking Action: Now that you know what you know, what are you going to do about it?

Reflection: What was it like to learn through inquiry? What did you notice about yourself as a learner? How will that impact that work you do with your students?

notice self learner what was it like inquiry impact work with students

Day 4: An inquiry into the first week of school…

Provocation: We used this post from What Ed Said to disrupt our comfortable thinking about what should take place the first days of school.

Then we gave time to grade and subject teams to collaboratively plan their first week of school, using the following resources.

Examples of Inquiry-Based First Week Activities:

What do you want to do on your first day of school?

What do you believe about learning?

Essential Agreements

Students Creating their learning space

Photos of student’s designing the classroom set-up

 Blog Posts:

10 things to do on the first day of school

Essential Agreements

What’s Your Story?

Who Owns the Learning?

First Impressions and the Inquiry Classroom

Tips for Creating a Classroom Agreement

Beginning of the Year Student Questionnaire 

Re-Thinking the Start of the Year

First Day Back Fun 

10 Back to School Icebreaker Games

3 Non-Icebreaker Things to Do the First Week of School 

8 First Day of School Activities

Why the first week of school needs to be vigorous 

Day 5: Reflection and Feedback…

Using this visual, we encouraged teachers to think about what they learned this week, and more importantly what action they took based on their learning.

action look like

Teachers then filled in post-its with their action and posted them on our action wall.

action post action wall

Finally, we asked for their feedback. We referred back to the 4 goals we introduced on the first day of orientation week and asked for “stars and wishes”  about what we did to accomplish those goals and what may have hindered those goals. We will keep this valuable feedback to help improve our staff orientation week next year!

stars and wishes example

After 5 days, our empty walls were filled with resources along with our teachers’ questions, thinking and action!

resource wall full walla

Now we are ready to start an amazing new school year!

How have your teachers prepared for a new year in the PYP?


Inquiring into PYP Classroom Set-up

 Provocation: If it looks, sounds and feels like a ‘regular’ classroom, its probably not PYP. 

typical classroom


June seems like a strange time for an inquiry into PYP classroom set-up. But we realize that many teachers are thinking about classroom set-up while they are taking down their classroom from the school year that just finished. We also realize that many teachers spend time in the summer thinking about classroom set-up, and many even come back to school early to get a head start on organizing their room. We wanted to make sure that we stayed ahead of this curve, and took the time to allow our teachers to reflect on and re-think the way they set up their PYP classrooms.

staff inquiry

We provided a collection a resources about PYP/inquiry-based learning spaces from a number of different blogs, school websites and PYP resources. The teachers were then given time to sort through the resources they felt were relevant to their learning.

First Impressions and the Inquiry Classroom

Learning Spaces

10 Ways to Think About Your Learning Space

What should my PYP classroom look like?

What does a PYP classroom look and sound like?

Visual Markers of a PYP Classroom – page 14

Inquiry Habitats

What our PYP Classrooms Look Like (International School of Helsinki)

What Does a PYP Classroom Look Like? (Video)

After reading through their self-selected resources, teaching teams worked together to make conclusions about how to set up a PYP classroom. Homeroom teachers and single-subjects teachers (who teach their subject in the students’ homeroom) all sat together to ensure everyone’s interests were being represented. They worked together to create a document that shows what PYP classrooms must have, should have, shouldn’t have and can’t have at our school. This sparked many interesting conversations!

“Is there really anything that belongs in the ‘can’t’ section?”

“What are we supposed to write? The classroom should be set up with the students, not for the students.”

“How do we know these sources actually represent what the PYP expects?”

Here are the insightful conclusions that resulted from inquiry and great discussions:

PYP classroom setup grade 1 PYP classroom setup grade 3 PYP classroom setup grade 4 PYP classroom setup KG1

Instead of us (PYP Coordinators) creating a checklist of requirements, we thought it was important to have staff own this process. That way the final product shows their understanding of what makes a PYP classrooms, as opposed to mandating their implementation of our understanding of what makes a PYP classroom.

We’re hoping to go through a similar inquiry with our new staff next fall to allow them to begin to construct their own understanding of PYP classroom set-up. We also plan on providing them with these awesome team-made resources!


Rethinking the Way We Plan

At our school, we realized we had very comfortable thinking about the way we plan for Units of Inquiry. We know what we plan, we know how we plan, but we’re not sure about the last time we slowed down to think about why we plan the way we do. So we thought it was time to rock the boat and disrupt our comfortable thinking about planning and focus on the why.

We used parts of Kath Murdoch’s Inquiry Cycle to structure a teacher inquiry into planning. Here is how it went:

Tuning In: How do you think a collaborative planning meeting should be structured in order to plan for a Unit of Inquiry?

Teachers tuned into their own understanding of planning for inquiry and sketched out a sample agenda of a collaborative planning meeting. Teachers then put these agendas aside to act as a time capsule, which would allow them to refer back to how their thinking about planning changed over the course of the meeting.

Sorting Out: What are you reading that connects, extends, and challenges the way we currently plan for inquiry? 

Teachers were given the following links to a variety of blog posts about planning for inquiry:

Assessing Understanding in the Planning Process

Planning for Learning

How Do You Plan?

Planning in RESPONSE to Learning

Planning for Inquiry

Planning for Inquiry: Example

How Healthy is Your Team Planning?

Planning for Concept Driven Learning

Reflecting on PYP Planners

Teachers spent 15 minutes independently sorting through these resources and recording their own discoveries based on the Visible Thinking Routine – Connect, Extend, Challenge.

indep inquiry 2 indep inquiry


Then, teachers had the opportunity to share their thoughts with one another and discuss. Common observations included:


  • we start from the end and decide the conceptual understandings we want our students to have
  • we design rubrics based on the key concepts
  • we take time to share successes and struggles in our classrooms
  • we spend time discussing and unpacking our own understanding of the big idea


  • We plan one provocation, but we should be planning a range of powerful provocations
  • We reflect at the end of each unit, but could involve students in that reflection process
  • We “tune in” to students’ prior knowledge but might want to pay more attention to their initial misconceptions


  • We should plan in response to learning based on students’ questions
  • We should explicitly plan for the development of transdisciplinary skills
  • We should resist the temptation to fill in the whole PYP planner before a Unit starts

Going Further: What parts of the PYP planner should be filled out before, during and after a Unit of Inquiry?

Thinking about the term ‘planning in response to learning’, teachers looked at a blank copy of the PYP Planner and identified which parts should be discussed and filled in prior to starting a Unit of Inquiry, which parts should be filled in on an ongoing basis throughout the Unit of Inquiry and which parts should be filled in after a Unit of Inquiry has finished. Teachers also identified the parts of the planner that should be kept from year to year and the sections that should be wiped clean.

collaborative reflection pyp planner 2 collaborative reflection pyp planner


Making Conclusions: As a team, design the agendas for collaborative PYP meetings before, during and after a Unit of Inquiry. 

My fellow PYP Coordinator and myself realized that as long we were creating the agendas for collaborative meetings, we are the owners of that planning process. So we wanted to give grade-level teams ownership over creating meeting agendas based on their own understanding of what planning for inquiry should look like. Each team’s collaborative meeting agendas were different and reflected their team’s understanding of how to plan for a Unit of Inquiry.

planning grade 2 crop planning KG crop

We then posted all of the team’s planning agendas in our Elementary Multipurpose Room, to allow teams to see the conclusions their colleagues made about planning for inquiry and hopefully inspire and challenge their own understanding further.

Taking Action: Now that you know what you know, what are you going to do about it?

I noted two, authentic, learner-initiated pieces of action that resulted from our inquiry into planning!

  • one teacher printed out a copy of the meeting agendas and posted them in her room so that her team could use them during informal planning meetings (without the facilitation of the PYP Coordinator)
  • a different teacher printed out a copy of the meeting agendas for her grade level and put them in her PYP Binder so she could bring them with her to any planning meeting she attended (formal or informal)

In the coming year, we plan to “live it, not laminate it” and actually use these agendas to structure each team’s collaborative planning meetings. Hopefully, as our collective understanding of inquiry grows and changes teams continue to reflect on and amend their planning agendas.

I wonder if any team included that process in their planning-plans? Maybe that will come about next time we reflect on and refine our collaborative planning processes!


How Children Learn Math

At our grade level math meetings, we have been discussing a very important question.

How do children learn math?

A powerful, and oftentimes perplexing question! Luckily, we are an IB school and the Primary Years Programme clearly lays out what they believe about how children learn math.

Simply put:

First, children need an opportunity to construct their own meaning about mathematical ideas and concepts. Then, they need the guidance and support to transfer their own meaning into conventional symbols, vocabulary and algorithms. Finally, they need a chance to apply their understanding. These three phases are fluid and children move back and forth through them in an on-going cycle.



The teams I work with have really taken interest in the phase of the cycle where students construct their own meaning. I think this may be because when we were students learning math, most of our teachers often jumped right into the second phase – conventional symbols, notations and algorithms.

“Today we are learning about fractions. This is what a fraction is…. This is how you write a fraction… This is what the different parts of the fraction are called…. Now you go try.”

math teacher

Our teachers are discovering that there are many benefits to allowing students to construct their own meaning first, before jumping into symbols. Not only are their students understanding math concepts more deeply and communicating their understanding more clearly, but when it comes time to “teach” to conventional skills, notations and vocabulary it end up taking less time and sticking much better!

So now for the million dollar question in teaching…

What does it actually look like in the classroom?

Here are a few examples across the grades of how teachers are helping students to construct their own meaning about math:

KG – Number Sense

This is a picture of an open-ended math center where students choose to play and no instructions are given in advance. Specific math manipulatives and writing tools are set out to try to lead students down specific paths and teachers and teaching assistants prompt with lots of questions.

KG Center c


Students have not been told that this is a ten-frame and have not been showed how to use a ten-frame. Yet, as the students play their curiosity drives them to experiment with how many squares fit inside and how many numerals fit inside. Allowing students this chance to interact with a ten-frame and construct their own ideas about it will make it much easier when it comes time to discuss “What mathematicians call this” and “How mathematicians use this”.

Grade 1 – Data Handling

In this grade 1 class the teacher gave each student a single piece of white paper and told them to pick a bunch of things and go find out which thing is the most liked in the class.

Grade 1 Data f

Students have not yet been taught how to collect data. In fact, the class had never discussed data in anyway before this activity. Students had to figure out their own method to record the choices and how many people liked each choice.

Grade 1 Data b


Some students wrote the names of each classmate beside each choice.

Grade 1 Data d

Some student drew a picture of each person next to their choice.

Grade 1 Data c


Some students took a “short cut” and made a tick to represent each student to save time.

The teacher now had 20 different student-generated strategies for collecting data and as a class they could discuss the pros and cons of each strategy. From here, a lesson about taking tallies is much more purposeful because students have a context of when to use tallies and why they are helpful.

Grade 2 – Fractions

How many ways can friends fairly share this pizza?

Grade 2 fractions


Before Grade 2 students ever heard the word “fraction” they were splitting things into equal parts. Students were cutting up squares, circles, and rectangles in multiple ways to “fairly” share them with different amounts of people.

Grade 2 fractions b


This provided a great context to introduce fraction vocabulary. Using the cut up pizzas, the teacher could ask many purposeful questions to help her students transfer their understanding of “fair shares” into the conventional understanding of fractions.

What is the fancy math word for ‘fair’?

What would a mathematician call something that has two equal parts?

What would a mathematician call something that has three equal parts?

If mathematicians call something with four equal parts fourths, and five equal parts fifths… does anyone want to guess what mathematicians call something with six equal parts? Ten equal parts? One hundred equal parts? ONE MILLION EQUAL PARTS!?!?!?!

Grade 3 – Area and Perimeter

Find something in the class and find the distance around the outside of it.

This grade 3 class was trying to figure out the distance around the outside of classroom objects without ever hearing the word perimeter or being taught the formula P = 2L + 2W.

Grade 3 Congress


These students were using logic to figure out that they could add up all the sides to find a distance around something. Some even discovered they could take a short cut when measuring a rectangle because both sets of sides were the same. One student even realized that when figuring out the distance around a square you could simply multiply the side by 4 to take a really quick short cut. Students were using rulers, cms, inches, blocks, paper clips… you name it. One student even cut a piece of string that could fit around the outside of her circular object and then held it against a ruler.

From here, the teacher is able to take their understanding and trade it for the conventional vocabulary and formulas for finding perimeter.

Grade 4 – Pattern and Function

There are 60 wheels. Some are on bicycles. Some are on tricycles. What combinations of bicycles and tricycles could there be?

Grade 4 Congress c


For this question, students were able to find the answers in any way that made sense to them. Some students drew wheels and put them in bundles of two and three. Some students split the wheels in half and figured out home many bikes and trikes would be in each half. Some students did repeated addition. Others did repeated subtraction. After one hour the most number of solutions found by one group was 4.

Grade 4 Congress a


So when the teacher said she had a “math short-cut” to show them how to find 12 answers in 15 minutes, she had 100% buy in from her students. How different their level of interest would have been if she started with “Today I am going to show you how to use a table to find patterns.”

Grade 5 – Number Operations

Why does 6 x 1/2 = 3?

Grade 5 Congress b


At the Grade 5 level, students are expected to have a solid understanding of multiplication. Students are also expected to have a solid grasp on fractions. However, multiplying fractions would be something brand new. So before this teacher taught her students how to multiply fractions, she gave them the chance to construct their own meaning first.

Grade 5 Congress


Some students went to the manipulatives shelf and took 6 “halves” and concretely put them together to discover that they could make 3 wholes. Others knew that multiplication was repeated addition, so they added 1/2 six times to discover the answer was 6/2 which is the same as 3. Other students approached the problem a different way. They drew a set of 6 objects and crossed out half, to show that half of 6 is 3. Now the teacher would be able to introduce the standard algorithm for multiplying a fraction by a whole number, and if that algorithm doesn’t make sense to someone, they have other self-generated and peer-generated strategies for finding the answer instead.


I’ve been hearing a lot about Math Wars lately, where people are either advocating for the importance of understanding in math (reform) versus the importance of skill computation in math (traditional).

I think we can have both.

If we allow students to construct their own meaning first, then help them transfer their understanding into symbols, then have them apply their understanding I believe we can have well-rounded mathematicians who can not only “do” math, but also deeply “understand” math.

What do you think?