Free Videos

So if you’re here it’s probably because you’re as excited about helping your children with math as we are.

Try exploring these free videos to give you a greater sense of what’s possible. Click each video and explore the power of decomposing numbers or how bar modeling can develop into one of your most powerful tools for solving word problems.

We hope this is helpful and would appreciate your feedback and questions.


                                                                                                                                                               - Sarah and the [Math]odology Team

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Monthly Showcase Videos


Mathodology Roundtable - The Art of Thin-slicing
Peter Liljedahl  & Sarah Schaefer  

The grand question asked in the session: How do we create and implement tasks for thin-slicing?


Peter answered this by listing out a four step process.

  1. Identify what students already know.
  2. Identify what you want students to accomplish by the end of the concept.
  3. Develop and group the tasks to fill this gap.
  4. Sequence tasks.


In his book, Building Thinking Classrooms, Peter shares the principles that Marton and Tsui discovered regarding variation theory; one of the theories that contributed to Peter's development of thin-slicing.


Principle 1: Variation in thin-slicing questions begins on the foundations of what students know. This may take a few questions of the same variation with in the sequence.


Principle 2: Only one thing can change from problem to problem. Too much change will inhibit students' flow in thinking and stop them from utilizing connections from the previous problems to successfully work through the current one.


What could this look like in a curriculum? The following is an example of how the think!Mathematics curriculum aligns with these principles in the development of the Guided Practice.

The concept: Subtraction with regrouping.


Notice the slight variation in number 1 from regrouping to subtract a 1-digit number, to now applying a second step of subtracting the tens.


Next, students are continuing to regroup and subtract, including from the tens, beyond the value of 10.


Lastly, we extend students application of renaming beyond regrouping. The set in question 3 lend themselves to the use of reasoning strategies like rounding up to the nearest ten, subtracting, then adjusting back. Furthermore asking the student to reason, versus solve.

Guided Practice source: think!Mathematics Second Edition Grade 2A


Math Concepts


Part-Whole Relationships

Decomposing Numbers-Operations

Adding and Subtracting Large Numbers

Multiplying Two-Digit Numbers










Key Ideas -

Beginning Bar Modeling

Bar Modeling Across Middle Elementary




Social Media Q/A

Instagram Post March 2023

Just curious, how would you solve the first one if a child has not started algebra as yet? That's the only method coming to mind. How else can I facilitate this?


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Math Practices​


Modifying an Anchor Task

Planning a



Mathodology Monday​

Building Thinking Classrooms

Sarah Schaefer and Dr. Peter Liljedahl​


Building Thinking Classrooms-Questioning

Sarah Schaefer and Dr. Peter Liljedahl ​

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Building Thinking Classrooms-Assessment

Sarah Schaefer and Dr. Peter Liljedahl​

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Building Thinking Classrooms

Classroom Setup

[Math]odology Favorites - Education​

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How you can be good at math, and other surprising facts about learning
| Jo Boaler | TEDxStanford​
Five Principles of Extraordinary Math Teaching
| Dan Finkel | TEDxRainier​
Assessment: The Silent Killer of Learning
|Eric Mazur ​
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Every kid needs a champion
| Rita Pierson​
The Power of Belief - Mindset and Success
|Eduardo Briceno​
Ability Grouping
|Professor John Hattie​

[Math]odology Favorites - Inspirational​


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Kodi Lee: Blind Autistic Singer WOWS And Gets GOLDEN BUZZER!
|America's Got Talent 2019​
Gary Woodland surprises Amy from Special Olympics Arizona 2019​

Be a Mr. Jensen- MUST WATCH!!

In the Media - About Singapore Math​


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Jade Educations​
Dan Rather- Take a Lesson from Singapore​