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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.
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- Sarah and the [Math]odology Team
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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.
- Identify what students already know.
- Identify what you want students to accomplish by the end of the concept.
- Develop and group the tasks to fill this gap.
- 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
Join us Monday, May 6th
7pm EST
With Sarah Schaefer and Fran Julien,
to learn more about
Summer Essentials
Registration available now!
Click here to register for the upcoming RoundtableMath Concepts
Number Bonds from Sarah Schaefer on Vimeo.
Part-Whole Relationships
Decomposing Numbers-Operations
Adding and Subtracting Large Numbers
Multiplying Two-Digit Numbers
Division Key Ideas from Sarah Schaefer on Vimeo.
Beginning Bar Modeling from Sarah Schaefer on Vimeo.
Key Ideas -
Division
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?
Math Practices
Anchor Task Modification from Sarah Schaefer on Vimeo.
Questioning Techniques from Sarah Schaefer on Vimeo.
Modifying an Anchor Task
Planning a
Lesson
Questioning
Techniques
Mathodology Monday
Building Thinking Classrooms
Sarah Schaefer and Dr. Peter Liljedahl
Building Thinking Classrooms-Questioning
Sarah Schaefer and Dr. Peter Liljedahl
Building Thinking Classrooms-Assessment
Sarah Schaefer and Dr. Peter Liljedahl
Building Thinking Classrooms
Classroom Setup
