Layered EducationWhat it looks like
- Finishes early and correctly, then waits or drifts
- Solves in their head and resists showing steps
- Asks "what if" questions beyond the lesson
Extension for Students Ready for More
Extension in Math
Richer problems on the same topic, not a second worksheet.
Why it happens
The student has already mastered the skill being practiced. More of the same problems adds no learning and can feel like a penalty for being quick. What helps is a harder question on the same idea.
Try this tomorrow
- Give a short pre-check, then skip practice the student has already mastered
- Swap in one open problem with many solution paths
- Ask for a second method, a proof, or a general rule
- Have the student write a new problem and solve it
- Praise depth of thinking, not speed
If two of you are in the room
Co-teaching pairs can split this between them, and swap who takes which part so both teachers work with every student.
One teacher
Leads the core lesson and practice for most of the class.
The other teacher
Runs a short extension seminar with a rich task. Next unit, the two teachers trade groups.
What the research can and cannot tell us
Compacting research was done with teachers in grades 2 to 6. Rich, open tasks are well supported by math education experts, but few controlled studies test them with advanced high school students.
Resources
9 resources for this topic, drawn from 7 organizations. Everything opens free, and the ones from other organizations open on their own sites.
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Youcubed Tasks, Filtered by Grade
Pick an open task for grades 9 to 12 that every student can start and advanced students can push far.
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Mathematics Assessment Project: High School Tasks
Choose an Expert task, which is less structured and needs strategy, for students who are done with routine practice.
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Classroom Challenges: Problem Solving Lessons
Full high school lessons built around one rich problem, with sample student work to critique.
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Illustrative Mathematics: High School Tasks by Standard
Find a deeper task on the exact standard you are teaching, so extension stays on topic.
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Creating a Low Threshold High Ceiling Classroom
Read how to run one task for the whole room: think time, partner talk, and questions that push further.
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Curriculum Compacting: The Three Steps
Follow three steps: name the goals, check who has already mastered them, and replace that practice with harder work.
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The Compactor Planning Form
Record what a student has mastered, how you know, and what extension work replaces it.
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Differentiate Content: Tiered Content and Compacting
See short examples of tiered content, learning contracts, and compacting. Examples are from younger grades and adapt up.
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How to Teach Deep Mathematical Thinking
Jo Boaler explains how to turn tasks in your current curriculum into rich tasks, such as asking for visual proof. Transcript included.
These resources are shared for professional learning and planning. They are meant to inform your professional judgment, not replace it. Each student's IEP and your district, state and federal requirements always come first. Listing a resource here is not an endorsement by Layered Education. This is educational information only, not legal advice.
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