Layered EducationWhat it looks like
- Counts on fingers or guesses at basic facts
- Stalls on fractions, negatives, or multi-step problems
- Copies steps without knowing why they work
Significant Skill Gaps in Secondary
Math Gaps
Early elementary math skills in an Algebra or Geometry class: how to teach both at once.
Why it happens
Math builds on itself. Missed number sense, facts, or fractions use up working memory, so little is left for the new idea. This reflects missed instruction, not ability.
Try this tomorrow
- Model one solved problem aloud, then solve the next one together
- Pair every equation with a drawing, number line, or table
- Hand out calculators so facts do not block the grade-level idea
- Run 5 minutes of fact or fraction practice, a few times a week
- Teach problem types (total, difference, change), not key words
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
Models the grade-level problem step by step with a visual and a worked example.
The other teacher
Runs a short small group on the prerequisite skill, then checks first attempts.
What the research can and cannot tell us
The strongest studies on explicit instruction, visual models, and word problem schemas come from kindergarten to grade 8. Evidence for the high school algebra guide is rated minimal to moderate. Adapt with care.
Keep in mind
A calculator or formula sheet used every day may need to be written into an IEP or 504 plan to be allowed on tests. Check with the case manager.
Resources
9 resources for this topic, drawn from 6 organizations. Everything opens free, and the ones from other organizations open on their own sites.
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Assisting Students Struggling with Mathematics: Summary
Six strong-evidence practices with how-to steps: systematic instruction, math language, representations, number lines, word problems, and timed practice.
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Teaching Strategies for Improving Algebra Knowledge: Summary
Use solved problems, teach structure, and compare strategies in Algebra. Includes sample problems and discussion prompts.
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Supporting Teaching of Algebra: Instructional Guide
Short how-to sections on explicit instruction, multiple representations, math language, word problems, graphic organizers, and brief fluency practice.
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Intensive Math Intervention: Instructional Delivery
Free slides, workbook, and activities on explicit instruction and moving from concrete to pictorial to abstract.
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Intensive Math Intervention: Instructional Strategies
Watch short videos of flashcard routines and word problem teaching. Covers brief fact practice, schemas, and math confidence.
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Schema Instruction for Word Problems
Teach students to spot the problem type and draw it. Covers total, difference, change, equal groups, comparison, and ratios.
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Basic Facts: Sample Lessons and Activities
Ready-made lessons, worksheets, flashcards, and score cards for short fact practice with one student or a small group.
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Calculator: Research
A fact sheet summarizing studies of calculators as an accommodation. Useful when deciding together who needs one.
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5 Ways to Free Up Working Memory in Math
Five quick moves, such as annotation, anchor charts, and manipulatives, that lower the load so students can reach harder problems. 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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Want help putting this to work?
Facilitated co-planning days give a pair protected time to pick a focal student, choose one thing to try, and plan who does what. The first call is free.