K-12 prerequisite knowledge map
Common Core & COVID Learning Loss
K-12 Common Core math standards structured as a prerequisite knowledge map, annotated with COVID-era learning loss research. Shows how pandemic disruptions to foundational skills propagate downstream through years of dependent content.
What this map shows
The map above is the entire Common Core Mathematics curriculum — every standard from kindergarten through high school — broken down into 773 atomic learning outcomes and linked by 851 prerequisite relationships.
Zoom in to see how a single 6th-grade standard depends on nine standards stretching back to 2nd grade. Pan to follow a chain forward and watch how disrupting any standard cascades into later grades. Click a node to see exactly which downstream standards rely on it.
Standards in red were directly disrupted by spring 2020 COVID school closures. Standards in yellow are downstream of disrupted content — kids will encounter them years later, with the upstream gap still there.
You’re looking at what a flat list of standards can never show: structure, dependency, and downstream risk.
How one disrupted lesson cascades through high school
In spring 2020, schools closed nationwide for an average of 13 weeks. For 6th graders in Massachusetts, that meant 27 specific math standards were never taught the way they should have been.
Here’s what happened to just one of them.
Directly disrupted
6.NS.8 — coordinate-plane problem solving
Solving real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
Downstream chain
- 1
7.G.4 · Grade 7
Area and circumference of circles.
- 2
7.G.6 · Grade 7
Real-world problems involving area, volume, and surface area.
- 3
8.G.8 · Grade 8
Applying the Pythagorean Theorem to coordinate distances.
- 4
G-GPE.1 / G-GPE.2 / G-GPE.3 / G-GPE.7 · High School
Deriving equations for circles, parabolas, ellipses — the entire coordinate geometry block.
A single missed lesson in 6th grade compromises content students will encounter at age 16. And 6.NS.8 wasn’t unusual — it was one of 27 directly disrupted standards in that grade alone. When the full cascade is traced, 27 directly disrupted standards turn into 37 downstream-impacted standards reaching into high school.
If you teach 9th grade and you’re wondering why your students are struggling with coordinate geometry — this is part of why.
The point isn’t that COVID is over. The point is that this kind of cascade analysis is always relevant. Every curriculum has fragile chains. Every disruption — a teacher quitting mid-year, a snowstorm closing schools for two weeks, a transfer student missing a unit — sends ripples through standards a list can’t show you.
What the network reveals that a list can’t
Once curriculum is a network, you can ask questions a list can’t answer. Three examples from the Common Core Math model:
Most depended-upon standard
4.NBT.1
Place value — that a digit in one place represents ten times the place to its right.
In our network analysis, 4.NBT.1 has the highest in-degree of any standard in the curriculum. Disrupt place value and the damage spreads further than disrupting almost anything else. If you have limited intervention resources after a disruption, the data says: protect the load-bearing standards first.
Most fragile standards
1.OA.6 / 2.OA.2 / 3.OA.7 / 3.OA.9 / G-CO.4
Standards that synthesize the most upstream knowledge.
These five tie for the highest synthesizing load — they sit downstream of so much else that any upstream gap shows up here first. They’re not fragile because they’re hard. They’re fragile because they reveal earlier gaps. When students struggle with 3.OA.7 (fluent multiplication within 100), the diagnostic question isn’t always “can they multiply?” It’s “what didn’t they get earlier?”
Longest learning chain
2.MD.6 → G-GPE.3
A 9-step prerequisite path spanning four grade bands.
“Derive the equation of an ellipse given the foci” (high school) sits at the end of a chain that begins in 2nd grade with “represent whole numbers as lengths on a number line.” Long chains are doubly important: they’re vulnerable to compounding upstream gaps, and they’re where the most powerful early interventions live.
This is what curriculum looks like when it’s a queryable model instead of a list of bullet points.
Why a list of standards isn’t enough
Common Core Mathematics is published as a list. 331 standards across 10 grade bands. Open the official document and you see paragraphs, numbered codes (4.NBT.1, 7.G.6, G-GPE.3), and grade groupings.
The list format hides the most important thing about the curriculum: how it connects.
Standards aren’t independent. Multiplying within 100 is a prerequisite for almost everything that follows. Place value holds up half the curriculum after 4th grade. Knowing that nothing in the list tells you so means three things go missing:
- You can’t see which standards are load-bearing. Disrupt teaching of one critical standard and the damage radius might span six grade levels — but you’d have no way to know which.
- You can’t trace cascading effects. When a 6th-grade lesson gets cut, what does that mean for 7th, 8th, and high school? In a list, this requires hours of expert review.
- You can’t reuse the analysis. Every new question — a new grade, a new state, a new disruption — starts from scratch.
A network map fixes all three. The relationships become first-class objects. The downstream impact becomes computable. The analysis becomes repeatable.
This map is what happens when you stop treating curriculum as a document and start treating it as data.
Modeled at scale
The full Common Core Math curriculum, modeled as a network:
The model is a directed acyclic graph — prerequisites flow in one direction, and every standard can be ranked by where it sits in the learning chain. Each node carries its grade, domain, and original Common Core code, so analyses translate directly back to classroom decisions.
Once built, the map is reusable. Change the input scenario — a different state, a different grade affected, a different timeline — and the analysis re-runs in seconds. No re-reading the standards. No manual prerequisite tracing. The dependencies live in the data.
Build this for your own curriculum
This map is built on a methodology — chunk standards into atomic outcomes, draw prerequisite relationships, make the graph queryable — that works for any structured curriculum framework.
Outcomap is the tool that lets you do it without writing code, hiring a research team, or maintaining a graph database.
What you can map:
- Accreditation frameworks — ABET, HLC, SACSCOC, WASC, QAA, NZQA, and others. Show how courses align to standards and where coverage gaps live. See the ABET Electrical Engineering example or the NZQA accreditation template.
- Higher education programs — degree programs, course sequences, prerequisite chains. See the MIT undergraduate curriculum for an example at scale.
- Self-paced learning pathways — concept maps, knowledge dependencies, modular courses. See the machine learning curriculum example.
- K-12 curricula — state standards frameworks, scope and sequence, vertical alignment across grades.
How Outcomap works:
- Upload your standards document, syllabus, or program spec. AI extracts entities and relationships.
- Refine the map in the visual editor. Add prerequisite chains, group nodes, draw cross-curricular connections.
- Publish, share, embed, or export. Live interactive maps that anyone can explore — no account required to view.
Data structure
A four-level hierarchy — Grade Band, Domain, Cluster, Micro-outcome — mirrors the official Common Core structure. Directed prerequisite edges between Micro-outcomes encode the dependency chains that make learning loss cumulative: a gap in one standard ripples forward into every standard that builds on it.
Entity types
- Grade Level / BandBroad grade groupings (Grade 1–8 and High School bands).
- DomainMajor mathematical domains within each grade band (e.g., Operations & Algebraic Thinking, Number & Operations).
- ClusterGroups of related standards within a domain (e.g., Understand place value, Apply properties of operations).
- Micro-outcomeIndividual Common Core standards — the atomic learning objectives students are expected to master.
Edge types
- RequiresDirected prerequisite edge between Micro-outcomes: the source standard must be mastered before the target.
Frequently asked questions
- What does this curriculum map show?
- It shows the entire Common Core Mathematics curriculum — every standard from kindergarten through high school — broken down into 773 atomic learning outcomes and linked by 851 prerequisite relationships. The map is annotated with research on the spring 2020 COVID school closures, showing how directly disrupted standards cascade into indirectly disrupted ones across later grades.
- Why model Common Core as a network instead of a list?
- Common Core Mathematics ships as a list of 331 standards, which hides the most important thing about the curriculum: how it connects. A network map makes prerequisite chains, dependency depth, and downstream risk explicit and computable. You can identify which standards everything else depends on, which standards are most vulnerable to upstream gaps, and how disruption to one lesson ripples through later years.
- Can I build a map like this for my school district or curriculum?
- Yes. The same network-mapping approach used here works for any structured curriculum — a state standards framework, a degree program, an accreditation rubric, or a single course. Outcomap is the tool: upload your existing documents, let AI draft the entity and relationship structure, refine it in the visual editor, and publish or embed the result.
Source. The network model and COVID disruption analysis are based on Modeling COVID-19 disruptions via network mapping of the Common Core Mathematics Standards by Luwen Huang, Kayla Bicol, and Karen E. Willcox (MIT Mapping Lab and the Oden Institute, UT Austin), 2022.
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