Mathematics & Logic
A payment plan, a map, a chart, and a probability claim can all demand mathematical judgment. Young people need actual Algebra I and Geometry competence as well as the habit of estimating, comparing, and checking whether the numbers answer the right question.
Practical Math Skills for Real Life
The Floor includes mathematical foundations. The broader map develops statistics, spatial reasoning, logical problem-solving, and quantitative decisions without confusing skepticism with mathematical mastery.
What young adults should be able to do by 18 · The formal Floor: Domain 2
The Floor for This Domain
The non-negotiable minimum. This is the contract, not the menu — what a floor-complete 18-year-old must actually be able to do.
- Handle the math real life throws at them: budgeting, tipping, unit conversions, splitting costs, reading a tax form, understanding a loan agreement, comparing deals
- Handle everyday mental math without reaching for a phone—tips, rough totals, quick comparisons
- Work with percentages, ratios, and basic statistics well enough to interpret news, polls, and data claims without being easily fooled
- Solve problems they haven't seen before by breaking them down logically—not panicking when there's no formula handed to them
- Read a graph, chart, or table and understand what it's actually saying, and what it might be hiding
- Think in estimates and sanity-checks—can spot when a number is way off before doing precise calculations
- Demonstrate competence in Algebra I and Geometry fundamentals—can follow a formula, rearrange it, plug in values, and reason about shapes, angles, and spatial relationships
- Reason about risk, likelihood, and tradeoffs in everyday decisions
Not on the Floor
- Calculus
- Geometric proofs
- Memorized formulas they'll never use
- "Show your work" ritual for its own sake
The Broader Map
The fuller landscape this domain engages over time. Inclusion here does not by itself make a competency mandatory.
Core Outcomes
- Master Algebra I & Geometry
- Apply quantitative reasoning in real-world problems
- Use logic & pattern recognition to solve novel tasks
Key Competencies
- Algebraic fluency & equation solving
- Spatial & geometric reasoning
- Data analysis & estimation
- Everyday mental math, estimation & numerical sanity-checking
- Applied math in budgeting, travel & probability
- Statistics & interpreting data sets
- Risk, probability & trade-off reasoning
- Pattern recognition & logical reasoning
- Procedural / algorithmic reasoning (designing clear step-by-step processes)
- Debugging processes & structured problem-solving
- Logic-puzzle fluency (e.g., LSAT style)
Evidence Examples
solved problems, budget sheets, code snippets, game-design docs, etc.
How It Builds
Mixed-runway domain. Number sense and quantitative reasoning build early. Procedures can come later. The goal is thinking mathematically, not performing school math.
Written for adults: developmental signals are prompts to investigate, not diagnoses or verdicts.
Early Childhood (18 months – 5 years)
On track
- Counts objects (not just reciting numbers)
- Understands more/less, bigger/smaller
- Recognizes basic shapes
- Sorts objects by attributes
- Beginning pattern recognition
- Enjoys puzzles and building
- Understands basic sequence (first, then, last)
Worth investigating
- No number sense by age 5 (can't count a few objects)
- Cannot compare quantities (more/less)
- No interest in patterns, puzzles, or building
What's building: Number sense. Quantity intuition. Pattern recognition. Spatial awareness.
Middle Childhood (6 – 9 years)
On track
- Solid with addition, subtraction; working on multiplication/division
- Can solve simple word problems
- Estimates reasonably before calculating
- Understands place value
- Tells time, counts money
- Recognizes patterns and extends them
- Comfortable with basic fractions (half, quarter)
Worth investigating
- Cannot do basic arithmetic by age 8 despite instruction (possible dyscalculia—investigate, support)
- No concept of estimation or magnitude
- Has adopted 'I'm not a math person' identity
- Complete math avoidance/anxiety
What's building: Arithmetic fluency. Estimation habit. Quantitative confidence. Problem-solving stance.
Late Childhood / Early Adolescence (10 – 13 years)
On track
- Fluent with arithmetic; fractions, decimals, percentages
- Can work with ratios and proportions
- Beginning algebraic thinking: variables, simple equations
- Understands basic statistics (mean, interpreting data)
- Can read and interpret charts/graphs
- Solves multi-step problems
- Estimates and sanity-checks naturally
- Beginning geometric reasoning: angles, area, spatial relationships
Worth investigating
- Cannot work with fractions or percentages
- No concept of variables or unknowns
- Cannot interpret basic charts or data
- Math identity fully negative; complete shutdown
What's building: Proportional reasoning. Algebraic thinking. Data literacy. Problem-solving confidence.
Adolescence (14 – 18 years)
On track
- Handles real-life math: budgeting, tipping, loans, conversions, comparisons
- Does everyday mental math without phone
- Works with percentages, ratios, basic statistics
- Solves novel problems by breaking them down
- Reads graphs/charts; knows what they show and hide
- Estimates and sanity-checks before precise calculation
- Uses algebraic thinking: works with variables, solves for unknowns, sees relationships
- Uses geometric reasoning: understands space, shape, measurement, spatial relationships
- Reasons about risk, probability, tradeoffs
Worth investigating
- Cannot do basic real-world math
- Cannot interpret data or statistics
- Panics at any unfamiliar math problem
- No estimation ability; can't spot unreasonable numbers
What's building: Functional numeracy. Data interpretation. Algebraic and geometric reasoning. Risk/tradeoff thinking.