Number sense & quantity
Develop magnitude, counting, place value, integers, rational numbers, estimation, and flexible representation of quantity.
My Journey CurriculumStart a conversation Accessible mathematics
Mathematics for
real decisions.
Arizona standards provide coherent mathematical progressions. My Journey makes those ideas visible, touchable, communicable, and useful—without treating speed, handwriting, or mental calculation as the only evidence of understanding.
Understanding before performance
Start with meaning.
Build toward symbols.
Every lesson identifies the essential mathematical relationship, begins from what the learner can already notice or do, and connects concrete experience, visual representation, language, and notation. Tools and accommodations support reasoning; they do not invalidate it.
Six connected strands
Concepts that connect
school and life.
The strands organize Arizona’s grade-level domains and high-school conceptual categories into a flexible instructional architecture. Precise standards will be mapped within each unit and learner pathway.
Operations & algebraic reasoning
Understand operations, patterns, expressions, equations, variables, functions, and the relationships that make procedures meaningful.
Ratios, rates & proportional thinking
Compare quantities, reason with rates, percentages, scale, and proportional relationships in visual and authentic contexts.
Measurement & geometry
Measure, compose, decompose, locate, transform, and reason about space, shape, units, perimeter, area, volume, and coordinate systems.
Data, statistics & probability
Ask statistical questions, collect and represent data, interpret variability, evaluate claims, and reason about likelihood and risk.
Financial & applied mathematics
Use time, money, schedules, budgets, comparison, change, distance, and estimation to make informed decisions in school, work, home, and community life.
Arizona Standards for Mathematical Practice
How learners think
matters, too.
The eight mathematical practices are taught in connected pairs so educators can see reasoning beyond the final answer and learners can build a durable problem-solving identity.
Make sense & persevere
Understand the situation, choose a starting point, monitor progress, and decide whether an answer is reasonable.
Reason & explain
Move between quantities and representations, notice relationships, justify a decision, and respond to another person’s reasoning.
Model & use tools
Represent with objects, drawings, diagrams, tables, graphs, equations, technology, calculators, or assistive tools chosen for purpose.
Attend to precision & structure
Communicate quantities and units clearly, notice repeated patterns, and use structure to make a problem more manageable.
One concept · three fluid routes
Different representations.
Shared mathematical meaning.
A learner may use one route for number and another for geometry or data. Route decisions come from current evidence, not a fixed label.
Explore & Connect
Build meaning through concrete experience and reliable response.
- Match, sort, compare, count, locate, combine, or choose
- Use objects, movement, images, number lines, ten frames, or digital manipulatives
- Communicate more, less, same, next, before, enough, or not enough
Observable evidence
A meaningful comparison, choice, action, representation, or consistent response under known access conditions.
Build & Use
Connect representations, strategies, and mathematical language.
- Represent one idea concretely, pictorially, verbally, and symbolically
- Choose and use a strategy, tool, operation, table, graph, or equation
- Explain a pattern, relationship, estimate, or solution step
Observable evidence
Greater strategy use, accuracy, explanation, independence, and connection across representations.
Apply & Lead
Use mathematics to reason, decide, design, and advocate.
- Model an authentic situation and identify relevant information
- Compare options, critique a claim, justify a choice, or revise a model
- Plan a budget, route, schedule, survey, design, or community solution
Observable evidence
Transfer of mathematical reasoning to a new problem, tool, environment, or consequential decision.
EngageNY-informed lesson architecture
Investigate, model,
practice, and debrief.
My Journey adapts EngageNY’s coherent mathematics lesson sequence while protecting processing time, conceptual understanding, multiple representations, assistive tools, communication access, and authentic application.
Fluency & access
Revisit a small, useful relationship through accessible practice. Fluency means efficient strategy use—not timed performance.
Application problem
Begin with a short, relevant situation that activates prior knowledge and gives the mathematics a purpose.
Concept development
Model and investigate the essential idea through concrete, representational, and abstract forms with explicit language and tools.
Guided practice
Solve, represent, compare, or explain with responsive prompting, feedback, and planned opportunities for choice.
Debrief & transfer
Discuss what worked, connect representations, revisit the target, and apply the idea with one meaningful change.
Example outcome pathway
Plan within a
weekly food budget.
The standard-connected idea stays shared: use quantities, operations, comparison, estimation, and reasoning to make a defensible decision.
Explore & Connect
Match items to prices, compare more and less, and choose whether a small set of items fits within a visual spending limit.
Build & Use
Add item prices, estimate the total, compare it with a budget, and explain one adjustment using a calculator or chosen representation.
Apply & Lead
Build and justify a weekly grocery plan, compare unit prices or alternatives, and revise the plan when one condition changes.
Alignment & attribution
Rigorous mathematics.
Responsive teaching.
This developing framework is connected to the Arizona Mathematics Standards and informed by Arizona’s guidance on academic achievement, inclusive practices, UDL, and specially designed instruction. Its lesson architecture is informed by the archived EngageNY mathematics modules. My Journey Curriculum is independently developed and is not endorsed by ADE or NYSED.
Structure in development
Next: the complete
mathematics scope and sequence.
Strand progressions, unit-level standards, lesson plans, assessments, manipulatives, and accessible resources will be added as the mathematics curriculum is mapped.
Discuss accessible math