AUA2 Graphing, Proportional Reasoning and Equations/Inequalities, catalog number MATH 5220, is the four-competency-unit portfolio in WGU's mathematics education sequence covering coordinate pairs and graphing, ratios and proportional reasoning, and equations and inequalities. The catalog lists it as a legacy performance-based portfolio assessment. The strand that decides most outcomes is proportional reasoning, because it is the concept that separates arithmetic thinking from algebraic thinking and it is the one most adults handle procedurally without ever having understood.
What MATH 5220 is actually testing
Proportional reasoning is the hinge of middle-grades mathematics and it is not the same as cross-multiplying. A learner reasoning proportionally recognizes that a relationship stays constant under scaling, can move between the ratio, the unit rate and the constant of proportionality, and knows when a situation is proportional and when it merely looks like it. A recipe scaled from four servings to six is proportional. A phone plan with a monthly fee plus a per-minute charge is not, and telling those apart is the competency being examined.
The graphing strand tests whether coordinates mean something to you beyond plotting. Slope as a rate of change, the vertical intercept as an initial value, and the visual signature of a proportional relationship passing through the origin are all connections a teacher has to make explicit. Portfolio evidence that plots points correctly and says nothing about what the graph shows demonstrates a technical skill and leaves the conceptual aspect unevidenced.
Equations and inequalities test the idea of equivalence under transformation. An equation is a claim of balance and every legal operation preserves that balance, which is why the procedures work. Inequalities add the one rule that trips both students and adults: multiplying or dividing by a negative reverses the direction, and being able to explain why rather than to remember that is the difference between knowing the rule and being able to teach it.
Turning portfolio requirements into a work plan
Scoring detail sits inside your Course of Study rather than in the catalog. Read the aspects before assembling anything, because portfolios grow by accumulation and the gaps are hard to see from inside. Each aspect is scored on its own against a three-point scale, and a 2 in each aspect passes the task.
Where the course is assessed by a performance assessment, build an inventory: one row per aspect, one named artifact per row. Any empty row is a return waiting to happen, and it takes an hour to find rather than a fortnight to fix afterwards.
The word budget, worked. Assume seven scored aspects and roughly 2,400 words of written commentary across the portfolio. Take 150 for a framing statement, leaving about 2,250 across seven aspects, or 320 each. Then move weight toward the conceptual explanations: the proportional reasoning aspect and any aspect asking you to justify a procedure deserve 430, funded by keeping straightforward computational commentary near 220.
Proportional reasoning is where the extra words earn most. Writing out why a unit rate and a constant of proportionality are the same number wearing different clothes is exactly the kind of explanation these portfolios are built to elicit, and it is rarely more than a paragraph once you have thought it through.
A structure that fits a proportional reasoning portfolio
Task directions define required components and govern wherever they speak. Where the arrangement is yours, this order groups evidence by strand and keeps commentary attached to it.
| Component | What belongs in it | How it tends to be scored |
|---|---|---|
| Overview | Where each requirement is evidenced in the portfolio | Prevents the evaluator hunting for material that exists |
| Coordinate work | Plotting, reading and interpreting points and lines | Scored for interpretation, not for accurate plotting alone |
| Slope and rate | Slope computed and explained as a rate of change in context | Context is the scoring surface; a number alone is thin |
| Proportional reasoning | Ratios, unit rates, constants of proportionality and scaling arguments | The heaviest strand and the one most often handled procedurally |
| Non-proportional contrast | A situation that resembles proportionality but is not, with the reason | Strong evidence of conceptual understanding and often omitted |
| Equations | Solving with each step justified by a property | Scored for justification rather than for arriving at the answer |
| Inequalities | Solutions, sign reversal explained, and solution sets represented | The sign rule explanation is a standard scoring point |
| Reflection | What the evidence shows and where your understanding is thinnest | Scored for specificity |
Include the non-proportional contrast even if the directions do not name it. One short artifact showing a linear relationship that does not pass through the origin, with an explanation of why proportional methods fail on it, demonstrates more than three correct proportion problems.
Evidence craft in a graphing and algebra portfolio
Mathematical evidence for teacher portfolios has to do double duty: be correct, and be readable by someone learning the idea.
- Label axes with quantities and units. An unlabelled graph cannot evidence interpretation, only plotting.
- Justify each solving step by name. Addition property of equality and multiplication property of equality are the sentences that turn steps into reasoning.
- Explain the inequality sign reversal rather than asserting it. A number line argument does it in two sentences.
- Show the unit rate explicitly in proportional work, and connect it to the slope and to the constant of proportionality in the same commentary.
- Keep equals signs honest. Writing a chain where consecutive expressions are not equal is the most visible error in algebraic writing.
- Cite any borrowed problem or definition in APA where the rubric asks for citation, and keep quotation minimal since WGU scans submissions for authenticity.
The strongest portfolios include a common student misconception with its diagnosis. Additive reasoning applied to a proportional situation, where a learner adds the same amount to both quantities instead of scaling, is the classic one and explaining it demonstrates exactly the knowledge a mathematics teacher needs.
What separates Competent from a returned portfolio
Everything is Competent or Not Competent, with no letter grades and no ordinary grade point average. Performance assessment work can be revised and resubmitted without a grade penalty, so a return costs time in a six-month flat-rate term rather than record.
Portfolios that clear on the first read tend to show:
- Every aspect matched to a locatable artifact and labelled as such.
- Graphs labelled with quantities and units, and interpreted in words.
- Proportional relationships connected across ratio, unit rate, table, graph and equation.
- At least one non-proportional situation analyzed as a contrast.
- Solving steps justified by named properties.
- The inequality sign rule explained rather than stated.
If your plan includes a proctored objective assessment for this course, the boundary is absolute. Proctored exams are yours to sit. Support is preparation: practice problems, drilled justifications and an honest readiness verdict. We never ask for portal credentials.
Seven mistakes that cost time in AUA2
- Cross-multiplying as the whole of proportional reasoning. It is a procedure, and the aspects are about the relationship underneath it.
- Unlabelled graphs. Without quantities and units on the axes, no interpretation claim can be evidenced.
- Steps without justifications. Solving correctly demonstrates fluency; naming the property demonstrates understanding.
- Asserting the sign reversal. Every adult remembers the rule. Explaining it is what the portfolio is asking for.
- No non-proportional example. Recognizing when proportional methods do not apply is half of proportional reasoning.
- Unmapped evidence. Artifacts an evaluator cannot associate with an aspect are scored as missing.
- Treating slope as a formula only. Rise over run computes a number. Saying what that number means for the two quantities in the situation is what the interpretation aspect asks for.
How support works on this course
These portfolios rarely fail on arithmetic. They fail on unexplained procedure and unmapped evidence. Send the rubric from your Course of Study, the task directions and your assembled material. The work comes back with an aspect-to-artifact map, proportional reasoning written out as a relationship rather than a method, graphs labelled and interpreted, solving steps justified by named properties, and a misconception artifact added where the portfolio has none.
Four competency units and a portfolio structure means the work spreads across weeks. In a six-month flat-rate term, starting it in the first month rather than the fourth is usually what decides whether it closes inside the term at all. There is also a compounding benefit worth naming. The explanations you write here are the explanations you will give in a classroom, so building them carefully now is not overhead on the degree. It is the first rehearsal of the job, done in a setting where a returned draft costs nothing but a rewrite.
Questions students ask about AUA2
Is AUA2 the same course as MATH 5220?
Why is proportional reasoning treated as so important?
How do I explain why an inequality sign reverses?
Proportional reasoning stuck at cross-multiplying?
Send the rubric and your portfolio material. Proportional work gets written as a relationship across ratio, rate, table, graph and equation, with evidence mapped to every aspect.
Where AUA2 sits in WGU's programs
The July 2026 catalog places this code in 1 current WGU program. Open a program page for the complete standard path and term positions. The live Degree Plan remains authoritative after transfer credit, substitutions, and mentor planning.
The assessments, one by one
The public catalog does not publish this course's PA/OA identity or task count. WGU Tutors publishes at most one PA manual per course and only from a WGU-controlled public rubric. Until that source exists, PA help begins from the student's real Course of Study and OA support remains preparation only.