Writing 30days Topics

Page Budget

The complete book must be ≤ 150 pages (target ~120). Budget:

Per-day targets:

• Single-topic day: opener (1 pg) + content (~1.5–2 pg) = ~2.5–3 pages total
• Double-topic day: opener (1 pg) + content (~2–2.5 pg) = ~3–3.5 pages total

How It Differs from Other Book Types

File Structure

in30Days.cls                            # Document class (orange-themed, chapter-based)
in30days_main.tex                       # Master document (template)
VM_packages/VMfunDays.sty              # Day-specific environments

topics_in30days/                        # Core day files (CCSS baseline)
    day-01-unit-rates-and-proportional-relationships.tex
    day-02-constant-of-proportionality-and-equations.tex
    ...
    day-30-simulating-compound-events.tex

topics_in30days_modified/               # Modified day files (state-specific)
    day-03-graphing-and-applying-proportional-reasoning.tex
    day-04-percent-problems-and-proportions.tex
    ...

topics_in30days_additional/             # Standalone bonus lesson files
    bonus-ch01-07-proportional-reasoning-with-scale-models.tex
    bonus-ch02-08-personal-financial-literacy.tex
    ...

initial_pages/in_30_days/               # Front matter
    00-welcome.tex                         # Welcome page (orange theme)
    01-how-to-use.tex                      # Guide to day-based box system
    02-your-30-day-plan.tex                # Bird's-eye overview of all 30 days
    03-progress-tracker.tex                # 30-day check-off grid
    (also reuses common/formula-reference.tex, common/key-vocabulary.tex)

The 30-Day Plan

Design Rationale

The day-to-topic mapping was designed using these principles:

1. All 30 days teach — no review days or celebration days.
2. Maximum 2 topics per day — no triple-topic days.
3. Content-aware pairing — study-guide topic file lengths were analyzed (40–69 lines) to ensure lighter topics share days and heavier topics stand alone.
4. Modification-aware grouping — when two topics in a double day are modified by overlapping state sets, they share a day file to minimize multi-variant complexity.
5. Pedagogical fit — paired topics are conceptually related and flow naturally together so the day tells a coherent "story."

Audience & Tone (Grade 7)

Students are 12–13 year olds in middle school. Content should:

• Use clear, confident language — these students can handle proper mathematical terminology.
• Use real-world contexts that resonate: sports statistics, shopping/budgeting, cooking (scaling recipes), phone plans, social media analytics, school event planning, part-time job earnings.
• Introduce formal vocabulary (e.g., "constant of proportionality," "reciprocal," "complementary angles") with brief plain-language definitions on first use.
• Maintain a supportive, no-nonsense tone — encouraging but not childish.
• Grade 7 is the year of proportional reasoning, rational number operations, and first encounters with geometric proofs — emphasize WHY, not just HOW.

Complete Day-to-Topic Mapping

Chapter 1 — Ratios and Proportional Relationships (Days 1–3)

Why ch01-01 + ch01-02? Computing unit rates and recognizing proportional relationships are the foundational skills of the chapter. Students compute unit rates with fractions, then immediately use them to test whether two quantities are proportional. Natural concept → application flow.

Why ch01-03 + ch01-04? Finding the constant of proportionality and writing equations ($y = kx$) are the same idea in two representations — one numerical, one symbolic. Students find $k$ from a table, then write the equation.

Why ch01-05 + ch01-06? Graphing proportional relationships and applying them to word problems are the capstone pair. Students graph, interpret $(0,0)$ and $(1,r)$, then apply all strategies in multi-step problems.

Chapter 2 — Percents in Everyday Life (Days 4–7)

Why ch02-01 + ch02-02? Solving percent problems and connecting percents to proportions are the same skill from two angles — students solve $\frac{x}{100} = \frac{\text{part}}{\text{whole}}$.

Why ch02-03 + ch02-04? Percent increase/decrease is the concept; markups, discounts, and sales tax are the immediate real-world applications. "Increase by 20%" = markup; "decrease by 15%" = discount.

Why ch02-05 + ch02-06? Tips, commissions, and simple interest are all "percent of an amount" applications. They share the formula structure (amount × rate) and make a cohesive "money math" day.

Why ch02-07 alone? Percent error is conceptually distinct — it involves absolute value and a specific formula. Students need focused attention on $\frac{|\text{estimated} - \text{actual}|}{|\text{actual}|} \times 100$.

Chapter 3 — Operations with Rational Numbers (Days 8–12)

Why ch03-01 + ch03-02? Defining integers/opposites and then adding them is a natural ramp-up. Day 8 answers "What are integers?" and "How do we add them?" in one lesson.

Why ch03-03 + ch03-04? Subtracting integers ($p - q = p + (-q)$) and extending to rational-number addition/subtraction are the same rule applied at different scopes — integers first, then fractions/decimals.

Why ch03-05 + ch03-06? Multiplying and dividing signed numbers share the same sign rules (same signs → positive, different signs → negative). Teaching them together reinforces this symmetry.

Why ch03-07 alone? Converting rational numbers to decimals (long division, detecting repeating patterns) is a distinct procedural skill that deserves its own day for mastery.

Why ch03-08 alone? This capstone day synthesizes all four rational-number operations in multi-step real-world problems. Students must choose operations, convert between forms, and check reasonableness.

Chapter 4 — Algebraic Expressions (Days 13–15)

Why ch04-01 + ch04-02? Writing/evaluating expressions and combining like terms are the two fundamental expression skills — create them, then simplify them.

Why ch04-03 + ch04-04? Expanding with the distributive property and factoring are inverse operations. Teaching them together helps students see $3(2x+5) = 6x+15$ in both directions.

Why ch04-05 + ch04-06? Adding/subtracting linear expressions and rewriting expressions for insight are the capstone skills. Students combine expressions and then interpret what the new form reveals (e.g., $a + 0.05a = 1.05a$).

Chapter 5 — Equations and Inequalities (Days 16–18)

Why ch05-01 + ch05-02? Writing and solving two-step equations are the same workflow: translate → solve → check. Splitting them would create an awkwardly thin "write but don't solve" lesson.

Why ch05-03 + ch05-04? Equations with the distributive property ($p(x+q) = r$) and multi-step real-world problems are both extensions of two-step solving. They build directly on Day 16 skills.

Why ch05-05 + ch05-06? Writing/solving inequalities and graphing them on a number line are inseparable — students write $px + q > r$, solve, and graph. Same topic, two representations.

Chapter 6 — Scale Drawings, Geometric Figures, and Angle Relationships (Days 19–21)

Why ch06-01 + ch06-02? Using scale drawings and reproducing them at a different scale are the same skill at two levels — read a scale, then create one. Both use scale factor reasoning.

Why ch06-03 + ch06-04? Drawing geometric figures under constraints and constructing triangles from three measurements are companion construction tasks. Day 20 is the "geometry tools" day.

Why ch06-05 + ch06-06? Cross-sections and angle relationships are both "seeing geometry in new ways" — slicing 3D shapes and finding unknown angles from supplementary/complementary/vertical pairs. They're conceptually distinct but share the "geometric reasoning" day.

Chapter 7 — Circles, Area, Surface Area, and Volume (Days 22–24)

Why ch07-01 + ch07-02? Parts of a circle (center, radius, diameter) and circumference ($C = \pi d$) are the natural introduction → formula pair. Students learn the vocabulary, then immediately use it.

Why ch07-03 + ch07-04? Circle area ($A = \pi r^2$) and composite-shape area are a learn → extend pair. Once students know circle area, they combine it with triangles and rectangles to find areas of complex shapes.

Why ch07-05 + ch07-06? Surface area and volume are the two key 3D measurement skills. Pairing them on one day lets students see both "wrapping" and "filling" the same prism, reinforcing the distinction.

Chapter 8 — Statistics: Sampling and Comparing Populations (Days 25–26)

Why ch08-01 + ch08-02? Defining populations/samples and then making inferences from random samples is a single concept arc: "What is a sample?" → "What can we learn from it?"

Why ch08-03 + ch08-04? Comparing populations visually (dot plots, box plots) and comparing with measures (mean, MAD, IQR) are two approaches to the same question: "How do these groups differ?"

Chapter 9 — Probability and Compound Events (Days 27–30)

Why ch09-01 + ch09-02? "What is probability?" defines the 0-to-1 scale; theoretical probability puts it to work with $\frac{\text{favorable}}{\text{total}}$. The definition alone would be too thin for a full day.

Why ch09-03 + ch09-04? Experimental probability (long-run relative frequency) and probability models (uniform vs non-uniform) are paired as "predicted vs observed" — students build a model, then test it experimentally.

Why ch09-05 + ch09-06? Sample spaces (lists, tables, tree diagrams) and finding compound-event probabilities are inherently paired — you build the sample space IN ORDER TO find probabilities. Separating them breaks the workflow.

Why ch09-07 alone? Simulating compound events is the capstone topic. Students design and run simulations using random-number generators — this synthesizes everything from the chapter's probability toolkit.

Totals Verification

• 4 single-topic days + 26 double-topic days = 30 days
• 4 topics (singles) + 52 topics (doubles) = 56 topics ✓

Writing Day Files

Day File Template

Every day file lives in topics_in30days/ and follows this structure:

% ============================================================================
% Day N — Day Title
% CCSS 7.XX.X.X
% Topics: chXX-YY Topic Name (+ chXX-ZZ Second Topic Name)
% Type: Single|Double (Light|Medium|Heavy)
% ============================================================================
\section{Day Title}

\dayPage{N}{Day Title}{%
    \begin{itemize}[leftmargin=6mm, itemsep=4pt]
        \item[\textcolor{funOrange}{\faCheck}] Goal 1
        \item[\textcolor{funOrange}{\faCheck}] Goal 2
    \end{itemize}
}

\minuteTimer{20}

\begin{quickLesson}{Key Concept}
% ≤ half page: state the rule, show one clear example, done.
\end{quickLesson}

\begin{workedExample}{Title}
% One example with step-by-step solution
\end{workedExample}

\mascotSays{One short fun sentence.}

\begin{dailyPractice}
\resetProblems
% 6 problems (single-topic) or 8 problems (double-topic)
\end{dailyPractice}

\begin{dailyChallenge}
\prob One challenge problem
\end{dailyChallenge}

\keyTakeaway{One-sentence summary.}

\dayComplete

Important rules:

• Do NOT include \begin{todaysGoals} — the \dayPage already displays goals.
• Do NOT add \newpage before \begin{dailyPractice} — let content flow naturally.
• The \section{Day Title} MUST come before \dayPage and use a concise title that describes the day's content (not just "Day N").

Double-Topic Days

When a day covers 2 topics, use \dayTopic{Title} to create sub-headers:

% ─── PART 1 ────────────────────────────────
\dayTopic{First Topic Title}

\begin{quickLesson}{Key Concept}
% ≤ ⅓ page per topic
\end{quickLesson}

\begin{workedExample}{Title}
% Brief example
\end{workedExample}

% ─── PART 2 ────────────────────────────────
\dayTopic{Second Topic Title}

\begin{quickLesson}{Key Concept}
% ≤ ⅓ page per topic
\end{quickLesson}

\mascotSays{Short fun sentence.}

\begin{dailyPractice}
\resetProblems

\practiceHeader{First Topic}
\prob ... % 4 problems

\bigskip
\practiceHeader{Second Topic}
\prob ... % 4 problems
\end{dailyPractice}

Each topic gets ~⅓ page teaching + 1 example. Combined practice = 8 problems total (4 per topic).

Day-Specific Environments (from VMfunDays.sty)

Environments from Other VM_packages

Day files can also use ALL environments from the standard VM_packages:

• Teaching: conceptBox, stepsBox, vocabBox, rememberBox, tipBox, mathRuleBox, keyIdea, etc.
• Examples: workedExample, errorBox, sideBySideExample, etc.
• Practice: practiceBox (use dailyPractice instead for 30-day format), codeBreaker, riddleBox
• Math visuals: fractionBar, areaGrid, barGraph, numberLine, etc.
• Engagement: \mascotSays{}, \encouragement{}, funFact, riddleBox, activityBox, etc.
• Answers: \answer{}, \answerTF{}, \answerMC{}, \answerExplain{}{}

Content Guidelines

1. Audience: 12–13 year olds (middle school). Clear language, proper math vocabulary introduced with definitions, real-world contexts relevant to the age group.
2. Ultra-concise lessons: Each quickLesson covers the concept in ≤ half a page. State the rule, show one clear example inline, done. No fluff.
3. One workedExample per topic — only when the concept needs an explicit step-by-step walkthrough. Do NOT use 2–3 examples.
4. No redundant boxes: Do NOT use todaysGoals (redundant with \dayPage), standalone rememberBox, or standalone tipBox. Fold important tips into the quickLesson body.
5. Practice counts:
   • 6 problems for single-topic days
   • 8 problems for double-topic days (4 per topic with \practiceHeader{})
   • Every problem MUST have an \answer{}, \answerTF{}, \answerMC{}, or \answerExplain{}{}.
6. One dailyChallenge per day (1 problem only). The challenge should be noticeably harder — multi-step, requiring synthesis, or connecting to real-world reasoning.
7. One \mascotSays{} per day — a single short, fun sentence that relates to the day's topic.
8. No \newpage before practice — let content flow naturally across pages.
9. Double-topic days: Each topic gets quickLesson (~⅓ page) + 1 workedExample. Combined dailyPractice with \practiceHeader{} separators.
10. Math always in $...$. Use \times and \div, not × or ÷.
11. Bold key terms on first use with \textbf{...}.
12. 2–3 goals max in the \dayPage itemize list (not 4+).
13. Difficulty progression within practice: Start with 1–2 direct application problems, then 2–3 that require a small twist or extra step, then 1–2 that embed the skill in a word problem or context.
14. Answer precision: All numerical answers must be fully simplified. Fraction answers in lowest terms. Decimal answers exact (no rounding unless the problem says so). Every answer key entry must be unambiguous.

Content Accuracy Checklist

Before finalizing any day file, verify:

• All \answer{} values are correct and fully simplified
• Fraction answers are in lowest terms
• Problems within scope — no concepts from later days
• LaTeX compiles without errors (balanced braces, no undefined commands)
• \dayPage number matches the day number in the filename
• Topic header comment matches the day's topic IDs from topics_config.yaml

State-Specific Handling

The 30-day book supports all 50 US states. 43 states use the pure CCSS curriculum (identical content). 7 states have customizations through two