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Writing Grade 7 Math Study Guide Topics

CRITICAL — Page Budget

The finished book MUST be 150–170 pages total (including front matter, all topics, and the answer key). There are 56 topics, so each topic averages roughly 2–3 printed pages. That means:

• Target: 60–90 lines of LaTeX per topic file. This is the single most important constraint. If your file is over 90 lines, cut it down. Every sentence must earn its place.
• A simple topic (e.g., "What Is Probability?") might be 55–70 lines (~1.5 pages).
• A dense topic (e.g., "Solving Equations with the Distributive Property") can go up to 100 lines (~2 pages) but no more.
• Never exceed 2 printed pages for any single topic.

When in doubt, cut. A short, clear explanation that a student actually reads beats a long one they skip.

The Book

This is a single-edition Grade 7 math book. Each topic should teach ONE concept clearly and give students practice — nothing more. Keep it tight.

Topic files live in topics/. File naming: ch01-01-slug-here.tex

Audience: 12–13 Year Olds (Grade 7)

Write for a smart, curious 12-year-old. These students have Grade 7 foundations — make every explanation dead simple but don't talk down to them.

• Use very short sentences. Aim for 8–12 words per sentence. One idea per sentence. If a sentence has a comma, consider splitting it.
• Use the simplest words possible. Say "find" not "determine." Say "shows" not "demonstrates." Say "same" not "equivalent" (until you define it). Write how you would talk to a kid.
• Simple first, formal second. Say "undo the operations backward" before "apply inverse operations." Always teach the real math term too, but lead with the plain-English version.
• Conversational, not textbook-stiff. Use "you" and "let's" freely. Keep it warm but not babyish.
• Connect to their world. Sports stats, video games, online shopping, cooking, phone plans, social media — use things they know.
• Be encouraging without overdoing it. One "Nice work!" is plenty. Skip filler praise.
• Cut any sentence that doesn't teach something. If you remove a sentence and the topic still makes sense, remove it.

Writing Style — Concise and Crystal Clear

Every word must earn its place. Here are concrete examples:

Rules:

• Delete transition sentences. "Let's see how this works" → just show it.
• Delete summary filler. "Now you know how to..." → cut it.
• One sentence per idea. If a sentence has "and" connecting two ideas, split it.
• No redundancy. If the conceptBox explains it, don't re-explain it in prose before the example.
• Definitions: one sentence. "The constant of proportionality is the value of $k$ in $y = kx$." Done.

Content Standards

Follow Common Core State Standards (CCSS) for Grade 7. The five domains are:

1. Ratios and Proportional Relationships (7.RP) — unit rates with fractions, proportional relationships, constant of proportionality, equations/graphs, percent problems, percent increase/decrease, markups/discounts, simple interest, percent error
2. The Number System (7.NS) — integers and opposites, adding/subtracting integers, rational number operations (all four), converting rationals to decimals, multi-step real-world problems with rational numbers
3. Expressions and Equations (7.EE) — writing/evaluating expressions, combining like terms, distributive property, factoring, adding/subtracting linear expressions, two-step equations, equations with distributive property, inequalities
4. Geometry (7.G) — scale drawings, geometric figures with given conditions, constructing triangles, cross-sections of 3D figures, angle relationships, circles (circumference, area), composite shapes, surface area, volume of prisms
5. Statistics and Probability (7.SP) — populations/samples, random sampling, comparing populations visually and with measures, probability concepts, theoretical/experimental probability, probability models, sample spaces, compound events, simulations

Numbers at this level: all rational numbers (positive and negative integers, fractions, decimals), proportional reasoning, two-step and multi-step problems, probability (0 to 1). This builds on Grade 7 — students work with signed rationals, proportional relationships, and basic probability.

Creative Freedom

You have access to 100+ environments and commands (see the toolkit reference below). There is no rigid template. Your job is to pick the combination that best serves each topic.

General principles:

• Teach the concept, then let them practice. That's the only hard structure rule.
• Be ruthlessly concise. Every environment, every sentence, every example must pull its weight. If something is "nice to have" but not essential — cut it.
• Limit teaching environments to 2–3 per topic. For example: one conceptBox + one workedExample + one mascotSays. That's usually enough. Don't stack four or five boxes.
• One worked example is usually enough. Add a second only if the concept has two clearly different cases (e.g., percent increase vs. percent decrease). Never more than two.
• Vary the flow between topics. If the last topic opened with a conceptBox, try a real-world scenario or a bold definition.
• Don't force environments. Only include a riddleBox if you have a great riddle. An empty filler environment is worse than nothing.
• Prefer compact environments. mascotSays, tipBox, and keyIdea take less space than exploreBox or activityBox. Use the lighter option when both work.

Things that tend to work well (use freely when they fit):

• \mascotSays{} — the owl giving a memorable shortcut or insight. Students love this.
• \tipBox{} — practical tricks ("To check a proportion, cross-multiply!")
• Visual math commands — \numberLine, \fractionBar, \fractionCircle, \barGraph, etc. A good visual is worth a page of explanation.
• \begin{workedExample} and \begin{sideBySideExample} — showing HOW to solve is the core of teaching.
• \begin{errorBox} — "find the mistake" is surprisingly effective for learning. Great for topics where common errors exist (integer signs, proportion setup, equation solving, percent increase/decrease).
• \begin{realWorld} — connecting math to life makes it stick. Especially powerful for percents, proportions, statistics, and probability topics.
• \sayLeft / \sayRight — dialogue-style explanations can break up dense content.

Things to use sparingly (they take lots of space):

• \begin{codeBreaker} — engaging but space-heavy. Use rarely, maybe 2–3 times in the whole book.
• \begin{mathTrail} — connected problem sequences. Reserve for review/capstone topics only.
• \begin{activityBox} — hands-on activities. This is a book, not a classroom. Use very rarely.
• \begin{storyProblem} — 1–2 sentences max for setup. Keep it short.
• \begin{riddleBox} — only if the riddle is genuinely good and short.
• \encouragement{} — a short motivational closer. Use on maybe half the topics, not all.

Opening ideas (pick what fits, vary between topics):

• A conceptBox that gets straight to the point
• A \begin{realWorld} scenario that motivates WHY this topic matters
• A conversation (\sayLeft / \sayRight) that introduces the key idea
• A \definitionSpotlight for a bold, clean definition
• An \begin{exploreBox} for discovery-based learning
• A \mascotSays{} that poses an intriguing question
• A \begin{riddleBox} that hooks the reader

Topic Structure (Guidelines, Not Rules)

A typical topic might flow like this — but feel free to deviate:

% ============================================================================
% Section X.Y — Topic Title
% CCSS 7.XX.X.X
% ============================================================================
\section{Topic Title}
\topicTitle{Topic Title}

\begin{learningGoals}
\begin{itemize}
    \item Goal 1
    \item Goal 2
    \item Goal 3 (2–4 goals is typical)
\end{itemize}
\end{learningGoals}

% --- Teaching (keep to 2–3 environments total) ---
% e.g., one conceptBox + one workedExample + one mascotSays

% --- Practice (NO \newpage — let content flow naturally) ---
\begin{practiceBox}{Title}
\resetProblems
% 4–5 problems with answers
\end{practiceBox}

Target: entire file = 60–90 lines.

Firm structural rules:

1. Start with \section{Title} (DO NOT add \topicTitle{} — the class file’s \section already renders a blue banner; adding \topicTitle creates a duplicate).
2. Include \begin{learningGoals} near the top (2 goals is ideal).
3. End with a practice section (usually practiceBox).
4. Every problem MUST have an answer (see Answer Rules below).
5. DO NOT put \newpage before the practice section. The \section command already forces a page break for each topic. Adding \newpage before practice wastes half a page of whitespace. Let content flow naturally — boxes are breakable and will split across pages.
6. keep it concise. Aim for 60–90 lines of LaTeX.

Everything in between is up to you — but keep it lean.

Practice Sections

Problem count: Aim for 4–5 problems per topic. Quality over quantity. A few well-chosen problems teach more than a long list.

• A computation topic might have 5 short drill problems.
• A conceptual topic might have 4 thoughtful ones.
• Never exceed 6 problems. Space is limited.

Difficulty progression: Start easy, end harder:

• Basic (2–3 problems): straightforward application
• Applied (1–2 problems): word problems or multi-step
• Challenge (0–1 problem): harder reasoning or error analysis

Problem types to mix and match:

• \prob — standard numbered problem
• \trueOrFalse — quick true/false statement
• \multiChoice — multiple choice
• \circleAnswer — circle the correct option
• \wordProblem — word problem with answer line
• \wrongAnswer — fix the mistake (inside errorBox)
• \sortCategory / \sortItem — sorting/classifying (inside sortBox)
• \codeClue — code breaker clues (inside codeBreaker)
• \trailStop — connected problems (inside mathTrail)
• Fill-in-the-blank with \answerBlank
• Input/output tables with fillTable
• Use \begin{multicols}{2} or {3} for compact layouts when problems are short.

Practice section structure:

• Start with \resetProblems inside the practiceBox.
• Use \practiceHeader[color]{Title} to organize subsections when you have different types (e.g., "Computation", "Word Problems", "Challenge").
• You can include standalone environments OUTSIDE the practiceBox too (like a challengeBox or codeBreaker after the main practice).

Answer Rules

Every single problem must have an answer. Place the answer command immediately after the problem.

Writing Good Answer Explanations (CRITICAL)

Use \answerExplain for nearly every problem. The student just learned this topic — if they couldn't solve a problem, a bare calculation won't help them either. The explanation is their mini-tutor.

Length: Each explanation should be 1–2 full printed lines (~80–200 characters). Walk the student through the reasoning step by step, not just the arithmetic.

What a good explanation includes:

1. What to do first — name the operation or strategy ("Find the unit rate by dividing…", "Set up a proportion…")
2. The key calculation — show the math with intermediate steps
3. Why it makes sense — a brief sanity check or connection back to the concept ("…which is the cost for one pound", "…this matches because a larger percent means a bigger discount")

Rules:

• Always prefer \answerExplain over \answer. Use bare \answer{} only when the answer is self-evident (e.g., "Write the equation" → \answer{$c = 8h$}).
• Name the strategy. Don't just show numbers — say "Divide…", "Set up…", "Multiply by the multiplier…".
• Show intermediate steps. If there are two operations, show both, not just the final result.
• Keep the tone simple. Same 8–12 word sentences as the teaching sections.
• For \answerTF{} problems, add a brief reason in the text before or after if the answer isn't obvious.

Visual Math Commands

Include at least one visual per topic. Choose based on the concept:

Ratios & Proportional Relationships: \barGraph, \fillTable, \numberLine — tape diagrams, ratio tables, coordinate graphs for proportional relationships Percents: \barGraph, \fractionBar, \areaGrid — percent bars, 10×10 grids, comparison visuals Integers & Rational Numbers: \numberLine, \funCompare — number lines with negative numbers, comparison visuals Expressions & Equations: \fillTable — balance diagrams (custom TikZ), algebra tile models, input/output tables Geometry & Angles: \areaGrid, \perimeterRect, \ruler — scale drawings, angle diagrams, cross-sections (custom TikZ) Circles, Area, SA, Volume: \fractionCircle, \areaGrid, \perimeterRect — circle diagrams, composite shapes, nets of 3D figures (custom TikZ) Statistics: \barGraph, \begin{picGraph} with \picRow — dot plots, box plots, side-by-side comparisons Probability: \fillTable, custom TikZ — tree diagrams, sample space tables, spinners

These are recommended but not every one needs to appear. Use the visuals that genuinely help explain the concept.

LaTeX Conventions

• Use $...$ for ALL math, even simple numbers in equations: $2x + 3 = 11$.
• Use \times for multiplication, \div for division. Never use × or ÷ directly.
• Use \textbf{...} to bold key terms on first use.
• Use \begin{itemize}[leftmargin=*] for tighter bullet lists.
• Use \hspace and \vspace sparingly — the environments handle spacing.
• Use \setcounter{funProblem}{N} if you need to continue numbering across sections.

Complete Environment & Command Toolkit

This is your full toolkit. You don't need to memorize it — scan for what fits each topic.

Teaching & Concepts

Examples & Solutions

Practice & Assessment

Engagement & Extras

Math Visuals

Answers

Creating New LaTeX Environments

If a topic genuinely needs a visual or interactive element that no existing environment provides, you may create new environments. Add them to the appropriate .sty file in VM_packages/ (or create a new .sty file if needed).

When creating new environments:

• Study existing .sty files to match the coding style, color conventions, and tcolorbox patterns.
• Use the project's color palette (funBlue, funGreen, funOrange, etc.).
• New environments should be self-contained and not depend on or modify existing environment internals.
• Add a clear header comment with name, usage signature, and description.

CRITICAL: Never modify existing environments or commands. They are shared across many topics and book types. Even a small change can break other sections. If an existing environment doesn't do exactly what you want, create a new one instead.

For the full environment reference with usage examples and code samples, see .agents/skills/latex_environments/SKILL.md.

Checklist (Sanity Check)

Before finishing a topic, verify:

• File is 60–90 lines of LaTeX (the #1 most important check)
• File is named ch<CC>-<SS>-slug.tex and placed in topics/
• Starts with \section{Title} (NO \topicTitle — the section banner handles it)
• Has \begin{learningGoals} with 2–4 bullet points
• Teaching uses at most 2–3 environments (e.g., one conceptBox + one workedExample + one mascotSays)
• At most 1–2 worked examples
• Includes at least one visual math command
• Practice section has 4–5 problems with \resetProblems and NO \newpage before it
• Every problem has a corresponding \answer{}, \answerExplain{}{}, \answerTF{}, or \answerMC{}
• Math is wrapped in $...$
• Sentences average 8–12 words — dead simple language
• No filler sentences — every sentence teaches something

Conciseness Lessons (Learned from Chapter 1 Rewrites)

These are concrete, tested techniques that cut topic files from 100–150 lines down to 60–90 without losing teaching quality.

What to cut

Structure rules for compact files

1. One header comment line. % CCSS 7.RP.A.1 — Topic Title
2. Two learning goals, not three or four. Two goals ≈ 5 lines. Four goals ≈ 8 lines. The extra goals rarely add value.
3. One conceptBox + one workedExample = enough teaching. Add a mascotSays or tipBox only if it adds a genuinely new insight, not repetition.
4. Inline solutions over solutionSteps. Write $k = 13.50 \div 3 = 4.50$ on one line instead of 3 \solStep lines.
5. Compact tables. Put table rows on one line: $2$ & $\$3.50$ \\ $4$ & $\$7.00$ \\. Skip \arraystretch.
6. 4–5 practice problems, not 6. Fewer, well-chosen problems beat a longer list. Cut the "medium" problems; keep easy + hard.
7. Use \answerExplain{}{} for nearly every problem. Write 1–2 full lines that walk the student through the reasoning. Only use bare \answer{} when the answer is self-evident.
8. No blank lines between \prob entries unless switching problem types.

The "earn its place" test

Before adding any environment, sentence, or problem, ask: If I remove this, does the student lose something important? If the answer is no, cut it. A 65-line file that teaches clearly is better than a 90-line file with padding.

Page-flow rules (critical for page budget)

• Never use \topicTitle{} in topic files. The \section{} command already renders a styled blue banner via the class file. Adding \topicTitle creates a duplicate header and wastes ~1cm of vertical space.
• Never use \newpage before practice sections. Each \section already forces a page break. A second \newpage before practice leaves half a page blank. Let content flow naturally into the practice box.
• All major boxes are breakable. conceptBox, workedExample, practiceBox, errorBox, warningBox, realWorld — they all break across pages automatically. Don’t try to prevent breaks; embrace them.
• Prefer inline content over boxed content when possible. A \mascotSays{} (minipage-based, ~3 lines) is lighter than an errorBox (tcolorbox, ~5+ lines) for the same message.
• Use \setstretch{1.25} in test/main files, not 1.4. The tighter line spacing saves ~10% vertical space across the book.
• Blank-page bug — page breaks must happen OUTSIDE \titleformat. Issuing \clearpage or \newpage inside \sectionBanner (which runs inside titlesec's \titleformat callback) causes a phantom blank page. The page break is shipped after the current page, but titlesec's internal state then ships an extra empty page before placing the banner. Fix: The page-break logic (\ifdim\pagetotal<50pt\else\newpage\fi) is placed in \AddToHook{cmd/section/before} in studyGuide.cls, which fires BEFORE titlesec processes the section. The \sectionBanner command itself must NOT contain any page-break commands.