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Refine math content layout and enhance readability: Update math-chapter-patterns.md to emphasize the use of aligned multi-line KaTeX for chained calculations. Revise Pythagorean theorem examples in _index.md and core.html to follow the new formatting guidelines. Update SKILL.md to reinforce the preference for aligned equations across all subjects. Modify feed.xml and sitemap.xml to reflect recent updates and new chapter additions for improved navigation.
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Hananoshika Yomaru
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6 changed files with 73 additions and 45 deletions
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@ -135,6 +135,8 @@ Live chapters live under `content/{subject}/{slug}/`:
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**Math checkpoints / dots:** follow [math-chapter-patterns.md](math-chapter-patterns.md); shared dot classes in `content/math/subject.scss`.
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**Math equation layout (all subjects):** for chained calculations, **always prefer multi-line KaTeX** and **always align at the equal sign** using `aligned` (e.g. `\begin{aligned} ... &= ... \\ ... \end{aligned}`). Do not write long one-line chains; aligned multi-line steps are the default for readability and mobile layout.
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### Interactive demo technology choices
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Interactive demos can use different technologies based on the learning goal and interaction type:
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@ -7,6 +7,20 @@ Use these conventions in `core.html` and `supplement.html` so every math chapter
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- Wrapper: `<div class="book-prose">`
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- Section titles: `<h2 id="…" class="book-prose__heading">`
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- In-chapter links: plain `<a href="/math/…/">` inside `.book-prose` (theme styles them)
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- For chained calculations, prefer aligned multi-line KaTeX:
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```html
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<p class="book-formula">\[
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\begin{aligned}
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b &= \sqrt{c^2-a^2} \\
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&= \sqrt{13^2-5^2} \\
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&= \sqrt{144} \\
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&= 12
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\end{aligned}
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\]</p>
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```
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This keeps equal signs aligned and avoids long single-line equations on mobile.
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## Checkpoints (required shape)
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@ -54,31 +54,37 @@ strand = "Measures, Shape & Space"
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<h3 id="find-hypotenuse" class="book-prose__heading">Find the hypotenuse</h3>
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<p><strong>Example.</strong> If \(a=9\) and \(b=12\), find \(c\).</p>
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<p class="book-formula">\[
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c = \sqrt{9^2 + 12^2}
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= \sqrt{81 + 144}
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= \sqrt{225}
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= 15
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\begin{aligned}
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c &= \sqrt{9^2 + 12^2} \\
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&= \sqrt{81 + 144} \\
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&= \sqrt{225} \\
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&= 15
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\end{aligned}
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\]</p>
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<p>The third side is 15 ft.</p>
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<h3 id="find-leg" class="book-prose__heading">Find a missing leg</h3>
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<p><strong>Example.</strong> If \(c=13\) and \(a=5\), find \(b\).</p>
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<p class="book-formula">\[
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b = \sqrt{c^2 - a^2}
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= \sqrt{13^2 - 5^2}
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= \sqrt{169 - 25}
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= \sqrt{144}
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= 12
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\begin{aligned}
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b &= \sqrt{c^2 - a^2} \\
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&= \sqrt{13^2 - 5^2} \\
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&= \sqrt{169 - 25} \\
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&= \sqrt{144} \\
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&= 12
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\end{aligned}
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\]</p>
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<h3 id="radical-form" class="book-prose__heading">Leave answers in simplest radical form</h3>
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<p><strong>Example.</strong> If \(c=10\) and \(a=2\), find \(b\).</p>
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<p class="book-formula">\[
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b = \sqrt{10^2 - 2^2}
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= \sqrt{100 - 4}
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= \sqrt{96}
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= \sqrt{16 \cdot 6}
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= 4\sqrt{6}
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\begin{aligned}
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b &= \sqrt{10^2 - 2^2} \\
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&= \sqrt{100 - 4} \\
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&= \sqrt{96} \\
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&= \sqrt{16 \cdot 6} \\
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&= 4\sqrt{6}
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\end{aligned}
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\]</p>
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<h2 id="common-pitfall" class="book-prose__heading">Common pitfall</h2>
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@ -43,31 +43,37 @@
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<h3 id="find-hypotenuse" class="book-prose__heading">Find the hypotenuse</h3>
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<p><strong>Example.</strong> If \(a=9\) and \(b=12\), find \(c\).</p>
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<p class="book-formula">\[
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c = \sqrt{9^2 + 12^2}
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= \sqrt{81 + 144}
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= \sqrt{225}
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= 15
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\begin{aligned}
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c &= \sqrt{9^2 + 12^2} \\
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&= \sqrt{81 + 144} \\
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&= \sqrt{225} \\
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&= 15
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\end{aligned}
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\]</p>
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<p>The third side is 15 ft.</p>
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<h3 id="find-leg" class="book-prose__heading">Find a missing leg</h3>
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<p><strong>Example.</strong> If \(c=13\) and \(a=5\), find \(b\).</p>
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<p class="book-formula">\[
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b = \sqrt{c^2 - a^2}
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= \sqrt{13^2 - 5^2}
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= \sqrt{169 - 25}
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= \sqrt{144}
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= 12
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\begin{aligned}
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b &= \sqrt{c^2 - a^2} \\
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&= \sqrt{13^2 - 5^2} \\
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&= \sqrt{169 - 25} \\
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&= \sqrt{144} \\
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&= 12
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\end{aligned}
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\]</p>
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<h3 id="radical-form" class="book-prose__heading">Leave answers in simplest radical form</h3>
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<p><strong>Example.</strong> If \(c=10\) and \(a=2\), find \(b\).</p>
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<p class="book-formula">\[
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b = \sqrt{10^2 - 2^2}
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= \sqrt{100 - 4}
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= \sqrt{96}
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= \sqrt{16 \cdot 6}
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= 4\sqrt{6}
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\begin{aligned}
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b &= \sqrt{10^2 - 2^2} \\
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&= \sqrt{100 - 4} \\
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&= \sqrt{96} \\
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&= \sqrt{16 \cdot 6} \\
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&= 4\sqrt{6}
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\end{aligned}
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\]</p>
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<h2 id="common-pitfall" class="book-prose__heading">Common pitfall</h2>
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@ -4,7 +4,21 @@
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<title>Open Free Books</title>
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<link>https://openfreebooks.org/</link>
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<description>Recent updates to Open Free Books pages and live chapters.</description>
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<lastBuildDate>Thu, 21 May 2026 23:42:19 GMT</lastBuildDate>
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<lastBuildDate>Fri, 22 May 2026 05:18:34 GMT</lastBuildDate>
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<item>
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<title>Coordinate geometry foundations</title>
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<link>https://openfreebooks.org/math/coordinate-geometry-foundations/</link>
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<guid isPermaLink="true">https://openfreebooks.org/math/coordinate-geometry-foundations/</guid>
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<pubDate>Fri, 22 May 2026 05:18:34 GMT</pubDate>
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<description>Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane.</description>
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</item>
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<item>
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<title>Pythagoras' theorem</title>
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<link>https://openfreebooks.org/math/pythagoras-theorem/</link>
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<guid isPermaLink="true">https://openfreebooks.org/math/pythagoras-theorem/</guid>
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<pubDate>Fri, 22 May 2026 05:18:34 GMT</pubDate>
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<description>Use Pythagoras' theorem and its converse in 2D problems and coordinate settings.</description>
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</item>
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<item>
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<title>Basic math notation</title>
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<link>https://openfreebooks.org/math/basic-math-notation/</link>
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@ -89,13 +103,6 @@
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<pubDate>Thu, 21 May 2026 16:54:30 GMT</pubDate>
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<description>Find equations of circles, tangents, and intersections using coordinate methods and distance.</description>
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</item>
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<item>
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<title>Coordinate geometry foundations</title>
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<link>https://openfreebooks.org/math/coordinate-geometry-foundations/</link>
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<guid isPermaLink="true">https://openfreebooks.org/math/coordinate-geometry-foundations/</guid>
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<pubDate>Thu, 21 May 2026 16:54:30 GMT</pubDate>
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<description>Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane.</description>
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</item>
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<item>
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<title>Deductive geometry</title>
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<link>https://openfreebooks.org/math/deductive-geometry/</link>
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@ -145,13 +152,6 @@
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<pubDate>Thu, 21 May 2026 16:54:30 GMT</pubDate>
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<description>Count outcomes with permutations and combinations, then compute probabilities in finite sample spaces.</description>
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</item>
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<item>
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<title>Pythagoras' theorem</title>
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<link>https://openfreebooks.org/math/pythagoras-theorem/</link>
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<guid isPermaLink="true">https://openfreebooks.org/math/pythagoras-theorem/</guid>
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<pubDate>Thu, 21 May 2026 16:54:30 GMT</pubDate>
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<description>Use Pythagoras' theorem and its converse in 2D problems and coordinate settings.</description>
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</item>
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<item>
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<title>Charts & averages</title>
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<link>https://openfreebooks.org/math/statistical-charts-averages/</link>
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@ -62,7 +62,7 @@
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</url>
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<url>
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<loc>https://openfreebooks.org/math/coordinate-geometry-foundations/</loc>
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<lastmod>2026-05-21T16:54:30.000Z</lastmod>
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<lastmod>2026-05-22T05:18:34.000Z</lastmod>
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</url>
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<url>
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<loc>https://openfreebooks.org/math/counting-and-numbers/</loc>
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@ -146,7 +146,7 @@
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</url>
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<url>
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<loc>https://openfreebooks.org/math/pythagoras-theorem/</loc>
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<lastmod>2026-05-21T16:54:30.000Z</lastmod>
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<lastmod>2026-05-22T05:18:34.000Z</lastmod>
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</url>
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<url>
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<loc>https://openfreebooks.org/math/quadratic-equations/</loc>
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