Education6 min read
Estimating Sales Tax From Friendly Blocks
Sales tax rates are awkward on purpose. Break the rate into blocks — 8.25% is 10% minus 2% plus a quarter of 1% — and the arithmetic becomes two easy steps.
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All articles, page 23
Articles 529–552 of 990, newest first. To read by subject instead, start from a category or a topic hub on the blog’s front page.
- Education7 min read
Famous Explorers in History, and the Guides Who Got Them There
Most famous voyages depended on navigators, interpreters and guides whose names were left off the record. Who they were, and what the evidence shows.
- Education5 min read
Fibonacci and Other Recursive Sequences
What makes a sequence recursive, how Fibonacci and Lucas numbers differ only in their seeds, and which golden ratio claims actually hold up.
- Education6 min read
Working Out the Original Price From a Sale Price
Reverse a discount by dividing, never by adding the percentage back. Here is why, plus the fraction shortcuts that make the division easy.
- Education6 min read
Finding the Rule: Difference Tables and Second Differences
A mechanical method for finding the rule behind a number pattern when inspection fails, using difference tables, constant rows and degree counting.
- Anime & Creative6 min read
When Tap-to-Fill Leaks: Fixing a Fill That Went Everywhere
A diagnostic order for the four ways a tap-to-fill goes wrong, and how to recover with undo, the two erasers and zoom instead of restarting the page.
- Education5 min read
Fluid and Crystallised Intelligence, and Why the Distinction Matters
One is reasoning with material you have never seen. The other is knowledge you already hold. They are measured differently and they age in opposite directions.
- Education5 min read
Converting Between Fractions, Decimals and Percents
One number, three notations. The anchors worth memorising, how to scale a denominator to 100, and the rule that says which fractions terminate as decimals.
- Education6 min read
The French Revolution: Causes, Phases and the Terror
A fiscal crisis, a constitutional phase, a war, the Terror and Thermidor are five different things. Separating them is what makes 1789 comprehensible.
- Education5 min read
Fun IQ Quizzes and Standardised Assessments Are Not the Same Thing
A shareable quiz and a normed assessment can use similar-looking questions and still be completely different objects. Here is the checklist that separates them.
- Education5 min read
Geometric Sequences: Constant Ratio, Explained
How to spot a constant ratio, why the nth-term rule uses an exponent, and what negative ratios and ratios below one do to a sequence.
- Education6 min read
Ghana, Mali and Songhai: Three Empires of the West African Sahel
Ghana, Mali and Songhai were three separate Sahelian states with different capitals, centuries and evidence. Here is how to tell them apart properly.
- Education7 min read
Great Zimbabwe, Mutapa and the Stone-Walled States of the South
Great Zimbabwe was built by Shona-speaking communities between about 1100 and 1450. What the excavations show, why it was abandoned, and what came next.
- Education7 min read
Grid Memory: Remembering Where, Not Just What
How grid and position memory tasks work, why location is its own kind of content, and the strategies that help on a grid but not on a list.
- Education6 min read
Growing Sequences: Where Simon-Style Games Break People
Why growing-sequence memory games break down in the middle of the list, what the serial position curve predicts, and how chunking moves the break point.
- Education6 min read
The Haitian Revolution and the Republic It Created
Enslaved people in Saint-Domingue destroyed slavery and French rule, founded Haiti in 1804, and were then billed by France for it. What the records show.
- Education5 min read
Helping a Child With Math Facts Without Making It Worse
What a supportive at-home session with number facts looks like, why the timer should come last, and how a parent's own attitude changes the outcome.
- Languages6 min read
Heritage Learners: Studying the Language You Half-Remember
A heritage learner arrives with listening ahead of reading and gaps in between. Why that profile needs a different study plan, with Shanghainese as the case.
- Education5 min read
Hijri Dates and Why Two Books Give Different Years for One Event
An AH year is about 11 days shorter than a CE year, so it straddles two of them. Here are the four reasons careful sources still convert it differently.
- Education6 min read
History Learning Apps and Free Courses Compared
Khan Academy, the OER Project, OpenLearn, Google Arts & Culture and our own app, compared on what each provider officially documents.
- Education6 min read
A Timeline of Inventions From Stone Tools to Reusable Rockets
An invention timeline that starts 2.6 million years ago, spans every inhabited continent, and explains why asking who invented something usually has no answer.
- Education6 min read
Timeline Building Tools Compared for History Study
Two different needs hide behind timeline app searches: building one and reading one. TimelineJS, Tiki-Toki, Preceden and our own app compared.
- Sports & GM6 min read
Hockey Career Archetypes: Scorer, Playmaker, Shutdown Defender or Netminder
What a scorer, playmaker, shutdown defender or netminder archetype commits you to in a hockey career mode, and how to pick one you can still play in season six.
- Action & Arcade6 min read
Holding First Place: What Changes Once the Crown Is on You
Reaching the top of a live io leaderboard inverts your incentives: rank can no longer improve, only fall. How to play the lead instead of playing for it.