Analytical topics for ages 11–12

The reasoning no subject teaches directly: spotting patterns, following a rule, working backwards from a result, and telling a sound argument from a plausible one.

The step up to secondary thinking — abstraction, formal terms and questions with more than one defensible answer.

20 topics · 120 hands-on stations · 1 free to try

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The Difference Ladder

Guessing at a series is a waste of time. Use the difference ladder: write the gaps underneath the terms, then the gaps of those gaps, until a row goes constant.

Row 1 is the series. Row 2 is the gap between neighbours. Row 3 is the gap between those gaps. Keep going until one row is constant — that row names the rule.
The series is arithmetic: it adds a fixed amount. Term n = first term + (n − 1) × gap, so you can jump to term 100 without listing anything.
The rule involves n². Squares, triangular numbers and expressions like 2n² + 1 all have a constant third row. Two rows down means squared.
If the gaps grow faster than the terms themselves, stop laddering — the rule is multiplication. Divide neighbouring terms instead and look for a constant ratio.

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Free printable worksheet

Ten questions from Number Series and Patterns on one page, with an answer key at the bottom — a PDF you can print for homework, a car journey or a classroom. No account needed and nothing to sign up for.

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A few of the Analytical topics at this age

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Number Series and Patterns
Free

The difference ladder — one method that cracks almost every series

🏗 The Difference Ladder · 🏃 Run the Ladder · 🔬 Watch the Ladder Settle · 🗂️ Name the Rule Family · 🔧 Find the Broken Term · 🎯 Practice Zone
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Letter and Alphanumeric Series

EJOTY, the 27 rule, and turning letters into arithmetic

🧰 The Letter Toolkit · ⏭️ Skip Through the Alphabet · ➡️ Continue the Series · 🏷️ Match Series to Rule · 📍 Position Arithmetic · 🎯 Practice Zone
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Analogies

The bridge sentence — say the relationship, then apply it word for word

🌉 The Bridge Sentence · 📖 Word Analogies · 🔢 Number Analogies · 🏷️ Name the Relationship · 🗂️ Sort by Bridge Type · 🎯 Practice Zone
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Classification and Odd One Out

The property checklist — and defending your criterion out loud

📋 The Property Checklist · 🔤 Odd Word Out · 🧮 Odd Number Out · 🗂️ Sort by Number Family · ⚖️ Defend Your Criterion · 🎯 Practice Zone
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Coding and Decoding

The crack sheet — a fixed order of tests that breaks an unknown code

🗝️ The Crack Sheet · 🎚️ Slide the Cipher · 🔍 Crack a Letter Code · 💬 Crack a Word Code · 🗂️ Name the Code Family · 🎯 Practice Zone