Grade 5 logic questions

Grade 5 logic questions: consecutive numbers, the Fibonacci sequence, fractions, age and money problems, systematic counting and paradoxes. Free printable PDF and solving strategies.

Logic questions in grade 5

Ages 10–12 are the bridge to middle school: fractions, multi-step problems and generalising begin. Logic questions playfully introduce pre-algebra thinking, systematic counting and the idea of proof.

Question types

• Consecutive numbers: finding three numbers with a given sum
• Sequences: Fibonacci and square numbers
• Fraction problems: numerator–denominator relationship
• Bar model: "Ali has 3 times as much money as Ece…"
• Systematic counting: handshakes, counting digits
• Logic paradoxes: "I am a liar"
• Optimisation: the largest area with a fixed perimeter

4-step strategy

1. Name the unknown: Give the number you're looking for a box or a letter.
2. Build a model: Show the relationship with a bar model, a table or a drawing.
3. Count systematically: List the possibilities so you don't miss any: handshakes, counting digits.
4. Generalise: Derive a rule from a small case, apply it to the big case and check.

Example: systematic counting

4 people shake hands: the first shakes 3 hands, the second 2, the third 1. Let your child use this pattern for 6 people; answer keys for the free PDF questions are not published.

📄 Grade 5 Logic Questions (free PDF)

Other grades: Grade 1 · Grade 2 · Grade 3 · Grade 4 · Free PDFs for ages 9 and up

Levelled next steps: packs

• Picture Sudoku 4×4 Pack — 48 puzzles, ages 6–8
• Number Sudoku 6×6 Pack — 48 puzzles, ages 9–12
• Way Home Mazes — 30 mazes, ages 6–8

All packs are A4 PDFs with solutions; prices include VAT, payment via Payhip.

Start for free

• Free activity PDFs — download and print right away.
• Puzzle of the Week — three new puzzles every Monday.
• Puzzle of the Day — one a day on screen.
• For more printable puzzle packs (A4 PDF with solutions, prices incl. VAT).