Number and letter series
Steady steps, doubling, alternating steps, growing differences, two series in turns, squares, cubes and Fibonacci. Letter series come with the alphabet on the sheet.
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Teaching guide: logical reasoning from Grade 3 to Grade 10
Reasoning means finding the rule behind some data and using it: that is what reasoning tests and maths competency tests ask for, and it gets better with practice. This free logical reasoning worksheet generator makes series, matrices, analogies and odd-one-out items that are different every time, with an answer key that states the rule of each item.
- For
- Elementary 3rd, 4th, 5th, 6th · Middle & High 7th, 8th, 9th, 10th (ages 8-15)
- Subject
- Mathematics › Logic & Patterns
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Figure series
An arrow that turns, a dot that moves round the frame, shapes that grow in number, shapes and fills that repeat: more things change at once at each level.
3 × 3 matrices
Like Raven matrices: each row and column follows a rule (the same, a progression or three values shared out) and pupils find the missing cell.
Analogies and odd one out
A is to B as C is to… with figures and with numbers (n → 3n + 1), and the odd one out among five figures or five numbers (multiples, primes, squares).
Exactly one answer
Every item is built from its rule and checked so that no other reasonable rule fits what is shown. Wrong options break the rule in just one place.
Answer key with the rule
The answer key circles the answer and writes the rule: +4 each time, Alternates +3 and ×2, The arrow turns 90°… Handy for marking and for explaining.
Frequently Asked Questions about the Logical Reasoning Worksheets
Which grades are these worksheets for?
Grades 3 to 10. Level 1 is for Grades 3-4, level 2 for Grades 5-6, level 3 for Grades 7-8 and level 4, with doubling differences, cubes and negative numbers, for Grades 9-10.
Are they good practice for reasoning tests such as the 11+ or CAT4?
Yes: they use the usual formats of reasoning tests (series, matrices, analogies, odd one out) with options to circle. Choose Mixed test to have them in turns, as in a test paper.
Which alphabet do the letter series use?
The English sheets use the 26-letter alphabet, printed above the series so pupils can count the steps (you can hide it in More options). The Spanish sheets use 27 letters, with Ñ.
What if a pupil finds a different rule?
Every series is checked against many rules (steady steps, alternating steps, two series in turns, multiplying, adding the previous terms…) and is only used when every rule that fits gives the same answer. A pupil who reaches the answer another way is also right.
Are there easier series for younger children?
Skip counting and simple number patterns are in the number sequences worksheet generator, and shape patterns for ages 3 to 6 in the patterns worksheet generator. For more logic, try sudoku and KenKen.
How do I print the answer key?
Press Print and choose Answer key (or Worksheet and answer key): the answer is circled in blue with the rule of each item underneath.
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