Number Mazes

Free puzzles to print

Each set: a Learn sheet with a worked example, 10 puzzles from easiest to hardest, and the answers.

• Level 1

  Ages 4–6 · Pre-K–K

  

  Count 1 to 10 on a square grid, then with tempting wrong turns, then on a honeycomb, and in the hardest puzzles to 15 or 20.

  On the sheet: “From 1, step on 2, 3, 4… to get out.”

  Print Level 1 (Letter)Other paper size: A4

• Level 2

  Ages 6–8 · Grades 1–2

  

  Mixes three kinds of maze. Make 10: step on facts that make 10 (near misses make 9 or 11). Doubles: step on doubles (near misses like 6 + 7). Skip counting: from a circled number, count by 10s to 100, then by 5s to 100 past near misses. Then count by 2s to 40, or by 10s from an odd start (3, 13, 23…). The hardest maze of each kind is a honeycomb.

  On the sheet: “Walk from START to END. Step only on facts that make 10.”

  On the sheet: “Walk from START to END. Step only on doubles, like 6 + 6.”

  On the sheet: “Skip count from the circled number. Find the way out.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  Multiples of 3, 4 or 5, then 6 to 9, then multiplication and division facts that may be off by a little.

  On the sheet: “Walk from START to END. Step only on squares that follow the rule: a multiple of a number, or a multiplication fact that is true (7 × 8 = 56).”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  Factors of a number, primes, then expressions where × comes before + and −.

  On the sheet: “Walk from START to END. Step only on squares that follow the rule. Do × before + and −: 2 + 3 × 4 = 2 + 12 = 14.”

  Print Level 4 (Letter)Other paper size: A4

The thinking it works on

• Working out facts, one after another

  Works out every fact on the way through the maze.

  De Brauwer, Verguts and Fias (2006) found that the extra time children needed for larger multiplication facts shrank between ages 9 and 11, when they matched adults. Source

• Counting in order

  Steps to the next number of the count, by 1s at Level 1 and by 2s, 5s or 10s at Level 2.

• Checking each step against a rule

  Asks of every cell whether it follows the rule.

  Lemaire and Fayol (1995) found that schoolchildren judging whether a multiplication was true used whether the answer should be odd or even. How they used it depended on their age and the problem. Source

• Ignoring the near miss

  Stops at the near miss, like 7 × 8 = 54, and works it out.

  Houdé and Guichart (2001) studied 9-year-olds who knew that a spread-out row has the same number. They still had to hold back the 'longer means more' idea, which slowed them on the next item. Source

• Thinking about multiples and factors

  Decides whether a number is a multiple, a factor or a prime.

  Sutarto and colleagues (2021) found that some fourth graders mixed up a number's multiples with its factors. Source

• Order of operations

  Does × before + and − when the rule says so.

  Lee and colleagues (2026) studied 578 middle school students. Accuracy fell and answers slowed as the multiply sign moved from the left of an expression to the middle or right. Source

• Going back when a path dies

  Retraces the last few cells at a dead end to find the wrong step.

  Asato, Sweeney and Luna (2006) found that skill on a tower-moving planning puzzle was still maturing through the teens, in 100 people aged 8 to 30. Source

Where is this thinking used?

• Receipts and bills: The sums are checked before paying.
• Checking someone's work: A calculation is tested before it's trusted.
• Checklists: A safety list or a recipe is followed step by step.
• Data entry: Proofreading numbers, where the error looks almost right.