Teaching objectives
What if mazes had numbers on the floor? In this lab a rabbit must cross grids full of digits to reach its carrot, but it can only step on squares that are multiples of the current number. Then the adventure gets harder: the path is no longer a grid but a series of branching operations where each choice adds, subtracts, or multiplies your score. Only one exact route leads to the goal.
What you'll learn
The student practises multiplication tables actively: if you can't spot the multiples of 8, you can't move forward. The second half of the lab trains operational reasoning — calculating several routes, comparing results, and picking the right one.
- Recognising at a glance whether a number is a multiple of 6, 7, 8, or 9 (rooms 1-8, 8×6 and 12×9 grids).
- Navigating mazes with backtracking: sometimes the correct path forces you to turn back.
- Following a trellis of branches (up or down) while accumulating addition, subtraction, and multiplication operations (rooms 9-13).
- Using divisibility to choose the correct final multiplication without computing every path (rooms 12-13).
- Ruling out impossible lanes by parity or membership in a multiplication table before calculating (rooms 14-16).
Key mathematical ideas
- The multiples of a number form a unique path through the grid: the graph of valid squares is a tree with no shortcuts, which ensures the student must follow it carefully.
- Accumulating operations step by step is an exercise in order of evaluation: each cell transforms the current number, not the starting number.
- Choosing the final multiplication by divisibility (which number's multiple is the target?) is the inverse reasoning of multiplication: from result to factors.
- In the 6-lane rooms, parity and the properties of the 7 or 5 times table allow routes to be eliminated without computing them — an intuitive introduction to divisibility rules.
Room-by-room contents
Room 1 · Multiples of 6 (8×6 grid)
The rabbit starts at the left edge and must reach the carrot at the right edge by stepping only on squares that are multiples of 6. The grid is 8×6 and the path is unique, though sometimes backtracking is needed.
Student tasks
- Trace the route of multiples of 6 to the carrot.
- Reach the exit without stepping on any number that is not a multiple of 6.
Room 2 · Multiples of 7 (8×6 grid)
Same 8×6 grid but now only squares that are multiples of 7 are valid. The 7 times table includes some large numbers (49, 63) that the student must recognise.
Student tasks
- Identify the squares that are multiples of 7 before starting to move.
- Complete the journey to the carrot.
Room 3 · Multiples of 8 (8×6 grid)
The 8×6 grid is filled with multiples of 8 mixed in with numbers that are not. Multiples of 8 are less frequent, so the path is tighter.
Student tasks
- Travel the maze stepping only on multiples of 8.
- Reach the exit without mistakes.
Room 4 · Multiples of 9 (8×6 grid)
Last 8×6 maze: now the table is the 9 times table. The trick of 9 (the digit sum equals 9) can help identify valid squares quickly.
Student tasks
- Use the 9 times table criterion to locate the valid squares.
- Complete the crossing to the carrot.
Room 5 · Multiples of 6 (12×9 grid)
The grid grows to 12×9: the path is longer and there are more traps. The 6 times table must be well consolidated to recognise multiples at a glance.
Student tasks
- Navigate the large grid of multiples of 6.
- Manage the necessary backtracking to reach the exit.
Room 6 · Multiples of 7 (12×9 grid)
The 12×9 grid with multiples of 7. With more rows and columns, multiples are more spread out and the process of elimination becomes more important.
Student tasks
- Identify the multiples of 7 in the enlarged grid.
- Reach the carrot following the only valid path.
Room 7 · Multiples of 8 (12×9 grid)
12×9 grid with the 8 times table. Multiples reach 80 and beyond; recognising 64, 72 or 80 at a glance is the key to moving ahead without hesitation.
Student tasks
- Cross the large grid using the 8 times table.
- Complete the journey to the exit.
Room 8 · Multiples of 9 (12×9 grid)
The largest grid in the block: 12×9 with multiples of 9. The path requires recognising large multiples such as 81 or 72 and planning several steps ahead.
Student tasks
- Use the digit-sum criterion to verify uncertain squares.
- Cross the full grid to the carrot.
Room 9 · Path of sums
The maze changes shape: there are now 3 columns and in each one the rabbit chooses to go up or down. Each square adds a number to a running total. The student starts at 0 and must arrive at exactly 11.
Student tasks
- Try combinations of up/down while calculating the running total.
- Find the only route that arrives at exactly 11.
Room 10 · Additions and subtractions
The trellis now mixes additions and subtractions. The total starts at 20 and the target is 24; some squares subtract, so a wrong choice can take you further from the goal.
Student tasks
- Calculate the effect of each branch before choosing.
- Arrive at exactly 24 starting from 20.
Room 11 · Multiply and add
The third trellis variant introduces multiplication alongside addition. Starting from 2, the target is 27; a ×2 square can radically change the running total.
Student tasks
- Understand how multiplication amplifies the accumulated number.
- Find the route that produces exactly 27.
Room 12 · Choose the multiplication (target 28)
The last column has three options: ×5, ×6 or ×7. The student must think about which number 28 is a multiple of before calculating all routes: only one multiplication can give that result.
Student tasks
- Reason about the divisibility of 28 to choose the correct multiplication.
- Complete the first two columns consistently with that choice.
Room 13 · Choose the multiplication (target 45)
Variant with target 45 and multipliers ×4, ×6 or ×9 in the last column. The student must identify which of those factors divides 45 in order to rule out the other two without calculating.
Student tasks
- Determine which number in the list is a factor of 45.
- Follow the correct route to arrive at 45.
Room 14 · The odd path
There are now 6 parallel lanes, each with 4 operations. Five lanes produce even results; only one reaches the odd target 27. The clue: an odd number cannot be the result of multiplying by an even number.
Student tasks
- Rule out lanes that end in multiplication by an even number.
- Calculate the remaining lane to confirm it arrives at 27.
Room 15 · Pick the multiplication (target 49)
Six lanes, each ending in a different multiplication (×2, ×7, ×3, ×2, ×5, ×6). The target 49 is a multiple of only ONE of those numbers: 7. On top of that, lanes ending in ×2 give even numbers, so they cannot reach 49 (which is odd) either. The student looks at the last multiplication of each lane and picks the only one that divides 49, without computing them all.
Student tasks
- Look at the last multiplication of each lane and find which number 49 is a multiple of.
- Follow that lane and check it reaches exactly 49.
Room 16 · The multiple of 5
Target 80: a multiple of 5 (ends in 0). Five lanes do not multiply by 5 and cannot produce that result; one does end in ×5. The student learns to look at the last digit of the target to guide the search.
Student tasks
- Recognise that 80 ends in 0 and that only a lane with ×5 can achieve it.
- Calculate that lane and verify it arrives at exactly 80.
Rooms to project
The most striking ones to show and discuss in class.