Teaching objectives
"I thought of a number, added 3, and got 15. What number did I think of?" With that hook, this secondary-school lab turns a guessing game into a first real encounter with linear equations in one unknown. Across 15 rooms of gradually increasing difficulty, students learn through riddles that grow into equations.
What you'll learn
Students internalize the idea that solving an equation means undoing operations in reverse order, and learn to recognize the formal structure N op A = R behind everyday situations.
- Rooms 1–2 introduce addition and the notation
N + 3 = 15; students verify that the solution is to subtract. - Rooms 3–4 repeat the pattern with multiplication (
N × 5 = 45) and discover that the inverse operation is division. - Rooms 5–7 scale up to two chained steps: students first guess the number, then write the equation
(N + 12) × 2 = 28, and finally solve it step by step. - Rooms 8–9 contain the key trap:
(N + 12) · 2versusN · 2 + 12; an interactive slider makes it visible that the order of operations produces different results. - Rooms 10–11 mix multiplication with subtraction, and division with addition, reinforcing the idea of inverse operations in new combinations.
- Room 12 presents three equations in a row with no hints, as a fluency check.
- Rooms 13–15 add three-step chains (add–multiply–subtract; subtract–divide–add; multiply–add–divide), requiring students to undo the full chain in the correct reverse order.
Key mathematical ideas
- A linear equation
N op A = Rhas exactly one solution: the value of the unknown. - Inverse operations: adding ↔ subtracting; multiplying ↔ dividing.
- Order of operations matters:
(N + 12) · 2 ≠ N · 2 + 12for most values of N. - Solving in several steps is equivalent to applying the inverse operation from the outside in (undoing in the reverse order they were applied).
- Algebraic notation with N is a precise way to write "the number I thought of" and makes the structure of the equation visible.
Room-by-room contents
Room 1 · I think of a number
Intuitive start: the teacher says "I thought of a number, added 3 and got 15". The student discovers the hidden number by trial and error before learning any notation.
Student tasks
- Guess which number, when 3 is added to it, gives 15.
- Enter the answer and check it.
Room 2 · You've solved an equation!
"Aha" moment: it is revealed that what the student just did is solve the equation <code>N + 3 = 15</code>. The notation and the idea of "undoing the operation" (N = 15 − 3) are explained. Then they practise with <code>N + 20 = 60</code>.
Student tasks
- Read the explanation of the equation <code>N + 3 = 15</code> and understand the concept of undoing.
- Solve <code>N + 20 = 60</code> applying the same idea.
Room 3 · I multiply by a number
New operation: the thought-of number is multiplied by 5 and gives 45. The student must find N, still without a visible formula, by direct reasoning.
Student tasks
- Find the number that, when multiplied by 5, gives 45.
Room 4 · Another equation solved!
The multiplication equation <code>N × 5 = 45</code> and its inverse operation — dividing — are introduced. The student immediately practises with <code>N × 4 = 80</code>.
Student tasks
- Understand that the inverse of × is ÷.
- Solve <code>N × 4 = 80</code> by undoing the multiplication.
Room 5 · Two steps in a row
First two-operation equation: (N + 12) × 2 = 28. The student solves the addition–multiplication chain by trial or reasoning.
Student tasks
- Find the number that, when 12 is added and the result multiplied by 2, gives 28.
Room 6 · Write the equation
The same statement from Room 5 is now presented as a writing exercise: the student fills in the blanks of the equation <code>(N + __ ) × __ = __</code> from the text.
Student tasks
- Fill in the blanks of the equation that represents "I added 12, multiplied by 2, and got 28".
Room 7 · Solve the equation
With the equation <code>(N + 12) × 2 = 28</code> already visible, the student solves it step by step: first undo the × 2 (divide), then undo the + 12 (subtract). The reverse order of undoing is reinforced.
Student tasks
- Undo the multiplication first: 28 ÷ 2.
- Then undo the addition: result − 12.
- Write the value of N.
Room 8 · Same number, different order
A subtle variation: now the operation is N × 2 + 12 = 28 (multiply first, then add), different from Room 5. The student solves it and notes the difference.
Student tasks
- Solve N × 2 + 12 = 28 by undoing in reverse order (first − 12, then ÷ 2).
Room 9 · Order matters
Interactive comparison room with a slider: the student sees (N + 12) · 2 and N · 2 + 12 simultaneously for the same value of N and verifies that they give different results. Visualises the distributive property and the impact of parentheses.
Student tasks
- Move the slider and observe how the two results change.
- Answer whether the two expressions are always equal or not.
Room 10 · Multiply and subtract
Equation N × 3 − 5 = 16. The student applies the undoing process with the new multiplication–subtraction combination.
Student tasks
- Solve N × 3 − 5 = 16 (first undo the subtraction, then the multiplication).
Room 11 · Divide and add
Equation N ÷ 3 + 4 = 9. Introduces division as the first operation and addition as the second; the student practises the reverse order of solving.
Student tasks
- Solve N ÷ 3 + 4 = 9 (first undo the addition, then the division).
Room 12 · Quick practice
Three two-step equations in a row with no hints or scaffolding. Consolidates the patterns learned before moving on to three operations.
Student tasks
- Solve the three equations one after another without help.
Room 13 · Three steps: add, multiply, subtract
First three-operation equation: (N + 5) × 2 − 3 = 17. The student must undo all three operations in reverse order.
Student tasks
- Identify the three operations in the statement.
- Undo in reverse order: first + 3, then ÷ 2, finally − 5.
- Check the value of N.
Room 14 · Three steps: subtract, divide, add
Equation ((N − 6) ÷ 2) + 3 = 7. Combines subtraction, division, and addition; the student practises a different undoing order from Room 13.
Student tasks
- Solve the equation ((N − 6) ÷ 2) + 3 = 7 step by step.
Room 15 · Three steps: multiply, add, divide
Lab closure: equation (N × 3 + 4) ÷ 2 = 8. Division as the last operation requires undoing the division first (multiply), then the addition, and finally the multiplication.
Student tasks
- Solve (N × 3 + 4) ÷ 2 = 8 by undoing all three operations.
- Verify by substituting N into the original statement.
Rooms to project
The most striking ones to show and discuss in class.