Algebra Thinking
Let the unknown be a box — what's inside?
Algebraic thinking means finding unknown quantities by keeping equations balanced. Whatever you do to one side, do to the other.
See It in Action
The Problem
A number is multiplied by 4 and then 6 is subtracted. The result is 26. What is the number?
Common Mistake
Guess and check: try 7 → 7×4=28 → 28−6=22 (no). Try 8 → 8×4=32 → 32−6=26. The number is 8.
Guess and check can work but it's slow and risky for harder numbers. Working algebraically is faster and always reliable.
Correct Approach
Let □ = the number. The equation: 4×□ − 6 = 26. Add 6 to both sides: 4×□ = 32. Divide both sides by 4: □ = 8.
Answer: 8
4 × 8 − 6 = 32 − 6 = 26. ✓
The Core Concept
Algebraic thinking at primary level is really about unknowns and balance. If a balance scale has 3 blocks on one side equalling 15 grams on the other, one block = 5 grams. The equation is 3 × □ = 15, so □ = 5.
The core principle is that an equation is like a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced. To find □ in 2×□ + 5 = 17, first subtract 5 from both sides (2×□ = 12), then divide both sides by 2 (□ = 6).
For word problems with unknowns, the strategy is: name the unknown (let □ = the starting number), write the equation from the problem description, then solve by undoing operations.
Common Mistakes to Avoid
Doing different operations to each side of the equation
The equation is a balance. Adding 6 to the left but not the right breaks the balance. Whatever you do to one side, do the same to the other.
Undoing operations in the wrong order
For 4×□ − 6 = 26, undo the subtraction first (add 6), then undo the multiplication (divide by 4). Work from the outside in.
Setting up the equation from the description incorrectly
"A number is doubled then 3 is added" → 2×□ + 3. "3 is added then the number is doubled" → 2×(□ + 3). The order of words matters.
Not writing an equation, just guessing
Writing the equation first forces you to think clearly about what the problem is saying. It also lets you check your answer by substituting back.
Try It Yourself
Three friends each have the same number of marbles. Together they have 54 marbles. How many does each friend have?
Hint: Let □ = number of marbles each friend has. Write an equation: 3 × □ = 54.
Key Tips
Always let □ (or n or x) represent the unknown BEFORE starting. Write it down.
Build the equation from the problem step by step: "a number is doubled" = 2×□.
Check your answer by substituting back into the original equation.
Ready to practise Algebra Thinking?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.