PSLE Mathematics Learning Guide · Guide 11
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An equation says that two quantities are equal. Solving an equation means finding the value of the unknown that makes that statement true.
If 3a + 5 = 20, the task is not to move symbols across an equals sign because “plus becomes minus”. The deeper idea is to preserve equality while undoing operations. Subtract 5 from both sides: 3a = 15. Divide both sides by 3: a = 5. Check: 3 × 5 + 5 = 20.
This guide develops the Primary 6 syllabus outcome on simple linear equations with whole-number coefficients. The working habit is: read the equation as a balance, identify the operation attached to the unknown, undo one operation at a time on both sides, then substitute the answer back into the original equation.
The MOE Primary Mathematics syllabus updated October 2025 lists simple linear equations with whole-number coefficient under Primary 6 Algebra. The SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples below are original eduKate teaching material.
The equals sign means “has the same value as”
In 7 + 3 = 10, the left side and right side have the same value.
In 2x + 4 = 18, the two sides must also have the same value. The unknown x is not a signal to start guessing blindly. It is a number that must preserve the equality.
The equals sign is not an instruction meaning “now write the answer”. It expresses a relationship between two expressions.
Use a balance model
Imagine two pans of a balance scale. If both sides are equal and you remove the same weight from each side, they remain equal. If you divide both sides into the same number of equal groups, equality remains.
For x + 7 = 19, remove 7 from both sides:
x + 7 − 7 = 19 − 7
x = 12.
For 4x = 28, divide both sides by 4:
4x ÷ 4 = 28 ÷ 4
x = 7.
Inverse operations undo each other
Addition is undone by subtraction. Multiplication is undone by division.
For x − 6 = 15, add 6 to both sides: x = 21.
For x/5 = 9, multiply both sides by 5: x = 45.
The phrase “move it to the other side and change the sign” may produce correct work in simple cases, but it hides the reason. The reliable idea is that the same valid operation is applied to both sides.
Undo operations in reverse order
In 3x + 4 = 25, x is first multiplied by 3 and then 4 is added. To isolate x, undo the outermost operation first:
3x + 4 = 25
3x = 21
x = 7.
Check: 3 × 7 + 4 = 25.
If you divide by 3 before removing 4, the equation becomes more complicated because the 4 is not part of 3x. Work from the outside back toward the unknown.
Be careful when the unknown appears before subtraction
x − 8 = 17 gives x = 25 because adding 8 to both sides undoes the subtraction.
But 30 − x = 12 is structurally different. One clear route is to reason: the amount removed from 30 leaves 12, so x = 30 − 12 = 18. Or preserve equality:
30 − x = 12
30 = 12 + x
x = 18.
Do not automatically write x = 12 + 30.
Read coefficient and division notation correctly
5x = 35 means five times x equals 35, so x = 7.
x/4 = 6 means x divided by 4 equals 6, so x = 24.
Guide 10 covers how these expressions are read: Algebraic Expressions and Substitution.
Translate a story into an equation only after naming the unknown
A pupil has some cards. After receiving 9 more, the pupil has 25. Let c be the original number of cards.
c + 9 = 25, so c = 16.
Another story: Four identical packs contain 36 stickers altogether. Let p be the number in each pack.
4p = 36, so p = 9.
The letter should represent one clearly named quantity. Changing what the letter represents halfway through a solution makes the equation unreliable.
Substitution is the final proof-of-fit check
If you solve 6x − 5 = 31 and obtain x = 6, substitute:
6 × 6 − 5 = 36 − 5 = 31.
The original equation is true, so the answer fits.
If substitution fails, do not merely change the final answer. Inspect the step where equality stopped being preserved.
Main worked workshop: fourteen original equation problems
1. Addition
x + 8 = 23.
Answer: x = 15.
2. Subtraction
x − 9 = 14.
Answer: x = 23.
3. Multiplication
7x = 56.
Answer: x = 8.
4. Division
x/6 = 5.
Answer: x = 30.
5. Two-step
4x + 3 = 27.
Reasoning: 4x = 24; x = 6.
6. Two-step subtraction
5x − 7 = 28.
Reasoning: 5x = 35; x = 7.
7. Unknown subtracted
40 − x = 13.
Answer: x = 27.
8. Check by substitution
3x + 2 = 20.
Answer: x = 6. Check: 18 + 2 = 20.
9. Word problem
After spending $12, Maya has $35 left. Let m be the original amount.
Equation: m − 12 = 35. Answer: m = 47.
10. Equal packs
Eight identical packets hold 72 counters. Let c be the number per packet.
Equation: 8c = 72. Answer: c = 9.
11. Fixed amount plus repeated amount
A game gives 4 points for each round plus a 3-point bonus. A player scores 27 points. Let r be the number of rounds.
Equation: 4r + 3 = 27. Answer: r = 6.
12. Identify the wrong step
2x + 5 = 17; learner writes 2x = 22.
Repair: Subtract 5 from both sides: 2x = 12, x = 6.
13. Equality audit
6x = 42; learner divides only the left side by 6.
Problem: Equality is broken. Divide both sides: x = 7.
14. Reverse-check
x/4 + 2 = 7.
Reasoning: x/4 = 5; x = 20. Check: 20/4 + 2 = 7.
A compact inverse-operation map
| Equation form | Undo first |
|---|---|
| x + a = b | subtract a |
| x − a = b | add a |
| ax = b | divide by a |
| x/a = b | multiply by a |
| ax + c = d | subtract c, then divide by a |
| ax − c = d | add c, then divide by a |
The table is a summary, not a replacement for the balance idea.
Common equation errors
Error 1: Apply an operation to only one side.
Error 2: Undo multiplication before removing an outside addition or subtraction.
Error 3: Treat 3x as x + 3.
Error 4: Solve correctly but never check in the original equation.
Error 5: Change what the letter represents midway through a word problem.
Independent transfer check
- x + 11 = 30
- x − 8 = 19
- 9x = 81
- x/7 = 6
- 3x + 5 = 26
- 4x − 6 = 30
- 50 − x = 21
- A fixed fee of $5 plus $3 per item gives a total of $26. Let n be the number of items. Write and solve an equation.
Independent-check answers
1. 19.
2. 27.
3. 9.
4. 42.
5. 7.
6. 9.
7. 29.
8. 3n + 5 = 26; 3n = 21; n = 7.
Parent and tutor guide
If a learner says “move 5 over and it becomes minus 5”, ask what operation was actually performed on both sides. This turns a memorised relocation rule back into equality-preserving reasoning.
For word problems, ask the learner to define the letter in words before writing the equation. For checking, require substitution into the original equation rather than into a rewritten intermediate line.
Separate translation errors from solving errors. A perfectly solved wrong equation is still a wrong model.
The learner’s final card
What does the letter represent? What operations are attached to it? Which operation should be undone first? Did I do the same thing to both sides? Does substitution make the original equation true?
Continue through the PSLE Mathematics Learning Guide
Use Guide 10: Algebraic Expressions and Substitution before this guide if notation is still unclear. Continue with Guide 12: Read Nets and 3D Solids by Tracking Faces and Adjacency.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and solutions are original eduKate teaching material. The guide stays with simple linear equations appropriate to the current Primary 6 syllabus.