PSLE Mathematics Learning Guide · Guide 10
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Algebra begins when a number is allowed to be unknown, variable or not yet specified, and a letter is used to hold its place without pretending the value is already known.
If a box contains a pencils and 3 more pencils are added, the new number is a + 3. If there are 3 identical boxes with a pencils in each, the total is 3a. If a pencils are shared equally among 3 pupils, each receives a/3.
The letter is not decoration and it is not always a label. It represents a number. The operation around it tells you how that number is related to another quantity.
This guide develops four current Primary 6 algebra jobs: using a letter to represent an unknown number, reading simple algebraic notation, simplifying simple linear expressions without brackets, and evaluating expressions by substitution. The MOE Primary Mathematics syllabus updated October 2025 lists these outcomes for Primary 6; the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus.
A letter represents a number, not a word
Suppose Mei has some stickers. Let m be the number of stickers Mei has. If she receives 5 more, she has m + 5.
The letter m does not mean “Mei”. It means the number of stickers assigned to that symbol. This distinction matters when more operations appear.
If each of 4 pupils has m stickers, the total is 4m, not m4 and not m + 4.
Read algebraic notation as operations
Common Primary 6 forms include:
- a + 3: three more than a
- a − 3: three less than a
- 3a: three times a
- a/3: a divided by 3
In algebra, 3a means 3 × a. The multiplication sign is normally omitted between a number and a letter.
Do not read 3a as “thirty-something” or as two separate digits. It is a product.
Translate words into algebra one relationship at a time
“A number x increased by 7” becomes x + 7.
“Five times a number n” becomes 5n.
“A number p divided equally among 4 groups” becomes p/4.
“Three less than a number k” becomes k − 3.
Order matters. “Three less than k” is k − 3, while “k less than 3” would describe 3 − k. Do not let familiar words choose the order without reading the full relationship.
Simplify by combining like terms
Like terms contain the same letter part.
3a + 2a = 5a because three groups of a plus two groups of a make five groups of a.
7b − 4b = 3b.
But 3a + 2 cannot become 5a. The constant 2 is not two groups of a.
Likewise, 4a + 3b cannot be simplified to 7ab or 7a because the terms represent different unknown quantities.
Keep constants separate from letter terms
Consider 4a + 3 + 2a + 5.
Combine letter terms: 4a + 2a = 6a.
Combine constants: 3 + 5 = 8.
Simplified expression: 6a + 8.
No further simplification is justified unless a value for a is given.
Substitution replaces the letter with its value
If a = 4, evaluate 3a + 2.
3a means 3 × a, so 3 × 4 + 2 = 12 + 2 = 14.
If b = 18, evaluate b/3 + 5.
18 ÷ 3 + 5 = 6 + 5 = 11.
Substitution should preserve the original operations. Replacing a with 4 in 3a does not create 34.
Keep the intended order of operations
Evaluate 2a + 7 when a = 5:
2 × 5 + 7 = 10 + 7 = 17.
Do not calculate 5 + 7 first and then multiply by 2. The expression says only a is multiplied by 2.
For expressions without brackets, use the ordinary order of operations taught in the primary syllabus.
An expression is not an equation
3a + 5 is an expression. It names a quantity.
3a + 5 = 20 is an equation. It states that two quantities are equal.
An expression does not ask you to solve for a unless additional information is given. You can simplify it, interpret it or evaluate it after a value is supplied.
Guide 11 will focus on equations and preserving equality.
Use context to check the expression
A taxi-style teaching example says a fixed charge is $4 plus $2 for each unit travelled. If n is the number of units, total cost is 4 + 2n.
Check with n = 0: the expression gives 4, matching the fixed charge. Check with n = 3: it gives 10.
These checks do not prove every algebraic model is correct, but they help reveal a reversed or missing operation.
Main worked workshop: fourteen original algebra-expression tasks
1. Write an expression
Sam has x marbles and receives 6 more.
Answer: x + 6.
2. Repeated groups
There are 5 boxes with n cards in each.
Answer: 5n.
3. Equal sharing
p sweets are shared equally among 8 pupils.
Answer: p/8.
4. Less than
A rope is y cm long. Another rope is 4 cm shorter.
Answer: y − 4.
5. Simplify
3a + 7a.
Answer: 10a.
6. Simplify
9b − 2b.
Answer: 7b.
7. Keep unlike terms separate
4m + 6.
Answer: Already simplified.
8. Combine letters and constants
2a + 5 + 3a + 4.
Answer: 5a + 9.
9. Evaluate
4a + 3 when a = 6.
Answer: 4 × 6 + 3 = 27.
10. Evaluate division form
b/5 + 2 when b = 35.
Answer: 35 ÷ 5 + 2 = 9.
11. Evaluate subtraction
7c − 4 when c = 3.
Answer: 21 − 4 = 17.
12. Translate a two-part cost
A service charges $3 plus $5 per item. Let n be the number of items.
Answer: 5n + 3.
13. Explain the difference
Compare 3a and a + 3.
Answer: 3a is three times a; a + 3 is three more than a.
14. Identify an invalid simplification
A learner writes 2a + 5a + 4 = 11a.
Repair: 2a + 5a = 7a, but 4 is a constant. Correct result: 7a + 4.
A translation table
| Words | Expression |
|---|---|
| 5 more than a | a + 5 |
| 5 less than a | a − 5 |
| 5 times a | 5a |
| a shared among 5 | a/5 |
| twice a, then add 3 | 2a + 3 |
| 3 plus four groups of a | 4a + 3 |
Four common algebra-reading mistakes
3a = 3 + a. Wrong: multiplication and addition are different relationships.
a + a = a². Wrong at this level: a + a = 2a. The expression a² means a × a.
2a + 3 = 5a. Wrong: unlike terms cannot be merged.
When a = 4, 3a = 34. Wrong: 3a means 3 × 4 = 12.
Independent transfer check
- Write an expression for “7 more than x”.
- Write an expression for “6 times n”.
- Simplify 4a + 3a.
- Simplify 5b + 2 + 2b + 7.
- Evaluate 3m + 4 when m = 8.
- Evaluate p/4 − 2 when p = 24.
- Explain why 4a + 3 cannot be simplified to 7a.
- A learner says 2x means the two-digit number formed by 2 and x. Explain the correct meaning.
Independent-check answers
1. x + 7.
2. 6n.
3. 7a.
4. 7b + 9.
5. 28.
6. 4.
7. 4a is four groups of the unknown a; 3 is a fixed constant, so they are unlike terms.
8. 2x means 2 multiplied by x.
Parent and tutor guide
Ask the learner to say the expression aloud before simplifying it: “three groups of a plus two groups of a”. This makes 5a more meaningful than a symbol-manipulation rule.
For substitution, write the value directly under or beside the letter and replace the letter in one step. If the learner writes 34 for 3a when a = 4, return to multiplication language rather than adding another rule.
When errors persist, separate four jobs: translate words, read notation, simplify, substitute. Success in one does not guarantee success in the others.
The learner’s final card
What number does the letter represent? What operation connects it to the other quantity? Are the terms truly alike? If a value is substituted, did every operation stay unchanged?
Continue through the PSLE Mathematics Learning Guide
Return to Guide 9: Divide Fractions by Asking How Many Groups Fit. Continue with Guide 11: Solve Simple Linear Equations by Preserving Equality and 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 suggested solutions are original eduKate teaching material. This guide stays within simple linear expression forms suitable for the current Primary 6 syllabus and does not treat later secondary algebra as assumed PSLE content.