Primary 6 Maths: Algebra
PSLE algebra is deliberately simple — one variable, expressions, and simple linear equations — but its notation trips many P6 students. What the syllabus actually requires, with worked examples.
Most schools typically cover this topic in Term 2, around weeks 1–3 — though every school sets its own sequence.
Primary 6 algebra is the smallest big topic in the syllabus. The MOE scope is deliberately narrow: one unknown, expressions like 2y + 3, evaluating by substitution, simplifying by collecting terms, and — the part many parents don't expect — solving simple linear equations such as 2y + 3 = 11 and forming an equation from a word problem. There are no simultaneous equations, no expanding brackets beyond a single multiplier, no factorisation.
So why do children lose marks on it? Notation. Algebra asks a P6 student to accept that 2y means "2 × y", that y + y + y collapses to 3y, and that a letter can stand for any number. Children who miss that shift try to get rid of the letter — usually by inventing a value for it.
The mistakes to watch for
- 3y read as "thirty-something". Children fresh from place value sometimes treat 3y like a two-digit number. 3y means 3 × y, full stop.
- Collecting unlike terms. 5a + 7 − 2a simplified to 10a — folding the 7 into the a-terms. Only like terms combine: 5a + 7 − 2a = 3a + 7.
- Substituting into the wrong expression. Evaluating 2y + 3 at y = 4 as 2 × (4 + 3) = 14 instead of 8 + 3 = 11. Order of operations still rules.
- Dropping units in cost problems. If a pen costs $y, three pens cost $3y — the dollar sign travels with the expression.
Seeing an expression as a box
Easy: expressions and a first equation
Easy: evaluate by substitution
Find the value of 3x − 4 when x = 5.
Show the worked solution
3 × 5 − 4 = 15 − 4 = 11.
Easy: simplify by collecting like terms
Simplify 4p + 6 + p − 2.
Show the worked solution
Collect the p-terms: 4p + p = 5p.
Collect the numbers: 6 − 2 = 4.
Answer: 5p + 4.
Easy: form an expression
Ravi is y years old. His sister is 5 years older. Write an expression for his sister's age.
Show the worked solution
Sister's age = y + 5.
Easy: solve a simple equation
Solve x + 9 = 20.
Show the worked solution
Subtract 9 from both sides: x = 20 − 9 = 11.
Exam: expressions from a story, simplifying, and solving
Exam: build the expression, then evaluate
A pen costs $y. A book costs $3 more than 2 pens.
(a) Express the cost of the book in terms of y.
(b) If y = 4, find the total cost of one pen and one book.
Show the worked solution
(a) Two pens cost $2y, so the book costs $(2y + 3).
(b) When y = 4: pen = $4; book = 2 × 4 + 3 = $11.
Total = 4 + 11 = $15.
Exam: simplify
Simplify 5a + 7 − 2a − 3.
Show the worked solution
Collect the a-terms: 5a − 2a = 3a.
Collect the numbers: 7 − 3 = 4.
Answer: 3a + 4.
Check with a = 2: original gives 10 + 7 − 4 − 3 = 10; simplified gives 6 + 4 = 10. ✓
Exam: solve a two-step equation
Solve 3y − 4 = 17.
Show the worked solution
Add 4 to both sides: 3y = 21.
Divide both sides by 3: y = 7.
Check: 3 × 7 − 4 = 21 − 4 = 17. ✓
Exam: form and solve an equation
Raju has $y. His sister has $3 less than twice as much money as Raju. Together they have $57. How much money does Raju have?
Show the worked solution
Sister's money = $(2y − 3). Together: y + (2y − 3) = 57.
3y − 3 = 57, so 3y = 60, and y = $20.
Check: Raju $20, sister $37 (2×20−3); total $57. ✓
Exam: substitution in a cost problem
A taxi ride costs $3 as a flat fee plus $2 for every kilometre travelled. Find the cost of a 9 km ride.
Show the worked solution
Cost = 3 + 2 × 9 = 3 + 18 = $21.
PSLE challenge: forming equations from harder stories
PSLE challenge: form and solve
Twice a number, minus 7, equals 25. Find the number.
Show the worked solution
Let the number be n: 2n − 7 = 25.
2n = 32, so n = 16.
PSLE challenge: ages now and in the future
Ethan is 4 years older than his sister. In 6 years, the sum of their ages will be 42. How old is Ethan now?
Show the worked solution
Let his sister's age now be s, so Ethan's age now is s + 4.
In 6 years: (s + 6) + (s + 4 + 6) = 42, so 2s + 16 = 42, giving 2s = 26, s = 13.
Ethan now = 13 + 4 = 17 years old.
Check: in 6 years, sister 19, Ethan 23; sum 42. ✓
PSLE challenge: simplify with brackets, then solve
Simplify 2(3x + 4) − x. Then solve 2(3x + 4) − x = 23.
Show the worked solution
Expand: 2(3x + 4) = 6x + 8. Subtract x: 6x + 8 − x = 5x + 8.
Solve 5x + 8 = 23: 5x = 15, so x = 3.
Check: 2(3×3+4) − 3 = 2×13 − 3 = 26 − 3 = 23. ✓
How to practise this topic
Algebra is the rare P6 topic where a small amount of well-chosen practice closes the gap quickly — the syllabus surface is small. Prioritise translating stories into expressions (the exam's favourite move) and substituting values with correct order of operations. A useful self-check habit: after simplifying, substitute a small number into both versions and confirm they match.
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 6 Algebra includes the concepts below. (P6-M-06 is Test Paper's own topic code, not an MOE reference.)
- Simple algebraic expressions
- Simplifying algebraic expressions
- Evaluating algebraic expressions
- Solving simple equations (linear)
- Forming equations from word problems
- Algebraic word problems
Before this topic
These topics feed into Algebra — if this one wobbles, check them first: Primary 6 Whole Numbers (All Operations) · Primary 6 Fractions · Primary 6 Decimals.
Where to go next
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