PSLE Mathematics Learning Guide · Guide 68 · Wintour V1.0 Companion to Guides 10 and 11
Return to the PSLE Learning Guide · Algebraic Expressions · Simple Linear Equations
A word problem becomes algebra only after one relationship is written faithfully.
The common failure is not equation solving. It happens earlier: the learner chooses the wrong unknown, reverses “more than” or “less than”, turns a multiplication relationship into addition, or writes an expression but never states what it is equal to.
This guide isolates the bridge:
name the unknown → translate each quantity in terms of that unknown → identify the equality statement → write one simple linear equation → solve while preserving equality → substitute back into the story.
The current Primary 6 syllabus includes using a letter for an unknown, simplifying/evaluating simple linear expressions, and solving simple linear equations with whole-number coefficients. This page stays subordinate to those owners and focuses on turning verbal relationships into the equation in the first place.
Choose one unknown that makes the rest easy to express
“Ben has 7 more stickers than Ali. Together they have 43.”
Let Ali have a stickers.
Then Ben has a+7.
Total statement:
a+(a+7)=43.
At Primary 6, a no-brackets route can also be written after combining:
2a+7=43.
2a=36.
a=18.
Ben=25.
An expression is not yet an equation
“Three more than twice a number” can be written 2n+3.
That is an expression.
If the problem says it equals 19, the equation is:
2n+3=19.
The equals sign comes from a stated balance or total relationship.
Translate “more than” in the correct order
“Mei has 5 more than Raj.”
If Raj=r, then Mei=r+5.
Do not write 5−r or r−5.
The person named after “more than” is usually the reference quantity.
Translate “less than” carefully
“Cara has 8 fewer than Dev.”
If Dev=d, then Cara=d−8.
If instead Cara=c, then Dev=c+8.
Both are correct representations when their definitions are stated clearly.
“Times as many” is multiplication, not addition
“A has 3 times as many as B.”
If B=b, then A=3b.
Not b+3.
The number 3 is a multiplicative scale factor.
Fraction relationships become multiplication
“A has 3/4 as many as B.”
If B=b, then A=3b/4.
For a simple Primary 6 equation, the numbers are often chosen so the relationship can be handled cleanly with whole-number operations or equivalent reasoning.
Equal groups create coefficients
“Four identical boxes contain 52 balls altogether.”
Let each box contain x balls.
4x=52.
x=13.
The coefficient 4 counts equal groups of x.
Fixed amount plus repeated amount
A service charges $6 plus $4 for each item. Total is $34.
Let n be the number of items.
4n+6=34.
4n=28.
n=7.
The fixed fee and repeated fee do different jobs and should not be merged before the relationship is written.
A total often creates the equality
“A has x. B has x+9. Together they have 51.”
The word “together” tells us:
x+(x+9)=51.
Then simplify to:
2x+9=51.
A stated difference can create the equality
“Five times a number is 28 more than the number.”
Let the number be n.
5n = n+28.
In a Primary-level method, subtract n from both sides:
4n=28.
n=7.
Age relationship at one moment
“A mother is 4 times her child’s age. Together they are 50 years old.”
Let child age=x.
Mother=4x.
x+4x=50.
5x=50.
x=10; mother=40.
If the problem changes time, update both ages before writing the new relationship.
Money relationship
Ben has $12 more than Ali. Together they have $68.
Let Ali=x.
Ben=x+12.
2x+12=68.
2x=56.
x=28; Ben=40.
Perimeter can become a linear equation
A rectangle has width x cm and length x+4 cm. Perimeter=40 cm.
2(length+width)=40.
2[(x+4)+x]=40.
At the current syllabus boundary, a tutor may first simplify the relationship arithmetically:
4x+8=40.
4x=32.
x=8.
Length=12 cm.
A multiplicative comparison can become an equation
A has twice as many as B. A also has 18 more than B.
Let B=x.
A=2x and A=x+18.
Therefore:
2x=x+18.
x=18.
A=36.
Two expressions for the same quantity create the equality.
Equality often comes from “two ways to describe the same quantity”
If one route says a distance is 3x+5 and another says it is 29, then:
3x+5=29.
If two descriptions both represent Ben’s money, set them equal.
The equals sign should have a meaning in the story.
A different unknown can make the equation easier or harder
“A is 7 more than B; total 43.”
If B=x → A=x+7 → 2x+7=43.
If A=y → B=y−7 → 2y−7=43.
Both are correct. Choose the unknown that makes the relationships easiest to express.
Do not solve from keywords alone
“More” does not always mean add immediately to every number.
“Times” does not always tell which quantity is the reference.
Read the full relationship and attach each operation to the quantities it connects.
Solving preserves equality
3x+7=31.
Subtract 7 from both sides:
3x=24.
Divide both sides by 3:
x=8.
Every move keeps both sides equal.
Guide11 develops this balance idea in full.
Substitute back into the story, not only the equation
If Ali=18 and Ben=25, check:
Ben has 7 more than Ali: 25−18=7.
Total: 18+25=43.
Both story conditions must hold.
A mathematically solved equation can still model the wrong story
Suppose “A has 5 less than B; total35.”
A learner writes A=x+5, B=x and solves correctly.
The algebra may be internally correct for that equation, but the equation models the opposite relationship.
Model correctness comes before equation-solving correctness.
Keep units attached after solving
If x represents metres, the answer is x metres.
If x represents number of tickets, it must fit a whole-ticket context.
If x represents dollars, cents may matter.
The symbol has a quantity meaning throughout the solution.
Main worked workshop: sixteen original equation-forming tasks
1.
A number plus7 is25.
Equation:x+7=25. x=18.
2.
Three times a number is36.
Equation:3x=36. x=12.
3.
Twice a number plus5 is27.
Equation:2x+5=27. x=11.
4.
Four times a number minus3 is29.
Equation:4x−3=29. x=8.
5.
Ben has6 more than Ali; total42.
Equation:2x+6=42. Ali18, Ben24.
6.
Cara has10 fewer than Dev; total70.
Equation:2x−10=70 if Dev=x. Dev40, Cara30.
7.
A has3 times B; total64.
Equation:x+3x=64. B16,A48.
8.
A has twice B and18 more than B.
Equation:2x=x+18. B18,A36.
9.
$5 fixed plus $3/item totals $29.
Equation:3n+5=29. n=8.
10.
Five equal packets plus2 loose items total47.
Equation:5x+2=47. x=9.
11.
A learner writes “4 more than x” as4x.
Repair:x+4.
12.
A learner writes “4 times x” asx+4.
Repair:4x.
13.
A learner writes an expression2x+7 but no equals sign when total31 is stated.
Repair:2x+7=31.
14.
A learner solves the wrong model perfectly.
Repair:recheck the verbal relationship before solving.
15.
Rectangle width x, length x+3, perimeter30.
Equation:4x+6=30. x=6; length9.
16.
Three equal groups plus one extra group of5 gives total41.
Equation:3x+5=41. x=12.
Diagnose the first weak link
Wrong unknown definition: quantity meaning unclear.
More/less reversed: comparison-order error.
Times translated as addition: multiplicative-language error.
No equality statement: expression/equation distinction error.
Equation solved correctly but story fails: modelling error.
A four-line modelling routine
1. Let x = …
2. Write every other related quantity in terms of x.
3. State the equality from total, difference or same-quantity description.
4. Solve and check in the original words.
Independent transfer check
- A number increased by9 is34.
- Four times a number plus2 is50.
- May has8 more than Jin; together54.
- A has5 times B; together72.
- A is twice B and also21 more than B.
- A service charges$7 plus$5/item; total$47.
- Width=x, length=x+5, perimeter42. Find dimensions.
- Explain why2x+5 is not yet an equation.
- Explain why “A has3 times B” becomes A=3B, not A=B+3.
- Give two story checks for a solved pair18 and25 when the conditions are “Ben has7 more than Ali; total43.”
Independent-check answers
1.x+9=34;x=25.
2.4x+2=50;x=12.
3.2x+8=54;Jin23,May31.
4.x+5x=72;B12,A60.
5.2x=x+21;B21,A42.
6.5n+7=47;n=8.
7.4x+10=42;x=8;width8,length13.
8.It names a quantity but does not state what that quantity equals.
9.“Three times” describes multiplicative scaling of B.
10.25−18=7 and18+25=43.
Wintour V1.0 return test
Change the unknown, reverse the comparison wording, swap a total for a difference, and move from money to length or counts. A robust learner should still build the equality from the relationship rather than hunt for keywords.
The learner’s final card
What does my letter represent? How can every other quantity be written from it? What exact sentence creates the equality? Did I preserve “more”, “less”, “times” and “total” correctly? Does my solved value make every original statement true?
Complete Batch 17
Use Guide 65: Combine Two Ratios, Guide 66: Reverse Circle Radius and Diameter, and Guide 67: Tank Flow Rate and Liquid Level.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All examples and solutions are original eduKate teaching material. This page is subordinate to the established algebra-expression and simple-equation owners and isolates word-to-equation modelling.