Primary 5 Maths | Solving Word Problems with Equations: Unknown, Translate, Check

2026-11-08

Tutor lesson-prep guides · Primary maths

Pupils usually attack a word problem by hunting for a formula: see “8 more” and add, see “30 altogether” and divide. The arithmetic is assembled by feel, so one changed number breaks everything. An equation is not faster, but every line of it can be justified.

Objectives — Pupils can: (1) state in one sentence what x stands for, including the unit; (2) translate a word problem sentence by sentence into an equation, where one equality gives one equals sign; (3) solve the equation, substitute back to check, and answer the question that was asked.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Inverse operations	Solve x plus 5 equals 12	7, by subtracting 5 from both sides
Expanding brackets	Expand 2(x plus 3)	2x plus 6
Substitution	Evaluate 3x plus 5 when x is 7	26

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Opening question	A brother has 8 more cards than his sister and together they have 30; ask what x should stand for	State the sister has x cards, with a unit
5-14 min	Choose the unknown	Three rules: one clear sentence, include the unit, prefer the smaller quantity	Write the unknown sentence themselves
14-24 min	Translate to an equation	One sentence, one relation: altogether means add, more means add, change means subtract	Turn four sentences into four statements
24-33 min	Solve it	Do the same operation to both sides; expanding removes brackets	Solve 3x plus 5 equals 26
33-40 min	Substitute and check	Put x back into the story and test every sentence	Check and write the answer sentence
40-45 min	Exit check	Collect two questions; mark whether the error is the unknown, the translation or the solving	Work independently

03 Teaching script (read it out)

Scene 1: Act 1: say who x is before anything else

Every question starts with the same sentence: “Let x be …”, and it must include the unit. Model it: “A brother has 8 more cards than his sister and together they have 30. Let x be the number of cards the sister has.” Then ask: and the brother? The answer is x plus 8.
Get pupils into the habit of writing both quantities on the left of the page as a relation table. If only x is written, the two people get muddled later. Pupils must do: write “sister x cards, brother x plus 8 cards” and say it out loud once.

Tutor line: “If you have not said who x is, I do not know whose number you are working with. One sentence, with the unit.”

Scene 2: Act 2: one sentence of English becomes one line of algebra

Cut the story into sentences and let each do one job. “Together they have 30” is the equals sign: x plus (x plus 8) equals 30. Solving gives 2x equals 22, so x is 11: sister 11 cards, brother 19.
Then a shopping problem: three books, pay 100 dollars, get 16 dollars change. Let each book cost x. Paying minus the change gives the cost: 3x equals 100 minus 16, which is 84, so x is 28. The key word “change” means subtract, not add.
Build a table on the board: altogether means add, more or longer or heavier means add, less or shorter or lighter means subtract, each or average means multiply or divide. Then add the warning: key words are hints, and you still ask whether the answer makes sense.

Pupils must do: write the equation for four short problems, equations only, no solving yet.

Scene 3: Act 3: solving means doing the same thing to both sides

An equation is not a copying exercise. From 3x plus 5 equals 26, subtract 5 from both sides to get 3x equals 21, then divide both sides by 3 to get x equals 7. Stress the words “both sides”: pupils most often operate on one side only, or forget to change a sign when moving a term.
With brackets, expand first: 2(x plus 3) equals 20 becomes 2x plus 6 equals 20, then 2x equals 14 and x equals 7.
After each line, ask pupils to write a small note at the end of it saying what they did, for example “subtract 5 from both sides”. Errors then become visible at a glance.

Tutor line: “An equation is a balance. Take 5 grams off the left pan and you must take 5 grams off the right pan, or it is no longer level.”

Scene 4: Act 4: substitution is why equations win

The strength of an equation is that it can always be checked. Put x equals 11 back into the story: sister 11 cards, brother 11 plus 8 is 19, together 11 plus 19 is 30, which matches. Show a wrong answer: if x came out as 15, then 15 and 23 give 38, which is not 30, so the work is wrong and must be re-examined.
Finish with the answer sentence: answer what was asked. If the question asks how many cards the brother has, write 19, not x equals 11. Many marks are lost here because the working value is handed in as the answer.

Pupils must do: check one problem themselves and write the full answer sentence.

04 Question types and worked steps

Type	Example	Steps	Answer
Two-step equation	3x plus 5 equals 26	Subtract 5, then divide by 3	x equals 7
With brackets	2(x plus 3) equals 20	Expand to 2x plus 6 equals 20	x equals 7
Two unknowns, a difference	Sister x, brother x plus 8, total 30	x plus (x plus 8) equals 30	x is 11, brother 19
Shopping and change	3 books, pay 100, change 16	3x equals 100 minus 16	x is 28 dollars

Sanity check (teach this): Three checks per question: the unknown sentence has a unit; substituting back makes every sentence of the story true; the answer sentence addresses the quantity actually asked for. For example, x equals 11 gives 11 plus 19 equals 30, which holds; a total of 38 would prove the equation or the solving is wrong.

05 Independent practice (3 questions)

Question	Answer	What to watch
Solve 4x minus 7 equals 25.	x equals 8	Did they change the sign when moving the term
Sister has x cards, brother has 8 more, together 30. How many does each have?	Sister 11, brother 19	Did they stop at x
A rectangle is 3 cm longer than it is wide and has a perimeter of 26 cm. Find both sides.	Width 5 cm, length 8 cm	Did they use twice length plus width

06 Common mistakes and what to say

Mistake	Student writes	Say this
Unclear unknown	Writing x without saying whose number it is	One sentence with the unit: x is the number of cards the sister has
Stopping at x	Answering 11 when asked about the brother	x is the sister. The brother has 11 plus 8, which is 19
Sign error when moving a term	Turning 4x minus 7 equals 25 into 4x equals 25 minus 7	Add 7 to both sides to get 4x equals 32, so x is 8
Skipping the check	Handing in x equals 15	Substitute: 15 and 23 give 38, not 30, so the work is wrong

07 Homework (paper, section and question numbers)

Independent practice on this page (questions 1 to 3) — Question 1: show each operation on both sides; question 2: write both answer sentences; question 3: start from twice length plus width
Primary maths test papers (word problems) — Do three equation word problems; each needs a “let x be” sentence and a substitution check
Primary maths chapter index (neighbouring topics) — Revise the P5 fraction division chapter and compare the checking habits of both topics

08 Exit check (last 5 minutes)

Question	Answer	Decision
What must the unknown sentence contain?	What x stands for, plus a unit	Cannot say: return to Act 1
Solve 3x plus 5 equals 26.	x equals 7	Answering 31 means the plus 5 was ignored
What is the first step in 4x minus 7 equals 25?	Add 7 to both sides, giving 4x equals 32	Subtracting 7 is a sign error
Why always substitute back?	To confirm every sentence holds, so a mistake shows up immediately	Cannot say: retaught in Act 4

09 Tutor FAQ

Pupils can get the answer by arithmetic, so why teach equations?

Arithmetic builds the answer step by step and each step has to be remembered; an equation writes the relation first, then follows rules. Once a problem has two unknowns or brackets, arithmetic gets messy while the equation keeps a fixed procedure, and it can always be checked.

My pupil keeps choosing the wrong unknown. What should I do?

Give one fixed routine: let x be the quantity the question asks for, or the smaller one, then immediately write the other quantity in terms of x. Writing both quantities down removes most of the confusion.

Should every question be checked?

Yes, at least for the first month. Substitution is the only self-correcting step in the topic and it costs very little: read the story again with x replaced. Once it is a habit, pupils catch their own errors before marking.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.