Word problems explained for parents (Australia)

Homework says Sam has 18 apples. He gives 5 to Mia and packs the rest into bags of 3. How many bags? and Australian parents watch a capable child freeze - not because the arithmetic is hard, but because the maths is buried in a story. A word problem (sometimes called a story problem) is everyday language with a number question hiding inside. The skill this page owns is the problem-solving approach: find what is asked, what is known, and which operation - then draw, act out, or sketch a light bar model before jumping to a number sentence.

This guide is for Year 1–Year 5. It does not reteach addition, subtraction, multiplication or division in depth - those umbrellas live on their own pages. Equal groups, arrays, remainders and part-part-whole stay where they belong too. Year maps: Year 1–Year 5 maths.

What a word problem is

A word problem is maths wrapped in a short story. Numbers appear as amounts of fruit, money, time, people or objects. The child must:

1. Understand the story (who, what happened)
2. Find the question (what is asked)
3. Find the knowns (what numbers and facts are given)
4. Choose an operation (or operations) that matches the meaning
5. Represent (draw, act out, bar sketch) then write a number sentence
6. Check whether the answer makes sense in the story

That sequence is the work. Circling every number and guessing +/−/×/÷ from a single keyword is a shortcut that breaks as soon as the wording gets tricky.

Not the same as the operation skill pages

Word problems use operations. This page owns the approach, not the skill deep-dives:

• Addition explained - joining / adding on
• Subtraction explained - take away / difference / how many more
• Multiplication explained - equal amounts / × meaning
• Division explained - sharing vs grouping
• Equal groups / arrays - pictures that make × and ÷ obvious
• Remainders - leftovers after equal sharing or grouping
• Part-part-whole - two parts make a whole (diagram language)
• Estimate before you add - ballpark check before or after calculating
• Money maths at home - story money contexts (light link only)

If the child can solve bare 8 + 5 but freezes on "eight stickers and five more", the gap is usually the story approach - not the fact itself.

A calm four-question routine

At the kitchen table, slow the rush with four spoken questions - before any pencil sum:

1. What is the story about? (apples, bags, Sam and Mia)
2. What is the question asking for? (how many bags - not how many apples left)
3. What do we already know? (18 apples; gave 5; bags of 3)
4. What happens in the story - join, take away, equal groups, share? (then pick +/−/×/÷)

Only after those four answers do you draw or write. This habit prevents the classic "I added all the numbers I saw" trap.

Draw, act out, or a light bar model first

Abstract number sentences land better after a picture the child can see:

Act it out. Use counters, Lego, fruit or coins. Give five away. Make groups of three with what is left. Count the groups. Say the answer in a full sentence: "Four bags."

Quick draw. Stick people, circles for apples, boxes for bags. Label the numbers from the story on the drawing - not on a blank sum first.

Light bar / strip model. A rough rectangle split into parts helps "how many more" and "altogether" stories without textbook jargon. Meaning first. Deeper part language: part-part-whole.

Then write the number sentence that matches the picture: 18 − 5 = 13; 13 ÷ 3 = 4 bags. Leftovers belong on remainders - do not invent a new rule here.

Keep the drawing or objects visible while you write. Symbols should label a story the child already understands.

Keywords that mislead (teach meaning, not hunting)

Many worksheets train children to hunt words: altogether = add; left = subtract; each = multiply; shared = divide. Those words often help - and they often lie.

Word / phrase	Sometimes…	But can also…
altogether	join / total (+)	total after a take-away first
left / left over	take away (−)	remainder after sharing
each	equal groups (×)	share equally (÷)
shared / share	divide	"give some" (−) in early stories
more / how many more	difference (−)	"3 more than" as add-on (+)
times	multiply	counting events, not ×

Home rule: never let one keyword choose the operation alone. Ask "What happens in the story?" If the keyword and the picture disagree, trust the picture and re-read the question.

Multi-step stories (calmly)

From about Year 3, stories often need two steps (give some away, then pack into bags). Teach children to:

1. Restate the final question
2. Spot the middle question ("how many left after giving 5?")
3. Solve step 1, box that answer as a new known, then do step 2
4. Check both steps against the original question

Do not skip the middle sentence. A light estimate ("about 4 bags or about 40?") catches wild multi-step answers.

Year by year: where story problems show up

Year 1 - short join / take-away / "how many more" with small numbers and objects (Year 1 maths; AC Year 1).

Year 2 - equal groups and arrays in stories; money and measure grow (Year 2 maths; AC Year 2).

Year 3 - related ×/÷ stories; clearer multi-step wording; leftovers in context (Year 3 maths; AC Year 3).

Year 4 - larger numbers; money, measure, multi-step; remainder decisions (Year 4 maths; AC Year 4).

Year 5 - denser multi-step and "which operation?" choice; leave vs round-up leftovers (Year 5 maths; AC Year 5).

Australian Curriculum Mathematics (version 9) builds problem-solving beside fluency through the primary years (Year 1–Year 5).

At home: four questions first, draw or act second, number sentence third, sense-check last.

Home games that do not feel like worksheets

Shop bag. A few items with pretend prices. "You have $10. Buy two things. How much left?" Light money only - deeper practice on money maths at home.

Kitchen share. "Twelve crackers, four plates - equal share." Act out before writing ÷. Meaning: equal groups.

Story flip. Same digits, new question: "18 stickers, give 5, bags of 3" vs "18 stickers shared among 3 friends." Different operations - keyword hunting is not enough.

"What is asked?" card. Child restates the question in their own words before any sum. Celebrate the restatement.

Guess then check. Rough estimate first ("more than 10 or less?"), then exact - light link to estimate before you add.

Keep games under ten minutes. If evenings fray - homework without tears.

A simple weekly home routine

1. Two minutes of story talk - read one short problem aloud; answer the four questions out loud; no writing yet.
2. Five minutes of one careful picture - counters or a quick draw; label knowns; only then write the number sentence.
3. Three minutes of a sense-check - "Does 4 bags sound right for 13 crackers in threes?"; light estimate; re-read the question.

Stop while friendly. Frequency beats duration. For shaky +/− rebuild via addition and subtraction; for equal groups and ×/÷ stories use multiplication, division and arrays.

Common mix-ups (and kinder fixes)

Adding every number in sight. Fix: restate the question; cross out numbers that are labels or red herrings; draw the story.

Keyword-only hunting. Fix: "What happens?" before naming +/−/×/÷; if altogether follows a take-away, the total is after the subtraction.

Skipping the middle step. Fix: write a mini-question for step 1; box that answer; use it as a known for step 2.

Right operation, wrong story answer. Writes "4" for 13 ÷ 3 when leftovers matter - or rounds up when leftovers should stay. Fix: "What happens to leftovers in this story?" - remainders.

Bare facts OK, stories freeze. Fix: more act-out and drawing; rebuild meaning on the matching operation page.

Tears over wordy sheets. Shrink the sheet; one carefully drawn story beats five panicked ones - homework without tears, maths anxiety.

Wider foundation worry: Is my child behind in maths?; calm signals: when to worry about maths.

How this links to other guides

• Addition / subtraction - join, take away, difference (not the story approach)
• Multiplication / division - × and ÷ meaning in stories
• Equal groups / arrays - pictures for × and ÷
• Remainders - leftovers in story context
• Part-part-whole - parts and wholes diagram language
• Estimate before you add - ballpark sense-check
• Money maths at home - story money contexts
• Year 1–Year 5 maths (Year 2, Year 3, Year 4)
• Maths Help hub - more parent guides

Ask the teacher: "For word-problem homework, do you want a drawing before the number sentence - and how should we mark multi-step working?"

FAQ

What is a word problem?

A short story with a maths question inside. Find what is asked, what is known, and which operation matches - usually after drawing or acting it out.

Should my child hunt for keywords like "altogether"?

Keywords are clues, not rules. If the keyword and the picture disagree, trust the picture and re-read the question.

My child knows their facts but freezes on stories. Why?

Often the gap is the approach - restating, choosing the operation, representing - not the bare fact. Use the four-question routine and one careful draw.

Do we need formal bar models?

A light strip or part-part-whole sketch helps. Match the class style. Aim for a clear picture of the story, not a perfect textbook diagram.

A calm next step

When the four questions, a quick draw or act-out, and a sense-check feel settled - and you want a wider number-skill snapshot at home - Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet story problems and related number ideas at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.

Story problems that mix operations still follow order of operations for parents.