Quick answer: Primary 3 Mathematics word problems become easier when pupils distinguish a change from a comparison, a whole from a part, an equal group from a remainder, and an area from a perimeter. This guide explains 200 useful words and question phrases and shows how to translate them into diagrams, number sentences and meaningful answers.
It is written for Singapore parents and pupils following the MOE Primary Mathematics syllabus updated October 2025. Primary 3 covers four-digit numbers, multiplication tables of 6 to 9, division with remainders, equivalent and related fractions, compound measurements and time, area and perimeter, angle concepts and bar graphs. The words below describe common problem situations across those topics. They form an independent teaching glossary, not an official MOE 200-word examination list. Some phrases are everyday language for reading questions rather than formal syllabus headings.
Start with what you need:
- The full list of 200 words and expressions
- Seven Primary 3 word problems explained
- Frequent reading mistakes and what to teach instead
- A four-week practice sequence
- FAQs and next reading
Top 200 Primary 3 Mathematics word-problem vocabulary
Each short entry explains a phrase in relation to the decision the pupil must make. Do not turn the entire list into spelling homework. Select words that currently cause uncertainty, teach them using counters or bar models, then ask the child to use the language in a different question the next day.
1. Reading the question before calculating — entries 1–20
- question statement — The sentences explaining the mathematical situation to be solved.
- given information — The numbers and facts supplied in the question.
- required answer — The specific quantity the question asks the child to find.
- unknown amount — A quantity that is not yet stated and must be worked out.
- starting quantity — The number of items before the story changes.
- ending quantity — The amount after all stated changes have happened.
- named person — The particular character whose items or money are being described.
- item count — How many objects a group contains rather than how large they look.
- measurement unit — The label such as cm, g or minutes attached to a quantity.
- time unit — The type of time measurement used in a story.
- single condition — One stated rule that must be true in the answer.
- combined conditions — Two or more rules that must be considered together.
- at first — A phrase pointing to the amount before an event.
- finally — A word pointing to the result after the events in the story.
- afterwards — A signal that the story has moved to a later stage.
- beforehand — A reference to a quantity or event earlier in the story.
- in all — A phrase that often asks for a total, but check the entire sentence.
- each of them — A phrase directing attention to a share for every person or group.
- remaining quantity — The number or measurement left after a stated action.
- answer sentence — A sentence naming the result and who or what it describes.
2. Addition and subtraction change stories — entries 21–40
- receives another — The collection grows because extra items are added.
- gets back — An earlier amount is returned to a person or group.
- joins the group — A new quantity is combined with an existing quantity.
- collected altogether — Separate collected quantities are combined into one total.
- additional items — New items that increase the previous count.
- added to the stock — The supply increases by a stated amount.
- transferred in — Items arrive from another place or collection.
- replenished — A quantity is restored by adding replacements.
- gave away — An amount decreases because items are passed to others.
- used up — An amount is consumed or spent.
- removed from the box — Items are taken out of a collection.
- spent on a purchase — Money is taken from a starting sum.
- lost during the trip — A starting count becomes smaller by a stated amount.
- donated a portion — Some items leave the owner’s collection.
- transferred out — Objects move away from a particular group.
- stock left — The amount still available after the change.
- total gained — The sum of all additions to a starting amount.
- total removed — The sum of everything taken away across the story.
- net change — The total increases minus the total decreases.
- undo the change — Use the inverse operation to recover the starting amount.
3. Comparisons and part–whole language — entries 41–60
- more than someone else — A comparison saying one person has a greater quantity.
- fewer than another group — A comparison saying one group has a smaller count.
- difference between counts — The numerical gap between two quantities.
- how much larger — A request to compare measurements or values by subtraction.
- how many fewer — A question asking for the gap between two item counts.
- same quantity — Two collections whose counts are equal.
- equalise the groups — Change amounts so that each group has the same number.
- matching pairs — One-to-one links used to see unmatched extra items.
- unmatched remainder — Items in the larger comparison group with no corresponding partner.
- whole amount — The complete amount made up of several parts.
- known part — A component whose quantity is already stated.
- missing part — A component calculated from the total and other known parts.
- part–whole diagram — A picture linking a total to its component quantities.
- comparison bars — Two drawn bars used to display quantities and their difference.
- longer comparison bar — The model segment showing the larger quantity.
- shorter comparison bar — The model segment showing the smaller quantity.
- difference segment — The unmatched part of the larger comparison bar.
- total of two groups — The result of combining both quantities, not their difference.
- compared with — A phrase indicating that a second amount provides the reference.
- one less than — A comparison showing a difference of exactly one.
4. Equal groups, multiplication and division — entries 61–80
- groups containing six — Equal groups with six items in every group.
- packets of seven — Collections containing seven items per packet.
- rows of eight — Arrays with eight objects in each horizontal row.
- nine in each basket — A group-size statement used with the number of baskets.
- number of identical sets — How many equally sized collections are formed.
- equal group size — The count of items held by one group.
- array arrangement — Objects placed in equal rows and columns.
- repeated addition statement — A sum showing the same group size several times.
- total across groups — The combined number from all equal groups.
- share into equal piles — Separate objects so every pile has the same count.
- number per pupil — The count received by each learner in equal sharing.
- number of containers — How many complete groups can hold the available items.
- division with leftovers — A division where some items remain after full groups are made.
- remainder — The quantity left that cannot make another complete group.
- complete packet — A group filled to the required packet size.
- incomplete packet — A group holding fewer than its stated full capacity.
- greatest full-group count — The largest number of complete groups possible.
- another container needed — A conclusion when leftovers cannot be carried separately.
- check by multiplication — Multiply the group count by group size and add the remainder.
- remainder below divisor — The rule that leftover items must be fewer than one full group.
5. Fraction words inside stories — entries 81–100
- equal pieces — Parts of a whole that are the same size.
- same-sized shares — Portions that represent equal fractions of an original amount.
- fraction of a cake — A part of the whole cake divided into equal pieces.
- fraction of a ribbon — A share of the ribbon measured relative to its full length.
- part coloured — The selected portion shown by shading a fraction diagram.
- part not coloured — The remaining unshaded portion of the same whole.
- one half of — One of two equal shares of the specified quantity.
- one third of — One of three equal shares of the specified whole.
- one quarter of — One of four equal shares.
- two thirds of — Two equal third-parts of a complete quantity.
- three quarters of — Three equal quarter-parts of one whole.
- fraction remaining — The share left after some equal parts have been removed.
- fractions of one whole — Fractions that all refer to the same original unit.
- like denominators — Fractions whose equal parts are of the same named size.
- unlike denominators — Fractions using differently sized parts that need alignment for comparison.
- equivalent parts — Different fraction names that cover the same amount.
- simplest fraction — A fraction reduced without changing its numerical value.
- common partition — A way to divide the whole into comparable equal parts.
- fraction comparison — Determine which equal-part amount is greater.
- fraction number sentence — An equation showing a correct relationship between fractions.
6. Money and everyday purchasing — entries 101–120
- money received — Cash added to a starting amount.
- money spent — Cash paid out for items or services.
- cost of one item — The price for exactly one item.
- cost of several items — The sum or product needed for a group purchase.
- dollars and cents — Singapore currency expressed using whole dollars and smaller cents.
- purchase receipt — A record of costs that can be added or checked.
- cash in hand — The money available before or after a purchase.
- exact amount paid — Money that equals the required price.
- change given back — Money returned when the amount tendered is more than the cost.
- price difference — How much more expensive one item is than another.
- same total cost — Two different purchases whose combined prices are equal.
- combined shopping cost — The total paid for several items.
- budget left — The money remaining after purchases.
- shared bill — A total cost divided among several people.
- unit price — The cost of a single item or stated unit.
- double the cost — Twice the original price amount.
- three times the price — Three copies of the same price.
- refund received — Money added back after an earlier purchase.
- amount to save — The difference between a savings target and money already saved.
- money check — Add the cost and change to confirm the cash originally handed over.
7. Units, time and measurement questions — entries 121–140
- distance travelled — The length of a journey.
- length measured — The end-to-end distance of an object.
- mass on a scale — The amount of matter indicated by a weighing device.
- liquid contained — The measured quantity of liquid within a vessel.
- kilometres and metres — Two units that may describe one distance.
- metres and centimetres — Two linked units for lengths.
- kilograms and grams — Two linked units for masses.
- litres and millilitres — Two linked units for liquid volumes.
- same unit first — A reminder to convert before comparing or combining measurements.
- total distance — The sum of the route segments travelled.
- difference in mass — How much heavier one object is than another.
- liquid poured out — Volume subtracted from the amount originally contained.
- starting time — The clock reading when an activity begins.
- finishing time — The clock reading when the activity ends.
- time taken — The elapsed duration between those clock readings.
- 24-hour notation — Writing afternoon or evening clock times with hours 13 through 23.
- after midnight — A time occurring after the new day begins.
- across the hour — A duration extending from one hour into the next.
- seconds elapsed — The number of seconds that have passed.
- timeline jumps — Separate short time intervals added to find a complete duration.
8. Area, perimeter, shape and angle words — entries 141–160
- surface covered — The area of a flat region.
- distance around — The perimeter of a figure’s outside boundary.
- rectangle length — A side dimension used in area and perimeter calculations.
- rectangle breadth — The perpendicular dimension paired with length.
- square-unit count — The number of unit squares needed to cover a region.
- number of boundary units — The total length units surrounding the region.
- missing side — A side length inferred from labelled neighbouring lengths.
- equal opposite sides — A property helping calculate a rectangle’s missing dimensions.
- right-angle corner — A corner that forms a quarter turn.
- turn at the vertex — The opening between two rays forming an angle.
- angle smaller than right angle — A turn narrower than 90 degrees.
- angle larger than right angle — A turn wider than 90 degrees.
- parallel edges — Lines staying the same distance apart in a plane.
- perpendicular edges — Lines meeting at a right angle.
- square grid — An arrangement of equal squares for drawing or measuring.
- rectangular floor — A real-life region whose area can be found by length times breadth.
- fence around a garden — A real-life example of finding perimeter, not area.
- tiles over a floor — A real-life example of area measured through equal squares.
- length unit in answer — Centimetres or metres used for a linear measurement.
- area unit in answer — Square centimetres or square metres used for a surface.
9. Reading bar graphs and data displays — entries 161–180
- bar graph title — The words indicating what a bar graph is about.
- category label — The name of a group represented by a bar.
- horizontal axis — The left-to-right line carrying labels or values.
- vertical axis — The up-and-down line carrying labels or values.
- graph scale — The numerical step between marked values on an axis.
- scale of five — An axis that increases by five per interval.
- scale of ten — An axis that increases by ten per interval.
- height of a bar — The vertical extent showing its represented quantity.
- length of a bar — The horizontal extent when categories use horizontal bars.
- greatest category — The group with the highest recorded quantity.
- least category — The group with the lowest recorded quantity.
- equal-height bars — Bars representing equal amounts on the same scale.
- category gap — The numerical difference between two groups.
- category total — The sum of items recorded for one category.
- combined graph total — The sum of quantities across all categories.
- graph comparison sentence — A statement citing two categories and their difference.
- graph conclusion — A claim supported by displayed values.
- missing graph entry — An unlabelled number inferred from other displayed information.
- read the scale before counting — Check each interval’s value instead of counting gridlines as ones.
- data-based question — A question whose facts are supplied by the display.
10. Bar-model strategy and checking words — entries 181–200
- draw one bar — Represent a whole quantity with one rectangle.
- split the bar — Divide the whole into labelled parts.
- align two bars — Place comparison models in corresponding positions.
- mark the difference — Show the unmatched portion when comparing two bars.
- label the whole — Write what the complete bar stands for.
- label each part — Identify the amount represented by every component.
- unknown box — A blank section standing for an amount not yet found.
- translate the sentence — Move from words to a picture or equation without altering meaning.
- choose an operation — Decide whether addition, subtraction, multiplication or division fits.
- operation reason — Explain why the selected calculation matches the story.
- draw before calculating — Make the relationships visible before using a written algorithm.
- calculate in steps — Use intermediate results rather than attempting a confusing single jump.
- check the story order — Apply changes in their stated sequence.
- reverse-operation check — Use a suitable inverse calculation to confirm a result.
- compare with an estimate — Make sure the final number is a plausible size.
- attach the correct unit — State books, dollars, metres or another appropriate label.
- answer the actual question — Avoid stopping at an intermediate number that was not requested.
- explain in a sentence — State what was found and why it makes sense.
- try different numbers — Test whether the same method works when values change.
- independent second example — A fresh question used to check understanding without prompts.
Seven worked questions: how the words change the mathematics
1. “Receives more” is a change, not a comparison
Question: A shop had 368 pencils. It received 145 more and sold 97. How many pencils are left? The starting quantity is 368. “Received” signals a gain: 368 + 145 = 513. “Sold” signals a reduction: 513 − 97 = 416 pencils. A pupil who adds all three numbers has noticed the quantities but not the events. Ask the child to explain the story aloud without numbers, then restore the numbers and write one calculation per change.
2. “How many more than” finds a gap
Question: Hari has 54 stickers and Mei has 39. How many more stickers does Hari have? Draw two bars starting at the same position. Match the first 39 units; the remaining segment of the longer bar is 54 − 39 = 15 stickers. “More” does not automatically mean addition: “got 15 more” describes growth, while “has 15 more than” compares existing amounts. This is why drawing two aligned bars often works better than circling keywords.
3. A remainder may or may not require another container
Question: A baker has 47 muffins and packs six muffins into each full box. How many full boxes can the baker make and how many muffins remain? 47 ÷ 6 = 7 remainder 5. Seven full boxes hold 42 muffins and five remain. If the question instead asks how many boxes are needed to carry all the muffins, the answer is eight boxes because the five leftover muffins still need a box. The division arithmetic did not change; the requested quantity did.
4. A fraction refers to a particular whole
Question: Two fifths of a ribbon is coloured red and one fifth is blue. What fraction is coloured? 2/5 + 1/5 = 3/5. What fraction remains uncoloured? 1 − 3/5 = 2/5. Every fifth is an equal part of the same ribbon. If the pieces came from different-sized ribbons, combining their fraction names directly would not necessarily describe a share of one common whole.
5. “How long did the journey take?” means duration
A bus leaves at 14:35 and arrives at 15:20. Count 25 minutes from 14:35 to 15:00 and 20 minutes to 15:20. The journey lasts 45 minutes. The finishing time is a clock reading; it is not a duration. Ask the pupil to draw the two jumps on a timeline and label each jump in minutes. The picture prevents mistakes such as subtracting hour and minute digits independently without considering their different bases.
6. Area and perimeter ask different questions about the same garden
A rectangular garden is 9 m by 4 m. “How much land does it cover?” asks for area: 9 × 4 = 36 m². “How long must the fence be?” asks for perimeter: 9 + 4 + 9 + 4 = 26 m. A student may know both formulas but still choose the wrong one when the problem is written in everyday language. Use tiles to explain area and string to trace perimeter.
7. A bar graph with a scale of five is not counted in ones
One class’s reading graph shows a bar at 20 books and another at 35 books. The difference is 15 books. If the vertical axis rises in steps of five, counting three grid steps between the bars is not the same as counting three books. A correct explanation names the scale first, converts bar heights to quantities, then compares the values. Ask pupils to state the two exact numbers as evidence for their conclusion.
Why a child can calculate correctly but still misunderstand a word problem
Arithmetic tells the child how to add, subtract, multiply or divide. Word problems ask the child to identify the relationship before selecting the arithmetic. This requires reading comprehension, precise vocabulary, a mental model of what changed and a check against the question’s target. The word “left” may describe subtraction, but “the bus turned left” describes direction. “More” may indicate an increase, a comparison or an extra amount that has already been included in a total. No single word should replace reasoning about the complete sentence.
The aim is to distinguish three structures. A change problem describes an amount before and after an event. A comparison problem describes two existing amounts and a gap. A part–whole problem describes how components make a total. Once students can name and draw those structures, the particular objects—stickers, marbles, money or bus passengers—can change without changing the underlying mathematics.
Seven mistakes worth diagnosing before more worksheets
- Circles “more” and always adds: contrast “receives more” with “has more than”.
- Changes the order of events: draw a starting box, a gain arrow, a loss arrow and a final box.
- Confuses the count of full boxes with boxes needed for every object: interpret leftovers against the exact question.
- Adds denominators of like fractions: draw one shared whole and count its already equal parts.
- Combines km and m as though they were the same unit: convert to one suitable unit first.
- Uses area units for a fence: contrast covering tiles with tracing the outer edge.
- Counts graph grid steps as individual items: read the axis labels and numerical scale aloud.
A reliable five-step reading routine for P3 Maths
Step 1: Read the final question first and name the target. Step 2: Read the story from the beginning and identify each amount, including its units and owner. Step 3: Decide whether the structure is a change, a comparison, a part–whole relationship or equal groups. Step 4: Draw counters, a short bar model, a table or a timeline where useful, and write a number sentence. Step 5: Check the size, units and wording of the final answer.
These steps need not be written out fully for every routine sum. They are especially helpful when a child feels stuck. The parent or tutor should fade out prompts over time: first model the questions, then ask the child to lead, then present a fresh problem without hints. Independent transfer is the goal.
Building abstraction through a changed story
Take a comparison problem with 54 stickers versus 39 stickers. Replace the stickers with 54 dollars versus 39 dollars. The numerical difference remains 15 because the mathematical relationship has not changed. Next change the numbers to 54 cm versus 39 cm, and attach the proper unit to the answer. Finally ask the pupil to write a new comparison question using the same structure. This moves knowledge from one familiar worksheet to a reusable mathematical idea.
Do the same with multiplication. Seven baskets of six oranges, seven bags of six buttons and seven trays of six biscuits all represent 7 × 6 = 42. But if the story asks how many groups of seven can be made from 42, division is required. Children should learn to explain the roles of group size, group count and total before they learn to recognise a superficial page layout.
Four weeks of Primary 3 Maths word-problem practice
Week 1 — Read, compare and identify changes
Practise two addition/subtraction change stories and two comparison stories on each learning day. Use aligned bar models with labels. Ask the child to give a spoken summary without numbers before calculating.
Week 2 — Equal groups, division and leftovers
Build arrays for multiplication tables of 6, 7, 8 and 9. Divide objects into full groups and interpret remainders in two different stories. Explain why the remainder must be smaller than the divisor.
Week 3 — Fractions, measurements and time
Colour equal fraction parts, convert compound lengths or masses where appropriate, and use a timeline for elapsed-time questions. Always attach a unit or explicitly name the whole being measured.
Week 4 — Area, perimeter, graph scales and mixed stories
Use a grid garden and a short bar graph. Ask the pupil to choose the correct question type without being told which topic it is. Repeat one earlier mistake in a changed story to test what has been learned.
For parents, students and tutors
Parents should observe the first incorrect interpretation, not just the final answer. A child who creates a wrong bar model needs help with reading relationships, while one who draws the correct model but makes an arithmetic slip needs calculation practice. Students can improve by labelling the unknown and speaking one sentence about the model. Tutors can assess the difference by giving the same underlying problem through a diagram, a number sentence and a real-life story.
More worksheets do not automatically repair a misunderstanding. Use one specific misconception, correct it with a model, then test understanding in a different context. Sign up for Mathematics tuition only after the child’s starting position is clear.
12-minute Primary 3 diagnostic quiz: read the words before solving
These twelve short checks are designed for a parent or tutor to read aloud. Ask the child to state the relationship, choose a drawing or calculation, and then give an answer sentence. A wrong answer is useful information: the first mistaken interpretation tells you what to explain next. The answer is provided immediately for quick checking.
- Change in two stages: A stall has 48 oranges. It receives 13 more and sells 9. How many remain? The stall has 48 + 13 − 9 = 52 oranges. Ask why 9 is removed rather than added; the action “sells” changes the stock downward.
- Comparison: One child has 65 cards and another has 47. How many more cards does the first child have? The difference is 65 − 47 = 18 cards. Draw aligned bars to make the gap visible.
- Find the missing starting relationship: A library now has 79 books after receiving 27 new books. How many were there before delivery? Work backwards: 79 − 27 = 52 books. The word “now” identifies the final total, not a value to add.
- Full groups and remainder: There are 53 cookies, with 8 in every full box. Six full boxes use 48 cookies and 5 remain. The division is 53 ÷ 8 = 6 remainder 5. If all cookies require a box, a seventh box is needed.
- Like fractions: Two sixths of a ribbon is green and three sixths is blue. How much of the same ribbon is coloured? The answer is 5/6. The six equal pieces remain sixths; they do not become twelfths.
- Unlike fractions: A pupil has 1/2 of a cake and eats 1/4 of the cake. How much is left? Rename 1/2 as 2/4 and subtract: 1/4 of a cake. Both fractions refer to the same cake.
- Compound distance: A walk is 2 km 300 m followed by 800 m. The total is 2,300 + 800 = 3,100 m, or 3 km 100 m. Convert to the same unit before adding.
- Elapsed time: A show starts at 3:45 pm and ends at 4:20 pm. Count 15 minutes to 4 pm and another 20 minutes: 35 minutes. A timeline is often clearer than subtracting the written clock numbers.
- Area: A rectangular mat measures 7 cm by 5 cm. Its covered area is 35 cm². Explain why the answer counts squares of surface, not the distance around the mat.
- Perimeter: The same mat measures 7 cm by 5 cm. Its perimeter is 7 + 5 + 7 + 5 = 24 cm. Show the child the boundary being measured and compare the units with the area answer.
- Bar-graph difference: Two bars show 30 pupils and 20 pupils on an axis marked every five. The difference is 10 pupils, not two pupils. Each scale step represents five people.
- Shopping total: A notebook costs $4.50 and a pen set costs $2.75. The total is $7.25. Ask the child to show the dollars and cents alignment and state whether the question requests total cost or change.
Choose the smallest useful diagram, not the prettiest one
A number line works well for ordered counts and durations. An array is clearer for equal rows and columns. A bar model helps when parts sum to a total or two existing amounts must be compared. A fraction strip makes equal pieces visible, and a square grid distinguishes area from length. A table is more helpful than a bar when a few related values change systematically. The choice of representation should follow the relationship, not the child’s favourite drawing style.
For every question, let the pupil try a model independently, then ask which labels would make it clearer to someone else. If a bar shows “15” but not whose fifteen objects they are, the problem is not fully represented. Add the owner or unit, check the operation and only then complete the answer. Over time, the pupil may no longer need to draw every obvious step: the purpose of a model is understanding, not producing artwork.
Three follow-up questions that test genuine understanding
After a correct response, ask “What if the numbers changed?” and see whether the same method still works. Ask “Can the question be answered another way?” to connect an inverse calculation, a table or a picture to the original reasoning. Finally ask “Why is your answer sensible?” A child who can justify the operation, the answer’s approximate size and the unit is developing a reliable mathematical habit, rather than depending on a recognised worksheet template.
Frequently asked questions
Are “more”, “left” and “altogether” reliable operation keywords?
They are clues, not universal rules. “More than” usually introduces a comparison while “gets more” describes an increase. Ask what happens to the amounts in the whole sentence.
Does P3 Mathematics include division with remainders?
Yes. Pupils should calculate a remainder and decide what it means for the real question, such as full boxes, leftover items or additional containers needed.
Must every P3 word problem use a bar model?
No. A timeline, array, table, number line or direct number sentence may be clearer. The model should make the relationship visible, not become a compulsory drawing exercise.
How should I use these 200 words?
Choose a small group connected to the child’s current mistakes. Show each phrase in a sentence, draw the relationship and use a fresh example on another day.
Are these official MOE examination vocabulary words?
No. This independent glossary supports the MOE Mathematics learning outcomes, including the important reading and reasoning needed to use those outcomes in questions.
Official source and next useful reading
Refer to the MOE Primary Mathematics syllabus, updated October 2025, and continue with eduKate’s complete P3 200-word Mathematics syllabus glossary, P2 Mathematics vocabulary foundation and Mathematics examination command words and notation guide. Use the two P3 articles together: one explains the topic vocabulary, while this guide explains how question wording connects the topics in stories.
