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Top 200 Vocabulary for Primary 5 Foundation Mathematics | MOE Fractions, Decimals and Essential Word Problems

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eduKate Asia

Quick answer: Primary 5 Foundation Mathematics helps pupils strengthen number sense, calculation, fractions, decimals, measurements, area, volume, angle reasoning and reading graphs. Its vocabulary includes simple but important expressions such as common factor, equivalent fraction, rate, perpendicular and elapsed time. This article explains 200 useful words and phrases and shows how to use them in understandable problems.

The MOE Primary Mathematics syllabus updated October 2025 explains that the Foundation pathway in P5–P6 revisits important Primary 1–4 ideas while introducing selected additional content. The P5 Foundation programme includes number reading up to ten million with specified limits on some operations, fractions, decimals to three places, rate, 24-hour time, area and perimeter, cuboid volume foundations, angle properties and tables or graphs. The 200 entries here are an independent teaching glossary, not 200 official terms pupils must memorise.

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Top 200 Primary 5 Foundation Mathematics words, explained simply

These terms build practical language for understanding actual questions. Teaching them does not mean giving a child 200 spellings to remember. Choose a short group based on what the child is learning, show the meaning with an object or drawing, let the child explain it aloud and later check it in a different story.

1. Number sense, place value and rounding (words 1–20)

  1. number name — The words used to read a numeral, such as three million.
  2. million group — A set of six zeroes after one, making 1,000,000.
  3. number to ten million — A whole-number reading range extending to 10,000,000.
  4. hundred-thousands comparison — Compare quantities at the 100,000 place before smaller places.
  5. place-value columns — Organised boxes for millions, thousands, hundreds, tens and ones.
  6. digit in context — A digit whose value depends on its column.
  7. value of the digit — What the selected digit contributes to the whole number.
  8. zero placeholder — A zero keeping the surrounding place values in their correct positions.
  9. large-number reading — Say each three-digit group and its place name in order.
  10. largest numeral — The greatest number among the displayed candidates.
  11. smallest numeral — The least number among the displayed candidates.
  12. order from least to greatest — Arrange the values in increasing order.
  13. order from greatest to least — Arrange the values in decreasing order.
  14. round to the nearest ten — Choose the closest multiple of ten.
  15. round to the nearest hundred — Choose the closest multiple of one hundred.
  16. round to the nearest thousand — Choose the closest multiple of one thousand.
  17. rounding choice — Use the digit immediately right of the rounding place.
  18. approximately — Indicates a value close to the exact amount.
  19. number pattern — An ordered list with a rule describing how values change.
  20. missing term in a pattern — The number that completes the stated sequence rule.

2. Addition, subtraction, multiplication and division (words 21–40)

  1. addition algorithm — A written method for combining whole numbers.
  2. subtraction algorithm — A written method for finding a difference.
  3. multiplication algorithm — A written sequence of steps for equal-group calculations.
  4. division algorithm — A written sequence of steps for sharing or grouping.
  5. regroup the tens — Exchange ten ones for a ten, or a ten for ten ones.
  6. regroup the hundreds — Exchange ten tens for a hundred, or reverse the exchange.
  7. add a three-digit number — Combine a number up to three digits with another quantity.
  8. subtract a three-digit number — Remove or compare a quantity written with up to three digits.
  9. two-digit by one-digit multiplication — An example is 24 × 3 = 72.
  10. two-digit by one-digit division — An example is 84 ÷ 4 = 21.
  11. multiply by ten — Make the value ten times larger.
  12. multiply by one hundred — Make the value one hundred times larger.
  13. divide by ten — Find one-tenth of the starting value.
  14. divide by one hundred — Find one-hundredth of the starting value.
  15. operation symbol — The sign that names addition, subtraction, multiplication or division.
  16. brackets — Grouping signs showing which part to calculate first.
  17. calculate in order — Follow the conventions governing multiple operations.
  18. mental addition — Add using place-value knowledge without writing every step.
  19. mental subtraction — Subtract by breaking the numbers into manageable parts.
  20. inverse check — Test a subtraction with addition, or a division with multiplication.

3. Factors, multiples and exact division (words 41–60)

  1. factor — A whole number that divides another exactly.
  2. multiple — A number produced by multiplying a given number by an integer.
  3. factor pair — Two whole-number factors whose product is the target number.
  4. common factor — A number dividing both target numbers without remainder.
  5. common multiple — A number appearing in both numbers’ multiplication sequences.
  6. division without remainder — A division that gives an exact whole-number answer.
  7. remainder zero — No items are left after forming complete equal groups.
  8. factor of thirty — An integer such as five or six that divides 30 exactly.
  9. multiple of four — A value in the four-times table.
  10. factor list — A systematic list of positive factors.
  11. multiples list — An increasing list obtained from successive times-table products.
  12. shared factor — A factor that belongs to two factor lists.
  13. shared multiple — A product common to two multiples lists.
  14. test a proposed factor — Divide the target value by the candidate number.
  15. one-digit factor — A factor represented by a single digit.
  16. one-digit multiple base — A number from one through nine whose multiples are listed.
  17. equal groups of objects — Collections containing the same number of objects each.
  18. group count — How many complete equal groups exist.
  19. items in each group — The size of one equal group.
  20. number bond from multiplication — A connection between a group count, group size and total.

4. Fractions as parts of wholes and sets (words 61–80)

  1. fraction — An equal-part quantity such as 3/5 of one whole.
  2. fraction bar — The line dividing numerator from denominator.
  3. numerator — The count of selected equal parts.
  4. denominator — The number of equal parts making one whole.
  5. unit fraction — One equal part of a whole, such as 1/6.
  6. proper fraction — A positive fraction smaller than one whole.
  7. part of a whole — A share of one object or continuous quantity.
  8. part of a set — A share of a group of separate objects.
  9. equal partitions — Pieces of identical size within one whole.
  10. fraction of six counters — A selected share from a collection of six items.
  11. shade three quarters — Colour three of four equal parts.
  12. unshaded remainder — The share not coloured or selected.
  13. equivalent fractions — Different fraction numerals representing the same amount.
  14. fraction strip — A rectangular model showing equal partitions.
  15. equivalent fraction model — A drawing comparing equal lengths with different partitions.
  16. simplest form — A fraction with no common factor greater than one in its numerator and denominator.
  17. simplify by dividing — Reduce both fraction entries by the same common factor.
  18. unlike fractions — Fractions with different denominators.
  19. comparison denominator — A shared denominator chosen for comparing fractions.
  20. fraction order — Arrange fractions from a smaller to a larger value.

5. Mixed numbers and fraction calculations (words 81–100)

  1. mixed number — A whole number combined with a proper fraction.
  2. improper fraction — A fraction whose numerator is at least its denominator.
  3. mixed-to-improper conversion — Count the whole units as equal fractional parts.
  4. improper-to-mixed conversion — Find whole groups of the denominator and any remaining parts.
  5. whole-number part — The complete units included in a mixed number.
  6. fractional remainder — The part of a mixed number smaller than a whole.
  7. add unlike fractions — Make equal-sized parts before combining.
  8. subtract unlike fractions — Express fractions with a common denominator before removing parts.
  9. denominator at most twelve — A boundary for the given denominators in Foundation fraction comparisons and sums.
  10. two denominator types — Fraction work using no more than two different given denominators where specified.
  11. add mixed numbers — Combine the whole parts and fractions, regrouping if needed.
  12. subtract mixed numbers — Remove whole and fractional parts, exchanging a whole when required.
  13. borrow one whole — Rename one unit as a fraction equal to 1.
  14. carry one whole — Regroup a fraction sum greater than or equal to one.
  15. proper fraction multiplied by whole — Example: 2/3 × 6 = 4.
  16. improper fraction multiplied by whole — Example: 5/4 × 4 = 5.
  17. proper fraction times fraction — Example: 1/2 × 3/4 = 3/8.
  18. fraction-of-quantity model — Use equal groups to find a fraction of a number.
  19. fraction multiplication drawing — Show a part taken from another part.
  20. check the fraction result — Decide whether the answer size fits the multiplication or addition.

6. Decimals and money place values (words 101–120)

  1. decimal notation — Writing fractional quantities using digits after a decimal point.
  2. decimal point — The dot separating whole-number and fractional positions.
  3. tenths — Equal parts created by dividing a whole into ten.
  4. hundredths — Equal parts created by dividing a whole into one hundred.
  5. thousandths — Equal parts created by dividing a whole into one thousand.
  6. decimal to three places — A decimal written through the thousandths column.
  7. decimal place-value chart — A table separating ones, tenths, hundredths and thousandths.
  8. compare decimals — Compare corresponding place values, adding harmless zeros if needed.
  9. order decimals — Arrange decimal values from smallest to largest or the reverse.
  10. fraction from a decimal — Represent a decimal as a fraction of a power of ten.
  11. decimal from a fraction — Express a suitable fraction as a base-ten numeral.
  12. round to whole number — Replace a decimal with its nearest integer.
  13. round to one decimal place — Keep tenths and use hundredths to decide.
  14. round to two decimal places — Keep hundredths and use thousandths to decide.
  15. align decimal points — Put matching places vertically for addition or subtraction.
  16. add decimal amounts — Combine decimals while preserving place values.
  17. subtract decimal amounts — Find a difference while maintaining place alignment.
  18. decimal multiplied by ten — Make the original decimal ten times larger.
  19. decimal divided by one hundred — Find one-hundredth of the original decimal.
  20. decimal money amount — Dollars and cents expressed with two decimal places.

7. Rate, metric conversions and duration (words 121–140)

  1. rate — An amount described for each one unit of another quantity.
  2. unit rate — The amount attached to exactly one item, hour or other unit.
  3. cost per item — The price of one item at a constant rate.
  4. amount per minute — A quantity occurring in one minute.
  5. number of units — How many items or time units are counted.
  6. rate times units — A method for finding the total amount.
  7. total divided by units — A method for recovering the rate.
  8. total divided by rate — A method for recovering the number of units.
  9. convert kilometres to metres — Use 1 kilometre = 1,000 metres.
  10. convert metres to kilometres — Divide the number of metres by 1,000.
  11. convert centimetres to metres — Use 100 centimetres = 1 metre.
  12. convert grams to kilograms — Use 1,000 grams = 1 kilogram.
  13. convert millilitres to litres — Use 1,000 millilitres = 1 litre.
  14. measurement in decimals — A converted metric quantity written using decimal numbers.
  15. time duration — The interval between when an event starts and ends.
  16. start time — The clock reading when the event begins.
  17. end time — The clock reading when the event finishes.
  18. 24-hour notation — A clock style using times such as 16:45.
  19. minutes after the hour — The number of minutes elapsed since the hour began.
  20. hours into minutes — Convert each hour to sixty minutes before adding leftovers.

8. Area, perimeter and cuboid volume foundations (words 141–160)

  1. area — The surface covered by a flat figure.
  2. perimeter — The total distance around the outer edge of a flat shape.
  3. square centimetre — A square unit of area written cm².
  4. square metre — A square unit of area written m².
  5. rectangle area — Length multiplied by width.
  6. square area — A side length multiplied by itself.
  7. rectangle perimeter — Twice the sum of length and width.
  8. square perimeter — Four times the side length.
  9. missing rectangle width — Area divided by the known length, if area and length are given.
  10. missing square side — The length found from a stated perimeter or area.
  11. composite rectangles — A shape formed by joining rectangular pieces.
  12. composite area — Add non-overlapping parts or subtract a missing rectangular region.
  13. outer boundary — The sides that count toward perimeter.
  14. internal line — A joining segment not included in the outside perimeter.
  15. cubic centimetre — A cube-shaped volume unit written cm³.
  16. cubic metre — A larger cube-shaped volume unit written m³.
  17. cube and cuboid — Solid shapes with six faces; a cube has equal square faces.
  18. unit cube model — Small blocks used to build and count solid volume.
  19. isometric grid — A grid allowing a simple drawing of a solid’s 3D appearance.
  20. volume measured in cubes — How many unit cubes fill a solid exactly.

9. Parallel lines, angles and rectangular shapes (words 161–180)

  1. parallel lines — Lines in a plane that never meet and stay equally separated.
  2. perpendicular lines — Lines that meet at right angles.
  3. right angle — An angle of ninety degrees.
  4. straight-line angles — Angles together forming 180 degrees on a straight line.
  5. angles at a point — Angles around a point adding to 360 degrees.
  6. vertically opposite angles — Equal angles on opposite sides of crossing lines.
  7. angle vertex — The common point where an angle’s arms meet.
  8. angle arm — One of the rays forming an angle.
  9. protractor — A tool marked in degrees to measure and draw angles.
  10. degree scale — The numbered markings on a protractor.
  11. angle notation — A symbol such as ∠ABC naming the angle at B.
  12. unknown angle — An angle whose value must be found.
  13. rectangle — A four-sided figure with four right angles.
  14. square — A rectangle with four equal sides.
  15. opposite sides — Two sides that do not share a corner.
  16. adjacent sides — Two sides meeting at one corner.
  17. parallel side pair — Two corresponding sides that maintain the same direction.
  18. draw a rectangle — Construct four right angles and two equal opposite side pairs.
  19. draw a square — Construct four equal sides meeting at right angles.
  20. angle-property explanation — State whether the result follows from a straight line, point or intersection.

10. Tables, bar graphs and explanation words (words 181–200)

  1. data table — A display storing values in labelled rows and columns.
  2. row heading — A label identifying a horizontal group of entries.
  3. column heading — A label identifying a vertical group of entries.
  4. table entry — One value at a row-and-column intersection.
  5. bar graph — A display using bars to represent numerical quantities.
  6. line graph — A display using connected plotted points to show values.
  7. graph title — A heading explaining which quantities are displayed.
  8. horizontal axis — The line generally running left to right in a graph.
  9. vertical axis — The line generally running bottom to top.
  10. graph interval — The numerical difference between adjacent scale marks.
  11. graph scale — The rule connecting positions on an axis with values.
  12. graph category — The group represented by one bar or point series.
  13. highest value — The largest number shown by the display.
  14. lowest value — The smallest number shown by the display.
  15. difference between categories — Subtract one displayed category total from the other.
  16. complete the table — Fill missing entries from given information.
  17. interpret the graph — Explain what the displayed data means.
  18. question target — The exact unknown the last sentence asks for.
  19. working steps — The calculation or drawing used to reach the result.
  20. reasonableness check — Confirm the answer fits the story, scale and units.

Seven worked questions that reveal what the words actually mean

1. Large numbers and rounding are not the same skill

Read 3,406,002 as “three million, four hundred and six thousand and two.” The zeros preserve the empty place values. A P5 Foundation learner may be asked to read numbers up to ten million, while comparing and ordering is specified up to 100,000 in the syllabus. For rounding, 48,562 to the nearest hundred becomes 48,600, because the tens digit 6 is at least five. Name the requested rounding place before looking at the deciding digit.

2. The difference between a factor and a multiple

Find the common factors of 12 and 18. Twelve has positive factors 1, 2, 3, 4, 6 and 12. Eighteen has 1, 2, 3, 6, 9 and 18. Their common factors are 1, 2, 3 and 6. Compare this with the common multiples of 3 and 4: 12, 24, 36 and so on. A factor divides a number exactly; a multiple is produced by multiplication. Draw groups to distinguish the two concepts rather than reciting one sentence repeatedly.

3. Unlike fractions first need the same-sized pieces

Calculate 1/3 + 1/6. Split each third into two equal sixths. One-third is 2/6, so 2/6 + 1/6 = 3/6 = 1/2. The final fraction is half of the original whole. An incorrect 2/9 means the child added both denominators and numerators while forgetting that denominators name the size of the parts. Fold a paper strip to show why this method cannot describe the correct quantity.

4. A fraction of a set has individual objects

Twelve apples are shared so that one-fourth of the apples go to Jo. Divide 12 by 4 to make four equal groups of three apples. Jo gets three apples. This differs visually from one-fourth of a rectangular cake, but the same equal-part relationship applies. When a learner can move between strips, counters and calculations, a fraction becomes a useful concept instead of one familiar picture.

5. Decimal place values and metric conversion

Convert 750 ml to litres: 750 ÷ 1,000 = 0.75 L. The numerical value is smaller because the litre is a larger unit; the physical amount has not changed. Now compare 0.75 and 0.705 by writing 0.750 and 0.705. Since 750 thousandths exceeds 705 thousandths, 0.75 is greater. Decimal length is not a reliable rule for comparing values: place values are what matter.

6. Rate and duration tell different stories

A machine fills 24 bottles in four minutes at a constant rate. Its rate is 24 ÷ 4 = 6 bottles per minute. At that rate, five minutes produces 6 × 5 = 30 bottles. If the machine starts at 14:35 and runs for 25 minutes, it finishes at 15:00. Rate compares a quantity per unit of time; duration tells how long the process lasted. The same problem can contain both but they must not be confused.

7. A rectangle area problem asks for a different quantity from its perimeter

A garden is 9 m long and 4 m wide. Its area is 9 × 4 = 36 m²; the perimeter is 9 + 4 + 9 + 4 = 26 m. If the question instead says the area is 36 m² and the length 9 m, the missing width is 36 ÷ 9 = 4 m. This is the reverse use of the same geometric relationship. Ask the child to sketch and label the rectangle before calculating.

What makes P5 Foundation Mathematics a distinct learning route?

Foundation Mathematics is not an informal description of “weak maths”. It is a named syllabus pathway for Primary 5 and 6. The 2025-updated syllabus says the route revisits key Primary 1–4 concepts and introduces a subset of the Standard content. This structure allows students to concentrate on essential mathematical understanding and use it in clearer, practical situations rather than moving at the same speed through every Standard topic.

It is important not to copy the P5 Standard checklist into a Foundation page. In P5 Standard, pupils study triangular area, percentage and several additional geometry properties. In P5 Foundation, those topic allocations differ, with some subjects being revisited from earlier years and percentage appearing in P6 Foundation. Parents and tutors should match the school’s actual pathway and the official document rather than assume both curricula have the same timetable.

Eight important learning gaps and practical fixes

  1. Reads large numbers but places digits wrongly: practise a labelled place-value chart, including zeros.
  2. Rounds to the wrong place: circle the required place, underline the deciding digit and name the nearest unit.
  3. Confuses factors with multiples: build equal groups, then compare factor and multiples lists.
  4. Adds unlike fractions directly: draw strips that show equivalent equal parts before adding.
  5. Counts only the selected fraction objects: identify the complete set, the number of equal shares and how many shares are selected.
  6. Thinks 0.705 is larger than 0.75 because it has more digits: write 0.750 and compare the place values.
  7. Multiplies when the question asks for a rate: write units as “items/minute” and divide total items by minutes.
  8. Uses m where the question asks for m²: connect the unit to the quantity being measured: distance or surface.

Why a vocabulary-first approach reduces unnecessary confusion

Mathematical vocabulary works best when words are attached to actions. A student might repeat “perimeter is around, area is inside” yet freeze when asked for a missing side. Encourage the next step: draw the rectangle, label what is known, explain how an equation represents the missing dimension, and check it by putting the result back in. The definition becomes a route to reasoning.

When words remain confusing, more complicated worksheets can hide the problem rather than fix it. A quick oral check is often more revealing: “Show me a factor of twelve; tell me why six is a factor. Now show me a multiple of twelve.” If the child can give examples in a new setting, the meaning is becoming stable. If not, return to counters or a number line before adding new terminology.

A four-week Foundation Mathematics support plan

Week 1 — Numbers, four operations and factors

Practise reading place-value charts and rounding. Use short multiplication or division tasks within the official calculation boundaries; connect each to equal groups. Make factor lists for small numbers and check them by division.

Week 2 — Fractions and decimal place value

Fold fraction strips and use small sets of counters. Rename fractions, practise the four operations included at this level, then show decimals on a place-value chart. Finish with a measurement conversion that retains the same physical quantity.

Week 3 — Rate, time, area and volume foundations

Set up a simple rate table using price per item or items per minute. Read a travel timetable in 24-hour notation. Measure rectangles, trace their perimeters and build block cuboids to understand cubic units.

Week 4 — Angle properties, graphs and self-explanation

Draw perpendicular and parallel lines; measure and name an angle. Compare bars and read a line graph from labelled scales. Ask the child to explain one question in everyday words before choosing the arithmetic.

Short, repeated sessions are usually easier to manage than a single exhausting study block. A child who can explain five words accurately and use them in changed questions has done meaningful mathematical work.

What students, parents and tutors can do next

Students: underline what the question asks, name the units and draw the relationship if the words feel unfamiliar. Parents: review the schoolbook and note which exact terms trigger confusion, rather than guessing that “all maths” needs help. Tutors: use a familiar example, one changed example and one independent explanation as a quick diagnostic. Sign up for Mathematics tuition only after the student’s starting position is clear.

Frequently asked questions

Is Primary 5 Foundation Mathematics just Primary 4 repeated?

No. It revisits selected earlier concepts and introduces additional concepts from a subset of the Standard syllabus. It has its own year-specific list of topics and expectations.

Is percentage part of P5 Foundation?

The October 2025 syllabus lists percentage as a new topic in Primary 6 Foundation, not in the P5 Foundation content list. Do not assume P5 Standard’s percentage sequence applies to P5 Foundation.

Does Foundation Mathematics include fractions and decimals?

Yes. P5 Foundation includes part–whole and part–set fractions, equivalent fractions, mixed numbers, fraction operations within stated scope and decimals to three places with specified calculations and conversions.

Does a P5 Foundation pupil need to know the area of triangles?

The new triangle-area content is under P6 Foundation. P5 Foundation emphasises areas and perimeters of rectangles, squares and composite figures made from them.

What should I do if my child is embarrassed about the pathway?

Describe the specific learning goal rather than attaching a label to the child. For example, “Let’s practise fraction pieces until you can explain why the denominator stays the same,” gives a clear task and visible progress. The pathway is a curriculum choice, not a judgment of a child’s potential.

Primary sources and useful next reading

Check the official MOE Primary Mathematics syllabus, updated October 2025, especially the P5 Foundation section. For parent pathway decisions, read the eduKate Primary Subject-Based Banding guide. Also compare the Primary 5 Standard Mathematics vocabulary guide and Primary 4 Mathematics foundation glossary to see how content is revisited and extended. These guides are independent explanations and not official MOE worksheets.