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Top 200 Vocabulary for Primary 5 Foundation Mathematics | Reading Word Problems, Rates and Bar Models

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by

eduKate Asia

Quick answer: Primary 5 Foundation Mathematics develops confidence with whole numbers, factors and multiples, fractions, decimals, rates, hours and minutes, area and perimeter, volume units, angles and graphs. The difficult part of a word problem may be understanding whether a quantity is per item, after a transfer, the whole or the missing side. This guide explains 200 useful words and phrases, then works through everyday examples and a four-week practice plan.

The MOE 2021 Primary Mathematics syllabus, updated October 2025, lists P5 Foundation content separately from P5 Standard. The Foundation curriculum includes multiplication and division algorithms up to two digits by one digit, equivalent fractions and mixed numbers, decimals to three places, rate, 24-hour time, rectangular area and perimeter, unit-cube volume, angles and reading tables, bar graphs and line graphs. P5 Foundation does not introduce percentage, triangle area or circle circumference as its new topics. Those should not be silently added to a P5 Foundation revision checklist. This 200-item list is an independent explanatory glossary rather than a mandated MOE vocabulary list.

Quick route through the article:

200 Primary 5 Foundation Mathematics question-language terms

Use the glossary as a reference alongside the child’s current school materials. Select the words that are causing misunderstandings, show their meaning with a diagram or simple number sentence, and return to them in a different context later. Multiword phrases matter because real questions explain whole situations, not isolated definitions.

1. Understand the starting information — words 1–20

  1. given total — The complete value already supplied by the question.
  2. unknown total — The whole amount that must be calculated from other facts.
  3. starting amount — The quantity before the described events.
  4. ending amount — The quantity after all stated changes.
  5. amount received — An increase in a person’s quantity.
  6. amount given away — A decrease from what the person owned.
  7. quantity transferred — An amount moved from one group to another.
  8. owner of the quantity — The person or group to whom a value belongs.
  9. named objects — The things being counted, such as pens or books.
  10. measurement label — A unit such as cm, kg or minutes.
  11. number of items — How many objects exist in a collection.
  12. number per packet — The count assigned to one equal group.
  13. cost per item — The price associated with one object.
  14. final question — The exact result that the reader must supply.
  15. relevant statement — A sentence containing necessary numerical facts.
  16. unrelated detail — A sentence that does not change the calculation.
  17. before the event — The stage prior to gaining or losing.
  18. after the event — The stage following a gain, loss or transfer.
  19. at the end — The finishing stage of the entire story.
  20. explain the target — Say in a short phrase what must be found.

2. Number size, rounding, brackets and factors — words 21–40

  1. number in numerals — A whole number written using digit symbols.
  2. number in words — A whole number written with a spoken number name.
  3. large-number grouping — Reading digits as millions, thousands and ones groups.
  4. thousands position — The place showing groups of one thousand.
  5. hundred-thousands position — The place showing groups of one hundred thousand.
  6. place-value digit — A digit whose numerical worth depends on its position.
  7. nearest ten — The closest multiple of ten.
  8. nearest hundred — The closest multiple of one hundred.
  9. nearest thousand — The closest multiple of one thousand.
  10. approximately equal — A relationship between a rounded estimate and an actual value.
  11. deciding digit — The digit immediately right of a required rounding place.
  12. number pattern step — The constant amount used to form a sequence.
  13. brackets first — A reminder to calculate the indicated grouped expression first.
  14. order of operations — The conventions governing calculations containing different operations.
  15. factor — A whole number that divides another number exactly.
  16. multiple — A number made by multiplying a stated value by a whole number.
  17. factor pair — Two whole numbers whose product equals the stated number.
  18. common factor — A factor shared by two specified numbers.
  19. common multiple — A number appearing in the multiples of two values.
  20. remainder zero — A sign that division was exact.

3. Add, subtract, compare and transfer — words 41–60

  1. altogether — Combine the named quantities into one complete amount.
  2. in total — The whole that includes all relevant parts.
  3. left after using — The original amount minus what has been used.
  4. difference between — The size of the gap between two numerical values.
  5. has more than — One amount is greater than a comparison amount.
  6. has fewer than — One amount is smaller than a comparison amount.
  7. increase by — Add the stated change to the original amount.
  8. increase to — Treat the stated amount as the new final total.
  9. decrease by — Subtract the stated change from the original amount.
  10. decrease to — Treat the stated amount as the new reduced total.
  11. one quantity moved — An amount is transferred rather than created.
  12. unchanged combined total — The sum stays fixed when items move only between the named groups.
  13. before-transfer gap — The difference between group amounts before moving items.
  14. after-transfer gap — The difference between group amounts after moving items.
  15. balance remaining — The amount available after the stated transactions.
  16. missing contribution — The amount that must be added to reach a known total.
  17. combined parts — Individual component quantities that form a whole.
  18. comparison bar — A rectangle diagram showing a larger and smaller amount.
  19. part–whole diagram — A model that splits one complete quantity into sections.
  20. work back from final — Reverse a change to find an earlier amount.

4. Equal groups and common number operations — words 61–80

  1. equal grouping — Make collections each containing the same number of items.
  2. times as many — Compare quantities using repeated copies, not a fixed difference.
  3. two times — Two equal copies of the referenced amount.
  4. three times — Three equal copies of the referenced amount.
  5. one group size — The number of objects in each equal group.
  6. number of groups — The count of equal collections.
  7. product of groups — The total found by multiplying group count by group size.
  8. division into shares — Split a total so everyone gets an equal amount.
  9. division into packets — Find how many complete groups of a stated size can be made.
  10. one-digit multiplier — The number from 1 to 9 used to multiply another quantity.
  11. two-digit number — A whole number represented by tens and ones.
  12. written multiplication — An organised algorithm for multiplying numbers.
  13. written division — An organised algorithm for separating into equal groups.
  14. multiplication table fact — A known product linking repeated groups.
  15. factor and product check — Confirm a multiplication by a related division.
  16. partial product — The result from multiplying one place-value part.
  17. tenfold quantity — A quantity multiplied by ten.
  18. hundredfold quantity — A quantity multiplied by one hundred.
  19. thousandfold quantity — A quantity multiplied by one thousand.
  20. divide by ten — Find one tenth of the stated amount.

5. Fractions of sets and mixed numbers — words 81–100

  1. whole set — The complete collection from which a fractional share is taken.
  2. equal set groups — Subcollections each having identical counts.
  3. fraction of a set — The share of objects selected from the original group.
  4. fraction of a whole — The share of a single complete quantity.
  5. numerator — The number counting selected equal parts.
  6. denominator — The number indicating the equal pieces forming one whole.
  7. proper fraction — A positive fraction smaller than one.
  8. improper fraction — A fraction whose numerator is at least its denominator.
  9. mixed number — A whole amount and a proper fraction written together.
  10. equivalent fraction — A new fraction name for the same value.
  11. common denominator — The shared denominator used to compare or combine fractions.
  12. like fractions — Fractions with equal denominators.
  13. unlike fractions — Fractions with different denominators.
  14. simplest fraction — A fraction reduced without changing its value.
  15. fraction remaining — The part still present after removal.
  16. fraction added — A fractional amount joined with another compatible quantity.
  17. fraction subtracted — A fractional part taken away from a quantity.
  18. fraction multiplied by a whole — A repeated copy of a proper or improper fraction.
  19. part of another part — A relationship represented by multiplying compatible fractional portions.
  20. fraction strip — A paper or diagram strip partitioned into equal fractional lengths.

6. Decimal words, money and unit conversion — words 101–120

  1. decimal point — The symbol separating whole and fractional decimal places.
  2. tenths — Equal parts representing one tenth each.
  3. hundredths — Equal parts representing one hundredth each.
  4. thousandths — Equal parts representing one thousandth each.
  5. decimal comparison — Determine which decimal amount is greater using place value.
  6. decimal addition — Combine decimal quantities with aligned place values.
  7. decimal subtraction — Find the difference between decimal quantities.
  8. round a decimal — Replace a number with a nearby stated precision.
  9. decimal estimate — A nearby value useful for checking the answer’s magnitude.
  10. decimal scaling — Multiplication or division by a power of ten.
  11. decimal money amount — A dollar-and-cent value written with a decimal point.
  12. exact currency amount — A price or payment expressed to the correct cents.
  13. dollars to cents — Multiply the number of whole dollars by one hundred.
  14. cent value — The part of a dollar represented by the two decimal positions.
  15. kilometres to metres — Express one kilometre as one thousand metres.
  16. metres to centimetres — Express one metre as one hundred centimetres.
  17. kilograms to grams — Express one kilogram as one thousand grams.
  18. litres to millilitres — Express one litre as one thousand millilitres.
  19. same units for addition — Use one compatible unit before combining measurements.
  20. unit-conversion check — Decide whether using a smaller unit should give a larger numeral.

7. Rates and everyday price comparisons — words 121–140

  1. rate — An amount of one quantity for a unit of another quantity.
  2. unit rate — The amount corresponding to exactly one comparison unit.
  3. cost per kilogram — The price for one kilogram of goods.
  4. dollars per item — The amount charged for one object.
  5. pieces per minute — The count produced during a single minute.
  6. litres per hour — The volume of liquid used or supplied in one hour.
  7. number of units — How many objects or equal measures are involved.
  8. total from a rate — Rate multiplied by the number of units.
  9. rate from a total — Total amount divided by unit count.
  10. unit count from a total — Total amount divided by the rate.
  11. higher unit price — A product costing more for one comparable unit.
  12. lower unit price — A product costing less for one comparable unit.
  13. same unit basis — Rates expressed with matching unit sizes.
  14. pack size — How many items are sold together.
  15. packet price — The money charged for the entire pack.
  16. per-person amount — The equal value assigned to each participant.
  17. rate table — A display of corresponding values at a constant rate.
  18. constant rate — A unit relationship that does not change across the story.
  19. compare fairly — Express quantities on the same per-unit basis before deciding.
  20. reasonable rate — A value that fits the stated total and unit count.

8. Time, area and perimeter questions — words 141–160

  1. starting time — The clock reading when an activity begins.
  2. finishing time — The clock reading when an activity ends.
  3. elapsed time — The duration between start and finish.
  4. time in hours — A duration expressed using hour units.
  5. time in minutes — A duration expressed using minute units.
  6. time across noon — An interval crossing from morning into afternoon.
  7. 24-hour clock — Time written from 00:00 through 23:59.
  8. duration line — A timeline showing how the minutes pass.
  9. area of rectangle — The surface covered by a rectangle.
  10. perimeter of rectangle — The distance around the rectangle’s boundary.
  11. area of square — The surface covered by a square.
  12. perimeter of square — The distance around a square.
  13. length of rectangle — One of the two perpendicular rectangle dimensions.
  14. breadth of rectangle — The other perpendicular rectangle dimension.
  15. missing rectangle side — A dimension recovered from area or perimeter and a known side.
  16. composite rectangular figure — A region formed by joining rectangles and squares.
  17. area by splitting — Find separate rectangular regions and add their areas.
  18. area by subtraction — Remove a missing rectangular region from a larger area.
  19. internal dividing edge — A line inside the figure not counted in perimeter.
  20. outer boundary — The shape’s exposed perimeter path.

9. Volume, angle properties and graphs — words 161–180

  1. cube — A solid with six identical square faces.
  2. cuboid — A solid with six rectangular faces.
  3. unit cube — One block representing a unit of volume.
  4. cubic centimetre — The volume of a cube with 1 cm edges.
  5. cubic metre — The volume of a cube with 1 m edges.
  6. isometric drawing — A 3D-looking sketch on an angled grid.
  7. solid length — One dimension of a cube or cuboid.
  8. solid width — A second perpendicular dimension.
  9. solid height — A third perpendicular dimension.
  10. angle vertex — The common endpoint of the two angle arms.
  11. degree — A unit measuring the size of an angle.
  12. straight-line angles — Adjacent turns that add to 180 degrees.
  13. angles around a point — The turns around one point that add to 360 degrees.
  14. vertically opposite angles — The equal angles on opposite sides of crossing lines.
  15. parallel lines — Straight lines in one plane that remain separated.
  16. perpendicular lines — Lines meeting at a right angle.
  17. table entry — A value found at a row-and-column intersection.
  18. bar graph — A display comparing quantities with bars.
  19. line graph — A display showing plotted values connected in an ordered sequence.
  20. graph scale — The numeric amount represented by each marked graph interval.

10. Reading strategies, checks and complete answers — words 181–200

  1. restate the story — Explain the problem in simpler words without changing conditions.
  2. identify the requested result — Name the unknown that the question wants.
  3. label the known parts — Place each supplied quantity on a model.
  4. draw equal sections — Use repeated bar units for a sharing or grouping question.
  5. draw two comparison bars — Make the gap between quantities visible.
  6. draw before-and-after bars — Display how quantities change across an event.
  7. mark a missing section — Show where the unknown amount belongs in a diagram.
  8. use a simple table — Organise related pairs of values before calculating.
  9. choose the operation — Select arithmetic based on relationships rather than trigger words.
  10. calculate in steps — Find meaningful intermediate results in the correct order.
  11. use one unit consistently — Avoid combining different measurement units without conversion.
  12. check the decimal place — Preserve place value during arithmetic and rounding.
  13. check the reference whole — Make sure a fraction refers to the intended complete amount.
  14. check the rate units — Confirm whether a value is per kilogram or per packet.
  15. check the area units — Use square units for the surface covered.
  16. check the perimeter units — Use linear units for boundary distance.
  17. estimate an answer — Predict a plausible numerical range.
  18. verify by reversing — Use a suitable inverse operation to test the result.
  19. answer with a label — State the object or measurement named by the calculated number.
  20. try a changed example — Test whether the same relationship works with new numbers.

Twelve worked P5 Foundation questions that show the relationship

1. Reading a large number needs place value

The numeral 1,205,040 is read as one million, two hundred and five thousand, and forty. Its zero digits still hold important positions. Write the number in three-digit groups and ask the pupil to identify the millions, thousands and ones groups. Reading and writing large numbers is part of P5 Foundation; comparing and ordering values should respect the syllabus’s stated range, up to 100,000, rather than assuming every large-number operation has the same bound.

2. “Increased by” differs from “increased to”

A stall has 245 notebooks and its stock increases by 130. The new stock is 245 + 130 = 375 notebooks. In another story, the stall’s stock increases to 375 after receiving 130 notebooks. The starting stock was 375 − 130 = 245. The same numbers appear but the unknown changes. Write “starting”, “change” and “final” above three simple boxes to help make the distinction visible.

3. Brackets preserve the meaning of grouped operations

Consider 6 × (8 + 2). The brackets make 8 + 2 one combined group, so 6 × 10 = 60. Without the brackets, 6 × 8 + 2 = 50 under the usual order of operations. This difference is not a cosmetic writing rule. It can represent six packets containing eight red and two blue pens each versus six packets of eight red pens plus only two loose blue pens.

4. Factors are not the same as multiples

The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 18 are 1, 2, 3, 6, 9 and 18. Their common factors are 1, 2, 3 and 6. Their common multiples include 36, 72 and 108. The first list consists of values that divide exactly; the second consists of values built by multiplication. Ask the pupil to show 12 as an array of three rows of four, then explain why three and four are factors.

5. Fractions of a set are groups of real objects

A box holds 20 balls. Three fifths are blue. Split twenty into five equal groups of four; three such groups contain 3 × 4 = 12 blue balls. The remaining eight balls are other colours. The denominator names the number of equal shares, and the numerator names how many shares are selected. If the pupil simply multiplies 20 × 3 and then divides without understanding the groups, use counters to show the reason behind the calculation.

6. Unlike fractions require comparable parts

A child has 1/2 m of ribbon and uses 1/4 m. To find the remaining amount, rename 1/2 as 2/4 and subtract: 2/4 − 1/4 = 1/4 m. The operation is not 1/2 − 1/4 = 0/−2. First describe the fractions as equal-size pieces of the same unit, then combine or remove those parts. P5 Foundation explicitly revisits equivalent fractions, comparisons and fraction operations.

7. “One half of one third” is a part of a part

One third of a garden is used for vegetables. Half that vegetable area is planted with carrots. The carrots occupy 1/2 × 1/3 = 1/6 of the complete garden. Draw a rectangle divided into three columns and two rows. The vegetable area takes two of the six small cells, and the carrot part takes one of the six. The reference whole is the entire garden, not only the vegetables.

8. Decimal conversion is a change of units, not quantity

A ribbon is 2.35 m long. Since one metre is 100 cm, it is 235 cm. The actual ribbon does not become longer; the number increases because centimetres are smaller units. Another example: 1,250 g is 1.25 kg. Teach this with a ruler and familiar masses rather than only a rule about moving the decimal point.

9. “Rate” means how much for one unit

Five identical notebooks cost $17.50. The unit price is 17.50 ÷ 5 = $3.50 per notebook. Eight notebooks at the same rate cost 8 × 3.50 = $28. A child who compares $17.50 for five notebooks with another seller’s $15 for three notebooks without finding unit prices may choose the wrong bargain. The word “per” identifies the two linked units and directs what should be divided.

10. Elapsed time is not a clock reading

An activity starts at 14:25 and lasts 1 hour 40 minutes. The finishing time is 16:05, or 4:05 pm. A timeline can show one hour to 15:25, then 35 minutes to 16:00, then another five minutes. The starting and finishing times are points in a day; the duration is how long the activity lasts. P5 Foundation includes the 24-hour clock and conversion between hours and minutes.

11. Area and perimeter answer different questions

A rectangular floor is 8 m long and 5 m wide. The amount of floor to tile is the area, 8 × 5 = 40 m². The length of skirting needed around the edge is the perimeter, 8 + 5 + 8 + 5 = 26 m. The same figure and measurements support two different questions. If a 3 m by 2 m corner is removed, the area becomes 34 m²; the boundary must be traced again to find perimeter correctly.

12. A graph’s scale is part of the data

A bar graph records 15 books read by one class and 25 by another, using an axis with marks every five. The difference is 10 books. Two marked steps separate the values, but each step represents five books. Ask the pupil to point to the labels and scale before writing the subtraction. P5 Foundation includes reading tables, bar graphs and line graphs; pie charts are listed as new content under P6 Foundation.

Why more arithmetic practice alone sometimes fails

Suppose a child correctly divides 20 by five but answers “four” when asked how many blue balls there are if three fifths of twenty are blue. The arithmetic 20 ÷ 5 = 4 is a useful intermediate result, but it represents one fifth, not three fifths. The mathematical mistake is selecting the final target. The next lesson should help the child label one unit and three units rather than assign more long division worksheets.

Similarly, a learner who correctly calculates 8 × 5 = 40 may use that result for the perimeter of an 8 m by 5 m garden. That child needs to distinguish covered surface from external boundary, not to drill multiplication. Ask pupils to explain what is being measured before choosing a formula. Use square tiles for area and a loop of string for perimeter.

Six practical methods for making question language visible

Use the before-and-after model. Draw a starting box, an arrow describing what changes and an ending box. This is effective for stock, savings and transfers. Use the equal-group model. Draw repeated small rectangles for sharing, multiplication or rate. Use a fraction strip. Divide a whole into equal parts, then select the relevant portion. Use a measurement diagram. Mark lengths and units before writing formulae. Use a timeline. Record start, finish and elapsed duration separately. Use a table. Organise related rates or graph values.

Do not force a bar model onto every question. An angle diagram should be inspected for marked right angles and parallel lines. A three-dimensional solid may be easiest to understand with unit cubes. A short number sentence can solve a straightforward calculation without an elaborate model. The best model is the one that makes the relationship and the unknown clear to the pupil.

Eight misconception repairs parents can use immediately

  1. Reads the number correctly but compares its zero digits wrongly: use a place-value chart and compare from the largest place.
  2. Rounding result looks unreasonable: identify the required place and the digit immediately to its right.
  3. Confuses the product with the group count: ask which quantity is “each” and which is “number of groups”.
  4. Multiplying fractions yields an implausibly larger portion: draw a fraction of a fraction before calculating.
  5. Rate units are reversed: write dollars per notebook rather than notebooks per dollar when the question asks for unit price.
  6. Subtracts clock numerals as though there were 100 minutes an hour: move along a timeline and regroup in 60-minute hours.
  7. Confuses the area unit and perimeter unit: name square units for surface and linear units for edges.
  8. Counts axis marks rather than represented values: read the graph scale and write numerical values before comparing.

Four-week P5 Foundation Mathematics word-problem plan

Week 1 — Understand large numbers and known totals

Practise naming digit places, comparing permitted number ranges, rounding and using brackets. Give change and comparison stories with small enough numbers for successful mental checking. Ask the pupil to name the starting quantity, final quantity and missing amount before calculating.

Week 2 — Fractions and decimals

Use real items for fractions of a set and folding paper for equivalent parts. Compare simple unlike fractions using common partitions, then calculate selected fraction operations. Make decimal place value visible through money and measurement examples. Focus on the correct reference whole.

Week 3 — Rates, time, area and perimeter

Compare costs per identical unit, work on the 24-hour clock and find the area or boundary length of simple rectangular figures. Use string and square-grid paper. Keep units attached to every intermediate result when they help interpretation.

Week 4 — Geometry, graphs and mixed application

Read unknown angles using properties of straight lines and vertically opposite angles. Sketch cubes and cuboids on simple grids, interpret tables and graphs, and mix problem types so the title does not reveal the operation. Return to one previously mistaken question with changed values.

Connecting Foundation Mathematics to everyday independence

Mathematical language is useful well beyond a test. A family comparing supermarket unit prices is using rate. Reading the time on a bus timetable is using clock and duration concepts. Measuring a tabletop for a cover uses rectangular area. Checking how much money remains after buying groceries uses subtraction. Understanding these ordinary situations helps children see a reason to learn Mathematics and practise it without constant formal drills.

The same words must remain precise across contexts. “Per kilogram” is not interchangeable with “per packet”, because a packet may contain a different mass. A fraction of the remaining money is not necessarily the same fraction of the original money. An area of 20 cm² is not 20 cm of boundary. Encourage the pupil to explain these distinctions in a sentence before writing the calculation.

A twelve-question diagnostic to use after a revision week

  1. Round 4,268 to the nearest hundred: 4,300.
  2. Find the common factors of 12 and 18: 1, 2, 3 and 6.
  3. Find 6 × (4 + 3): 42.
  4. Find 2/5 of 25 items: 10 items.
  5. Add 1/2 and 1/4: 3/4.
  6. Find half of one third: 1/6.
  7. Convert 2.4 m to centimetres: 240 cm.
  8. Five identical packets cost $25. Find price per packet: $5.
  9. Convert 2 hours 20 minutes into minutes: 140 minutes.
  10. Find the area of a 7 cm by 6 cm rectangle: 42 cm².
  11. Find its perimeter: 26 cm.
  12. A graph bar reaches 30 on a scale of ten. Its value is 30, not three.

The purpose of the check is to find the first misunderstanding. A learner who gives a correct result with an incorrect explanation may still need the model. One new example a few days later is a better test of transfer than repeating the same question immediately from memory.

What tutors, teachers and families should prioritise

Parents can ask for a spoken explanation before a calculation. Teachers can give two similar questions where only the target changes. Tutors can use the same numerical structure with real-life objects, a diagram and a number sentence to see whether a pupil can transfer the idea. The priority is independent understanding within the right curriculum level, not racing through a Standard Mathematics workbook when the learner is taking Foundation Mathematics.

Additional support should match the error. A child struggling with the word per benefits from comparing unit prices in a shop story. A child with a correct model but incorrect multiplication needs numerical fluency. A child with anxiety around long word problems may benefit from short, successful tasks with gradually reduced prompts. Sign up for Mathematics tuition only after the student’s starting position is clear.

Frequently asked questions

Is percentage a Primary 5 Foundation Mathematics topic?

Percentage is listed as new content under Primary 6 Foundation in the updated MOE syllabus, not in the P5 Foundation content list. Begin with the current P5 Foundation topics such as fraction, decimal and rate relationships.

Does P5 Foundation include rate?

Yes. Pupils learn the meaning of amount per unit and use the relationship among rate, total amount and number of units.

Are angle properties part of P5 Foundation?

Yes. The syllabus includes drawing and measuring angles, angles on a straight line, around a point and vertically opposite angles, as well as finding unknown angles.

Does P5 Foundation include area of triangles?

The specified P5 Foundation area section covers rectangles, squares and composite figures made from them. Triangle area is listed as new content under P6 Foundation.

Does every word-problem phrase need memorising?

No. Select the phrases connected to current learning and explain their meaning through diagrams and new problems.

Official syllabus and next reading

Check the MOE Primary Mathematics syllabus updated October 2025, especially the P5 Foundation tables. Use the P5 Foundation 200-word topic glossary, the P6 Foundation 200-word syllabus guide and the distinct P5 Standard word-problem article if you need to compare pathways. These explanations are independent and are not official school assessment papers.