Grade 6 Mathematics (CAPS): a term-by-term guide for parents and learners

Course guides › Grade 6 › Mathematics

← Back to main menu

Grade 6 Mathematics is the last year of the Intermediate Phase, so it pulls together everything from Grades 4 and 5 and stretches it: numbers up to nine digits, all four operations with large numbers, fractions, decimals and percentages, and more formal geometry, measurement and data handling.

Each summary below explains what the topic covers, how to tackle it, and the mistake learners make most often. The examples use our own numbers, not questions from the course or the memo.

Below, all 42 topics of our Grade 6 Mathematics (CAPS) course are summarised term by term, in the order schools teach them: what each topic covers, how to approach it, and the mistake learners make most often. The summaries are based on the course’s term Parent Memos, written in our own words, so nothing here gives away the answers to course questions.

Course status: available. Grade 6 Mathematics (CAPS) is one course for the whole year (Terms 1 to 4). Price: R100 per subject per year.

Open the Grade 6 Mathematics course

On this page

The course at a glance

  • One course for the whole year: 42 topics across Terms 1 to 4 (11, 9, 11, 11 per term).
  • Every topic has a lesson, worked examples, a 15-question quiz with hints on wrong answers, and extra practice. Quizzes can be retaken, and there is no pass mark to fail.
  • Printables for every term: a Learner Coursebook to write in and a Parent Memo with the answers and explanations.
  • Listen mode reads each page aloud.

How marks are given in Grade 6 Mathematics

  • 1-mark questions test one fact or one quick step. Only the final answer counts, so check it.
  • 2-mark questions usually give a mark for the method and a mark for the correct answer with its unit.
  • 3- and 4-mark questions are longer calculations or multi-step problems. Marks are given for each correct step, so clear working still earns marks after a small slip.
  • Estimate first. It earns no marks on its own, but it catches place-value and sign mistakes before they cost marks.

Term 1: Whole numbers and the four operations

Term 1 is about whole numbers: mental maths, place value to nine digits, rounding, primes, factors and multiples, and adding, subtracting, multiplying and dividing big numbers, ending with word problems.

Term 1 topics:

  1. Mental maths: number facts and quick strategies
  2. Place value: 9-digit numbers, number names and expanded notation
  3. Ordering, comparing and rounding off
  4. Prime numbers
  5. Adding and subtracting big whole numbers
  6. Properties of whole numbers and inverse operations
  7. Multiples, factors and prime factors
  8. Multiplying big whole numbers
  9. Many operations: brackets and the order of operations
  10. Dividing big whole numbers (with remainders)
  11. Solving problems with whole numbers: money, measurement, ratio and rate
Read the Term 1 topic summaries (11 topics)

1.1 Mental maths: number facts and quick strategies

Fast recall of times tables and number bonds frees up thinking for bigger sums. Strategies such as doubling and halving help: 25 × 16 = 50 × 8 = 400.

Watch out for: Counting on fingers instead of learning the facts by heart.

1.2 Place value: 9-digit numbers, number names and expanded notation

Each digit’s value depends on its place, up to hundred millions. 407 052 316 is four hundred and seven million, fifty-two thousand, three hundred and sixteen, and in expanded notation 400 000 000 + 7 000 000 + 50 000 + 2 000 + 300 + 10 + 6.

Watch out for: Leaving out a zero placeholder when writing the number in digits.

1.3 Ordering, comparing and rounding off

Compare numbers from the left, digit by digit. To round, look at the digit to the right of the place you are rounding to: 638 472 rounded to the nearest 1 000 is 638 000.

Watch out for: Rounding each digit in turn instead of looking only at the next digit.

1.4 Prime numbers

A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11 …). 1 is not prime, and 2 is the only even prime.

Watch out for: Calling 1 a prime number, or 9 or 15 primes because they are odd.

1.5 Adding and subtracting big whole numbers

Use column methods or breaking down for big numbers. 528 346 + 271 589 = 799 935. Estimate first by rounding: about 530 000 + 270 000 = 800 000.

Watch out for: Misaligning columns so thousands are added to hundreds.

1.6 Properties of whole numbers and inverse operations

Commutative, associative and distributive properties let you rearrange sums. Inverse operations check answers: if 7 284 − 3 196 = 4 088, then 4 088 + 3 196 should give 7 284.

Watch out for: Thinking subtraction or division is commutative.

1.7 Multiples, factors and prime factors

Multiples come from multiplying (multiples of 6: 6, 12, 18 …). Factors divide exactly. Prime factors break a number into primes: 60 = 2 × 2 × 3 × 5.

Watch out for: Mixing up factors and multiples.

1.8 Multiplying big whole numbers

Multiply big numbers with the column method or by breaking down: 347 × 26 = 347 × 20 + 347 × 6 = 6 940 + 2 082 = 9 022.

Watch out for: Forgetting the placeholder zero in the tens row.

1.9 Many operations: brackets and the order of operations

The order of operations is brackets first, then multiplication and division, then addition and subtraction: 18 − 4 × 3 = 6, but (18 − 4) × 3 = 42.

Watch out for: Working strictly left to right.

1.10 Dividing big whole numbers (with remainders)

Long division works place by place. 4 375 ÷ 12 = 364 remainder 7. In a word problem, decide whether to round the answer up, down or keep the remainder.

Watch out for: Ignoring the remainder when the context needs one more bus, box or trip.

1.11 Solving problems with whole numbers: money, measurement, ratio and rate

Word problems combine money, measurement, ratio and rate. Underline what is asked, pick the operation, estimate, solve and check: three pens at R14.50 each cost R43.50.

Watch out for: Answering with a number but no unit.

Try at home in Term 1:

  • Read a big number from a news story aloud and write it in expanded notation together.
  • Play “factor pairs”: choose a number such as 48 and race to list every pair that multiplies to it.

Back to the topic list · Back to main menu

Term 2: Patterns, number sentences, fractions, percentages and decimals

Term 2 moves from number sentences and patterns to common fractions, percentages and decimal fractions, including how they relate to each other.

Term 2 topics:

  1. Number sentences
  2. Numeric patterns: sequences
  3. Input and output values: flow diagrams and tables
  4. Geometric patterns
  5. Common fractions: compare, order, add and subtract
  6. Fractions of whole numbers and fraction problems
  7. Percentages and equivalent forms
  8. Decimal fractions: place value, counting, comparing and ordering
  9. Decimal fractions: add, subtract, multiply by 10 and 100, and solve problems
Read the Term 2 topic summaries (9 topics)

2.1 Number sentences

A number sentence uses symbols to show a relationship, with a box or letter for the unknown: 7 × □ + 5 = 61, so □ = 8. Learners write and solve them from word problems.

Watch out for: Doing the operations in the order the words appear instead of solving for the unknown.

2.2 Numeric patterns: sequences

A numeric pattern follows a rule. In 5, 12, 19, 26 … the rule is “add 7”, so the 10th term is 5 + 9 × 7 = 68.

Watch out for: Finding the next term but not stating the rule.

2.3 Input and output values: flow diagrams and tables

A flow diagram applies a rule to each input to get an output. With the rule “× 4 then − 3”, the input 9 gives 33. Learners also work backwards to find inputs.

Watch out for: Reversing the operations in the wrong order when working backwards.

2.4 Geometric patterns

Geometric patterns grow by adding shapes in a regular way. Learners describe the rule and predict a later pattern, for example how many matchsticks are in the 8th shape.

Watch out for: Drawing every shape instead of using the rule.

2.5 Common fractions: compare, order, add and subtract

To compare or add fractions, make the denominators the same: 2/3 + 1/4 = 8/12 + 3/12 = 11/12. Mixed numbers can be converted to improper fractions.

Watch out for: Adding the denominators as well as the numerators.

2.6 Fractions of whole numbers and fraction problems

A fraction of a whole number divides by the denominator, then multiplies by the numerator: 3/8 of 64 = 64 ÷ 8 × 3 = 24.

Watch out for: Multiplying by the denominator instead of dividing.

2.7 Percentages and equivalent forms

A percentage is a fraction out of 100: 35% = 35/100 = 0.35. Learners convert between fractions, decimals and percentages and find percentages of amounts, such as 25% of R180 = R45.

Watch out for: Treating 5% as 0.5 instead of 0.05.

2.8 Decimal fractions: place value, counting, comparing and ordering

Decimals extend place value to tenths, hundredths and thousandths. 0.6 is greater than 0.58 because 6 tenths beat 5 tenths.

Watch out for: Thinking a longer decimal is always bigger.

2.9 Decimal fractions: add, subtract, multiply by 10 and 100, and solve problems

Line up the decimal commas (or points) to add and subtract: 7.45 + 2.8 = 10.25. Multiplying by 10 or 100 moves every digit one or two places to the left: 3.62 × 100 = 362.

Watch out for: “Adding a zero” to multiply decimals by 10, which gives the wrong answer.

Try at home in Term 2:

  • Halve a recipe and work out the new amounts as fractions.
  • Look at a “30% off” sticker and work out the new price together.

Back to the topic list · Back to main menu

Term 3: Geometry and measurement: shapes, angles, transformations and space

Term 3 covers length, 2D shapes and angles, symmetry and transformations, 3D objects and their nets, then perimeter, area and volume.

Term 3 topics:

  1. Length: measuring and converting mm, cm, m and km
  2. 2D shapes: polygons, rectangles and parallelograms
  3. Angles
  4. Symmetry
  5. Transformations: rotation, translation, reflection, tessellations, enlargements and reductions
  6. 3D objects: faces, edges, vertices and nets
  7. Viewing objects (bonus topic)
  8. Perimeter
  9. Area
  10. Volume
  11. Temperature (bonus topic)
Read the Term 3 topic summaries (11 topics)

3.1 Length: measuring and converting mm, cm, m and km

10 mm = 1 cm, 100 cm = 1 m and 1 000 m = 1 km. Learners measure with rulers and tapes and convert: 2.35 m = 235 cm.

Watch out for: Multiplying when they should divide (or the other way round) during conversions.

3.2 2D shapes: polygons, rectangles and parallelograms

Polygons are closed shapes with straight sides. Rectangles have four right angles; parallelograms have two pairs of parallel sides. Learners sort shapes by their sides and angles.

Watch out for: Saying a square is not a rectangle.

3.3 Angles

Angles are measured in degrees with a protractor. Acute is less than 90°, right is 90°, obtuse is between 90° and 180°, straight is 180° and reflex is more than 180°.

Watch out for: Reading the wrong scale on the protractor.

3.4 Symmetry

A line of symmetry divides a shape into two mirror halves. A rectangle has two, a square has four and a circle has infinitely many.

Watch out for: Drawing the diagonals of a rectangle as lines of symmetry.

3.5 Transformations: rotation, translation, reflection, tessellations, enlargements and reductions

Translation slides a shape, reflection flips it over a line, and rotation turns it around a point. Enlargement and reduction change its size but keep its shape. Tessellations cover a surface with no gaps.

Watch out for: Changing the shape’s size during a translation or reflection.

3.6 3D objects: faces, edges, vertices and nets

3D objects have faces, edges and vertices: a cube has 6 faces, 12 edges and 8 vertices. A net is the flat pattern that folds into the object.

Watch out for: Counting the hidden edges twice, or not at all.

3.7 Viewing objects (bonus topic)

This older CAPS topic asks learners to draw objects as seen from the front, side and top. Our course includes it for completeness even though the current ATP leaves it out.

Watch out for: Drawing a 3D sketch when a flat view is asked for.

3.8 Perimeter

Perimeter is the distance around a shape. For a rectangle 14 cm long and 9 cm wide: 2 × (14 + 9) = 46 cm.

Watch out for: Adding only two sides.

3.9 Area

Area is the space inside a shape in square units. A rectangle of 14 cm by 9 cm has an area of 126 cm². Learners count squares and use length × breadth.

Watch out for: Writing cm instead of cm² for area.

3.10 Volume

Volume is the space a 3D object takes up, measured in cubic units. A box 5 cm × 4 cm × 3 cm has a volume of 60 cm³.

Watch out for: Adding the dimensions instead of multiplying them.

3.11 Temperature (bonus topic)

Temperature is measured in degrees Celsius with a thermometer. This older CAPS topic is included even though the current ATP does not list it.

Watch out for: Reading the thermometer scale in steps of 1 when each mark is 2 degrees.

Try at home in Term 3:

  • Measure a room with a tape measure and work out its perimeter and floor area.
  • Unfold a cereal box to see its net.

Back to the topic list · Back to main menu

Term 4: Measurement, time, data handling and probability

Term 4 covers mass, time and time zones, capacity, data handling with graphs, mode and median, position and movement, probability and a short history of measurement.

Term 4 topics:

  1. Mass: grams and kilograms
  2. Time: 12-hour and 24-hour time, calendars and time intervals
  3. Time zones
  4. Capacity and volume: ml, l and kl
  5. Data handling: collecting and organising data
  6. Data handling: graphs and reading data
  7. Data handling: mode and median
  8. Solving problems with all four operations (whole numbers and fractions)
  9. Position and movement: grids and directions
  10. Probability: coins, dice and spinners
  11. History of measurement
Read the Term 4 topic summaries (11 topics)

4.1 Mass: grams and kilograms

1 000 g = 1 kg. Learners read kitchen and bathroom scales and convert: 2.4 kg = 2 400 g.

Watch out for: Reading the scale without checking what each small mark stands for.

4.2 Time: 12-hour and 24-hour time, calendars and time intervals

12-hour time uses a.m. and p.m.; 24-hour time runs from 00:00 to 23:59. 7:40 p.m. is 19:40. Learners work out time intervals across the hour: 08:45 to 11:20 is 2 hours 35 minutes.

Watch out for: Subtracting times as if an hour had 100 minutes.

4.3 Time zones

The world is divided into time zones. Places east of us are ahead and places west are behind, so learners add or subtract hours.

Watch out for: Moving the clock in the wrong direction.

4.4 Capacity and volume: ml, l and kl

1 000 ml = 1 l and 1 000 l = 1 kl. Learners read measuring jugs and convert: 1.75 l = 1 750 ml.

Watch out for: Mixing up capacity (how much a container holds) with mass.

4.5 Data handling: collecting and organising data

Data can be collected with tally tables and questionnaires and organised in frequency tables.

Watch out for: Tallies grouped wrongly: the fifth stroke crosses the other four.

4.6 Data handling: graphs and reading data

Learners draw and read bar graphs and pictographs, and read pie charts, always checking the title, labels and scale.

Watch out for: Starting the bars at a value other than zero.

4.7 Data handling: mode and median

The mode is the value that appears most often; the median is the middle value when the data is in order. For 3, 7, 7, 9, 12, the mode is 7 and the median is 7.

Watch out for: Finding the median without ordering the data first.

4.8 Solving problems with all four operations (whole numbers and fractions)

Mixed problems use all four operations with whole numbers and fractions. Learners decide the steps, estimate and check.

Watch out for: Choosing an operation from a key word without reading the whole problem.

4.9 Position and movement: grids and directions

Positions on a grid are given with letters and numbers, and directions with compass points and steps.

Watch out for: Giving the row before the column when the map says otherwise.

4.10 Probability: coins, dice and spinners

Probability describes how likely something is. A coin has two equally likely outcomes; a dice has six. Learners record results of experiments and compare them with what they expect.

Watch out for: Thinking that after three heads, tails is “due”.

4.11 History of measurement

People once measured with body parts and objects, such as hand spans and paces, before standard units like the metre and kilogram made measurements fair everywhere.

Watch out for: Thinking non-standard units give the same result for everyone.

Try at home in Term 4:

  • Collect data on the colours of cars passing your house for ten minutes, then draw a bar graph.
  • Look at a world clock and work out what time it is in London when it is 15:00 in South Africa.

Back to the topic list · Back to main menu

Common mistakes in Grade 6 Mathematics (and how to fix them)

  • Calling 1 a prime number.
  • Working left to right regardless of the signs in mixed calculations.
  • Lining up decimals by the last digit instead of by the comma.
  • Mixing up perimeter, area and volume units (cm, cm², cm³).
  • Reading graph scales wrongly: check what each gridline is worth first.

Tips for parents

  • Little and often. Fifteen minutes on most school days works better than a long session once a week.
  • Print the term’s Learner Coursebook so working is done on paper, and keep the Memo.
  • Use shopping for percentages and decimals: specials, discounts and change.
  • Practise times tables to 12 × 12; they carry primes, factors, division and fractions.
  • Get ready for Grade 7 by making sure fractions and decimals are solid by Term 4.

Frequently asked questions

How much does the Grade 6 Mathematics course cost?

R100 per subject for the year. It is one course for the whole year, with Terms 1 to 4 inside it, so there is nothing extra to pay per term.

How does access work?

Tap Open course on this page or on the Grade 6 course card. It takes you to the course page on Coursebox, our learning platform, in a new tab, where you’ll see the price and how to join (R100 per subject per year, as listed on our site). A parent or guardian signs up there with their own name and email address, and the learner then signs in with that account. Please use a nickname for your child, not their full name or school.

Does it follow CAPS and what my child does at school?

Yes. The topics on this page follow the CAPS curriculum for Grade 6 Mathematics and the DBE’s Annual Teaching Plan order, so Term 1 topics are taught in Term 1, and so on. Schools can move a topic by a week or two, so check your child’s term plan.

Are the answers to the course quizzes on this page?

No. This page explains each topic in our own words so you can help at home. The worked answers to every course question are in the Parent Memo for each term, which comes with the course.

Why are some topics marked as bonus topics?

The 2023/24 Annual Teaching Plan leaves out a few topics from the 2011 CAPS, such as viewing objects and temperature. Our course still covers them briefly so your child is prepared if their school includes them.

Ready to start?

The whole year of Grade 6 Mathematics is in one course for R100, with printable coursebooks and memos for every term.

Open the Grade 6 Mathematics course
← Back to main menu

All Grade 6 guides · All course guides

Sources and review

This summary is based on our own Grade 6 Mathematics (CAPS) course and its four term Parent Memos, the DBE’s CAPS document for Mathematics Grades 4–6 (Intermediate Phase), and the DBE’s Annual Teaching Plan for Grade 6. Past national and provincial papers were used only to see which topics are tested and how. All explanations and examples on this page are our own. Last reviewed: 1 November 2026. AI Buddies is an independent project and is not endorsed by the Department of Basic Education.