Grade 7 Mathematics (CAPS): a term-by-term guide for parents and learners

Course guides › Grade 7 › Mathematics

Grade 7 is the first year of the Senior Phase, and Maths changes gear. Learners meet negative numbers (integers), exponents, formulae with letters, percentages, profit and loss, simple interest, angle facts, surface area and volume, and statistics such as the mean and median. These ideas lead straight into algebra in Grades 8 and 9.

This guide explains what our Grade 7 Mathematics (CAPS) course covers in each term, the key ideas with short worked examples, the mistakes that cost marks, and how parents can help. It follows the CAPS Mathematics curriculum for Grades 7–9 and the DBE’s 2023/24 Annual Teaching Plan order.

The course is taught by Zack, one of the two brothers behind AI Buddies. The tone suits Grade 7s, who see themselves as nearly grown up: clear, direct and practical, with real contexts like data bundles, taxi fares, sport statistics and small businesses.

The course at a glance

• One course for the whole year: 47 sub-chapters across Terms 1 to 4 (12, 10, 12 and 13), about 205 pages in total.
• Every sub-chapter has four pages: Learn with Zack, Worked examples (step by step), Test your understanding (15 questions) and Practise more (15 more at Core, Stretch and Exam level).
• About 1 400 quiz questions, each with a hint that works through the full answer and names the usual mistake. Quizzes can be retaken at any time.
• Printables for every term: a Learner Coursebook with every Test and Practise question and space for working, a Parent Memo with full working, and an exam-style practice test with its memo.
• Listen mode reads each page aloud; numbers, units and working are shown in the pictures.
• Price: R100 per subject for the year.

What’s covered, term by term

CAPS splits Senior Phase Maths into five content areas. For Grade 7 the weighting is Numbers, Operations and Relationships 30%, Patterns, Functions and Algebra 25%, Space and Shape 25%, Measurement 10% and Data Handling 10%. The course follows the ATP order below.

Term 1: Whole numbers, common fractions and decimal fractions

• Whole numbers: calculations and the order of operations; prime factors, LCM and HCF; ratio and rate; financial maths (profit, loss, discount, VAT, budgets, simple interest, hire purchase, exchange rates)
• Common fractions: simplifying, ordering and comparing; adding and subtracting; multiplying and fractions of amounts; percentages
• Decimal fractions: place value, ordering and rounding; adding and subtracting; multiplying and dividing; equivalent forms (fraction, decimal, percentage)
• Term 1 practice test with memo

Term 2: Exponents, integers, patterns and functions

• Exponents: squares and square roots; cubes and cube roots; exponential form and the order of operations
• Integers: counting, ordering and comparing; adding and subtracting; properties and problems in context (temperature, money, height)
• Numeric and geometric patterns: constant difference and ratio, and the rule linking each term to its position
• Functions and relationships: flow diagrams and tables; formulae and number sentences
• Term 2 practice test with memo, covering Terms 1 and 2

Term 3: Geometry

• Angles: measuring and classifying with a protractor; lines, rays and segments; parallel and perpendicular lines
• Constructions with ruler, compass and protractor; parts of a circle
• 2D shapes: triangles; quadrilaterals; similar and congruent figures; unknown sides and angles
• Transformations: translations, reflections and rotations; lines of symmetry; enlargements and reductions
• 3D objects: polyhedra, faces, edges, vertices and nets
• Term 3 practice test with memo

Term 4: Measurement, data handling and probability

• Perimeter of regular and irregular polygons; area of squares, rectangles and triangles; area units and problems
• Surface area and volume of cubes and rectangular prisms; capacity, units and problems
• Data handling: collecting data; organising it (tallies, frequency tables, stem-and-leaf); mean, median, mode and range; bar graphs and histograms; pie charts, interpreting and reporting
• Probability: outcomes, frequency and relative frequency
• Term 4 practice exam with memo, covering Terms 1 to 4

A note on algebra. CAPS 2011 and the 2015 national paper include simple algebraic expressions and equations in Grade 7, but the 2023/24 ATP doesn’t list them separately. The course covers formulae, substitution and solving number sentences by inspection in Term 2.

Key ideas, with worked examples

Order of operations

When a calculation mixes operations, everyone must get the same answer, so there is an agreed order: brackets, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Worked example. 20 − 3 × 4: first 3 × 4 = 12, then 20 − 12 = 8 (not 68). 3 + 2² × 5: 2² = 4, 4 × 5 = 20, 3 + 20 = 23. But (3 + 2)² = 5² = 25.

Prime factors, HCF and LCM

Write each number as a product of primes by dividing by the smallest prime that works. The HCF takes the primes the numbers share; the LCM takes every prime the most times it appears. HCF problems are about splitting into equal groups; LCM problems are about things happening again at the same time.

Worked example. 180 = 2 × 2 × 3 × 3 × 5 and 84 = 2 × 2 × 3 × 7. They share 2, 2 and 3, so the HCF is 12. For 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3, the LCM is 2 × 2 × 3 × 3 = 36.

Ratio, rate and sharing

A ratio compares quantities of the same kind, and the order matters. To share in a ratio, add the parts, find one part, then multiply. A rate compares different kinds of quantity; the unit rate (the amount for one) lets you compare deals.

Worked example. Share R600 in the ratio 2 : 3. 2 + 3 = 5 parts; 600 ÷ 5 = R120 per part; so R240 and R360. Check: 240 + 360 = 600. 3 kg of apples for R54 is 54 ÷ 3 = R18 per kg.

Financial maths

Profit is selling price minus cost price. A discount is taken off; VAT (15% in South Africa) is added on. Simple interest is charged on the original amount only: amount × rate × years.

Worked example. A 20% discount on R450 shoes: 450 ÷ 100 × 20 = R90 off, so you pay R360. Borrow R2 000 at 10% simple interest for 3 years: R200 a year × 3 = R600 interest, so you repay R2 600.

Fractions, decimals and percentages

Add or subtract fractions only when the denominators match (use the LCM). To multiply, multiply tops and bottoms. To find a percentage of an amount, divide by 100 and multiply. Percentage change is the change divided by the original amount. In South Africa decimals are written with a comma.

Worked example. 2⁄3 + 1⁄4 = 8⁄12 + 3⁄12 = 11⁄12. A R300 taxi fare rises by 12%: 12% of 300 = R36, new fare R336. A phone drops from R2 500 to R2 000: 500 ÷ 2 500 × 100 = 20% decrease. 0,375 = 37,5%.

Exponents and roots

7² means 7 × 7 = 49, and 4³ means 4 × 4 × 4 = 64. The square root and cube root undo squaring and cubing. Learn the squares to 12² and the cubes to 6³.

Worked example. A square has an area of 64 cm², so each side is √64 = 8 cm. A cube-shaped box holds 216 cm³, so each edge is ∛216 = 6 cm. Watch out: √(9 + 16) = √25 = 5, not 3 + 4 = 7.

Integers (negative numbers)

On a number line, numbers get bigger to the right, so −2 is bigger than −7. Adding a negative is the same as subtracting; subtracting a negative is the same as adding. A change is always new minus old.

Worked example. 3 + (−5) = 3 − 5 = −2. 2 − (−6) = 2 + 6 = 8. A diver at −18 m rises to −5 m: the change is −5 − (−18) = 13 m up. A balance of R150 after a R220 debit is −R70 (overdrawn).

Patterns, flow diagrams and formulae

Link each term to its position so you can find any term quickly. To find a rule from a table, see how much the output goes up when the input goes up by 1. In a formula, substitute the numbers for the letters and multiply before you add.

Worked example. 5, 8, 11, 14: the difference is 3, and each term is 3 × position + 2, so term 10 is 3 × 10 + 2 = 32. A taxi charges R15 plus R8 per km: a 6 km trip costs 6 × 8 + 15 = R63.

Angles and shapes

Angles on a straight line add up to 180°, angles around a point to 360°, and the angles of a triangle to 180°. In an isosceles triangle the base angles are equal. Every square is a rectangle, but not every rectangle is a square.

Worked example. One angle on a straight line is 65°, so the other is 180° − 65° = 115°. An isosceles triangle has a top angle of 40°: the base angles share 140°, so each is 70°.

Area, surface area and volume

Area of a rectangle = length × breadth; area of a triangle = ½ × base × perpendicular height. Surface area is the total area of all the faces (the net). Volume of a rectangular prism = length × breadth × height. 1 cm³ holds 1 mℓ, and 1 m³ holds 1 kℓ.

Worked example. A triangle with base 10 cm and height 6 cm has area ½ × 10 × 6 = 30 cm². A cube with 4 cm edges has surface area 6 × 4² = 96 cm² and volume 4³ = 64 cm³. 1 m² = 10 000 cm² (not 100).

Data handling and probability

The mean is the total divided by the number of values; the median is the middle value once the data is in order; the mode is the most common value; the range is the largest minus the smallest. Probability is the number of outcomes you want divided by the total number of equally likely outcomes.

Worked example. For 4, 7, 9 and 12 the mean is 32 ÷ 4 = 8. For 3, 5, 8 and 10 the median is (5 + 8) ÷ 2 = 6,5. The probability of rolling an even number on a die is 3⁄6 = ½; 22 heads in 50 tosses is a relative frequency of 0,44.

Common mistakes (and how to fix them)

• Working strictly left to right. 20 − 3 × 4 is 8, not 68. Brackets and exponents come first, then × and ÷, then + and −.
• Adding the denominators. ½ + ½ is 1, not 2⁄4. Make the denominators the same, add the numerators, keep the denominator.
• Thinking −7 is bigger than −2. Think of temperature: −2 °C is warmer than −7 °C.
• Squaring by doubling. 5² is 25, not 10, and √16 is 4, not 8. Don’t mix up squares and cubes either: 3² = 9 but 3³ = 27.
• Percentage change from the wrong amount. Always divide the change by the original amount, not the new one. And 8% = 0,08, not 0,8.
• Decimal places when multiplying. 0,6 × 0,4 = 0,24 (two decimal places), and multiplying by a number less than 1 makes the answer smaller.
• Forgetting the half in a triangle’s area, or using the sloping side as the height. Look for the right-angle mark.
• Wrong area and volume conversions. 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³. The length factor is squared for area and cubed for volume.

Tips for parents

• Insist on written working. The Learner Coursebook has every Test and Practise question with space for working, and the question numbers match the course. Tests in Grade 7 give marks for method, not just answers.
• Use the Parent Memo as a coach’s sheet. It has full working and the explanation for each answer, so you can check work without having to re-learn the maths.
• Talk money. Discounts on specials, VAT on a till slip, interest on a store card, data bundle prices per GB: Grade 7 financial maths is everyday life.
• Keep a times-table and squares list visible until squares to 12² and cubes to 6³ are automatic; they speed up exponents, area and volume.
• Geometry needs tools. A protractor, compass and ruler cost little and make Term 3 much easier.
• Respect independence. Grade 7s like to work alone. Agree on a routine (for example, one sub-chapter every school day) and check the quiz score and coursebook at the end of the week.

Frequently asked questions

How much does the Grade 7 Mathematics course cost?

R100 per subject for the year. It is one course with Terms 1 to 4 inside it.

How does access work?

Tap Open course on this page or on the Grade 7 course card. It takes you to the course page on Coursebox, our learning platform, in a new tab. Enrolment is through Coursebox: a parent or guardian signs up there with their own name and email address, and the learner then signs in with that account. The price is R100 per subject per year. Please use a nickname for your child, not their full name or school.

Does it follow CAPS and the school’s term plan?

Yes. It follows the CAPS Mathematics Grades 7–9 curriculum for Grade 7 and the DBE’s 2023/24 Annual Teaching Plan order. Exam-style questions were modelled on the 2015 national Grade 7 Mathematics paper and adapted, not copied.

Can my child use it on a phone?

Yes. It works in a phone’s web browser, and Coursebox has a free Android and iPhone app where learners sign in with the same email and password.

Does it use a lot of data?

Lessons are pictures and short text with quizzes, and there are no videos, so data use is low. The printable coursebooks, memos and practice tests are PDF downloads.

Is there an Afrikaans version?

The Grade 7 Mathematics course is in English, with Listen mode reading each page aloud.

My child struggles with negative numbers. Where should they start?

Start with Term 2, Integers: counting, ordering and comparing. It uses a number line and real contexts like temperature and bank balances before moving on to adding and subtracting.

Is there exam preparation?

Yes. Every term ends with a printable practice test and memo, and the Term 4 practice exam covers Terms 1 to 4. Practise more pages include Exam-level questions.

Start Grade 7 Maths with Zack

Open the course, pick a term, and start with any sub-chapter’s Learn page. The whole year is one course for R100, with printables and a practice test every term.

Sources and review

This guide is based on our Grade 7 Mathematics (CAPS) course content, the DBE’s CAPS Mathematics Grades 7–9 document (2011), the 2023/24 Grade 7 Mathematics Annual Teaching Plan, and the 2015 Annual National Assessment for Grade 7 Mathematics. Last reviewed: 31 October 2026. AI Buddies is an independent project and is not endorsed by the Department of Basic Education.