All 10 chapters — Patterns, Lines & Angles, Number Play, Data Handling, Primes, Perimeter & Area, Fractions, Constructions, Symmetry and Integers.
| Sequence | An ordered list of numbers following a rule |
| Pattern | A repeated or predictable arrangement |
| Triangular number | Sum of first n counting numbers: 1+2+3+...+n |
| Square number | A number that equals n × n for some counting number n |
| Cube number | A number that equals n × n × n |
| Complete graph | A figure where every point is connected to every other point |
| Koch Snowflake | A fractal shape made by repeatedly adding triangles to sides |
Triangular number dots: Row 1 has 1 dot, row 2 has 2 dots, row 3 has 3 dots, etc. Each triangular number is the total dots in the triangle. — T(1)=1, T(2)=3, T(3)=6, T(4)=10
Square number dots: Dots arranged in a square grid. 1×1=1, 2×2=4, 3×3=9, 4×4=16. Notice each square is formed by adding the next odd number as an L-shaped border.
Complete graph K(n): K(2)=1 line, K(3)=triangle (3 lines), K(4)=complete quadrilateral (6 lines), K(5)=pentagram+pentagon (10 lines).
Koch Snowflake: Start with equilateral triangle. On each side, add a smaller equilateral triangle at the middle third. Repeat infinitely for a fractal.
Everyday examples of mathematics — temples, structures, daily life applications.
Recognising and extending number sequences, completing pattern tables.
Shape sequences — drawing the next shape and describing the formation rule.
Regular polygons, complete graphs — connecting shapes to number sequences.
Stacked squares, stacked triangles, Koch Snowflake — advanced pattern exploration.
| Point | A location in space, represented by a dot |
| Line segment | Part of a line with two fixed endpoints |
| Ray | Part of a line with one endpoint, extending infinitely |
| Vertex | The common point where two rays meet to form an angle |
| Acute angle | An angle less than 90° |
| Right angle | An angle exactly equal to 90° |
| Obtuse angle | An angle between 90° and 180° |
| Straight angle | An angle exactly equal to 180° |
| Reflex angle | An angle between 180° and 360° |
| Protractor | A tool used to measure and draw angles |
Angle types visual: Acute angle — arms close together (like a narrow V). Right angle — arms form an L with a small square at vertex. Obtuse angle — arms spread wider than L. Straight angle — arms form a flat line.
Protractor placement: Centre point on vertex, baseline aligned with one ray. Read the scale where the other ray crosses — use the inner or outer scale depending on which starts at 0°.
Clock angles: 12 o'clock = 0°, 3 o'clock = 90°, 6 o'clock = 180°, 9 o'clock = 270°.
Identifying and drawing basic geometric elements.
Understanding what angles are and how they are formed.
Using superimposition and other methods to compare angles.
Identifying right angles in the environment and shapes.
Acute, obtuse, right, straight and reflex angles.
Estimating angles without marked scales.
Using a protractor to measure angles accurately.
Practice measuring various angles and finding unknown angles.
Common mistakes when using a protractor and how to avoid them.
Real-world angle applications — clocks, doors, slopes.
Constructing angles of given measures using a protractor.
| Supercell | A cell whose value exceeds all its adjacent cells in a grid |
| Digit sum | Sum of all digits of a number, repeated until single digit |
| Palindrome | A number (or word) that reads the same in both directions |
| Kaprekar constant | 6174 — the fixed point of the Kaprekar routine for 4-digit numbers |
| Estimation | Finding an approximate value by rounding |
| Rounding | Replacing a number with the nearest ten, hundred, etc. |
Supercell grid: A rectangular grid of numbers where you circle cells that are larger than all their neighbours. Corner cells have 2 neighbours, edge cells have 3, interior cells have 4.
Number line jumps: Showing skip counting (by 2s, 3s, 5s) as arcs on a number line — landing spots reveal multiples and patterns.
What are supercells and how to identify them in number grids.
More practice with supercells — finding largest neighbours.
Patterns on number lines, jumps and skip counting.
Finding digit sums and exploring their properties.
Number play with clock arithmetic, calendar patterns and Kaprekar’s routine.
Quick mental calculation strategies.
Rounding, estimating sums, differences and products.
Number games — winning strategies and logical reasoning.
| Data | Raw facts and figures collected for analysis |
| Tally marks | Lines used for counting, grouped in fives: ∣∣∣∣ crossed = 5 |
| Frequency | How many times a value occurs in data |
| Pictograph | A graph using pictures/symbols to show data |
| Key / Scale | Tells what each symbol represents in a pictograph |
| Bar graph | A graph using rectangular bars to compare quantities |
| Title | The heading that describes what the graph shows |
Tally marks example: Counting favourite fruits — Apple: ∣∣∣∣ ∣∣ (7), Banana: ∣∣∣∣ (5), Mango: ∣∣∣ (3). Transfer to a frequency table.
Bar graph structure: X-axis shows categories (horizontal), Y-axis shows frequency with a uniform scale. Each bar is the same width. Title on top. Scale marked at equal intervals.
Methods of data collection — surveys, observations.
Recording data using tally marks and frequency tables.
Understanding and computing frequency from raw data.
Extended data collection exercises and organisation.
Reading and drawing pictographs to represent data.
Interpreting bar graphs — extracting and comparing data.
Constructing bar graphs from given data sets.
| Factor | A number that divides another number exactly |
| Multiple | The product of a number with any counting number |
| Prime number | A number with exactly two factors (1 and itself) |
| Composite number | A number with more than two factors |
| HCF | Highest Common Factor — the largest factor shared by two numbers |
| LCM | Lowest Common Multiple — the smallest multiple shared by two numbers |
| Co-prime | Two numbers with HCF = 1 |
| Perfect number | A number equal to the sum of its factors (excluding itself). E.g., 6 = 1+2+3 |
| Twin primes | A pair of primes differing by 2 |
Sieve of Eratosthenes: Write numbers 1 to 100 in a grid. Cross out 1. Circle 2 and cross out all its multiples. Circle 3 and cross out all its multiples. Continue with 5, 7. All remaining uncrossed numbers are prime.
Factor tree: Break a number into two factors, then keep breaking until all leaves are prime. E.g., 60 → 6 × 10 → (2×3) × (2×5) → 60 = 2² × 3 × 5.
Finding common multiples through a fun game context.
Understanding factors using number-line jumps.
Identifying primes, Sieve of Eratosthenes, properties of primes.
Breaking numbers into prime factors using factor trees.
Pairs of numbers with no common factor other than 1.
Rules for divisibility by 2, 3, 4, 5, 6, 9, 10.
| Perimeter | Total distance around a closed shape |
| Area | Amount of surface a shape covers, in square units |
| Unit square | A square with side 1 unit — used to measure area |
| Tangram | A Chinese puzzle of 7 pieces that form a square |
| Grid paper | Paper with squares used for measuring area |
Rectangle with labels: Length (l) on the longer side, breadth (b) on the shorter side. Perimeter goes all around: l + b + l + b = 2(l+b). Area fills the inside: l × b square units.
Grid paper area counting: An irregular shape on squared paper. Count full squares inside, estimate partial squares using the half rule. Add up for total area.
Same area, different perimeter: A 1×12 rectangle and a 3×4 rectangle both have area 12 sq units, but perimeters are 26 and 14 units respectively.
Understanding perimeter as the total boundary length.
Perimeter problems using a running track context.
Finding perimeter of shapes drawn on dot grids.
How splitting and rejoining shapes changes perimeter.
Introduction to area as the surface covered by a shape.
Exploring area relationships using tangram pieces.
Counting squares to find area of irregular shapes.
Finding all rectangles with a given area.
Relating triangle area to rectangle area.
Arranging unit squares to form different shapes and areas.
Calculating perimeter and area from a house floor plan.
| Numerator | Top number — how many parts are taken |
| Denominator | Bottom number — how many equal parts the whole is divided into |
| Unit fraction | A fraction with 1 as the numerator |
| Equivalent fractions | Different fractions representing the same value |
| Simplest form | Fraction reduced so HCF of numerator and denominator is 1 |
| Like fractions | Fractions with the same denominator |
| Unlike fractions | Fractions with different denominators |
Fraction of a shape: A circle divided into 4 equal parts. Shading 3 parts shows ¾. The denominator (4) is total parts; numerator (3) is shaded parts.
Fraction wall: Rows of equal-length bars divided into 1, 2, 3, 4, 5, ... equal parts. Shows equivalent fractions visually: ½ aligns with 2/4, 3/6, etc.
Number line: Mark 0 and 1, divide into equal segments. For fifths: 0, 1/5, 2/5, 3/5, 4/5, 1. Helps compare and order fractions.
Understanding and generating equivalent fractions.
Expressing fractions with a common denominator.
Reducing fractions to their simplest form.
Ordering and comparing fractions using different methods.
Adding like and unlike fractions.
Subtracting fractions with same and different denominators.
| Compass | A tool with two arms for drawing circles and arcs |
| Arc | A part (curve) of a circle |
| Radius | Distance from centre to any point on a circle |
| Diameter | A line segment through the centre connecting two points on a circle; = 2 × radius |
| Diagonal | A line segment connecting two non-adjacent corners of a polygon |
| Bisect | To divide into two equal parts |
| Dot paper | Paper with evenly spaced dots for drawing shapes accurately |
Rectangle with diagonals: Draw rectangle ABCD. Diagonals AC and BD cross at point O. AO = OC and BO = OD (bisection). AC = BD (equal diagonals).
Square on dot paper: Connect 4 dots forming a square. All sides span the same number of dots. Tilt the square 45° for a tilted square whose side length involves the Pythagorean theorem.
Circle with compass: Fix one arm at the centre, rotate the pencil arm 360°. All points on the curve are exactly one radius away from the centre.
Creating geometric artwork using constructions.
Analysing and replicating wave patterns.
Constructing squares of different sizes on dot paper.
Drawing rectangles with given dimensions on dot paper.
Open-ended geometric exploration activities.
Decomposing rectangles into smaller shapes.
Multi-step constructions combining various techniques.
Properties and constructions involving diagonals of polygons.
Advanced constructions using diagonals.
| Line of symmetry | A line that divides a shape into two identical mirror halves |
| Mirror line | Another name for line of symmetry |
| Rotational symmetry | A shape maps onto itself when rotated by less than 360° |
| Order of rotation | Number of times a shape maps onto itself in one full turn |
| Angle of rotation | The smallest angle for the shape to look the same: 360°/n |
| Shape | Lines of Symmetry | Rotational Order | Angle |
|---|---|---|---|
| Equilateral triangle | 3 | 3 | 120° |
| Square | 4 | 4 | 90° |
| Rectangle | 2 | 2 | 180° |
| Regular pentagon | 5 | 5 | 72° |
| Regular hexagon | 6 | 6 | 60° |
| Circle | ∞ | ∞ | any angle |
| Parallelogram (non-rect.) | 0 | 2 | 180° |
Lines of symmetry of a square: Draw a square. It has 4 lines: one horizontal (through midpoints of top and bottom), one vertical (through midpoints of left and right), and two diagonals.
Paper cutting symmetry: Fold paper along the line of symmetry, cut a shape, unfold. The result is symmetric about the fold line. Predicting the unfolded shape is a key skill.
Rotational symmetry of a windmill: A 4-bladed windmill looks the same every 90° turn. Order = 4, angle = 90°.
Identifying lines of symmetry in shapes and figures.
Predicting outcomes of punching holes and cutting folded paper.
Understanding rotation and order of rotational symmetry.
Combining line and rotational symmetry concepts.
| Integer | Any positive whole number, negative whole number, or zero |
| Positive integer | Numbers greater than zero: +1, +2, +3, ... |
| Negative integer | Numbers less than zero: −1, −2, −3, ... |
| Additive inverse | The number that, when added to a given number, gives 0 |
| Zero pair | A pair of +1 and −1 tokens that cancel each other |
| Magnitude | The size of a number regardless of sign (absolute value) |
Number line with integers: A horizontal line with 0 at centre, positive integers marked at equal intervals to the right (+1, +2, +3, ...) and negative integers to the left (−1, −2, −3, ...). Arrows show the line extends infinitely both ways.
Building/lift model: Ground floor = 0, floors above = positive (+1, +2, +3), basement levels = negative (−1, −2, −3). Going up = adding positive, going down = adding negative.
Token model: Green circles represent +1, red circles represent −1. To show +3, use 3 green tokens. To show −2, use 2 red tokens. To add (+3)+(−2): place all tokens, cancel 2 zero pairs, 1 green remains = +1.
Temperature/altitude diagram: A vertical number line with sea level (or 0°C) in the middle. Positive values above, negative values below. Shows real-world meaning of integers.
Adding positive integers using a lift/elevator model.
Adding negative integers — going below ground floor.
Ordering integers on a number line, greater than and less than.
Subtracting integers using the building floors model.
Representing and operating with integers on a number line.
Adding and subtracting larger integers.
Using positive and negative tokens to model addition.
Subtracting integers using the token model.
Advanced token model subtraction with cancellation.
Credits, debits and account balances using integers.
Altitude and depth — above and below sea level.
Positive and negative temperatures, rises and falls.
Filling grids and magic squares with integers.
Exploring patterns in an extended number grid with negatives.