1. Number Systems and Factors
- Place value in large numbers and decimals
- Comparing, ordering, rounding, and estimating
- Whole numbers and decimal numbers
- Factors and multiples
- Prime and composite numbers
- Prime factorization at an introductory level
- Divisibility rules
- Greatest common divisor / highest common factor
- Least common multiple
- Integers in simple contexts such as temperature, elevation, and gains/losses
- Number lines and visual models

2. Operations with Whole Numbers and Decimals
- Addition, subtraction, multiplication, and division of whole numbers
- Decimal operations up to appropriate grade-level precision
- Efficient mental calculation strategies
- Standard written methods
- Order of operations
- Estimation and reasonableness checks
- Money, measurement, and time calculations
- Multi-step operation problems
- Error identification in calculations

3. Fractions, Percentages, and Ratio
- Fraction concepts and equivalence
- Comparing and ordering fractions
- Fraction operations: addition, subtraction, multiplication, and simple division cases
- Decimals and fraction-decimal conversion
- Percent as “per hundred”
- Percent of a quantity
- Simple percent increase and decrease
- Ratios: part-part and part-whole relationships
- Equivalent ratios
- Unit rate and introductory proportional reasoning
- Real-life contexts such as discounts, recipes, maps, and comparisons

4. Patterns, Algebra, and Early Equations
- Numeric and visual patterns
- Growing and shrinking sequences
- Input-output tables and function rules
- Expressing rules in words and symbols
- Variables and simple algebraic notation
- Writing expressions from words or contexts
- Evaluating expressions by substitution
- Operation properties in algebraic form
- Simplifying expressions at an introductory level
- One-step and two-step equations
- Balance models and equality reasoning

5. Measurement and Geometry
- Metric measurement: length, mass, capacity, time, and temperature
- Unit conversions within the metric system
- Perimeter and area of rectangles, triangles, parallelograms, and composite figures
- Volume of cubes and rectangular prisms
- Surface area using nets at an introductory level
- Circumference and circle measures at an introductory level
- Angle types and angle measurement
- Use of protractors in simple contexts
- Time, timetables, and elapsed time
- Measurement in practical contexts

6. 2D and 3D Geometry, Symmetry, and Transformations
- Properties of polygons and quadrilaterals
- Classification of 2D shapes by sides, angles, and symmetry
- Triangles and angle relationships
- Parallel and perpendicular lines
- Line symmetry and rotational symmetry
- Transformations: translation, reflection, rotation, and enlargement at an introductory level
- Tessellations and geometric patterns
- 3D solids and their properties
- Nets of 3D shapes
- Scale drawings and similarity at an introductory level
- Coordinate plotting in the first quadrant and, where appropriate, all four quadrants

7. Data Interpretation and Statistics
- Data collection and organization
- Tables, bar graphs, line graphs, pictographs, and line plots
- Pie charts where appropriate
- Introductory histograms or box plots where appropriate
- Mean, median, mode, and range
- Comparing simple data sets
- Variability and spread at an introductory level
- Designing and critiquing data displays
- Misleading graphs and incomplete information
- Drawing conclusions from data

8. Probability and Strategic Reasoning
- Probability language: certain, likely, unlikely, impossible
- Simple probability calculations
- Equally likely outcomes
- Experimental and theoretical probability
- Simple events and compound outcomes
- Tree diagrams and outcome tables at an introductory level
- Probability in games, spinners, dice, and real-life scenarios
- Fair and unfair games
- Strategy-based probability reasoning

9. Quantitative, Logical, and Visual-Spatial Reasoning
- Number puzzles and reasoning from clues
- Logic grids and matching problems
- Balance-scale and weighing puzzles
- Classification and odd-one-out problems
- Always/sometimes/never reasoning
- Error analysis and correcting flawed reasoning
- Shape analogies and visual classification
- Pattern grids and matrix puzzles
- Rotation, reflection, folding, and orientation puzzles
- Combining and decomposing shapes
- Non-verbal reasoning tasks

10. Mathematical Modelling and Real-World Mathematics
- Multi-step problem solving in real contexts
- Budgeting, money, change, and cost comparison
- Unit price and best-buy decisions
- Discounts, markups, and simple tax contexts
- Maps, recipes, timetables, and schedules
- Measurement-based real-life problems
- Tables, diagrams, and simple equations as models
- Working backwards and estimation strategies
- Designing or analyzing simple fair games or plans
- Open-ended “What if...?” style reasoning in age-appropriate contexts