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Linear number sequences
Algebra
Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule
Long multiplication (age 10+)
Multiplication & Division
Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication
Measurement Conversions
Measurement
Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
Measuring length (age 10+)
Measurement
Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units
Measuring temperature
Number Representation & Place Value
Use negative numbers in context (temperature, finance, sea level); calculate intervals across zero
Miles & Kilometres
Measurement
Convert between miles and kilometres using the approximate relationship (5 miles ≈ 8 km)
Multi-step problems: choosing operations
Multiplication & Division
Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts
Multiplication as scaling
Fractions
Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1
Multiplying and dividing (age 10+)
Multiplication & Division
Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart
Multiplying fractions (age 10+)
Fractions
Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
Number Pattern Relationships
Algebra
Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
Numbers on a number line
Geometry
Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin
Numbers to Ten Million
Number Representation & Place Value
Solve number and practical problems involving reading, writing, ordering, comparing, rounding, and negative numbers up to 10,000,000
Order of operations
Multiplication & Division
Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
Order of operations (age 10+)
Mathematical Thinking
Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently
Parts of a circle
Geometry
Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius
Patterns with Powers of Ten
Number Representation & Place Value
Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)
Perimeter (age 10+)
Measurement
Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically
Place Value × 10 and ÷ 10
Number Representation & Place Value
Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left
Plotting points in the first quadrant
Geometry
Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context
Probabilities Sum to One
Probability
Understand that when all possible outcomes of a trial are listed, their probabilities must add up to 1; use this to find the probability of an event NOT happening: P(not A) = 1 − P(A); apply this shortcut to avoid counting all unfavourable outcomes directly
Ratio (age 10+)
Multiplication & Division
Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts
Ratio Problems
Ratio & Proportion
Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
Reading and writing numbers (age 10+)
Number Representation & Place Value
Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning