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Comparing measurements
Data & Statistics
Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers
Complementary events
Probability
Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))
Compound Units
Ratio & Proportion
Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
Coordinate Transformations
Geometry
Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
Coordinates (age 11+)
Algebra
Plot and read coordinates in all four quadrants of the Cartesian plane, using positive and negative x- and y-values to describe positions precisely
Decimal place value (age 11+)
Number Representation & Place Value
Round numbers and measures to an appropriate degree of accuracy including to a specified number of decimal places or significant figures
Decimals and fractions (age 11+)
Fractions
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
Dividing fractions
Fractions
Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions
Dividing Quantities by Ratio
Ratio & Proportion
Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole
Expanding Single Brackets
Algebra
Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers
Experimental probability
Probability
Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
Expressions & Equations Vocabulary
Algebra
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
Factors, multiples, and primes (age 11+)
Multiplication & Division
Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property
Fractions on a number line
Number Representation & Place Value
Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line
Fractions on a number line (age 11+)
Number Representation & Place Value
Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations
Generating Sequences
Algebra
Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither
Measuring angles (age 11+)
Geometry
Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements
Mixed & Improper Fractions
Fractions
Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
Multiplying fractions (age 11+)
Fractions
Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
Numbers on a number line
Number Representation & Place Value
Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements
Numbers on a number line
Algebra
Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
One Quantity as a Fraction
Ratio & Proportion
Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in context
Percentages as Fractions
Ratio & Proportion
Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
Pictograms and tally charts (age 11+)
Data & Statistics
Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type