GCSE Statistics₈₃₈₂

Integers, fractions, decimals and percentages

• Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and $\frac{\mathsf{7}}{\mathsf{2}}$ or 0.375 and $\frac{\mathsf{3}}{\mathsf{8}}$ ). Recognise that some fractions can be written as recurring decimals.
• Identify and work with fractions in ratio problems.
• Interpret fractions and percentages as operators.

Structure and calculation

• Order positive integers, decimals and fractions.
• Understand and use the symbols =, ≠, <, >, ≤, ≥
• Apply the four operations to integers, decimals and simple fractions (proper and improper), and mixed numbers.
• Understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals).
• Understand and use standard form.
• Recognise and use relationships between operations, including inverse operations eg cancellation to simplify calculations and expressions; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals.
• Substitute numerical values into formulae and expressions, including scientific formulae.
• Understand and use standard mathematical formulae; rearrange formulae to change the subject.
• Work with coordinates on Cartesian grid.

Measures and accuracy

• Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate.
• Estimate answers; check calculations using approximation and estimation, including answers obtained using technology.
• Use compound units such as speed, rates of pay, unit pricing.
• Round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding.

Ratio, proportion and rates of change

• Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1.
• Use ratio notation, including reduction to simplest form.
• Divide a given quantity into two parts in a given part: part or part: whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving probability).
• Relate ratios to fractions and vice versa.
• Define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages.
• Understand and use the general equation of a straight line $\mathit{y}\mathsf{=}\mathit{m}\mathit{x}\mathsf{+}\mathit{c}\mathit{ }$ where $\mathit{c}$ is the intercept with the $\mathit{y}\mathsf{-}$ axis and $\mathit{m}\mathsf{=}\frac{\mathsf{(}{\mathit{y}}_{\mathsf{1}}\mathsf{-}{\mathit{y}}_{\mathsf{2}}\mathsf{)}}{\mathsf{(}{\mathit{x}}_{\mathsf{1}}\mathsf{-}{\mathit{x}}_{\mathsf{2}}\mathsf{)}}$