Number

Topics

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Sample objectives

What this unit covers

• Structure and calculation: Order positive and negative integers, decimals and fractions, and use equality and inequality symbols correctly.
• Structure and calculation: Apply the four operations and place value to positive and negative integers, decimals, fractions and mixed numbers.
• Structure and calculation: Use inverse relationships, cancellation and the conventional priority of operations with brackets, powers, roots and reciprocals.
• Structure and calculation: Use primes, factors, multiples, HCF, LCM and prime factorisation, including product notation and uniqueness of factorisation.
• Structure and calculation: Use a systematic method to list all possibilities without omissions or repetitions.
• Structure and calculation: Use the product rule for counting to find the number of outcomes in successive choices.
• Structure and calculation: Use positive integer powers and corresponding square, cube and higher roots, and recognise common powers.
• Structure and calculation: Estimate powers and roots of any positive number using nearby known values.
• Structure and calculation: Calculate with roots and apply the laws of integer indices.
• Structure and calculation: Interpret and calculate with fractional indices, linking powers to roots.
• Structure and calculation: Calculate exact values involving fractions and multiples of pi.
• Structure and calculation: Simplify surd expressions and rationalise denominators while retaining exact values.
• Structure and calculation: Write, interpret and calculate with numbers in standard form using integer powers of ten.
• Fractions, decimals and percentages: Convert fluently between terminating decimals and their equivalent fractions.
• Fractions, decimals and percentages: Convert recurring decimals to fractions and convert suitable fractions to recurring decimals.
• Fractions, decimals and percentages: Identify and use fractions when solving ratio problems.
• Fractions, decimals and percentages: Apply fractions and percentages as operators on quantities.
• Measures and accuracy: Use standard units for mass, length, time, money and compound measures, including decimal quantities.
• Measures and accuracy: Estimate answers and use approximation to check calculations, including results obtained with technology.
• Measures and accuracy: Round numbers and measurements to a stated accuracy and express simple rounding or truncation error intervals with inequalities.
• Measures and accuracy: Apply and interpret limits of accuracy in measured or rounded values.
• Measures and accuracy: Find and use upper and lower bounds to calculate limits for combined quantities.