Number and proportion
Build and connect the representations and methods in number and proportion.
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Before you begin
Build and connect the representations and methods in number and proportion.
Learning goals
- Calculate with integers and rational numbers
- Compare and order numbers and representations
- Identify primes, factors and multiples
- Use prime factorisation to find HCF and LCM
- Round, estimate and judge numerical accuracy
- Use integer, zero, negative and fractional indices appropriately
- Represent and simplify ratios of quantities
- Share a quantity in a specified ratio
- Relate part-to-part ratios to part-to-whole fractions
- Interpret a percentage relative to its base
- Recover a whole or original amount from a percentage part
- Calculate percentage changes and contextual amounts
- Model and solve direct or inverse proportional relationships
- Use rate, speed, distance and time relationships
- Convert compatible measurement units
Syllabus statements covered
- primes and prime factorisation • finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation • negative numbers, integers, rational numbers, real numbers, and their four operations • calculations with calculator • representation and ordering of numbers on the number line • use of the symbols <, >, ⩽, ⩾ • approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) • use of standard form A × 10^n, where n is an integer, and 1 ⩽ A < 10 • positive, negative, zero and fractional indices • laws of indices
- ratios involving rational numbers • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion
- expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • increasing/decreasing a quantity by a given percentage • reverse percentages
- average rate and average speed • conversion of units (e.g. km/h to m/s)
- primes and prime factorisation
- finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers and their four operations
- calculations with calculator
- representation and ordering of numbers on the number line
- use of <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)
- ratios involving rational numbers
- writing a ratio in its simplest form
- problems involving ratio
- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage (including concept of percentage point)
- reverse percentages
- problems involving percentages
- concepts of average rate, speed, constant speed and average speed
- conversion of units (e.g. km/h to m/s)
- problems involving rate and speed
- map scales (distance and area)
- direct and inverse proportion
- use of standard form A×10^n , where n is an integer, and 1 ≤ A < 10
- positive, negative, zero and fractional indices
- laws of indices
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Signed numbers and rational calculationG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use a number line and inverse operations to calculate with negative integers, fractions and decimals.
- Primes, squares, cubes and rootsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Recognise primes and interpret calculator squares, cubes and roots before using the result.
- Prime factorisation, HCF and LCMG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Express composites in prime factors to find common factors, common multiples and roots.
- Rounding and estimationG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Choose decimal places or significant figures and use a separate estimate to check a calculation.
- Integer powers and standard formG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Separate a repeated-factor exponent from a multiplier and express a number with a valid standard-form coefficient.
- Index laws and rational powersG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Justify zero, negative and fractional exponents while retaining non-zero and real-domain conditions.
- Ratios and equal sharesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use equal-sized ratio units to compare and share quantities with whole-number terms.
- Fractional ratios and common unitsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Rename every ratio term by the same multiplier and convert unlike units before comparing.
- Percentages and parts of a wholeG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Name the reference whole before converting or finding a percentage part.
- Reverse percentages and percentage changeG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Identify the original whole before finding it or measuring a change.
- Percentage points and relative changeG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Distinguish a difference between percentages from a percentage change relative to the original rate.
- Direct and inverse proportionG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Identify a constant ratio or constant product and state the model assumptions.
- Map scales and area factorsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Convert map lengths in common units and square a length factor for corresponding areas.
- Speed and average ratesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Calculate totals before averaging rates and convert both the distance and time units.
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