Number and proportion
Build and connect the representations and methods in number and proportion.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
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
- Round, estimate and judge numerical accuracy
- Interpret integer power notation
- 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
- negative numbers and primes (exclude prime factorisation) • integers and their four operations • four operations on fractions and decimals (including negative fractions and decimals) • calculations with calculator, including squares, cubes, square roots and cube roots • 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) • use of index notation for integer powers • use of standard form A × 10^n, where n is an integer, and 1 ⩽ A < 10
- comparison between two or more quantities by ratio • dividing a quantity in a given ratio • ratios involving fractions and decimals • equivalent ratios • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion
- expressing percentage as a fraction or decimal • finding the whole given a percentage part • expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • finding one quantity given the percentage and the other quantity • increasing/decreasing a quantity by a given percentage • finding percentage increase/decrease
- rates and average rates (including the concepts of speed and average speed) • conversion of units (e.g. km/h to m/s)
- negative numbers and primes (exclude prime factorisation)
- integers and their four operations
- four operations on fractions and decimals (including negative fractions and decimals)
- calculations with calculator, including squares, cubes, square roots and cube roots
- 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)
- comparison between two or more quantities by ratio
- dividing a quantity in a given ratio
- ratios involving fractions and decimals
- equivalent ratios
- writing a ratio in its simplest form
- expressing percentage as a fraction or decimal
- finding the whole given a percentage part
- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- finding one quantity given the percentage and the other quantity
- increasing/decreasing a quantity by a given percentage
- finding percentage increase/decrease
- direct and inverse proportion
- rates and average rates (including the concepts of speed and average speed)
- conversion of units (e.g. km/h to m/s)
- use of index notation for integer powers
- use of standard form A × 10^n , where n is an integer, and 1 ≤ A < 10
- map scales (distance and area)
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 calculationG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Use a number line and inverse operations to calculate with negative integers, fractions and decimals.
- Primes, squares, cubes and rootsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Recognise primes and interpret calculator squares, cubes and roots before using the result.
- Rounding and estimationG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Choose decimal places or significant figures and use a separate estimate to check a calculation.
- Integer powers and standard formG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Separate a repeated-factor exponent from a multiplier and express a number with a valid standard-form coefficient.
- Ratios and equal sharesG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Use equal-sized ratio units to compare and share quantities with whole-number terms.
- Fractional ratios and common unitsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Rename every ratio term by the same multiplier and convert unlike units before comparing.
- Percentages and parts of a wholeG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Name the reference whole before converting or finding a percentage part.
- Reverse percentages and percentage changeG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Identify the original whole before finding it or measuring a change.
- Direct and inverse proportionG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Identify a constant ratio or constant product and state the model assumptions.
- Map scales and area factorsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Convert map lengths in common units and square a length factor for corresponding areas.
- Speed and average ratesG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Calculate totals before averaging rates and convert both the distance and time units.
No lessons match your search. Try a shorter phrase, or show all lessons.