About this topic
Before you begin
Use prime factors, index laws, percentages and proportion to calculate accurately and interpret scales and rates in G2 Mathematics.
Learning goals
- Calculate with integers and rational numbers
- Compare and order numbers and representations
- Identify primes, factors and multiples
- Express a positive integer as a complete product of primes
- Find squares and cubes with linked source and result prime products
- Find exact positive square and cube roots with linked prime products
- Use prime factorisation to find HCF and LCM
- Round a signed decimal to a stated number of decimal places
- Round a nonzero number to a stated number of significant figures
- Estimate a four-operation calculation by rounding its inputs first
- Round, estimate and judge numerical accuracy
- Evaluate rational numerical expressions with nonnegative integer powers and signed bases
- Write a positive finite decimal in normalized standard form
- Evaluate a positive base to a negative or fractional power when the result is rational
- Use integer, zero, negative and fractional indices appropriately
- Express a ratio part as a fraction of the whole
- Share a quantity in a specified ratio
- Represent and simplify ratios of quantities
- Relate part-to-part ratios to part-to-whole fractions
- Simplify a two- or three-term ratio of rational quantities
- Interpret a percentage relative to its base
- Express one quantity as a percentage of another, including above 100%
- Find a quantity after a stated percentage increase or decrease
- Recover a quantity before a stated percentage increase or decrease
- Find an increase as a percentage of the original
- Find a decrease as a percentage of the original
- Recover a whole or original amount from a percentage part
- Calculate percentage changes and contextual amounts
- Construct a direct-proportion expression from positive paired data and predict a new value
- Construct an inverse-proportion expression from positive paired data and predict a new value
- Model and solve direct or inverse proportional relationships
- Calculate corresponding map and ground distances with compatible units
- Calculate corresponding map and ground areas using the squared length scale
- Determine a map's 1-to-n length scale from corresponding distances
- Calculate average speed from all distances and elapsed times of a multi-stage journey
- Convert speeds between kilometres per hour, metres per minute, metres per second and centimetres per second
- Calculate the average rate of a quantity over several stages, including pauses and stages given as rates
- 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 <, >, ⩽, ⩾
- 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
- Comparison between two or more quantities by ratio
- Relationship between ratio and fraction
- Dividing a quantity in a given ratio
- Ratios involving rational numbers
- 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
- 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
- Finding percentage increase/decrease
- Reverse percentages
- Relationships between distance, time and speed
- Writing speed in different units (e.g. km/h, m/min, m/s and cm/s)
- Calculation of speed, distance or time given the other two quantities
- 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)
- Comparison between two or more quantities by ratio
- Relationship between ratio and fraction
- Dividing a quantity in a given ratio
- Ratios involving rational numbers
- Equivalent ratios
- Writing a ratio in its simplest form
- Problems involving ratio
- Expressing percentage as a fraction or decimal
- 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)
- Finding percentage increase/decrease
- Reverse percentages
- Problems involving percentages
- Relationships between distance, time and speed
- Writing speed in different units (e.g. km/h, m/min, m/s and cm/s)
- Concepts of average rate, speed, constant speed and average speed
- Conversion of units (e.g. km/h to m/s)
- Calculation of speed, distance or time given the other two quantities
- 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
Choose a lesson
Work through them in order.
- Not startedSigned numbers and rational calculationNextUse a number line and inverse operations to calculate with negative integers, fractions and decimals.
- Not startedPrimes, squares, cubes and rootsNextRecognise primes and interpret calculator squares, cubes and roots before using the result.
- Not startedPrime factorisation, HCF and LCMNextExpress composites in prime factors to find common factors, common multiples and roots.
- Not startedRounding and estimationNextChoose decimal places or significant figures and use a separate estimate to check a calculation.
- Not startedInteger powers and standard formNextSeparate a repeated-factor exponent from a multiplier and express a number with a valid standard-form coefficient.
- Not startedIndex laws and rational powersNextJustify zero, negative and fractional exponents while retaining non-zero and real-domain conditions.
- Not startedRatios and equal sharesNextUse equal-sized ratio units to compare and share quantities with whole-number terms.
- Not startedFractional ratios and common unitsNextRename every ratio term by the same multiplier and convert unlike units before comparing.
- Not startedPercentages and parts of a wholeNextName the reference whole before converting or finding a percentage part.
- Not startedReverse percentages and percentage changeNextIdentify the original whole before finding it or measuring a change.
- Not startedPercentage points and relative changeNextDistinguish a difference between percentages from a percentage change relative to the original rate.
- Not startedDirect and inverse proportionNextIdentify a constant ratio or constant product and state the model assumptions.
- Not startedMap scales and area factorsNextConvert map lengths in common units and square a length factor for corresponding areas.
- Not startedSpeed and average ratesNextCalculate totals before averaging rates and convert both the distance and time units.
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