Content:
MA4-FRC-C-01
Compare fractions using equivalence
- Determine the highest common factor (HCF) of two whole numbers
- Examine methods of generating equivalent fractions
- Simplify fractions by using methods, including determining the HCF of the numerator and denominator or repeated simplification using common factors
- Create fractions with the same denominator to compare their sizes
- Compare and order fractions with different denominators
Round decimals to a specified degree of accuracy using approximations
- Round decimals to a given number of decimal places
- Apply the notation \( \approx \) as a symbol of numerical approximation
- Reason why an approximation may be more appropriate than an exact answer and vice versa
Identify and make use of the relationship between fractions, decimals and percentages to carry out simple conversions
- Define rational numbers as numbers that can be written in the form \( a \over b \), where \( a \) and \( b \) are integers and \( b \ne 0 \)
- Classify fractions and percentages as rational numbers
- Recognise and explain that numbers with terminating or recurring decimals are rational
- Represent fractions as decimals (terminating and recurring) and percentages
- Represent terminating decimals as fractions and percentages
- Represent improper fractions as mixed numbers and decimals, and vice versa
- Represent percentages as fractions and decimals
Examine the concept of irrational numbers
- Identify and define irrational numbers as numbers that cannot be written in the form \( a \over b \) where \( a \) and \( b \) are integers and \( b \ne 0 \)
- Find approximations of irrational numbers using digital tools
- Locate the approximate position of irrational numbers on a number line
Order and compare the value of fractions, decimals and percentages
- Locate positive and negative fractions, decimals and mixed numbers on a number line to compare their relative values
- Compare and order fractions, mixed numbers, decimals (terminating and recurring) and percentages
Solve problems that involve the addition and subtraction of fractions
- Represent addition and subtraction of fractions with the same or unrelated denominators
- Solve problems involving adding and subtracting fractions and mixed numbers, including finding a common denominator
- Solve problems that involve subtracting a fraction from a whole number, with and without the use of digital tools
Solve problems that involve the multiplication and division of fractions and decimals
- Compare and generalise the effect of multiplying or dividing by a number with magnitude between zero and one
- Represent multiplication and division of decimals
- Represent multiplication and division of fractions, including mixed numbers
- Multiply and divide decimals, using digital tools to solve problems
- Multiply and divide fractions and mixed numbers, with and without using digital tools to solve problems
- Compare initial estimates with the results of calculations
- Apply knowledge of fractions and decimals of quantities to solve problems
- Apply knowledge of multiplication and division of fractions and decimals to solve problems
Represent one quantity as a fraction, decimal or percentage of another, with and without the use of digital tools
- Represent one quantity as a fraction, decimal or percentage of another by considering appropriate units
- Calculate percentage increases and decreases in various contexts
- Examine the financial applications of percentage increase and decrease, including profit and/or loss as a percentage of cost price or selling price
Solve problems that involve the use of percentages
- Apply knowledge of percentages to calculate quantities in various contexts
- Apply knowledge of percentage increases and decreases to solve problems in various contexts
- Solve real-life problems involving percentages using the unitary method or other techniques
- Solve financial problems involving percentages, specifically considering GST, profit and loss