- MA4-FRC-C-01 represents and operates with fractions, decimals and percentages to solve problems
📖 Prior Knowledge
| Content | Prerequisite relationships |
|---|---|
| Represents Numbers A | - Compare and order decimals up to 3 decimal places → Approximate decimals to a given number of places - Approximate decimals to a given number of places (revisited content) |
| Represents Numbers B | - Recall equivalent percentages, decimals and fractions → Convert between fractions, decimals and percentages - Find 10%, 25% and 50% of a quantity → Find a percentage of a quantity |
| Additive Relations B | - Add and subtract decimals → Multiply and divide decimals |
| Multiplicative Relations A | - Determine the factors of a whole number → Find the highest common factor (HCF) |
| Multiplicative Relations B | - Multiply and divide decimals by powers of 10 → Convert a decimal divisor to a whole number |
| Representing Quantity Fractions B | - Order fractions with related denominators → Create and record equivalent fractions - Create and record equivalent fractions (revisited content) - Add and subtract fractions with related denominators → Add and subtract fractions and mixed numbers - Find a non-unit fraction of a whole number → Solve problems with fractions and decimals of quantities |
Compare fractions using equivalence.pdf
- Determine the highest common factor (HCF) of 2 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.pdf
- Round decimals to a given number of decimal places
- Apply the notation ≈ as a symbol of numerical approximation
- Reason why an approximation may be more appropriate than an exact answer and vice versa
Identify terminating and recurring decimals.pdf
- Use either dot or vinculum notation for recurring (repeating) decimals
- Classify decimals as recurring or terminating
Identify and make use of the relationship between fractions, decimals and percentages to carry out simple conversions.pdf
- Define rational numbers as numbers that can be written in the form , where and are integers and
- 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.pdf
- Identify and define irrational numbers as numbers that cannot be written in the form , where and are integers and
- 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.pdf
- 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.pdf
- 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.pdf
- 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.pdf
- 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.pdf
- 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