numberandalgebra core

📖 Prior Knowledge

ContentPrerequisite 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