Mathematics / Year 7 / Number and Algebra / Number and place value

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)

Elaborations
  • defining and comparing prime and composite numbers and explaining the difference between them
  • applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation
General capabilities
  • Numeracy Numeracy
ScOT terms

Indices,  Prime numbers

Moving Image

What are factors?

What are factors? Watch as the jelly babies in this clip show you! What are the factors of 12? How many factors does the number 11 have? Try explaining to a friend what a prime number is.

Moving Image

Patterns, primes and Pascal's Triangle

Are you intrigued by patterns? Check out Vi Hart as she explains how to visualise patterns in prime numbers, using Ulam's Spiral. Watch as Vi creates patterns, using Pascal's Triangle to explore relationships in number. See what happens when she circles the odd numbers. What rule does she use to create the final pattern?

Teacher resource

Fascinating prime numbers

Use this teaching resource to investigate prime numbers with your students. Go back in time to the ancient Greeks (around 300 BC) to find out how Euclid demonstrated that there is an infinite number of primes. Investigate ways to identify prime numbers using algebra and square numbers and how to represent large primes using ...

Teacher resource

TIMES Module 19: Number and Algebra: multiples, factors and powers - teacher guide

This is a 33-page guide for teachers. It introduces the concepts of primes, composites, prime factorisation, factors, multiples, odd and even numbers, the least common multiple and the highest common factor.

Moving Image

Graham's number

If you were asked what the biggest number you can think of is, what would you say? Infinity? Well, what about the biggest finite number you can think of? Mathematician Ron Graham came across such a gigantic number in his research that, to capture its massive size, he and his colleagues needed to come up with new methods ...

Audio

The beauty of prime numbers

A prime number is a number that only has two factors: one and itself. Listen to Adam Spencer and Richard Glover discussing prime numbers. They cover how we define these numbers and how and why prime numbers are widely used in internet encryption.

Moving Image

Small scale measurements

What units of measurements do we use to describe incredibly small things like blood cells and atoms? Watch as you are taken on a journey to explain the different units of measurement that we use to describe the very small.

Moving Image

Zero the hero

What is the role of zero as a placeholder for large numbers such as 1 million, 1 billion and 1 trillion? Find out about the notion of place value and powers of ten through the act of bead counting.

Teacher resource

reSolve: Prime factorisation

This sequence of four lessons explores prime factorisation. Students solve a puzzle using factor strings, play a dice game to learn about prime numbers, develop a method for finding all of the factors of a number, and engage in an investigation of highest common factors and lowest common multiples of two numbers, and how ...

Moving Image

Prime numbers and unbreakable codes

Imagine if anyone was able to read all our secret, encrypted messages and information. Watch and find out how scientists at the Australian National University are developing a new encryption system using quantum physics and quantum computing.

Interactive resource

Exploring square roots

Build a square on a grid to cover a given number of units. Notice that each side of the square equals the square root of the area. Calculate the area of each square and work out the square root. For example, calculate the length of each side needed for a square to cover 81 units. Calculate the area of squares bordering ...

Interactive resource

Circus towers: square pyramids

Work out how many acrobats are needed to form pyramid-shaped human towers. Start by building a square pyramid with five acrobats: four acrobats in the base layer and one acrobat standing on their shoulders. Examine a table and graph of the total number of acrobats in the towers. Predict the number of acrobats needed to ...

Teacher resource

Square roots and square numbers

This is a website designed for both teachers and students that deals with square roots of square numbers from the Australian Curriculum for year 7 students. It contains material on products of squares and square roots, prime factorisation and square roots of non-perfect squares. There are pages for both teachers and students. ...

Teacher resource

The laws of arithmetic and their use in algebra

This is a website designed for both teachers and students that refers to algebraic notation, the laws of arithmetic and the use of these laws in algebra from the Australian Curriculum for year 7 students. It contains material on algebraic notation, the commutative and associative laws, the use of brackets and the orders ...

Moving Image

Understanding exponents: 2

This resource is a short video presentation, with audio commentary, in which the meaning of exponents or powers of a number is explained. In the numerical example used the presenter explains the difference between evaluating the power of a number and the product of two numbers.

Teacher resource

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use the three content strands ...

Teacher resource

reSolve: Real numbers - Sum of squares

This lesson explores Diophantus' hypothesis that all natural numbers can be expressed as the sum of no more than four square numbers. Students are invited to work in small groups to express natural numbers up to 120 as a sum of squares and share this on a whole-class grid. The resource develops students' fluency in identifying ...

Teacher resource

TIMES Module 24: Number and Algebra: negatives and the index laws in algebra - teacher guide

This is a 19-page guide for teachers. It extends the use of pronumerals to include negative numbers. Algebraic notation is discussed. It includes substitution, adding like terms, the use of brackets, multiplying terms and using algebra to describe number patterns.

Teacher resource

TIMES Module 19: Number and Algebra: whole number arithmetic - teacher guide

This is a 17-page guide for teachers, a module that introduces addition of whole numbers.

Interactive resource

Exploring order of operations

Work through mathematical operations in an algorithm. Perform calculations with integers where the order of operations is important. Start with two-step operations such as 6+10x2. Move on to numerical expressions involving several operations and notation such as parentheses and indices. Solve numerical expressions quickly ...