Unit 1: Prime Numbers and Factorisation

Unit 1: Prime numbers and factorisation

Planning guidance

Unit objectives

Within this unit, students will learn to:

· Find the factors and multiples of a number

· Find prime numbers

· Find the prime factors of a number

· Determine HCF and LCM by prime factorisation

· Find squares, square roots, cubes and cube roots using prime factorisation

· Use indices to record repeated multiplication

· Calculate with the use of a calculator

Tasks and questions in this unit focus predominantly on prime numbers and prime factorisation, given students' prior learning on factors and multiples. The use of a calculator is not built into the tasks. However, any additional lessons during this period and/or homework time should be used to enable students to familiarise themselves with the use of calculators.

This unit should take two weeks and there are two sections of work to cover: factors, multiples and primes and using prime factors.

Suggested Structure

The actual number of lessons spent on each section will depend on the individual class and the number of lessons available to teachers. We suggest the following based on a total of 6, 8 or 10 lessons over two weeks:

Section / 6 lessons / 8 lessons / 10 lessons
Factors, multiples and primes / 3 / 3-4 / 4-5
Using prime factors / 3 / 4-5 / 5-6

Factors, multiples and primes

Objectives

· Find factors and multiples of a number

· Understand the definition of a prime number

· Identify prime numbers

· Recognise square numbers

In this unit students work to develop their understanding of properties of number by exploring factors, multiples and primes. Often, simple concepts are hard to define and time should be spend ensuring students understand the meaning of these key words before moving on.

Once students are secure in finding factors and multiples they can explore prime numbers. There are lots of discussions to be had here, for example thinking about why 2 is the only even prime number and why 1 is not a prime number. Students should be encouraged to develop their reasoning skills by talking through these ideas with their peers.

For further guidance, including the Department Tasks for this section, click Factors, multiples and primes under the Planning resources on the main page for this unit.

Using prime factors

Objectives:

· Find the prime factors of a number using a factor tree or repeated division method

· Determine HCF of two (or more) numbers

· Determine LCM of two (or more) numbers

· Use index notation

· Find squares, square roots, cubes and cube roots using prime factorisation

· Use a calculator efficiently

We have not included instructional slides in this pack as we appreciate teachers will teach prime factorisation in a variety of different ways. Instead, here we include lots of problems that can be used to explore prime factorisation, such as the uniqueness of prime decomposition.

Factor trees are the most commonly used method to do this. Students should appreciate that regardless of how they decompose numbers at each stage, the final answer will be the same and the ‘Making 36’ slide can be used to support students understanding of this.

Venn diagrams are used extensively in this unit to support finding HCFs and LCMs. It’s important that students do develop an understanding of the number structure here and don’t rely on listing methods.

Students can explore the structure of square numbers, and how to square root very large number through prime factorisation.

For further guidance, including the Department Tasks for this section, click Using prime factors under Planning resources on the main page for this unit.