Properties of Number

Place Value

Adding and Subtracting Integers

Multiplying Integers

Dividing with Integers

Multiplying and Dividing by a Power of Ten

Multiples of a Number

Factors of a Number

Prime Numbers

Square and Cube Numbers

Order of Operations

Use of a Calculator

Order of Operations

Written Methods for Real Life Problems

Multiples and Lowest Common Multiples

Highest Common Factors

Powers and Roots

Place Value

Prerequisite Knowledge

• read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
• represent and use number bonds and related subtraction facts within 20
• add and subtract one-digit and two-digit numbers to 20, including zero
• solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

Success Criteria

• Understand and use place value
• Order positive integers
• Apply the four operations, including formal written methods, to integers
• Recognise and use relationships between operations
• Use the concepts and vocabulary of prime numbers, factors (divisors) and multiples

Key Concepts

• Students need to be very secure in their knowledge of applying the place value table to identify the value of any digit.
• Understanding the additive and multiplicative number properties are vital building blocks for the remainder of this course. For example, 2 x 3 = 3 x 2 and 2 + 3 = 3 + 2.
• When calculating factors of integers it is beneficial to use factor pairs rather individual values.
• Use the place value table to demonstrate column addition and subtraction.

Common Misconceptions

• Students often define a prime number as ‘divides by 1 and itself’. This leads to the incorrect assumption of 1 to be prime number.
• When subtracting, students may find knowing when to ‘borrow’ confusing and instead incorrectly subtracting the smaller digit from the larger one. E.g., 43 – 25 = 22
• Aligning the correct value digits for column addition and subtraction can prove troublesome. Encourage use of the place value table.