Properties of Number

August 23, 2016

Properties of number is a key topic for Foundation GCSE maths students as it lays the groundwork for fractions, standard form, ratio and percentages. Throughout this topic students learn the importance of place value and the order of operations.

Properties of number takes place in Term 1 of Year 9 and is followed by fractions and mixed numbers.

Properties of Number Lessons

Place Value

Adding and Subtracting Integers

Multiplying Integers

Dividing with Integers

Multiples of a Number

Factors of a Number

Prime Numbers

Square and Cube Numbers

Order of Operations

Use of a Calculator

Revision Lessons

Order of Operations

Written Methods for Real Life Problems

Multiples and Lowest Common Multiples

Highest Common Factors

Powers and Roots

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.

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