Properties of Number

August 23, 2016

Properties of numbers is a key topic for Foundation GCSE maths students as it lays the groundwork for fractions, standard form, ratios 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
Number: Interactive Lessons
Short Multiplication
4 Part Lesson
Short Multiplication
How to multiply integers and decimals by a single digit.
Number: Interactive Lessons
Short Division
4 Part Lesson
Short Division
How to use the box method to divide by a single-digit integer.
Number: Interactive Lessons
Prime Numbers
4 Part Lesson
Prime Numbers
How to work out which numbers are prime by their factors.
Number: Interactive Lessons
Place Value
4 Part Lesson
Place Value
How to recognise the value of a numerical digit using the place value table.
Number: Interactive Lessons
Multiples of a Number
4 Part Lesson
Multiples of a Number
How to work out the multiples of a number.
Number: Interactive Lessons
Factors of an Integer
4 Part Lesson
Factors of an Integer
How to work out the factor pairs of a number.
Number: Interactive Lessons
Order of Operations
4 Part Lesson
BODMAS and the Order of Operations
How to break down a calculation using the order of operations.
Number: Interactive Lessons
Addition and Subtraction with Integers
4 Part Lesson
Addition and Subtraction with Integers
How to add and subtract with integers using place value.
Number: Interactive Lessons
Using Calculator Efficiently
4 Part Lesson
Using Calculator Efficiently
How to apply the order of operations using a calculator.
Number: Interactive Lessons
Square and Cube Numbers
4 Part Lesson
Square and Cube Numbers
How to work out square and cube numbers using multiplication.
Number: Interactive Lessons
Multiplying and Dividing by Tens
4 Part Lesson
Multiplying and Dividing by Tens
How to use the place value to multiply and divide by 10, 100 and 1000.
Additional Resources
Number: Interactive Lessons
Multiplying and Dividing by 10, 100 and 1000
Extended Learning
Multiplying and Dividing by 10, 100 and 1000
Additional practice applying multiplying and dividing by 10, 100 and 1000.
Number: Interactive Lessons
Factors and Factor Pairs
Extended Learning
Factors and Factor Pairs
Additional practice working out factors and the highest common factor of two numbers.
Number: Interactive Lessons
Extended Learning - Primes
Extended Learning
Prime Numbers
Additional practice identifying and using prime numbers.
Number: Interactive Lessons
Extended Learning - Order of Operations
Extended Learning
Order of Operations
Additional practice using the order of operations to work out calculations.
Number: Interactive Lessons
Problem Solving - Place Value
Problem Solving
Place Value
Students are challenged to solve a range of problem solving questions involving place value.
Number: Interactive Lessons
Revising Multiples and Lowest Common Multiples
Revision
Multiples and Lowest Common Multiples
Revision lesson on multiples for exam students.
Number: Interactive Lessons
Revising Powers and Roots
Revision
Powers and Roots
Revision lesson on powers and roots for exam students.
Number: Interactive Lessons
Revising Highest Common Factors
Revision
Highest Common Factors
Revision lesson on the highest common factor for exam students.
Number: Interactive Lessons
Revising Written Methods for Real Life Problems
Revision
Written Methods for Real Life Problems
Revision lesson on using written to solve real life problems for exam students.
Number: Interactive Lessons
Revising Order of Operations
Revision
Order of Operations
Revision lesson on applying the order of operations for exam students.
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 than 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 a 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 the use of the place value table.

Mr Mathematics Blog

Complex Numbers

September 19, 2022

Scheme of Work for A-Level Further Mathematics: Year 1: Pure: Complex Numbers

Promoting your Maths Department on Open Evening

September 6, 2022

Five practical tips for promoting your mathematics department on open evening.

Problem Solving Maths Lessons

September 1, 2022

Four problem solving lessons to develop student’s mathematical reasoning and communication skills.