Number & Algebra
Integers and Order of Operations
Year 5 · Year 6
- ✓Understand and identify negative numbers (integers) in real-world contexts.
- ✓Locate and represent integers on a number line.
- ✓Apply the order of operations (BODMAS) to solve numerical expressions involving whole numbers.
- ✓Perform calculations involving addition, subtraction, multiplication, and division in the correct order.
Key concepts
Integers are whole numbers, including positive numbers, negative numbers, and zero. Negative numbers are numbers less than zero. They are used to represent quantities that are 'below zero' or 'in the opposite direction' from positive numbers. Examples include temperatures below freezing, debt, or depths below sea level.
A number line is a visual tool used to represent numbers. Zero is usually in the middle. Positive numbers are to the right of zero, and negative numbers are to the left of zero. The further a number is to the right, the greater its value. The further a number is to the left, the smaller its value.
When a calculation involves more than one operation (like addition, subtraction, multiplication, or division), we need a specific order to ensure everyone gets the same answer. This order is called the 'Order of Operations', often remembered by the acronym BODMAS:\n* Brackets: Do any calculations inside brackets first.\n* Orders: (Powers or indices – not typically covered in detail for Years 5-6 in this context, so we will focus on the other operations).\n* Division and Multiplication: Work from left to right, doing any division or multiplication as you come to them.\n* Addition and Subtraction: Work from left to right, doing any addition or subtraction as you come to them.
Key facts to remember
- 1Integers include positive whole numbers, negative whole numbers, and zero.
- 2Negative numbers are less than zero and are found to the left of zero on a number line.
- 3The further left a number is on the number line, the smaller its value.
- 4BODMAS stands for Brackets, Orders (powers), Division/Multiplication, Addition/Subtraction.
- 5Division and Multiplication have equal priority and are performed from left to right.
- 6Addition and Subtraction have equal priority and are performed from left to right.
- 7Calculations inside brackets must always be completed first.
Worked examples
Example 1
Represent the following numbers on a number line: -3, 0, 4, -1. Then order them from smallest to largest.
Answer
Smallest to largest: -3, -1, 0, 4.
Example 2
Calculate: 12 + 6 ÷ 3 - 2 × 4
Answer
6
Remember to do division and multiplication before addition and subtraction.
Example 3
Calculate: (15 - 7) × 3 + 20 ÷ 5
Answer
28
Brackets always take priority!
Common mistakes
- ✗Ignoring the order of operations and calculating from left to right without considering BODMAS.
- ✗Mixing up the order of division/multiplication or addition/subtraction (e.g., doing addition before subtraction when subtraction comes first from the left).
- ✗Incorrectly placing negative numbers on a number line (e.g., thinking -3 is greater than -1).
- ✗Forgetting to complete all operations inside brackets before moving on.
Exam tips
- ★Always write down the BODMAS acronym to help you remember the order.
- ★Underline or highlight the part of the calculation you are about to do in each step to keep track.
- ★Draw a number line if you are unsure about the order or position of negative numbers.
- ★Show all your working step-by-step, even for simple calculations, to avoid errors and allow for partial marks.
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