Calculation
Order of Operations (BODMAS)
Year 3 · Year 4 · Year 5 · Year 6
- ✓Understand that mathematical operations must be performed in a specific order to ensure consistent results.
- ✓Recall and correctly apply the BODMAS acronym to solve calculations.
- ✓Accurately perform calculations involving brackets and a combination of addition, subtraction, multiplication, and division.
- ✓Solve multi-step problems by correctly identifying and executing operations in the proper sequence.
Key concepts
When you have a calculation with more than one operation (like addition, subtraction, multiplication, or division), it's important to do them in the correct order. If you don't, you might get a different answer! The 'Order of Operations' is a set of rules that tells us which part of a calculation to do first, second, and so on. This ensures everyone gets the same correct answer.
BODMAS is a helpful acronym (a word made from the first letters of other words) that tells us the order to perform operations in. Each letter stands for a different type of operation: * **B** - **Brackets**: Always do anything inside brackets first. * **O** - **Orders**: This stands for powers (like 2²) or roots (like √9). These are usually covered in Key Stage 3 and beyond, so you won't typically see them in Key Stage 2 problems. For your calculations, you will mostly focus on Brackets, Division, Multiplication, Addition, and Subtraction. * **D** - **Division** and **M** - **Multiplication**: These come next. If you have both division and multiplication in the same calculation, you work from left to right. * **A** - **Addition** and **S** - **Subtraction**: These come last. If you have both addition and subtraction in the same calculation, you work from left to right.
Key facts to remember
- 1BODMAS is an acronym that helps you remember the order of operations.
- 2Always perform operations inside **B**rackets first.
- 3For Key Stage 2, the 'O' for Orders (powers/roots) is usually not encountered.
- 4**D**ivision and **M**ultiplication have equal priority; work from left to right.
- 5**A**ddition and **S**ubtraction have equal priority; work from left to right.
- 6Each step of a calculation should be written out clearly.
- 7The order of operations ensures everyone gets the same answer to a calculation.
Worked examples
Example 1
Calculate: 3 + 4 × 2
Answer
11
Remember, without BODMAS, if you did 3 + 4 first, you would get 7 × 2 = 14, which is incorrect.
Example 2
Calculate: (10 - 4) + 3 × 2
Answer
12
Example 3
Calculate: 12 ÷ (2 + 4) × 3 - 5
Answer
1
Always work through division and multiplication from left to right before moving to addition and subtraction.
Common mistakes
- ✗Not doing operations inside brackets first.
- ✗Performing addition or subtraction before multiplication or division.
- ✗Doing multiplication before division (or vice versa) when they appear together, without considering the left-to-right rule.
- ✗Doing subtraction before addition (or vice versa) when they appear together, without considering the left-to-right rule.
- ✗Trying to do too many steps at once, leading to errors.
Exam tips
- ★Write down 'BODMAS' at the top of your page to remind yourself of the order.
- ★Underline the part of the calculation you are going to do next in each step.
- ★Show all your working out, step-by-step. This helps you check your work and can earn you marks even if your final answer is wrong.
- ★Double-check your calculations, especially the basic arithmetic (addition, subtraction, multiplication, division) at each stage.
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