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Order of operations (BIDMAS)
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Foundational skills
Recall the BIDMAS hierarchy
\[ \text{Example: } \times \text{ vs } + \]
Which operation should be performed first?
Identify the first operation
\[ \text{Example: } 5 + 3 \times 2 \rightarrow \times \]
Identify which operation calculates first.
Evaluate add/subtract only
\[ 10 – 3 + 4 \]
Work left to right with + and -.
Evaluate mult/div only
\[ 12 \div 3 \times 2 \]
Work left to right with x and ÷.
Two operations
Multiplication with add/sub
\[ 3 + 4 \times 2 \]
Evaluate expression with x and +/-.
Division with add/sub
\[ 15 – 12 \div 3 \]
Evaluate expression with ÷ and +/-.
Three or more operations
Mixed priorities (3 ops)
\[ 3 + 4 \times 2 – 5 \]
Expressions like 3 + 4 x 2 – 5.
Four operations mixed
\[ 20 – 3 \times 4 + 8 \div 2 \]
Expressions with +, -, x, ÷.
Brackets basics
Brackets with add/sub
\[ (3 + 2) \times 4 \]
(3 + 2) x 4 type questions.
Op before brackets
\[ 5 \times (3 + 2) \]
5 x (3 + 2) type questions.
Brackets advanced
Two separate brackets
\[ (2 + 3) \times (4 + 1) \]
(2 + 3) x (4 + 1)
Nested brackets
\[ ((2 + 3) \times 2) + 4 \]
((2 + 3) x 2) + 4 etc.
Indices
Square with operations
\[ 3^2 + 4 \]
3² + 4 or 4 + 3²
Cubes with operations
\[ 2^3 + 5 \]
2³ + 5 etc.
Square roots with ops
\[ \sqrt{16} + 5 \]
√16 + 5 or √(9+7) etc.
Brackets and indices
\[ 2 \times (3 + 1)^2 \]
2 x (3 + 1)² etc.
Full BIDMAS
\[ (2 + 3)^2 \times \sqrt{4} + 5 \]
Bracket, Index, Mult, Add
Special cases
Insert brackets (2 ops)
\[ 2 + 3 \times 4 = 20 \rightarrow (2 + 3) \times 4 \]
Make the statement true.
Timer (Optional)
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