053e. Order of Operations with Integers

Learning Intentions

To know the convention for determining order of operations in an expression involving more than one operation
evaluate arithmetic expressions involving more than one operation with positive and/or negative numbers

Understand the four operations: addition, subtraction, multiplication and division
Understand that brackets change the order in which parts of an expression are evaluated
Know how to add, subtract, multiply and divide positive and negative integers
Understand that multiplication and division are performed before addition and subtraction
Be able to work from left to right when operations have the same priority
Recognise that a negative number is different from subtraction as an operation

Evaluate using the correct order of operations:
a) $5 + 3 \times 4$
b) $18 - 2 \times 7$
c) $24 \div 6 + 2$

Evaluate expressions with negative numbers:
a) $- 3 + 4 \times 5$
b) $12 - 3 \times (- 2)$
c) $- 20 \div 5 + 7$

Evaluate expressions with brackets:
a) $(6 + 2) \times 3$
b) $4 \times (7 - 9)$
c) $(18 - 6) \div 3$

Evaluate expressions with brackets and negative numbers:
a) $(- 4 + 9) \times 2$
b) $3 \times (5 - 8)$
c) $(- 12) \div (- 3) + 4$

Evaluate expressions with several operations:
a) $14 - 6 \div 2 + 3$
b) $8 + 3 \times 2 - 7$
c) $(- 5) + 12 \div 3 \times 2$

Evaluate expressions with integers and brackets:
a) $2 \times (3 + 4) - 5$
b) $18 \div (2 + 1) + (- 4)$
c) $(- 2) \times (6 - 9) + 1$

Evaluate using the correct order of operations:
a) $6 + 2 \times 5$
b) $20 - 3 \times 4$
c) $30 \div 5 + 1$

Evaluate expressions with negative numbers:
a) $- 4 + 3 \times 6$
b) $10 - 2 \times (- 3)$
c) $- 24 \div 6 + 5$

Evaluate expressions with brackets:
a) $(5 + 4) \times 2$
b) $3 \times (8 - 10)$
c) $(21 - 9) \div 4$

Evaluate expressions with brackets and negative numbers:
a) $(- 3 + 7) \times 4$
b) $2 \times (4 - 9)$
c) $(- 15) \div (- 5) + 6$

Evaluate expressions with several operations:
a) $16 - 8 \div 4 + 2$
b) $7 + 4 \times 3 - 6$
c) $(- 6) + 15 \div 5 \times 2$

Evaluate expressions with integers and brackets:
a) $3 \times (2 + 5) - 4$
b) $24 \div (3 + 1) + (- 2)$
c) $(- 3) \times (7 - 10) + 2$

Evaluate:
a) $4 + 2 \times 3$
b) $15 - 3 \times 2$
c) $18 \div 3 + 5$
Evaluate:
a) $- 2 + 5 \times 4$
b) $14 - 2 \times (- 3)$
c) $- 16 \div 4 + 9$
Evaluate with brackets:
a) $(3 + 5) \times 2$
b) $6 \times (4 - 7)$
c) $(20 - 8) \div 2$
Evaluate with brackets and negative numbers:
a) $(- 1 + 6) \times 3$
b) $4 \times (2 - 5)$
c) $(- 18) \div (- 6) + 7$
Evaluate:
a) $12 - 4 \div 2 + 6$
b) $9 + 2 \times 5 - 8$
c) $(- 7) + 18 \div 3$
Evaluate:
a) $2 \times (4 + 1) - 3$
b) $16 \div (2 + 2) + 5$
c) $(- 4) \times (3 - 7)$
Evaluate:
a) $5 + (- 3) \times 2$
b) $24 \div (- 6) + 1$
c) $3 \times (- 2) + 7$
Evaluate:
a) $(- 8) + 4 \times 3$
b) $20 - (- 2) \times 5$
c) $(- 12) \div 3 - 2$

Explain why $5 + 3 \times 4 \neq 32$ .
A student evaluates $18 - 6 \div 3$ as $4$ . Explain the mistake.
Explain why $3 \times (4 - 6)$ gives a different answer from $3 \times 4 - 6$ .
A student says $- 2 + 5 \times 4 = 12$ because they added first. Explain why this is incorrect.

A game score is calculated by the expression $10 + 3 \times (- 2)$ . Find the score.
A diver’s position is modelled by $4 + (- 3) \times 5$ . Find the final position.
A lift starts at floor $- 2$ and follows the expression $- 2 + 4 \times 3$ . Find the final floor.
A bank balance changes according to $20 - 3 \times 8$ . Find the final balance.
A temperature change is modelled by $(- 5) + 12 \div 3 \times 2$ . Find the final temperature.
A pattern is given by $2 \times (6 - 9) + 4$ . Evaluate the expression.

Students may perform operations strictly from left to right instead of following the order of operations
Students may not recognise that multiplication and division must be completed before addition and subtraction
Students may ignore brackets or treat them as decorative symbols
Students may confuse a negative sign with subtraction as an operation
Students may not work left to right when multiplication and division appear together
Students may make sign errors when multiplying or dividing negative integers
Students may think $- 3^{2}$ and $(- 3)^{2}$ have the same meaning in later work, so careful bracket use should be reinforced
Students may simplify part of an expression correctly but then lose track of the remaining operations