009. Order of Operations in Arithmetic

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

Understanding basic arithmetic operations: addition, subtraction, multiplication, division
Knowledge that multiplication and division have higher priority than addition and subtraction
Understanding parentheses and their role in changing order of evaluation
Familiarity with simple calculations and ability to perform operations accurately

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

Include parentheses to change order:
a) $(5 + 3) \times 2$
b) $18 - (6 \div 3)$

Combine multiple operations:
a) $12 + 6 \times 3 - 4$
b) $20 \div 5 + 3 \times 4$

Use a mixture of parentheses and multiple operations:
a) $(12 + 6) \times (3 - 1)$
b) $24 \div (3 + 1) + 5$

a) $7 + 4 \times 5$
b) $20 - 8 \div 2$

a) $(7 + 4) \times 5$
b) $20 - (8 \div 2)$

a) $15 + 9 \times 2 - 6$
b) $18 \div 3 + 7 \times 2$

a) $(10 + 5) \times (4 - 2)$
b) $30 \div (5 + 1) + 6$

Evaluate:
a) $6 + 3 \times 4$
b) $12 - 8 \div 2$
c) $7 \times 2 + 5$
Evaluate with parentheses:
a) $(6 + 3) \times 4$
b) $12 - (8 \div 2)$
c) $(7 \times 2) + 5$
Evaluate mixed operations:
a) $10 + 5 \times 2 - 3$
b) $16 \div 4 + 9 - 2$
c) $8 + 12 \div 3 \times 2$
Evaluate using parentheses:
a) $(10 + 5) \times (2 - 1)$
b) $16 \div (4 + 2) + 3$
c) $(8 + 12) \div (3 \times 2)$

Explain why $5 + 3 \times 2$ is not $16$ .
A student writes $12 - 6 \div 3 = 2$ . Explain the mistake.
Why do parentheses change the order of operations?
Compare $7 + 3 \times 2$ and $(7 + 3) \times 2$ . Explain the difference in answers.

A shop sells $3$ pens for $2$ dollars each and a notebook for $5$ dollars. How much does a customer pay if they buy $3$ pens and $1$ notebook?
A factory produces $20$ items per hour. On Monday, they make $3$ hours in the morning and $2$ hours in the afternoon. How many items are produced?
Evaluate $50 - 6 \times 3 + 4$ using correct order.
Evaluate $(24 + 16) \div 4 \times 2$ .
A bus travels $15$ km in the morning and $20$ km in the afternoon. It stops $3$ times for $2$ km each. How far does it travel in total?

Students may perform operations strictly left to right without following order of operations
Students may ignore multiplication/division precedence over addition/subtraction
Students may misplace parentheses or ignore them
Students may incorrectly evaluate expressions with multiple layers of parentheses
Students may treat subtraction or division as commutative
Students may not check work by reverse operations