# Stage 4 multiplication and division - order of operations

Students can:

• determine which operation in a number sentence should be completed first, second, third, and so on
• identify when grouping symbols should be used
• identify the correct order of operations in number sentences.

## Activities to support the strategies

### Activity 1: Investigate order of operations

Students may not yet be aware that calculations can generate different answers, depending on the order in which they are done.

Students should use the activity 'Calculations generating different answers' to investigate.

Calculations generating different answers worksheet (PDF 83.24KB)

As a class, discuss:

• Which answers changed when done on a calculator?
• What are the common elements of the answers with changed answers?

Calculations for further investigation worksheet (PDF 93.16KB)

calculations for further investigation
Calculation First step Second step Answer when using calculator in question 1
1. 13 +  25             13 + 25 = 38 insert answer                            38
2. 13 + 25 x 4 25 x 4 = 100 13 + 100 = 113                           113
3. 25 x 4 + 13 25 x 4 = 100 100 + 13 = 113                           113

As a class, discuss:

Did you get the same answer for the final step in 'calculations for further investigations' AND the answer when using the calculator in 'calculations generating different answers'?

• What are the common elements of step 1?
• What are the common elements of step 2?
• What rules might be useful when adding, subtracting, multiplying and dividing?

Ask students to copy and complete this statement

• When doing questions with different operations (+, - , x, ÷), it is important to apply the correct order of operations. Any _________ and _________ operations should be done first, followed by any _________ and _________ operations.

Correct response: Any multiplication and division operations should be done first, followed by any addition and and subtraction operations.

### Activity 2a: Ordering operations

In pairs, ask students to determine which operations should be done first, second and third in the expressions and calculate the answers for the activity 'Which operation is first, second and third?'

Question 1 Question 2 Question 3
Question  5 + 7 x 12 + 4  29 - 5 + 3 x 3  1 x 9 + 1 x 5
First step = 5 + 84 + 4 = 29 - 5 + 9 = 9 + 1 x 5
Second step = 89  + 4 = 24 + 9 = 9 + 5
Answer = 93 = 33 = 14

Which operation is first, second and third? (PDF 117.7KB)

• Ask pairs of students to share their answers with another pair of students, discuss any differences and determine the group’s final answer.
• Ask groups of four to share with another four students. The two groups discuss any differences and determine the whole group’s final answer.

### Activity 2b: Grouping symbols

( ) are called parentheses

[ ] are called brackets

{ } are called braces

These grouping symbols can be used together or separately in any mathematical expression, as a way of grouping values together.

Ask students to copy and complete this statement

• When doing questions with different operations (+, - , x, ÷), it is important to apply the correct order of operations. Any grouping symbols - parentheses (), brackets [] or braces {} - should be completed first, followed by any _________ and _________ operations, then any _________ and _________ operations.

Correct response: Multiplication and division first, followed by addition and subtraction

Students complete the activity 'Calculations with grouping symbols'

Question 1 Question 2 Question 3
Question (13 + 25) x 4 13 + (25 x 4) 13 + 25 x 4
First step = 38 x 4 = 13 + 100 = 13 + 100
Answer = 152 = 113 =  113

## References

### Australian curriculum

ACMNA151: Apply the associative, commutative and distributive laws to aid mental and written computation

### NSW syllabus

MA4-4NA: Communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

## Teacher resources

Lesson plans and activities

Stage 3 multiplicative thinking teaching strategies (staff only)