# 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: modelled

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.

CalculationAnswer without using calculatorAnswer when using calculator
1. 13 + 25insert answer insert answer
2. 13 + 25 x 4insert answer insert answer
3. 25 x 4 + 13insert answer insert answer

View and print  – Calculations generating different answers (PDF 83.24KB)

As a class, discuss:

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

Students complete the activity calculations for further investigation for further investigation.

View and print  – Calculations for further investigation (PDF 93.16KB)

CalculationFirst stepSecond stepAnswer when using calculator in question 1
1. 13 +  25            13 + 25 = 38insert answer                           38
2. 13 + 25 x 425 x 4 = 10013 + 100 = 113                          113
3. 25 x 4 + 1325 x 4 = 100100 + 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?

3. 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 (insert answer) and (insert answer) operations should be done first,

followed by any (insert answer) and (insert answer) operations.

### Activity 2  – guided

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 1Question 2Question 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
Third stepinsert answerinsert answerinsert answer
Answer= 93= 33= 14

View print - 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, discuss any differences and determine the group’s final answer.
2. Ask the group of 9 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 (insert answer) and (insert answer) operations, then any (insert answer) and (insert answer) operations.

( ) 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.

3. Students should complete the activity Calculations with grouping symbols.

Students complete the activity 'Calculations with grouping symbols'

Question 1Question 2Question 3
Question(13 + 25) x 413 + (25 x 4)13 + 25 x 4
First step= 38 x 4= 13 + 100= 13 + 100
Second stepinsert answerinsert answerinsert answer
Third stepinsert answerinsert answerinsert answer
Answer= 152= 113=  113

4. Practise order of operations further using activities from Funbrain.

### Extension

Students studying Stage 5 mathematics will also need to investigate the order to implement more complex operations, such as exponents, roots and fractional expressions.

Students complete the activity 'Calculations involving complex operations'.

Question 1Question 2Question3
Question6 x 2 2 6 + 2 243 x  82 -  3  x  52
First step= 6 x 4= 6 + 4= 64 x 64 - 3 x 25
Secondinsert answerinsert answer= 4096 - 75
Thirdinsert answerinsert answer=
Answer= 24= 10= 4021

## 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

## Resources

• Funbrain - Operation order from Fun brain teaches about the importance of the order of operations
• Maths interactive -This interactive mathematics resource allows the user to explore the order of operations (brackets, exponents, multiplication, division, addition and subtraction)
• The Numbers Game - A game styled on the British TV show Countdown, where contestants use 6 numbers and the usual operations and brackets to make the target number. This program has a great bonus – after you have found a solution (or not), the program will then list all of the solutions. Available for download.
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