# 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.

Calculation | Answer without using calculator | Answer when using calculator |
---|---|---|

1. 13 + 25 | insert answer | insert answer |

2. 13 + 25 x 4 | insert answer | insert answer |

3. 25 x 4 + 13 | insert 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.

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?

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 number | 1 | 2 | 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 step | insert answer | insert answer | insert 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 ( ) 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 |

Students complete the activity 'Calculations with grouping symbols'

Question number | 1 | 2 | 3 |
---|---|---|---|

Question | (13 + 25) x 4 | 13 + (25 x 4) | 13 + 25 x 4 |

First step | = 38 x 4 | = 13 + 100 | = 13 + 100 |

Second step | insert answer | insert answer | insert answer |

Third step | insert answer | insert answer | insert answer |

Answer | = 152 | = 113 | = 113 |

View and print – calculations with grouping symbols (PDF 111.66KB)

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 number | 1 | 2 | 3 |
---|---|---|---|

Question | 6 x 2 ^{2 } | 6 + 2 ^{2} | 4^{3 }x 8^{2 } - 3 x 5^{2} |

First step | = 6 x 4 | = 6 + 4 | = 64 x 64 - 3 x 25 |

Second | insert answer | insert answer | = 4096 - 75 |

Third | insert answer | insert answer | = |

Answer | = 24 | = 10 | = 4021 |

View and print – Calculations involving complex operations (PDF 93.16KB)

## References

### Australian curriculum reference: ACMNA151

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

### NSW syllabus reference: 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.