Multiplication & Division

Learning Experiences

Multiplication & Division

OUTCOME

A student:

MA3-6NA:

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

TEACHING POINTS | Students could extend their recall of number facts beyond the multiplication facts to 10 × 10 by also memorising multiples of numbers such as 11, 12, 15, 20 and 25, or by utilising mental strategies, eg ’14 × 6 is 10 sixes plus 4 sixes’. |

The simplest multiplication word problems relate to rates, eg ‘If four students earn $3 each, how much do they have all together?’ Another type of problem is related to ratio and uses language such as ‘twice as many as’ and ‘six times as many as’. | |

An ‘operation’ is a mathematical process. The four basic operations are addition, subtraction, multiplication and division. Other operations include raising a number to a power and taking a root of a number. An ‘operator’ is a symbol that indicates the type of operation, eg +, –, × and ÷. | |

Refer also to background information in Multiplication and Division 1. |

Language | Students should be able to communicate using the following language: multiply, multiplied by, product, multiplication, multiplication facts, area, thousands, hundreds, tens, ones, double, multiple, factor, divide, divided by, quotient, division, halve, remainder, fraction, decimal, equals, strategy, digit, estimate, speed, per, operations, order of operations, grouping symbols, brackets, number sentence, is the same as. |

When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, eg ‘cost of goldfish = …’, ‘cost of plants = …’, ‘total cost = …’. | |

Grouping symbols’ is a collective term used to describe brackets [ ], parentheses ( ) and braces { }. The term ‘brackets’ is often used in place of ‘parentheses’. | |

Often in mathematics when grouping symbols have one level of nesting, the inner pair is parentheses ( ) and the outer pair is brackets [ ], eg 360÷[4×(20−11)]. |

Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123) | select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers |

select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainder | |

– estimate solutions to problems and check to justify solutions {Problem Solving, Reasoning, Critical and creative thinking} | |

use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiples | |

solve word problems involving multiplication and division, e.g. ‘A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?’ {Critical and creative thinking} | |

– use appropriate language to compare quantities, e.g. ‘twice as much as’, ‘half as much as’ {Communicating, Critical and creative thinking} | |

– use a table or similar organiser to record methods used to solve problems {Communicating, Problem Solving, Information and communication technology capability} | |

recognise symbols used to record speed in kilometres per hour, e.g. 80 km/h {Literacy} | |

solve simple problems involving speed, e.g. ‘How long would it take to travel 600 km if the average speed for the trip is 75 km/h?’ {Critical and creative thinking} |

Explore the use of brackets and the order of operations to write number sentences (ACMNA134) | use the term ‘operations’ to describe collectively the processes of addition, subtraction, multiplication and division |

investigate and establish the order of operations using real-life contexts, e.g. ‘I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?’; this can be represented by the number sentence 6 × 10 + 2 × 4 but, to obtain the total cost, multiplication must be performed before addition {Literacy, Critical and creative thinking, Work and enterprise} | |

– write number sentences to represent real-life situations {Communicating, Problem Solving, Literacy} | |

recognise that the grouping symbols ( ) and [ ] are used in number sentences to indicate operations that must be performed first {Literacy} | |

recognise that if more than one pair of grouping symbols are used, the operation within the innermost grouping symbols is performed first | |

perform calculations involving grouping symbols without the use of digital technologies, e.g. 5+(2×3)=5+6 =11 (2+3)×(16−9)=5×7 =35 3+[20÷(9−5)]=3+[20÷4] =3+5 =8 | |

apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies, e.g. 32+2−4=34−4 =30 addition and subtraction only, therefore work from left to 32÷2×4=16×4 =64 multiplication and division only, therefore work from left to right 32÷(2×4)=32÷8 =4 perform operation in grouping symbols first (32+2)×4=34×4 =136 perform operation in grouping symbols first 32+2×4=32+8 =40 perform multiplication before addition {Work and enterprise} | |

– investigate whether different digital technologies apply the order of operations {Reasoning, Information and communication technology capability, Critical and creative thinking} | |

recognise when grouping symbols are not necessary, eg 32 + (2 × 4) has the same answer as 32 + 2 × 4 |

Learning Experiences

To be added

WE ARE CLOSED FOR THE HOLIDAYS – DECEMBER 21 – JANUARY 4 2021

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Australia