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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 memorising multiples of numbers such as 11, 12, 15, 20 and 25. They could also utilise mental strategies, eg ’14 × 6 is 10 sixes plus 4 sixes’. |
| In Stage 3, mental strategies need to be continually reinforced. | |
| Students may find recording (writing out) informal mental strategies to be more efficient than using formal written algorithms, particularly in the case of multiplication. | |
| An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse operations; multiplication and division are inverse operations. | |
| The area model for two-digit by two-digit multiplication in Stage 3 is a precursor to the use of the area model for the expansion of binomial products in Stage 5. |
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, round to. |
| In mathematics, ‘quotient’ refers to the result of dividing one number by another. | |
| Teachers should model and use a variety of expressions for multiplication and division. They should draw students’ attention to the fact that the words used for division may require the operation to be performed with the numbers in the reverse order to that in which they are stated in the question. For example, ‘divide 6 by 2’ and ‘6 divided by 2’ require the operation to be performed with the numbers in the same order as they are presented in the question (ie 6 ÷ 2). However, ‘How many 2s in 6?’ requires the operation to be performed with the numbers in the reverse order to that in which they are stated in the question (ie 6 ÷ 2). | |
| The terms ‘ratio’ and ‘rate’ are not introduced until Stage 4, but students need to be able to interpret problems involving simple rates as requiring multiplication or division. |
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100) | use mental and written strategies to multiply three- and four-digit numbers by one-digit numbers, including: {Critical and creative thinking} – multiplying the thousands, then the hundreds, then the tens and then the ones, eg 673×4=(600×4)+(70×4)+(3×4)=2400+280+12=2692 – using an area model, e.g. 684 × 5 – using the formal algorithm, e.g. 432 × 5 |
| use mental and written strategies to multiply two- and three-digit numbers by two-digit numbers, including: {Critical and creative thinking} – using an area model for two-digit by two-digit multiplication, e.g. 25 × 26 – factorising the numbers, e.g. 12 × 25 = 3 × 4 × 25 = 3 × 100 = 300 – using the extended form (long multiplication) of the formal algorithm, e.g. | |
| use digital technologies to multiply numbers of up to four digits {Information and communication technology capability} | |
| – check answers to mental calculations using digital technologies {Problem Solving, Information and communication technology capability} | |
| apply appropriate mental and written strategies, and digital technologies, to solve multiplication word problems {Literacy, Information and communication technology capability, Critical and creative thinking} | |
| – use the appropriate operation when solving problems in real-life situations {Problem Solving} | |
| – use inverse operations to justify solutions {Problem Solving, Reasoning, Critical and creative thinking} | |
| record the strategy used to solve multiplication word problems {Literacy} | |
| – use selected words to describe each step of the solution process {Communicating, Problem Solving, Literacy} |
Solve problems involving division by a one-digit number, including those that result in a remainder (ACMNA101) | use the term ‘quotient’ to describe the result of a division calculation, e.g. ‘The quotient when 30 is divided by 6 is 5’ |
| recognise and use different notations to indicate division, e.g. 25÷4, 4)25, 25/4 {Literacy} | |
| record remainders as fractions and decimals, eg 25÷4=6 1/4 or 6.25 {Literacy} | |
| use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is no remainder, including: {Critical and creative thinking} – dividing the hundreds, then the tens, and then the ones, e.g. 3248 ÷ 4 3200÷4=800 40÷4=10 8÷4=2 so 3248÷4=812 – using the formal algorithm, eg 258 ÷ 6 43 6)258 | |
| use mental and written strategies to divide a number with three or more digits by a one-digit divisor where there is a remainder, including: {Critical and creative thinking} – dividing the tens and then the ones, e.g. 243 ÷ 4 240÷4=60 3÷4=3/4 so 243÷4=60 3/4 – using the formal algorithm, e.g. 587 ÷ 6 97 5/6 6)258 | |
| – explain why the remainder in a division calculation is always less than the number divided by (the divisor) {Communicating, Reasoning, Critical and creative thinking} | |
| show the connection between division and multiplication, including where there is a remainder, e.g. 25 ÷ 4 = 6 remainder 1, so 25 = 4 × 6 + 1 | |
| use digital technologies to divide whole numbers by one- and two-digit divisors {Information and communication technology capability} | |
| – check answers to mental calculations using digital technologies {Problem Solving, Information and communication technology capability} | |
| apply appropriate mental and written strategies, and digital technologies, to solve division word problems {Literacy, Information and communication technology capability, Critical and creative thinking} | |
| – recognise when division is required to solve word problems {Problem Solving} | |
| – use inverse operations to justify solutions to problems {Problem Solving, Reasoning, Critical and creative thinking} | |
| use and interpret remainders in solutions to division problems, eg recognise when it is appropriate to round up an answer, such as ‘How many 5-seater cars are required to take 47 people to the beach?’ {Critical and creative thinking} | |
| record the strategy used to solve division word problems {Literacy} | |
| – use selected words to describe each step of the solution process {Communicating, Problem Solving, Literacy} |
Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) | round numbers appropriately when obtaining estimates to numerical calculations |
| use estimation to check the reasonableness of answers to multiplication and division calculations, e.g. ’32 × 253 will be about, but more than, 30 × 250′ |
To be added
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