Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
Add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies
<ul>
<li>using drawings, physical and virtual materials, and number combinations within 10 to add and subtract collections to 20</li>
<li>adding and subtracting numbers within 20, using a variety of representations and strategies, such as counting on, counting back, partitioning and partpart-whole knowledge of numbers to 10; for example, using partitioning and combining 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12</li>
<li>developing and using strategies for one-digit addition and subtraction based on part-part-whole relationships for each of the numbers to 10 and subitising with physical and virtual materials; for example, 8 and 6 is the same as 8 and 2 and 4</li>
<li>representing story problems involving addition and subtraction of numbers within 20 using a Think Board; recognising and using + and − symbols and the equal sign (=) to represent the operations of addition and subtraction; and showing and explaining the connections between any materials used using the language of plus and minus, and the numbers within the story problem</li>
<li>creating and performing addition and subtraction stories told through Aboriginal and/or Torres Strait Islander dances</li>
</ul>
Add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies
<ul>
<li>using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5</li>
<li>using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93</li>
<li>representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation</li>
<li>using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54</li>
<li>using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’</li>
<li>using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences</li>
</ul>
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
<ul>
<li>applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem</li>
<li>using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems</li>
<li>matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve</li>
<li>formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences</li>
</ul>
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
<ul>
<li>partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)</li>
<li>using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36</li>
<li>exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place</li>
</ul>
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
<ul>
<li>using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts</li>
<li>recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives</li>
<li>practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts</li>
<li>systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns</li>
</ul>
Develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
<ul>
<li>using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers, for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate</li>
<li>using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 × 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 × 18 = 180, then halving 180 to get 90; or applying the associative property of multiplication, where 5 × 18 becomes 5 × 2 × 9, then 5 × 2 × 9 = 10 × 9 = 90 so that 5 × 18 = 90</li>
<li>using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence</li>
<li>using materials or a diagram to solve a multiplication or division problem, by writing a number sentence and explaining what each of the numbers within the number sentence refers to</li>
<li>representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation</li>
<li>using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems; for example, for 16 × 4, thinking 10× 4 and 6 × 4, then 40 + 24 = 64, or a double double strategy where double 16 is 32, double this is 64, so 16 × 4 is 64</li>
</ul>
Recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator
<ul>
<li>using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in multiplication facts up to 10 × 10; and using the arrays to explain the related division facts</li>
<li>using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6, and recording and explaining the connections to the × 3 and × 6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …</li>
<li>using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as ‘to multiply a number by 9 you multiply by 10 then take the number away’: 9 × 4 = 10 × 4 − 4, so 9 × 4 is 40 − 4 = 36; or using multiples of 3 as ‘to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again’</li>
<li>using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30, which is 42</li>
</ul>
teaching resource
Input Output Machine Worksheet Set
Updated: 04 Apr 2025
Use this input output machine worksheet set to introduce your students to number patterns while giving them computational practice.
Use this input output machine worksheet set to introduce your students to number patterns while giving them computational practice.
A Varied Input Output Machine Worksheet Set
Engage your students with this input output machine worksheet set that features ‘Maths Machines’ that help reinforce key mathematical concepts. Students will work to discover the rule that turns an input number into the correct output, practising essential skills like addition, subtraction, and division. Each worksheet provides an exciting challenge that encourages critical thinking, while adorable robot illustrations keep students entertained. Answer keys are included for quick and easy assessment!
This input output machine worksheet set includes the following worksheets:
‘Make 2’ Maths Machines (addition or subtraction rules)
‘Make 3’ Maths Machines (addition or subtraction rules)
‘Make 4’ Maths Machines (division rules)
‘Make 5’ Maths Machines (division rules)
Using This Function Machine Worksheet Set
This function machine worksheet set is great for independent practice, but has other uses as well! Here are some examples to get you started.
Timed Test Alternative – Use the ‘Make 4’ and ‘Make 5’ worksheets as a fun alternative to division fact timed tests.
Exit Ticket – Cut maths machine singles or pairs apart to use as an exit ticket to assess understanding after a lesson.
Maths Stations – Print this input output machine worksheet set on cardboard and laminate each page. Put the set in your maths stations with a supply of whiteboard markers for your students to complete over and over again!
‘Scoot’ Activity – Cut the maths machines on these worksheets apart and place them around the room. Students travel from robot to robot, writing the answer to each on a piece of paper.
Download This Function Machine Worksheet PDF
Our function machine worksheet PDF is also available in editable Google Slides format. To grab your copy, click the drop-down arrow on the download button and choose the format that works for you.
This resource was created by Kaylyn Chupp, a teacher and a Teach Starter collaborator.
More Input and Output Machines Worksheets and Activities
We have many additional input and output machines worksheets and activities available at your fingertips! Take a look at the selection below.
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
Add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies
<ul>
<li>using drawings, physical and virtual materials, and number combinations within 10 to add and subtract collections to 20</li>
<li>adding and subtracting numbers within 20, using a variety of representations and strategies, such as counting on, counting back, partitioning and partpart-whole knowledge of numbers to 10; for example, using partitioning and combining 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12</li>
<li>developing and using strategies for one-digit addition and subtraction based on part-part-whole relationships for each of the numbers to 10 and subitising with physical and virtual materials; for example, 8 and 6 is the same as 8 and 2 and 4</li>
<li>representing story problems involving addition and subtraction of numbers within 20 using a Think Board; recognising and using + and − symbols and the equal sign (=) to represent the operations of addition and subtraction; and showing and explaining the connections between any materials used using the language of plus and minus, and the numbers within the story problem</li>
<li>creating and performing addition and subtraction stories told through Aboriginal and/or Torres Strait Islander dances</li>
</ul>
Add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies
<ul>
<li>using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5</li>
<li>using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93</li>
<li>representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation</li>
<li>using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54</li>
<li>using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’</li>
<li>using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences</li>
</ul>
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
<ul>
<li>applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem</li>
<li>using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems</li>
<li>matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve</li>
<li>formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences</li>
</ul>
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
<ul>
<li>partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)</li>
<li>using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36</li>
<li>exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place</li>
</ul>
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
<ul>
<li>using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts</li>
<li>recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives</li>
<li>practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts</li>
<li>systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns</li>
</ul>
Develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
<ul>
<li>using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers, for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate</li>
<li>using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 × 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 × 18 = 180, then halving 180 to get 90; or applying the associative property of multiplication, where 5 × 18 becomes 5 × 2 × 9, then 5 × 2 × 9 = 10 × 9 = 90 so that 5 × 18 = 90</li>
<li>using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence</li>
<li>using materials or a diagram to solve a multiplication or division problem, by writing a number sentence and explaining what each of the numbers within the number sentence refers to</li>
<li>representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation</li>
<li>using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems; for example, for 16 × 4, thinking 10× 4 and 6 × 4, then 40 + 24 = 64, or a double double strategy where double 16 is 32, double this is 64, so 16 × 4 is 64</li>
</ul>
Recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator
<ul>
<li>using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in multiplication facts up to 10 × 10; and using the arrays to explain the related division facts</li>
<li>using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6, and recording and explaining the connections to the × 3 and × 6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …</li>
<li>using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as ‘to multiply a number by 9 you multiply by 10 then take the number away’: 9 × 4 = 10 × 4 − 4, so 9 × 4 is 40 − 4 = 36; or using multiples of 3 as ‘to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again’</li>
<li>using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30, which is 42</li>
</ul>
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