Multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies
<ul>
<li>making and naming arrays and using bar models to solve simple multiplication or sharing problems; for example, making different arrays to represent 12 and naming them as ‘3 fours’, ‘2 sixes’, ‘4 threes’ and ‘6 twos’, using physical or virtual materials to make arrays or using bar models to demonstrate that ‘3 fours’ is equal to ‘4 threes’</li>
<li>finding the total number represented in an array by partitioning the array using subitising and number facts; for example, describing how they determined the total number of dots arranged in a ‘3 fives’ array by saying, ‘I saw 2 fives, which is 10, and then 5 more, which makes 15’</li>
<li>recognising problems that can be solved using division and identifying the difference between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of 3</li>
<li>using a Think Board to solve partition and quotition division problems; for example, sharing a prize of $36 between 4 people, using materials, a diagram and skip counting to find the answer, and explaining whether the answer ‘9’ refers to people or dollars</li>
<li>using materials or diagrams, and skip counting, to solve repeated equal-quantity multiplication problems; for example, writing a repeated addition number sentence and using skip counting to solve the problem ‘Four trays of biscuits with 6 on each tray – how many biscuits are there?’</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context
<ul>
<li>modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition, subtraction, multiplication or division to solve the problem and justifying the choice of operation, such as ‘I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part’</li>
<li>modelling and solving simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division, for example, ‘If each member of our class contributes $5, how much money will we have in total?’</li>
<li>modelling and solving practical problems such as deciding how many people should be in each team for a game or sports event, how many teams for a given game can be filled from a class, or how to share out some food or distribute money in whole dollar amounts, including deciding what to do if there is a remainder</li>
<li>modelling and solving the problem ‘How many days are there left in this year?’ by using a calendar</li>
<li>modelling problems involving equal grouping and sharing in Aboriginal and/or Torres Strait Islander children’s instructive games; for example, in Yangamini from the Tiwi Peoples of Bathurst Island, representing relationships with a number sentence and interpreting and communicating solutions in terms of the context</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>
Recall multiplication facts up to 10 x 10 and related division facts
Elaborations
using known multiplication facts to calculate related division facts (Skills: Numeracy, Critical and Creative Thinking)
View this topic on www.australiancurr...
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
Multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation
Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Use this set of division posters in your classroom when teaching different mental maths strategies.
Division Strategies
Are your students needing help recalling their division facts? If you are looking for tips and tricks to help them divide numbers within 100, look no further! Even though there may not be as many strategies as there are when adding or subtracting, there are some helpful ways students can tackle some of those hard-to-remember math problems. Teach Starter has created a set of division posters that you can use in your classroom to help them increase their math fluency!
With this download, you will receive 1 title poster and 4 strategy posters covering the following:
use a known fact
halve
think multiplication in reverse
halve a half.
How to Make the Most of Your Mental Maths Posters
Print the posters and display them in your classroom for students to reference when doing independent work.
Print the posters, slip them into clear sleeves and use them in your guided groups as a reminder.
Print the posters, slide them into a clear sleeve, and hang them on a ring as a reference tool for a maths group.
We’ve also come up with bonus ways to turn posters into interactive tools that really make your lessons stick!
📂 Place copies in students’ homework folders for reference.
💻 Provide posters as digital resources for virtual students.
🧠 Test students’ memories by showing them the poster, then hiding it and having them tell you what they remember.
✅ Incorporate posters into your lesson wrap-up: students write on a sticky note what they learned from the lesson and place it on the poster.
Before You Download
This resource prints as a PDF. Please use the Download button to access the colour version of this resource.
Multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies
<ul>
<li>making and naming arrays and using bar models to solve simple multiplication or sharing problems; for example, making different arrays to represent 12 and naming them as ‘3 fours’, ‘2 sixes’, ‘4 threes’ and ‘6 twos’, using physical or virtual materials to make arrays or using bar models to demonstrate that ‘3 fours’ is equal to ‘4 threes’</li>
<li>finding the total number represented in an array by partitioning the array using subitising and number facts; for example, describing how they determined the total number of dots arranged in a ‘3 fives’ array by saying, ‘I saw 2 fives, which is 10, and then 5 more, which makes 15’</li>
<li>recognising problems that can be solved using division and identifying the difference between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of 3</li>
<li>using a Think Board to solve partition and quotition division problems; for example, sharing a prize of $36 between 4 people, using materials, a diagram and skip counting to find the answer, and explaining whether the answer ‘9’ refers to people or dollars</li>
<li>using materials or diagrams, and skip counting, to solve repeated equal-quantity multiplication problems; for example, writing a repeated addition number sentence and using skip counting to solve the problem ‘Four trays of biscuits with 6 on each tray – how many biscuits are there?’</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context
<ul>
<li>modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition, subtraction, multiplication or division to solve the problem and justifying the choice of operation, such as ‘I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part’</li>
<li>modelling and solving simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division, for example, ‘If each member of our class contributes $5, how much money will we have in total?’</li>
<li>modelling and solving practical problems such as deciding how many people should be in each team for a game or sports event, how many teams for a given game can be filled from a class, or how to share out some food or distribute money in whole dollar amounts, including deciding what to do if there is a remainder</li>
<li>modelling and solving the problem ‘How many days are there left in this year?’ by using a calendar</li>
<li>modelling problems involving equal grouping and sharing in Aboriginal and/or Torres Strait Islander children’s instructive games; for example, in Yangamini from the Tiwi Peoples of Bathurst Island, representing relationships with a number sentence and interpreting and communicating solutions in terms of the context</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>
Recall multiplication facts up to 10 x 10 and related division facts
Elaborations
using known multiplication facts to calculate related division facts (Skills: Numeracy, Critical and Creative Thinking)
View this topic on www.australiancurr...
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
Multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation
Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts
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