Tasks in this sequence
Task 1 • Finding multiplication
Students learn that multiplication is about how many groups and how much in each group.
Task 2 • Mangoes and apples
Students learn that the array is a powerful representation of the ‘how many’ groups and ‘how much in each group’ structure of multiplication.
Task 3 • Making arrays
Students complete an activity that builds their understanding of the array as a representation of multiplication.
Task 4 • Hidden fruit
Students learn that multiplying ‘how many’ by ‘how much’ gives the whole.
Task 5 • Rolling arrays
Students play a game to build their understanding that multiplying how many by how much gives the whole.
Task 6 • Lemon arrays
Students learn that related multiplication and division facts can be recorded as a fact family.
Task 7 • Making fact families
Students continue to build their understanding that related multiplication and division facts can be recorded as a fact family.
Task 8 • Finding fact families
Students revisit the reSolve Market picture and use fact families to record the multiplication.
Sequence implementation
This time plan is just one way that you might choose to implement this sequence. We have based this plan on 50minute lessons, with some tasks split across two lessons. The timing provided in the tasks’ documentation align with this implementation advice.
Week 1  Week 2  

Monday  Task 1 • Finding multiplication
 Task 6 • Lemon arrays

Tuesday  Task 2 • Mangoes and apples
 Task 6 • Lemon arrays

Wednesday  Task 3 • Making arrays
 Task 7 • Making fact families

Thursday  Task 4 • Hidden arrays
 Task 8 • Finding fact families

Friday  Task 5 • Rolling arrays
 Task 5 • Rolling arrays

Curriculum and syllabus alignment
Achievement standards
Students use mathematical modelling to solve practical problems involving single—digit multiplication and division, recalling multiplication facts for twos, threes, fours, fives and tens, by using a range of strategies.
Australian Curriculum V9 alignment
Number
Multiply and divide one and twodigit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Algebra
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
Sequence design overview
Multiplication involves students being able to recognise and work with equalsized groups, and to differentiate between how many and how much (Siemon et al, 2021). This sequence uses the array as a powerful model to express the distinction between how many and how much, which forms the foundation for the idea of factorfactorproduct. This supports student understanding of the relationship between multiplication and division and informs the building of fact families.
How many and how much: In multiplication, students need to work out two things: ‘how many groups’ and ‘how much in each group’. Students need to be able to distinguish between the two quantities which make up the whole. The twodimensional nature of the array makes the distinction between these quantities visible, as the count of how many indicates the number of rows, where the count of how much indicates the number in each row.
Fact families: Multiplication and division are about equalsized groups. The two operations are related, which means that when we know one fact, we actually know four (for square numbers there are just two). The array powerfully represents the relationship between multiplication and division, as it makes the factorfactorproduct idea visible.
Sequence Framework
This Sequence Framework presents an overview of the key elements in this sequence.
Learning goals  Students’ mathematical activity  Representation  Context  

Task 1  Multiplication is about coordinating two ideas: how many groups and how much in each group.  Students identify examples of multiplication in the reSolve Market picture, including examples of equal groups and arrays.  Multiplication is represented as equalsized groups and arrays.  The reSolve Market is introduced through an illustration with examples of multiplication as equalsized groups and arrays. 
Task 2  The array powerfully represents the ‘how many groups’ and ‘how much in each group’ structure of multiplication.  Students investigate relationships between different collections of fruit represented in equal groups and the array.  Multiplication is represented as equalsized groups and arrays. The different representations have been carefully designed to illustrate properties and relationships.  The different displays of fruit have been carefully designed to model multiplicative properties and relationships. 
Task 3  The array powerfully represents the ‘how many groups’ and ‘how much in each group’ structure of multiplication.  Students create arrays for a given total and investigate the relationship between how many rows and how much in each row.  Students create their own arrays given how many and how much.  A Build activity in which students create their own arrays and record the corresponding multiplication fact. 
Task 4  Multiplying how many by how much gives the whole: how many x how much = the whole  Students calculate the amount of fruit in partially hidden arrays. They work out how many and how much to find the whole.  Partial arrays and hidden groups build the relationship between:
 The back of the reSolve Market with boxes partially unpacked or hidden. 
Task 5  Multiplying how many by how much gives the whole: how many x how much = the whole  Students create arrays and record corresponding multiplication facts through the context of a game.  Students create an array based on how many and how much and record this as a multiplication fact.  A game to build students’ understanding of the relationship between how many, how much, and the whole. 
Task 6  Related multiplication and division facts can be recorded as a fact family. A family of facts is clearly modelled in the array.  Students organise equalsized bags of fruit into different arrays. They determine the family of facts that are represented by each array.  Multiple equalsized bags converted into arrays, recording the corresponding fact family for each array.  Equalsized bags of lemons, limes and kiwifruit are unpacked by the grocer to display as an array in the Market store. 
Task 7  Related multiplication and division facts can be recorded as a fact family. A family of facts is clearly modelled in the array.  Students create arrays for a given total and record the family of facts that are represented by each array.  Students create arrays based on how many and how much and record the corresponding fact family.  A Build activity in which students create their own arrays and record the corresponding fact family. 
Task 8  Related multiplication and division facts can be recorded as a fact family.  Students revisit the reSolve Market picture and record the fact families for the different examples of multiplication that can be seen.  Return to the example of multiplication in the reSolve Market and recording corresponding fact families.  Return to the example of multiplication in the reSolve Market and recording corresponding fact families. 