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**Related topic**

develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder (AC9M4N06)

- 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
- using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for \(5 \times 18\), using the fact that double \(5\) is \(10\) and half of \(18\) is \(9\); or using \(10 \times 18 = 180\) and halve \(180\) is \(90\); applying the associative property of multiplication, where \(5 \times18\) becomes \(5 \times 2 \times 9\), then \(5 \times 2 \times 9 = 10 \times 9 = 90\) so that \(5 \times 18 = 90\)
- 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
- 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
- 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
- using place value partitioning, basic facts and an area or region to represent and solve multiplication problems, such as \(16 \times 4\), thinking \(10 \times 4\) and \(6 \times 4\), \(40 + 24 = 64\) or a double, double strategy where double \(16\) is \(32\), double this is \(64\), so \(16 \times 4\) is \(64\)
- using materials or diagrams to develop and explain division strategies; for example, finding thirds, using the inverse relationship to turn division into a multiplication

Associativity, Commutativity, Distributivity, Number operations