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**Related topic**

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator (AC9M4A02)

- using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in the \(10 \times 10\) multiplication facts; using the arrays to explain the related division facts
- 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 \(6\); recording and explaining the connections to the \(\times3\) and \(\times6\) multiplication facts: \(3, 6, 9,\) … doubled is \(6, 12, 18,\) …
- 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”; \(9 \times 4 = 10 \times 4\space – \space4\), so \(9 \times 4\) is \(40 \space– \space4 = 36\); using multiple of \(3\) as “to multiply a number by \(9\) you multiply by \(3\), and then multiply the result by \(3\) again”
- 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 \(6 \times 7\), knowing that \(7\) is made up of \(2\) and \(5\), and using an array to show that \(6 \times 7\) is the same as \(6 \times 2 + 6 \times 5 = 12 + 30\) which is \(42\)
- using known multiplication facts up to \(10 \times 10\) and the inverse relationship of multiplication and division to establish corresponding division facts
- designing, creating and playing instructive card games that involve the recall, recognition and explanation of the \(10 \times 10\) multiplication facts and related division facts

Commutativity, Distributivity, Division, Multiplication tables