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Multiplication Written Methods Written Methods • Throughout their years at school, children should progress from informal jottings and number line methods to formal efficient written methods. • By the end of Year 3, children should be confident using short efficient written methods for all four operations + - x ÷ • Children become secure with these methods with regular practice and should be able to apply skills to problem solving. Arrays • An array provides a visual representation of a multiplication sum. Through this, the language of multiplication is introduced. 4 groups of 3 3 lots of 4 4+4+4 3+3+3 3 times 4 3 x 4 = 12 Blank Number Line • An empty number line let’s us show multiplication as repeated addition by counting on in multiples or ‘lots’. 2x5 +2 +2 +2 +2 +2 0 2 4 6 8 10 1x2 0 2 2x2 4 3x2 6 4x2 8 5x2 10 Partitioning Method • Partitioning method splits two digit numbers into Tens and Units before multiplying. This is in preparation for formal short method. 13 x 2 10 + 3 2 13 x 8 10 + 3 8 1 0 x 2= 30 3 x 2= 6 30 + 6 = 36 1 0 x 8= 80 3 x 8= 24 80 + 24 = 104 Your Turn! • Can you use the partitioning method to solve these multiplications? • 45 x 6 = • 32 + 5 = • 32 + 3 = Column Multiplication • Partitioning method leads onto a compact efficient written method. This method requires a solid understanding of place value. TU 23 x 3 69 TU 57 x 5 285 3 7 x 5 = 35 Carry the tens beneath the line 5 x 5 =25 ADD the carried tens 25 + 3 = 28 Column Multiplication • Rules of column multiplication – Start with the biggest number – Align the columns H T U – Times from the units first – Carry tens below the answer line of the next column – Add on carried tens TU 42x5= + Your Turn! • Can you use the column method to solve these multiplications? •37x4= •28x3= •256x3= Column Multiplication • Once children are confident multiplying TU x U we extend to TU x TU using an expanded method first. TU 3 x 30 23 x 33 20 600 60 9 (3 x 3) 6 0 (20 x 3) 3 90 9 9 0 (30 x 3) + 6 0 0 (20 x 30) 759 1 Column Multiplication • Once children are confident multiplying TU x U we extend to TU x TU using an expanded method first. TU 23 x 33 9 (3 x 3) 6 0 (20 x 3) 9 0 (30 x 3) + 6 0 0 (20 x 30) 759 1 T 2 x 3 6 +6 9 75 1 U 3 3 9 (23 x 3) 0 (23 x 30) 9