Multiplication Written Methods Written Methods Throughout their years

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’. 2 x 5 +2 0 +2 +2 2 4 6 8 10 1 x 2 0 2 x 2 2 4 3 x 2 4 x 2 6 8 10 5 x 2

Partitioning Method • Partitioning method splits two digit numbers into Tens and Units before multiplying. This is in preparation formal short method. 2 1 0 x 2= 30 3 x 2= 6 30 + 6 = 36 8 1 0 x 8= 80 3 x 8= 24 80 + 24 = 104 13 x 2 10 + 3 13 x 8 10 + 3

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 42 x 5= +

Your Turn! • Can you use the column method to solve these multiplications? • 37 x 4= • 28 x 3= • 256 x 3=

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 30 3 20 60 x 3 90 9

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 TU 23 x 33 6 9 (23 x 3) + 6 9 0 (23 x 30) 759 1