23 x 7 = ? The array method (grid method) There are 23 biscuits in a packet. How many biscuits An array can be created to represent 23 lots are there altogether in 7 packets? of 7 (or the inverse) and the two digit numbers partitioned (see the blue lines). 23 = 10 + 10 + 3 Here 23 has been partitioned into tens and ones. Each part is then multiplied by 7. The . . . . . . . . . . . . . . . . . . . . . . . subtotals are to give the total answer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . = 161 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Children can also partition the numbers . . . . . . . . . . . . . . . . . . . . . . . involved into other parts, depending on their personal strengths and preferences. 70 + 70 + 21 To be more efficient, boxes can be drawn to represent the parts of an array. When boxes are used these should be drawn proportionally. 72 x 38= The array method also works when A car is 72cm long. A train is 34 times longer. How multiplying bigger numbers. Again, long is the train? partition the numbers into a proportional grid and multiply each separate section. This needs a good understanding of place value 70 x 30 can be accessed using 7 x 3 – but misconceptions around x 10, x 100 will need to be attended to. This method can be extended for multiplying larger numbers such as 327 x 24. Partition the hundreds, tens and ones into a larger 3 x 3 grid. Top row 2100 + 60 = 2160 – Next row 560 + 16 = 576 – Total = 2736 This could be extended for those children who have a very secure understanding of place value and fluency in multiplication to use a more compact method.
23 x 7 = ? There are 23 biscuits in a packet. How many biscuits are there altogether in 7 packets? 23 = 10 + 10 + 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 + 70 + 21 The array method (grid method) An array can be created to represent 23 lots of 7 (or the inverse) and the two digit numbers partitioned (see the blue lines). Here 23 has been partitioned into tens and ones. Each part is then multiplied by 7. The subtotals are to give the total answer. = 161 Children can also partition the numbers involved into other parts, depending on their personal strengths and preferences. To be more efficient, boxes can be drawn to represent the parts of an array. When boxes are used these should be drawn proportionally. 72 x 38= A car is 72cm long. A train is 34 times longer. How long is the train? Top row – 2100 + 60 = 2160 Next row – 560 + 16 = 576 Total = 2736 The array method also works when multiplying bigger numbers. Again, partition the numbers into a proportional grid and multiply each separate section. This needs a good understanding of place value – 70 x 30 can be accessed using 7 x 3 but misconceptions around x 10, x 100 will need to be attended to. This method can be extended for multiplying larger numbers such as 327 x 24. Partition the hundreds, tens and ones into a larger 3 x 3 grid. This could be extended for those children who have a very secure understanding of place value and fluency in multiplication to use a more compact method.
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