Teach-Primary-Issue-19.7

However, another thing can be drawn out. Consider how much smaller than 100 each of the products is: 10 × 10 = 100 11 × 9 = 99 (1 less) 12 × 8 = 96 (4 less) 13 × 7 = 91 (9 less) 14 × 6 = 84 (16 less) This reveals an amazing pattern: the products are decreasing in a pattern of square numbers! Does this work just for this example sequence? Or could it also be true for other sequences? Investigate… Area and perimeter One of the requirements from the Year 6 national curriculum is to ‘Recognise that shapes with the same areas can have different perimeters and vice versa’ . In this statement, we are asking children to explore the same mathematical idea as we explored above. For example, children can be asked to calculate the perimeter and area of these two rectangles ( Fig. 1 ): Whilst the rectangles have the same perimeter, they don’t have the same area. Rectangle B has side lengths that are closer together in value, therefore it has a larger area. Children can create their own example rectangles to test this theory further. The largest product There is another way in which we can explore the same big mathematical idea. Consider this task ( Fig. 2 ): To begin with, pupils can explore different possible combinations of multiplication calculations. Then, you can emphasise the first level of reasoning: to maximise the product, we must place our largest digits in the most significant columns. Put the digits 8 and 5 in the tens positions. Does it matter which way around we position the digits 4 and 0? Yes! The product is maximised when the numbers being multiplied are as close together as possible . 80 × 54 has a larger product than 84 × 50. Why is this? The picture below demonstrates ( Fig. 3 ): Both calculations include 80 × 50. For 84 × 50, we have 4 more lots of 50. For 80 × 54, we have 4 more lots of 80. This gives us a larger product. In exploring this big mathematical idea in any of these ways, children will be practising their calculation skills in multiplication. But they will get so much more from engaging in these tasks. They will have to spot patterns, test new ideas with their own questions and try different ways. Pupils will have a context in which to explain their thinking clearly, giving relevant examples and explaining what they have found. They will be stretched personally as well as mathematically, and it will enable them to experience what it means to be a true mathematician. TP Gareth Metcalfe is the director of I See Maths and the author of the Deconstructing Word Questions , I See Reasonin g and I See Problem-Solving eBooks. @gareth_metcalfe iseemaths.com I SeeMaths: GarethMetcalfe Position the digits 0, 4, 5 and 8 to make the product as large as possible. Fig. 2 x = 0 4 5 8 8 8 80 50 4 5 5 4 0 x x 0 4 80 50 4 Rectangle A 4cm 9cm Rectangle B 6cm 7cm Fig. 1 Fig. 3 www.teachwire.net | 51 MA THS S P E C I A L