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Enrichment in Mathematics – Number Digit Sum Teachers Notes This could be used as a starter, plenary or homework. Although pupils could find an answer from laborious use of a calculator, teachers should encourage pupils to look for ‘short cuts’ by thinking of number pairs (combinations to make 100 or 10) The task is made easier by using the techniques for the number sum so this could be omitted to make the task harder. Solution Sum of numbers: Pair the numbers to make 100, e.g. 1 with 99, 2 with 98, etc. Hence 49 with 51, leaving both 50 and 100 unpaired. Total is therefore (49 × 100) + 100 + 50 Total = 5050 Sum of digits: Firstly check how many times the digit 1 is used 1 11 21 31 41 51 61 71 81 91 there are 10 1’s in the ‘units column’ 10 11 12 13 14 15 16 17 18 19 there are 10 1’s in the ‘tens column’ So each digit will be used 20 times either in the units or tens Total = 20 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 1 (which is the 1 used in 100) Total = (20 × 45) + 1 Total = 901 Worcestershire Numeracy Team Enrichment Activities Enrichment in Mathematics – Number Digit Sum Think of all the digits that make the sequence: 1, 2, 3, 4, 5, 6, 7, ………………………………99, 100 What is the sum of these numbers? (easy!) What is the sum of the digits? Worcestershire Numeracy Team Enrichment Activities