Written methods Which four consecutive odd numbers sum to 120? [N4.1 Extension Plenary] Which four consecutive odd numbers sum to 120? Write down four pairs of 3-digit numbers whose sum is 901. Megan writes these six numbers on pieces of card. She picks two of the cards and writes down their product. Which pair of numbers gives: i) the largest product, ii) a 3-digit number ending in 7, iii) a number between 100 and 500 ending in 3, iv) a number less than 1000 ending in 1? 4) Put in the decimal points to turn this grid into a magic square. Preamble A set of four numerical puzzles/investigations for pupils to work through individually or in pairs, but with a greater group discussion towards the end to share ideas. For example (1) may be solved by “brute force” but division by 4 which gives 30, suggests that the numbers are close to 30 etc. Although (2) seems very easy pupils do need to think and use non-calculator methods. Possible content Calculations (integer and decimals) without the aid of a calculator, informal trial and improvement. Resources None. Solution/Notes 27 + 29 + 31 + 33 = 120 Pupils own answers. i) 61  48 = 2928 ii) 11 and 17 4) iii) 17  29 = 493 iv) 61  11 = 671 Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010