Patterns, squares and roots N1.4 Core Plenary This is the sequence of triangular numbers. 1 3 6 10 15 … Find a number which is both a triangular number and a square number. These numbers are part of the sequence of triangular numbers. Work out what numbers are represented by a .  300 325  378 Preamble This activity practises finding triangular and square numbers. It is pupils’ explanations and strategies which are important, rather than just finding the correct answer. Pupils will find both problems more difficult if they fail to work systematically. In the second sequence, pupils may need reminding to check their pattern using the final term. A further check is that the sums of consecutive terms form a sequence of square numbers. Possible content Recognition of triangular and square numbers, generating triangular sequences. Resources None. Solutions/Notes Numbers which are both triangular and square include 1, 36, 1225 (thereafter they become quite large). Many pupils may forget about 1. In the second pattern, calculating 325 – 300 = 25 gives the rule to find the previous term (subtract 24) and the next term (add 26). 276 300 325 351 378