These resources have been reviewed and selected by STEM Learning’s team of education specialists for factual accuracy and relevance to teaching STEM subjects in UK schools.

Patterns and Generalisations

This SMILE resource contains four packs of games, investigations, worksheets and practical activities supporting the teaching and learning of patterns and generalisations, from finding number patterns on a hundred-square grid to exploring converging sequences.

Patterns and generalisations pack one contains nine work cards with a wide variety of activities covering finding number patterns on a hundred-square grid, doubling patterns, number patterns in geometry, and patterns in the nine times table.

Patterns and generalisations pack two contains eight work cards with activities requiring students to investigate number patterns formed by cutting string, explore repeating number patterns on a calculator, investigate number patterns on the mystic rose, and spotting number patterns when organising a tournament.

Patterns and generalisations pack three contains six work cards with activities in which students investigate the page numbers in a newspaper, look at patterns formed on a billiard table, explore patterns on a Chinese triangle, and look at patterns in Pascal’s triangle resulting in a Fibonacci sequence.

Patterns and generalisations pack four contains eight work cards with activities covering patterns on Shongo networks, the Queen’s moves on a chess board, forming sequences from diagrams, using number patterns in proof, geometric progressions, and converging sequences.

SMILE (Secondary Mathematics Individualised Learning Experiment) was initially developed as a series of practical activities for secondary school students by practising teachers in the 1970s. It became a complete individualised scheme based around a network of activity cards and assessments.

Related resources include answers to all of the cards and test books and answers.

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