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**Related topic**

recognise and use rules that generate visually growing patterns and number patterns involving rational numbers (AC9M6A01)

- investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern; looking for patterns in the way the numbers increase/decrease
- using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, \(1 ÷ 9, 2 ÷ 9, 3 ÷ 9\)…, \(210 \times 11, 211 \times 11, 212 \times 11\)…, \(111 \times 11, 222 \times 11, 333 \times 11\)…, or \(100 ÷ 99, 101 ÷ 99, 102 ÷ 99\)…
- creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their \(\$2.50\) for an incursion as \(2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50\) …
- investigating the number of regions created by successive folds of a sheet of paper: one fold, \(2\) regions; \(2\) folds, \(4\) regions; \(3\) folds, \(8\) regions, and describing the pattern using everyday language
- creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using \(3\) for one triangle, \(5\) for \(2\) triangles, \(7\) for \(3\) triangles and describing the pattern as, “Multiply the number of triangles by \(2\) and then add one for the extra toothpick in the first triangle”

Mathematical expressions, Sequences (Number patterns), Rational numbers