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P6 Growing patterns and tables

Pattern

Q17 — circles in a growing pattern

One step of the worked solution to Pattern, drawn in pencil.
9 steps, drawn in pencil

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The pattern behind it: Growing patterns and tables

Find the rule, so Figure 250 is no harder than Figure 4.

In this one. Neither colour follows a rule on its own because the colours take turns — add the two rows into one Total row, and the pattern appears at once: each new ring is 4 circles longer than the last.

The first threeeach one adds 3Figure 14Figure 2+3Figure 3+3Any figure3n + 1Figure nFigure 250 = 751

How to spot it

A row of figures or a table of numbers is shown for the first few terms only, and the question asks for a term far further along, such as 'Figure 6' or 'Figure 250'.

Common mistake

Children extend the sequence one term at a time by drawing or counting. Finding the fixed step or relationship lets them jump straight to the term asked for.

Try one like it

Challenging Grey and white triangles — Figure 250 Figure n is a triangle of small white and grey triangles. Given the counts for Figures 1–4, find (a) Figure 5's counts, (b) the to…
All 4 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

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