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P1 Growing patterns and tables

Today’s problem — free all day, every step. Every day has one.

Dot pattern — Figure 6

A pattern is made up of dots. Figure 1 has 4 dots, Figure 2 has 7 dots and Figure 3 has 10 dots. How many dots will there be in Figure 6?

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19 dots.

✎  14 practice questions
One step of the worked solution to Dot pattern — Figure 6, drawn in pencil.
7 steps, drawn in pencil

The pattern behind it: Growing patterns and tables

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

In this one. When the step between terms is a constant, you never have to draw the figure — the figure number and the count sit one table apart, so extend the table by adding the step each time.

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

Standard continue a number sequence 20, 25, 30, __. What comes next?
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.

A PDF, and a note when new solutions go up.