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P1 Growing patterns and tables

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

Mrs Tan is setting out chairs in rows for a wedding dinner.

Mrs Tan is setting out chairs in rows for a wedding dinner. Row 1 has 6 chairs, Row 2 has 10 chairs, and Row 3 has 14 chairs. How many chairs will be in Row 5?

One step of the worked solution to Mrs Tan is setting out chairs in rows for a wedding dinner., drawn in pencil.
6 steps, drawn in pencil

See all 6 steps

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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. When the same amount is added from each row to the next, you reach a later row by adding that step again and again to a row you already know — the table does the work, so there is no need to draw the chairs.

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.