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P3 Growing patterns and tables

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

Farmer Aziz puts fence posts around square flower beds.

Farmer Aziz puts fence posts around square flower beds. Bed 1 uses 5 posts, Bed 2 uses 8 posts, and Bed 3 uses 11 posts. How many posts will Bed 6 need?

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Bed 6 needs 20 posts.

One step of the worked solution to Farmer Aziz puts fence posts around square flower beds., drawn in pencil.
6 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 same amount is added each time, the table is the method — keep adding the step, bed by bed, instead of trying to draw the sixth figure.

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 Continue this number pattern: 3000, 3500, 4000, __. What is the next number?
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.