Identify growing patterns

A growing pattern is understood as an ordered sequence of quantities or figures in which each term increases according to a consistent rule, such as adding the same number of objects, tiles, or units; the rule can be interpreted from visual arrangements, numbers, tables, or a number line. The learner describes the change from one term to the next, extends the pattern, and predicts nearby terms, without requiring formal algebraic notation or generalized nth-term formulas.

Detailed Explanation: Identify growing patterns

A growing pattern gets bigger by following the same rule each time. To identify the rule:

Look at two terms next to each other.
Find how much the pattern grows.
Check that the same amount is added each time.
Use the rule to find the next terms.

Example

A pattern shows the number of tiles in each figure:

Figure	1	2	3	4
Number of tiles	3	6	9	12

Step 1: Compare neighboring terms.

From Figure 1 to Figure 2:

6-3=3

From Figure 2 to Figure 3:

9-6=3

From Figure 3 to Figure 4:

12-9=3

Step 2: Describe the rule.

The number of tiles increases by $3$ each time. The rule is:

Add $3$ to find the next term.

Step 3: Extend the pattern.

Starting with $12$ tiles in Figure 4:

12+3=15

So Figure 5 has $15$ tiles.

Then:

15+3=18

So Figure 6 has $18$ tiles.

The extended pattern is:

3,\ 6,\ 9,\ 12,\ 15,\ 18

Always check that the same amount is added from one term to the next.

Learn by doing: Identify growing patterns

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Patterning - Next in Growing Shape Pattern

Earned ?