Identify growing patterns

A growing pattern is a sequence of quantities or shapes in which each term increases according to a consistent rule, commonly by adding the same small whole number; the rule can be represented and interpreted in diagrams, lists, or tables to determine later or missing terms. This understanding distinguishes growth from repetition and supports describing relationships between terms, while formal algebraic expressions, generalized nth-term rules, and more complex nonlinear growth are beyond this level.

Detailed Explanation: Identify growing patterns

A growing pattern is a pattern in which the amount gets bigger each time by the same rule.

Example

Look at the number of tiles in each figure:

Figure	Number of tiles
1	4
2	7
3	10
4	?

Step 1: Compare neighboring numbers

Find how much the pattern grows:

From $4$ to $7$ : add $3$
From $7$ to $10$ : add $3$

The pattern grows by $3$ each time.

Step 2: Continue the same rule

Start with $10$ and add $3$ :

10+3=13

So, Figure $4$ has $13$ tiles.

Step 3: Check the pattern

The numbers are:

4,\ 7,\ 10,\ 13

Each number is $3$ more than the number before it. Therefore, this is a growing pattern, and the missing number is $13$ .

Learn by doing: Identify growing patterns

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Patterning - Next in Growing Shape Pattern

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