A growing pattern is a sequence where each step is larger than the one before, following a consistent rule. Unlike repeating patterns (which cycle through the same unit), growing patterns build on themselves — each step adds new elements. A staircase that gains one block per step, an L-shape that extends by one tile on each arm, or a number sequence that increases by a fixed amount are all growing patterns. Analyzing how and why a pattern grows connects visual reasoning to numerical reasoning and lays the groundwork for understanding functions.
Build growing patterns with physical tiles or blocks so students can see each step. Use a table to record the step number and the count of tiles at each step. Ask: "How many tiles were added this step? Is it the same amount each time?" Have students predict the count at step 10 or step 20 using their rule. Draw the pattern on grid paper to make the growth visible. Compare growing patterns with different rates of growth (add 1 each time vs. add 3 each time).
You have been working with repeating patterns (circle-square-circle-square) and number patterns (3, 6, 9, 12). Now you are going to explore a special kind of pattern that does something different: it grows. Each step is bigger than the one before, and the way it grows follows a rule.
Imagine building a staircase out of blocks. Step 1 is just 1 block. Step 2 adds a column of 2 blocks next to it, making 3 blocks total. Step 3 adds a column of 3, making 6 total. You can see the staircase getting taller and wider — that is a growing pattern. The visual growth (the staircase shape getting bigger) connects to a number pattern (1, 3, 6, 10...) and a growth rule (each step adds one more block than the previous step added).
The simplest growing patterns add the same amount each step. If you build with square tiles and add 2 tiles at each step, you get: 2, 4, 6, 8, 10. The growth is constant — the pattern gets bigger by the same amount every time. But some growing patterns are more interesting: they add more and more each step. The staircase pattern adds 2, then 3, then 4, then 5. The growth itself is growing. These patterns produce numbers that increase faster and faster.
To analyze a growing pattern, make a table with two columns: the step number and the count. Then look at the differences between consecutive counts. If the differences are constant (always +3), you have a simple growing pattern. If the differences change in a regular way (increasing by 1 each time), you have a more complex pattern with its own rule. Either way, the table turns a visual pattern into a number pattern, making the rule easier to spot. This table-based analysis — looking at inputs, outputs, and the relationship between them — is exactly what you will do later with functions and equations.