Create your own growing geometric pattern. Draw it up to Stage 4 and describe how it grows. Complete a table showing stage number and number of shapes.

Here is the solution to Question 3:

3.1 Create your own growing geometric pattern. Draw it up to Stage 4.

• Stage 1: A single square. $$\boxed{\text{ } }$$
• Stage 2: A $2 \times 2$ arrangement of squares (total 4 squares). $$\boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } }$$
• Stage 3: A $3 \times 3$ arrangement of squares (total 9 squares). $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$
• Stage 4: A $4 \times 4$ arrangement of squares (total 16 squares). $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$ $$\boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } } \boxed{\text{ } }$$

3.2 Describe how your pattern grows.

The pattern grows by forming a larger square at each stage. The side length of the square increases by one unit at each subsequent stage. For example, Stage 1 is a $1 \times 1$ square, Stage 2 is a $2 \times 2$ square, and so on.

3.3 Complete a table showing Stage number and number of shapes.

Stage Number (n)	Number of Shapes
1	1
2	4
3	9
4	16

3.4 Write a rule for your pattern in words.

The number of shapes at any given stage is the square of the stage number.