From the image you provided, we see a series of math pattern problems. Let's break down the patterns and how to create expressions for each:

1. Problem 10 (Circles):

   • The pattern shows an increasing number of circles in each step.
   • From left to right:
     • Step 1: 3 circles
     • Step 2: 6 circles
     • Step 3: 9 circles
   • The pattern increases by 3 circles at each step, suggesting an arithmetic progression. The general expression for the number of circles at step $n$ is: $3n$ This means that in the 7th step, there would be $3 \times 7 = 21$ circles.

2. Problem 11 (Squares):

   • The pattern shows squares arranged in a progressively increasing grid.
   • Step 1: 1 square
   • Step 2: 4 squares (2x2)
   • Step 3: 9 squares (3x3)
   • The number of squares follows a quadratic sequence where the number of squares in step $n$ is $n^2$. Therefore, the expression is: $n^2$ For the 7th figure, the number of squares would be $7^2 = 49$.

3. Problem 12 (Rectangular Tiles):

   • The pattern shows a grid of tiles increasing by one row and one column each time.
   • Step 1: $2 \times 2$ grid (4 tiles)
   • Step 2: $3 \times 3$ grid (9 tiles)
   • Step 3: $4 \times 4$ grid (16 tiles)
   • Again, this is a quadratic pattern. The number of tiles at step $n$ is $n^2$. Thus, the expression is: $n^2$ In the 7th step, the number of tiles is $7^2 = 49$.

4. Problem 13 (Linear Tiles):

   • The pattern shows increasing rows of horizontal tiles.
   • Step 1: 2 tiles
   • Step 2: 3 tiles
   • Step 3: 4 tiles
   • The pattern increases by 1 tile each step. The general expression is: $n + 1$ So for the 7th step, the number of tiles is $7 + 1 = 8$.

5. Problem 14 (Circle Clusters):

   • The pattern shows clusters of circles.
   • Step 1: 9 circles
   • Step 2: 16 circles
   • Step 3: 25 circles
   • This is a quadratic pattern where the number of circles in step $n$ is $n^2$. Thus, the expression is: $n^2$ In the 7th step, there would be $7^2 = 49$ circles.

Would you like any further details or clarifications on these patterns?

Here are 5 related questions for further practice:

1. How would the pattern change if the growth rate doubled?
2. What if you were given geometric sequences instead of arithmetic?
3. How would you modify these expressions for a 10th figure instead of a 7th?
4. Can you create a real-world scenario that fits one of these patterns?
5. How would the expressions change if the increase was non-linear (e.g., exponential growth)?

Tip: Always look for common differences or ratios to identify the type of sequence—whether arithmetic, geometric, or quadratic.