1. The problem asks: How many rectangles of all sizes are there in a 3x3 grid of squares? Remember, squares are also rectangles. 2. To find the total number of rectangles in a grid, use the formula: $$\text{Number of rectangles} = \frac{m(m+1)}{2} \times \frac{n(n+1)}{2}$$ where $m$ is the number of rows and $n$ is the number of columns. 3. For a 3x3 grid, $m=3$ and $n=3$. 4. Calculate the number of horizontal line pairs: $$\frac{3 \times (3+1)}{2} = \frac{3 \times 4}{2} = 6$$ 5. Calculate the number of vertical line pairs: $$\frac{3 \times (3+1)}{2} = 6$$ 6. Multiply these to get the total number of rectangles: $$6 \times 6 = 36$$ 7. Therefore, there are 36 rectangles of all sizes in the 3x3 grid. Final answer: **36 rectangles**.