1. **Stating the problem:** We are asked to group algebraic expressions with their corresponding model cards representing variables and expressions. 2. **Understanding the models and expressions:** - A 3x3 grid of squares labeled $n$ represents $n$ multiplied by itself 9 times, or $n \times n \times n \times n \times n \times n \times n \times n \times n$, but more simply, it is a square of side $3n$, so the area is $(3n)^2$. - A vertical rectangle composed of two stacked squares labeled $n$ and $2$ with the expression $n + n + n$ beside it represents adding $n$ three times, which is $3n$. - A small rectangle divided into two parts horizontally labeled $n$ and $3$, with $2$ above it on the left, represents $2(n + 3)$. - A vertical rectangle labeled $n 6$ likely represents $n + 6$. - A sequence of three small squares labeled $n n n$ represents $n + n + n = 3n$. 3. **Matching expressions to models:** - The 3x3 grid of $n$ squares corresponds to the expression $(3n)^2$ because the side length is $3n$ and area is side squared. - The vertical rectangle with two stacked squares labeled $n$ and $2$ corresponds to $n + n + n = 3n$. - The small rectangle with $n$ and $3$ horizontally and $2$ above corresponds to $2(n + 3)$. - The vertical rectangle labeled $n 6$ corresponds to $n + 6$. - The sequence of three $n$ squares corresponds to $3n$. 4. **Summary of groupings:** - $(3n)^2$ matches the 3x3 grid of $n$ squares. - $3n$ matches the vertical rectangle with stacked $n$ and $2$, and also the sequence of three $n$ squares. - $2(n + 3)$ matches the small rectangle with $n$ and $3$ horizontally and $2$ above. - $n + 6$ matches the vertical rectangle labeled $n 6$. 5. **Additional expressions:** - $2n$ and $2n + 6$ are expressions that can be related to doubling $n$ and adding 6, but no direct model is described for these. - $n^2$ corresponds to a square of side $n$, but no such model is explicitly described. - $n + 3$ is a simple sum, possibly related to the small rectangle parts. **Final answer:** - Models with expressions: - 3x3 grid of $n$ squares: $(3n)^2$ - Vertical rectangle with stacked $n$ and $2$: $3n$ - Sequence of three $n$ squares: $3n$ - Small rectangle with $n$ and $3$ horizontally and $2$ above: $2(n + 3)$ - Vertical rectangle labeled $n 6$: $n + 6$