Question

pick the model that represents this division equation.
2 ÷ 3 1/3 = ?
hint: use a related multiplication equation.

Explanation:

Step1: Convert mixed number to fraction

$3\frac{1}{3} = \frac{3\times3 + 1}{3} = \frac{10}{3}$

Step2: Rewrite division as multiplication

$2 \div \frac{10}{3} = 2 \times \frac{3}{10} = \frac{6}{10} = \frac{3}{5}$

Step3: Analyze the models

The first model asks: what portion of 2 is equal to 3 full 3-block units? No, this does not match.
The second model asks: how much total is there when 2 is the size of 3 full 3-block units? No, instead, interpret the division as: how many groups of $3\frac{1}{3}$ fit into 2? Wait, correct model: the first model has the total labeled as 2, and the question is the first 3 full blocks (3 units). Wait no, re-express the division as: we want to find how many times $3\frac{1}{3}$ goes into 2, or equivalently, what is $x$ where $x \times 3\frac{1}{3} = 2$. So $x = \frac{3}{5}$, meaning the first model: the total length is 2, and the question is the length of 3 full 3-block sections? No, wait the first model: the entire bar is 2, and the question mark is 3 full 3-unit blocks. The value of 3 full 3-unit blocks is 3, which is more than 2, no. Wait the second model: the first 2 full 3-unit blocks are labeled 2, so each 3-unit block is 1. Then $3\frac{1}{3}$ is a 3-unit block plus 1 unit, so the total question mark is $3\frac{1}{3}$, but we are doing $2 \div 3\frac{1}{3}$. Wait no, correct model: the first model represents "what is $x$ such that $x$ is the part of 2 that equals $3\frac{1}{3}$? No, wait let's calculate the value of each small block. In the first model, total length 2 is equal to 3 full 3-block sets plus 1 block, so total blocks: $3\times3 +1=10$ blocks. So each block is $\frac{2}{10}=\frac{1}{5}$. Then the question mark is 3 blocks, which is $3\times\frac{1}{5}=\frac{3}{5}$, which is our answer. That matches $2 \div 3\frac{1}{3}=\frac{3}{5}$. The first model's question mark is 3 blocks, which equals $\frac{3}{5}$, which is the result.

Answer:

The correct model is the top (unboxed) one, where the total length is labeled 2, and the question mark covers the first 3 full 3-block groups.