The question asks to describe four common meanings of $\frac{1}{3}$, using specific fraction models. Based on the images provided, we are tasked to illustrate these meanings through four models:

1. Part of a Whole

• Explanation: This interpretation means dividing a whole object or quantity into equal parts and considering one of these parts. In the case of $\frac{1}{3}$, it represents one out of three equal parts of a whole.
• Drawing: Imagine a circle (or another object like a rectangle) divided into three equal sections. One of the three parts would represent $\frac{1}{3}$.
• How it works for $\frac{1}{3}$: If you have a pizza and you divide it into 3 equal slices, $\frac{1}{3}$ is one slice.

2. Point on a Number Line

• Explanation: Fractions can be shown as points on a number line between whole numbers. For $\frac{1}{3}$, it lies between 0 and 1.
• Drawing: Draw a number line from 0 to 1, and divide the distance into three equal parts. The point one part away from 0 is $\frac{1}{3}$.
• How it works for $\frac{1}{3}$: If we divide the segment between 0 and 1 into three equal sections, $\frac{1}{3}$ would be the first marker after 0.

3. Division

• Explanation: Fractions represent division. $\frac{1}{3}$ means 1 divided by 3.
• Drawing: To illustrate, consider three equal groups or sections.
• How it works for $\frac{1}{3}$: If you take 1 object and split it into 3 parts, each part represents $\frac{1}{3}$ of the object.

4. Part of a Group

• Explanation: Fractions also represent part of a set or group. $\frac{1}{3}$ would mean 1 out of 3 elements from a group.
• Drawing: Imagine a set of 3 objects (like 3 apples), and one apple is selected to represent $\frac{1}{3}$.
• How it works for $\frac{1}{3}$: If there are 3 apples and you choose 1, you have taken $\frac{1}{3}$ of the group.

Do you need more details or illustrations for these concepts?

Here are 5 relative questions to explore:

1. How would $\frac{2}{3}$ be represented on a number line?
2. Can you describe how $\frac{1}{4}$ differs from $\frac{1}{3}$ in terms of part of a group?
3. How would you divide a square to show $\frac{1}{3}$ of it?
4. How does understanding $\frac{1}{3}$ as division help in real-life scenarios?
5. What is another way to visualize fractions like $\frac{2}{3}$ beyond the four common models?

Tip: Fractions are not just part of a whole, but they also describe relationships between quantities, such as ratios and rates!