4)) Which diagram represents the equation \( 10+f=17 \) ?

To represent the equation \( 10 + f = 17 \) with a diagram, you can use a **bar model** (also known as a **part-whole diagram**). Here's how you can visualize it: ### Bar Model Representation 1. **Whole Bar:** Start with a single long bar that represents the total value, which is **17** in this case. 2. **Part Bars:** Divide this bar into two parts: - **First Part:** A smaller section labeled **10**. - **Second Part:** Another smaller section labeled **\( f \)** (the unknown). 3. **Visual Layout:** ``` |-----------|--------| 10 f ``` - **Full Length:** Represents **17**. - **Left Section:** Represents **10**. - **Right Section:** Represents **\( f \)**. ### Explanation - **Whole (17):** The entire length of the bar shows the total value of 17. - **Parts (10 and \( f \)):** The bar is split into two parts where one part is known (10) and the other part is unknown (\( f \)). - **Equation Relationship:** This visual division directly corresponds to the equation \( 10 + f = 17 \), showing that the sum of the two parts equals the whole. ### Solving for \( f \) Using the diagram: \[ 10 + f = 17 \] Subtract 10 from both sides to solve for \( f \): \[ f = 17 - 10 \] \[ f = 7 \] ### Final Diagram with Values ``` |-----------|--------| 10 7 ``` This final diagram shows that \( f = 7 \), completing the equation \( 10 + 7 = 17 \). ### Alternative Diagram Types If you're using other types of diagrams, such as **number lines** or **objects (like blocks or icons)**, the same principles apply: - **Number Line:** Mark points at 10 and 17, showing the distance between them as \( f = 7 \). - **Objects:** Use 10 objects in one group, 7 in another, totaling 17 objects. These visual representations help in understanding the relationship between the known and unknown quantities in the equation.