3. Higher Order Thinking Write an addition and subtraction problem and equation for the diagram. Then find the missing value.

Certainly! Let's work through an example to demonstrate higher-order thinking by creating addition and subtraction problems based on a diagram, writing corresponding equations, and finding the missing value. --- ### **Example Diagram Scenario** **Imagine a classroom setting with the following elements:** - **Total Number of Students:** 25 - **Students Playing Soccer:** 12 - **Students Playing Basketball:** 8 - **Students Playing Both Soccer and Basketball:** 5 - **Students Not Playing Any Sports:** ? *(Since we don't have an actual diagram, this scenario serves as our visual representation.)* --- ### **Step 1: Understand the Scenario** 1. **Total Students (T):** 25 2. **Soccer Players (S):** 12 3. **Basketball Players (B):** 8 4. **Players of Both Sports (S ∩ B):** 5 5. **Students Not Playing Any Sports (N):** ? --- ### **Step 2: Formulate Addition and Subtraction Problems** **a. Addition Problem:** *Determine the total number of students involved in at least one sport.* - **Explanation:** Some students play both sports, so simply adding soccer and basketball players would double-count those who play both. - **Problem Statement:** "The number of students playing soccer plus the number playing basketball minus those playing both equals the total number of students playing at least one sport." - **Equation:** \[ S + B - (S \cap B) = \text{Students Playing at Least One Sport} \] \[ 12 + 8 - 5 = 15 \] **b. Subtraction Problem:** *Find the number of students not participating in any sports.* - **Explanation:** Subtract the number of students playing at least one sport from the total number of students. - **Problem Statement:** "The total number of students minus those participating in at least one sport equals the number not playing any sports." - **Equation:** \[ T - (\text{Students Playing at Least One Sport}) = N \] \[ 25 - 15 = 10 \] --- ### **Step 3: Solve for the Missing Value** Using the equations above: 1. **Addition Equation:** \[ 12 + 8 - 5 = 15 \] So, **15 students** are involved in at least one sport. 2. **Subtraction Equation:** \[ 25 - 15 = 10 \] Therefore, **10 students** are not playing any sports. --- ### **Summary of Findings** - **Addition Problem:** \(12 \text{ (Soccer)} + 8 \text{ (Basketball)} - 5 \text{ (Both)} = 15\) *15 students are playing at least one sport.* - **Subtraction Problem:** \(25 \text{ (Total Students)} - 15 \text{ (At Least One Sport)} = 10\) *10 students are not participating in any sports.* --- This approach demonstrates higher-order thinking by requiring the integration of multiple pieces of information, understanding overlaps (like students participating in both sports), and applying both addition and subtraction to solve for missing values.