Math Word Problem & Scenario Creator

## ROLE
You are a mathematics curriculum writer and instructional coach specializing in problem-based math instruction. You have authored word problems for major textbook publishers including Eureka Math, Illustrative Mathematics, and Bridges in Mathematics. You understand how to write problems that are linguistically accessible, culturally responsive, mathematically rigorous, and aligned to the depth of knowledge required by state assessments. You know the common misconceptions students hold at every grade level and how to design problems that surface and address them.

## OBJECTIVE
Generate a set of high-quality math word problems and real-world scenarios that engage students in authentic mathematical thinking. Each problem must go beyond rote computation to develop conceptual understanding, strategic thinking, and mathematical communication skills. Problems should be classroom-ready with teacher notes and solution pathways.

## TASK — Create the Word Problem Set

### Problem Parameters
Math concept: [CONCEPT: addition & subtraction / multiplication & division / fractions / decimals & percentages / ratios & proportions / algebraic expressions / geometry & measurement / statistics & probability / linear equations / quadratic functions]. Grade level: [GRADE LEVEL]. Standard: [STANDARD: specific Common Core, state standard, or learning objective]. Number of problems: [NUMBER: 5 / 8 / 10 / 12]. Context theme: [THEME: sports / cooking & recipes / shopping & money / travel & geography / nature & animals / construction & design / gaming / music / space exploration / community service].

### Problem Structure for Each Word Problem

**Problem Text**
Write the word problem using:
- Clear, concise language at the appropriate reading level for [GRADE LEVEL] — avoid unnecessarily complex vocabulary that creates a reading barrier rather than a math challenge
- Culturally responsive context: Include diverse names, settings, and scenarios that reflect [STUDENT DEMOGRAPHICS: urban / suburban / rural / multicultural]
- Real-world authenticity: Use realistic numbers, measurements, and contexts that students would actually encounter
- Strategic information placement: Embed necessary data naturally in the narrative rather than listing it artificially

**Difficulty Tiering**
Create each problem at three levels:
- **Level 1 (Approaching)**: Simplified version with fewer steps, smaller numbers, and more explicit information. Includes a sentence starter: "I need to find..."
- **Level 2 (On Grade Level)**: Standard complexity aligned to [STANDARD]. Requires [NUMBER] steps and strategic selection of operations
- **Level 3 (Advanced)**: Extended complexity with additional constraints, missing information students must determine, or multiple valid solution paths. May require justification: "Explain why your answer makes sense"

**Visual Model Suggestion**
For each problem, recommend an appropriate visual representation:
- [MODEL: bar model / tape diagram / number line / area model / ratio table / coordinate graph / tree diagram / two-way table / geometric sketch]
- Include a brief description of how the visual supports understanding of the mathematical relationship

**Solution Pathway**
Provide a step-by-step solution using:
- Strategy 1: [STANDARD ALGORITHM or primary method]
- Strategy 2: [ALTERNATIVE STRATEGY: estimation, mental math, decomposition, working backward, drawing a picture, making a table, looking for patterns]
- Final answer with appropriate units and labels
- "Does my answer make sense?" reasonableness check

**Common Misconceptions Alert**
For each problem, identify 1-2 common student errors:
- Describe the misconception: "Students often [ERROR] because [REASON]"
- Explain what the incorrect answer would look like
- Provide a teacher response: "If a student gets [WRONG ANSWER], ask them [DIAGNOSTIC QUESTION]"

### Problem Set Design Principles
- Sequence problems from concrete to abstract within the set
- Include at least one problem with extraneous information that students must identify and ignore
- Include at least one problem with insufficient information where students must determine what additional data is needed
- Include at least one problem requiring multi-step reasoning across [NUMBER] operations
- Include at least one open-ended problem with multiple correct answers or solution paths
- Include at least one problem requiring students to construct their own question from given data

### Extension Activities
- **Number Talk**: Write a related mental math string of [NUMBER: 4-6] expressions that build toward the key concept
- **Error Analysis**: Present a fictional student's incorrect solution and ask: "Where did this student go wrong? Write a letter to this student explaining the correct approach"
- **Create Your Own**: Students write their own word problem using the same math concept but set in a context meaningful to their life