Algebra Word Problems

Word problems are algebra's purpose. 'A train leaves Chicago...' becomes 60t = d. The original question is the control — does the answer make sense? Indirect aim: applied mathematics, preparation for physics, problem-solving.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 10-12

Objectives

• Translate word problems to algebraic equations
• Solve and interpret
• Handle age, mixture, and rate problems
• Verify answers in original context

Materials

• Word problem collection
• Problem-solving template
• Calculator
• Solution journal

Instructions

1. Age problem: 'John is 3x Mary's age. In 10 years, John will be twice Mary. How old now?' Let Mary = x. John = 3x. In 10: 3x+10 = 2(x+10). Solve: x=10. Mary=10, John=30. Check: in 10 years, 40 = 2×20 ✓. 2. Mixture: '10L of 20% salt + xL of 50% salt to get 30%. Find x.' 0.2×10 + 0.5x = 0.3(10+x). Solve: x=5. 3. Rate: 'Two trains ...'. 4. Practice varied types. 5. Always verify in original context. 6. File solutions.

Educator tip

Setup is harder than solving. Spend time translating words to symbols.

Assessment

Observe correct translation, solution, and verification.

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