Multi-Step Word Problems

Grade 5 Math – Strategy, Notes & Formulae

From Words to Expressions

• Identify keywords: add (total), subtract (left), multiply (times/fold), divide (each/group)
• Write an expression (no equals sign) that matches the problem.
• Example: "Three times the sum of 6 and 7" → \(3 \times (6+7)\)
• "15 divided by the difference of 8 and 3" → \(15 \div (8-3)\)

Solve Multi-Step Problems with Expressions

• Use order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (L→R), Addition/Subtraction (L→R)
• For each step, solve inside parentheses first, then follow operations.
• Example: "Twice as many apples as oranges, with 4 oranges and 10 more apples":
  \(2 \times 4 + 10 = 8 + 10 = 18\) apples.

Use Equations with Unknowns

• Let a letter (n, x, y) stand for the unknown.
• Write an equation for the problem, then solve for the variable.
• Example: "n + 12 = 27"
  \(n = 27 - 12 = 15\)
• "Three times a number plus 5 is 20." → \(3x + 5 = 20 \implies 3x = 15 \implies x = 5\)

Check Reasonableness & Remainders

• Estimate each step before exact calculation to check if answers make sense.
• Handling remainders: When dividing, consider the context:
  • Drop remainder (if you need groups completely filled)
  • Round up (if everyone gets something, e.g., buses, boxes)
  • Leave as a fraction/decimal (if problem allows)
• Example: "27 cookies shared among 4 kids": \(27 \div 4 = 6\) R3, each kid gets 6 cookies, 3 left over.

Multiplicative Comparison

• Word clues: "times as many", "twice", "three times", etc.
• Example: "Sally has 4 times as many marbles as Tom. Tom has 7":
  \(4 \times 7 = 28\) marbles

Quick Problem-Solving Checklist

1. Read every part carefully
2. Underline/identify key info and numbers
3. Determine what to find (unknown/variable)
4. Translate into expressions/equation(s)
5. Solve step by step using order of operations
6. Write a sentence answer, check units
7. Estimate for reasonableness (does answer make sense?)