Word Problems Solved - A Parent and Teacher Guide to Mathematical Reasoning

“I can do the maths, but I don’t understand word problems!” Many students can compute perfectly but freeze when faced with written problems. Word problems aren’t just maths—they’re reading, reasoning, and mathematics combined. Here’s how to help students master this essential skill.

Why Word Problems Are Hard

Multiple Skills Required:

• Reading comprehension
• Identifying relevant information
• Choosing appropriate operations
• Mathematical computation
• Checking if the answer makes sense

Weak in any area? The whole problem becomes difficult.

Language Complexity:

• Ambiguous phrases (“how many more” could mean add or subtract)
• Extra information that’s not needed
• Missing information assumed from context
• Technical vocabulary
• Multi-step reasoning required

The Four-Step Problem-Solving Framework

Teach this systematic approach for every word problem:

Step 1: Understand the Problem

Actions:

• Read twice, slowly
• Highlight or underline the question
• Identify what you need to find
• Restate in your own words

Questions to ask:

• What is the problem asking for?
• What information do I have?
• What information do I need?

Red flags:

• Can’t explain what the problem asks
• Doesn’t know where to start
• Mixing up information

Step 2: Make a Plan

Actions:

• Decide what operation(s) to use
• Think about a strategy
• Draw a picture or diagram
• Estimate a reasonable answer

Questions to ask:

• What strategy might work?
• Have I solved similar problems?
• Does a picture help?
• About how big should the answer be?

Red flags:

• Randomly choosing operations
• No strategy, just “trying stuff”
• Unrealistic estimates

Step 3: Carry Out the Plan

Actions:

• Do the calculations carefully
• Show your working
• Keep track of multi-step work
• Stay organized

Questions to ask:

• Am I answering the right question?
• Did I do the calculations correctly?
• Do I need more steps?

Red flags:

• Calculation errors
• Answering wrong question
• Losing track in multi-step problems

Step 4: Check and Reflect

Actions:

• Does the answer make sense?
• Check calculations
• Use opposite operation to verify
• Answer with appropriate units and labels

Questions to ask:

• Is this reasonable?
• Did I answer what was asked?
• Can I explain my solution?

Red flags:

• Clearly unreasonable answers (negative ages, huge prices)
• No checking performed
• Can’t explain reasoning

Key Words Strategy (Use with Caution!)

Traditional keyword lists (“altogether” = add, “difference” = subtract) can help, but don’t over-rely on them. Context matters more than single words.

Problems with keywords:

• “How many more” can mean add or subtract depending on context
• Keywords can trick students (“more” in “3 more than 5 times a number” needs multiplication AND addition)
• Students stop thinking, just look for keywords

Better approach: Understand the situation, then choose operations logically.

Problem Types and Strategies

Join/Part-Whole Problems

Example: “Emma had 12 stickers. Her friend gave her 8 more. How many does she have now?”

Strategy: Picture or act it out. Start with 12, add 8. Total is what we need.

Operation: Addition (joining groups)

Separate/Take Away Problems

Example: “A shop had 45 apples. They sold 17. How many are left?”

Strategy: Picture or act it out. Start with 45, remove 17.

Operation: Subtraction (taking away)

Compare Problems

Example: “Tom has 23 cards. Sarah has 35 cards. How many more does Sarah have?”

Strategy: Draw both amounts, see the difference.

Operation: Subtraction (comparing)

Tricky bit: “How many more” sounds like addition but needs subtraction!

Equal Groups Problems

Example: “4 friends share 20 chocolates equally. How many does each get?”

Strategy: Draw groups, distribute evenly.

Operation: Division (sharing)

Array/Area Problems

Example: “A garden is 6 metres long and 4 metres wide. What’s the area?”

Strategy: Draw rectangle, think of rows and columns.

Operation: Multiplication (repeated addition in rows)

Multi-Step Problems

Example: “Books cost $8 each. Jane buys 3 and pays with$50. How much change?”

Strategy: Break into steps.

• Step 1: Total cost = 3 × $8 =$24
• Step 2: Change = $50 -$24 = $26

Multiple operations needed: Identify each step clearly.

Visualization Strategies

1. Draw a Picture: Simple sketch of the situation helps understanding.

2. Use a Diagram:

• Bar models (comparison bars)
• Tape diagrams (for ratios)
• Number lines (for operations)

3. Act It Out: Use objects to physically model the problem.

4. Make a Table or Chart: Organize information systematically.

Scaffolding for Struggling Students

Simplify the Language:

• Rewrite with simpler words
• Break long sentences into shorter ones
• Remove unnecessary information first

Provide Sentence Starters:

• “I need to find…”
• “The important information is…”
• “I will use ___ because…”

Use Manipulatives: Counters, blocks, or drawings make abstract concrete.

Practice Problem Types Separately: Master join problems before moving to compare problems.

Building Problem-Solving Confidence

1. Start with Simpler Numbers: Same problem structure, easier computation. “Sarah had 147 cards” becomes “Sarah had 10 cards”

2. Remove Extraneous Information: Give core problem first, add complexity later.

3. Provide the Question: Start with “How many are left?” then build to finding questions themselves.

4. Co-construct Solutions: Think aloud together: “Let’s see, what is this asking…”

5. Celebrate Process Over Answer: “Great strategy using a picture!” matters more than correct answer.

Common Mistakes and Fixes

Mistake: Using all numbers in random operations Fix: Identify what the question asks before choosing operations

Mistake: Not reading carefully Fix: Always read twice, underline key information

Mistake: Giving up immediately Fix: “What’s ONE thing you know about this problem?”

Mistake: Unrealistic answers (negative people, $1,000 for milk) Fix: ALWAYS estimate first: “About how much should this be?”

Creating Your Own Word Problems

Writing problems helps understanding! Have students:

• Write problems for given numbers (8, 3, 24)
• Create problems matching operations (write a subtraction problem)
• Make problems from real situations (class attendance, lunch orders)

This reverses thinking and deepens comprehension.

Assessment Beyond Correctness

Look for:

• Clear problem-solving process
• Appropriate strategy selection
• Logical reasoning
• Ability to explain thinking

Don’t only assess:

• Final answer correctness
• Speed
• Following one specific method

Practice Sources

Real Life: Shopping, cooking, sports scores, travel planning

Games: Logic puzzles, strategy games

Daily Situations: “If we leave at 3:00 and it takes 45 minutes…”

Quality Worksheets: Progressively challenging, varied problem types

The Bottom Line

Word problem success comes from systematic strategies, visualization skills, and lots of practice. Don’t rush. Build confidence through gradual challenge increase. When students approach problems methodically and check their thinking, they become powerful problem-solvers—a skill valuable far beyond mathematics.