Solved Exercises on Worked Solution Strategy in Grade 4

Master worked solution strategy: problem-solving methods, step-by-step approaches, and systematic techniques through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Multi-Step Problem
Exercise 1
Sarah has 24 stickers. She gives 8 to her friend and then buys 15 more stickers. How many stickers does she have now? Show your worked solution strategy.
Definition:

Worked Solution Strategy: A systematic approach to solving problems by breaking them into clear, sequential steps with explanations.

Worked Solution Method:
  1. Read the problem carefully and identify what is being asked
  2. Identify the given information
  3. Break the problem into smaller steps
  4. Solve each step sequentially
  5. Check your work and state the final answer
Initial Stickers
24
Gives Away
-8
Buys More
+15
Final Count
24 - 8 + 15 = 31
Step 1: Identify the initial amount

Sarah starts with 24 stickers

Step 2: Calculate after giving away

24 - 8 = 16 stickers remaining

Step 3: Calculate after buying more

16 + 15 = 31 stickers

Step 4: Verify the calculation

24 - 8 + 15 = 31

Sarah has 31 stickers now.
Final answer:

Sarah has 31 stickers. The worked solution strategy involved: (1) Starting with 24, (2) Subtracting 8 given away, (3) Adding 15 bought, (4) Result: 31 stickers.

Applied rules:

• Sequential Operations: Perform operations in the order they occur in the problem

• Step-by-Step Verification: Check each step before proceeding to the next

• Clear Documentation: Show each step with explanation

2 Pattern Recognition
Exercise 2
Find the next three numbers in this pattern: 5, 10, 15, 20, __, __, __. Use the worked solution strategy to explain your answer.
Definition:

Pattern Recognition: Identifying the rule that governs a sequence of numbers or objects.

Pattern
5, 10, 15, 20, ...
Rule
Add 5 each time
Next Three
25, 30, 35
Step 1: Examine the sequence

Look at: 5, 10, 15, 20

Step 2: Find the pattern

10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5

Step 3: Identify the rule

Add 5 to get the next number

Step 4: Apply the rule

20 + 5 = 25, 25 + 5 = 30, 30 + 5 = 35

Next three numbers: 25, 30, 35
Final answer:

The next three numbers are 25, 30, 35. The pattern is counting by 5s (adding 5 each time).

Applied rules:

• Pattern Analysis: Look for consistent differences between terms

• Rule Consistency: The same operation applies to all terms

• Sequential Application: Apply the rule repeatedly to generate new terms

3 Comparison Problem
Exercise 3
Tom has 3 bags of marbles. Each bag has 12 marbles. Jane has 2 bags of marbles. Each bag has 15 marbles. Who has more marbles? Use the worked solution strategy to solve this.
Definition:

Comparison Problem: A problem that requires calculating two or more quantities and comparing them to determine which is greater or lesser.

Tom's Marbles
3 × 12 = 36
Jane's Marbles
2 × 15 = 30
Comparison
36 > 30
Step 1: Calculate Tom's total marbles

Tom has 3 bags × 12 marbles per bag = 36 marbles

Step 2: Calculate Jane's total marbles

Jane has 2 bags × 15 marbles per bag = 30 marbles

Step 3: Compare the totals

Tom has 36 marbles, Jane has 30 marbles

Step 4: State the comparison

Since 36 > 30, Tom has more marbles

Tom has more marbles (36 vs 30).
Final answer:

Tom has more marbles. Tom has 36 marbles (3 × 12), and Jane has 30 marbles (2 × 15).

Applied rules:

• Individual Calculation: Calculate each person's total separately

• Direct Comparison: Compare the final totals

• Clear Explanation: State which is greater and by how much

Detailed Summary: Worked Solution Strategy
Key Concepts and Definitions

Worked Solution Strategy: A systematic approach to solving problems by breaking them into clear, sequential steps with explanations.

Step-by-Step Method: Breaking complex problems into smaller, manageable parts.

Problem Decomposition: Dividing a complex problem into simpler components.

Sequential Operations: Performing mathematical operations in the correct order.

Pattern Recognition: Identifying rules that govern sequences or sets of data.

Verification: Checking that each step and the final answer is correct.

Core Rules and Principles
  • Read Carefully: Understand what the problem is asking before solving.
  • Identify Information: Separate given information from what needs to be found.
  • Plan Sequentially: Determine the order of operations needed to solve.
  • Document Steps: Show each step with clear explanations.
  • Verify Results: Check that each step and final answer makes sense.
Step-by-Step Methods

For Multi-Step Problems:

  • Read the problem completely
  • Identify what information is given
  • Determine what is being asked
  • Break the problem into smaller steps
  • Solve each step in order
  • Combine results if needed
  • Verify the final answer

For Pattern Recognition:

  • Examine the given sequence
  • Calculate differences between consecutive terms
  • Identify the pattern rule
  • Apply the rule to find missing terms
  • Verify the pattern works for all terms

For Comparison Problems:

  • Calculate each quantity separately
  • Record each result clearly
  • Compare the final totals
  • State which is greater or lesser
  • Explain the reasoning
Examples - Simple to Advanced

Simple Examples:

  • Addition: 5 + 3 = 8 (one step)
  • Pattern: 2, 4, 6, 8 (add 2 each time)
  • Comparison: 7 vs 5 (7 is greater)

Intermediate Examples:

  • Multi-step: 10 + 5 - 3 = 12
  • Pattern: 10, 20, 30, 40 (add 10 each time)
  • Comparison: 3 × 4 vs 2 × 7 (12 vs 14)

Advanced Examples:

  • Multi-step with multiple operations
  • Complex patterns with multiple rules
  • Multi-variable comparison problems
Tips, Tricks, and Common Pitfalls

Tips and Tricks:

  • Always write down what you know and what you need to find
  • Use scratch paper to work out calculations
  • Check your work by doing the opposite operation
  • Label each step clearly
  • Estimate your answer first to check reasonableness

Common Pitfalls:

  • Skipping steps or doing calculations mentally
  • Forgetting to perform operations in the correct order
  • Not verifying the final answer
  • Misreading the problem
  • Stopping before completing all required steps
Key Notes for Memorization
  • "Read first, then solve"
  • "Show your work step by step"
  • "Check your answer makes sense"
  • "Pattern = Find the rule"
  • "Compare = Calculate then compare"
Worked Solution Strategy Rules and Methods
Problem → Steps → Solution → Verification
Worked Solution Process
Problem Types
Multi-step, Pattern, Comparison
Different Problem Categories
Solution Steps
Read → Plan → Solve → Check
Problem-Solving Process
Verification
Reasonableness Check
Ensuring Accuracy
Key definitions:

Worked Solution: A complete solution showing all steps and reasoning

Sequential Operations: Performing mathematical operations in the correct order

Problem Decomposition: Breaking complex problems into simpler parts

Complete methodology:
  1. Read: Carefully read the problem and identify what is being asked
  2. Plan: Decide on the steps needed to solve the problem
  3. Solve: Execute each step in order, showing work clearly
  4. Check: Verify that each step and the final answer is correct
Tip 1: Always write down what you know and what you need to find.
Tip 2: Show each step clearly with explanations.
Tip 3: Check your work by estimating first.
Tip 4: Use scratch paper for complex calculations.
Common errors: Skipping steps, incorrect order of operations, not verifying answers, misreading problems.
Good practices: Document all steps, verify calculations, use systematic approaches, check reasonableness.
Worked Solution Strategies & Visual Guide
Given Information → Steps → Final Answer
Solution Pathway
Multi-Step Problems
Sequential Operations
Step-by-Step Approach
Pattern Recognition
Find Rule → Apply Rule
Pattern Analysis
Comparison Problems
Calculate → Compare → Conclude
Direct Comparison
Strategy Categories:

Multi-Step Problems: Breaking complex problems into smaller, sequential steps

Pattern Recognition: Identifying rules that govern sequences or sets

Comparison Problems: Calculating quantities and comparing results

Verification Methods: Ensuring solutions are accurate and reasonable

Solution Framework:
Step Action Purpose 1 Read Carefully Understand the problem 2 Identify Info Separate given from unknown 3 Plan Steps Determine solution order 4 Solve Execute calculations 5 Verify Check accuracy
Multi-Step Rule: Perform operations in the order they occur in the problem.
Pattern Rule: Look for consistent differences or operations between terms.
Verification: Always check that your solution makes sense in context.
Documentation: Show all steps clearly to avoid errors.
Essential Solution Facts:

• Always read the entire problem before starting calculations

• Break complex problems into smaller, manageable steps

• Show your work clearly to track progress

• Verify that your answer is reasonable and makes sense

• Different problem types require different solution approaches

Worked Solution Strategy Laws, Methods, Rules, and Expressions
Solution = (Given Info) → (Steps) → (Answer) → (Verification)
Solution Structure
Key definitions:

Worked Solution Strategy: A systematic approach to solving problems by breaking them into clear, sequential steps with explanations

Sequential Operations: Performing mathematical operations in the correct order to solve problems

Problem Decomposition: Breaking complex problems into simpler, manageable components

Complete methodology:
  1. Understand: Read the problem carefully and identify what is being asked
  2. Plan: Determine the steps needed to solve the problem
  3. Execute: Carry out each step in order, showing work clearly
  4. Verify: Check that each step and the final answer is correct
Tip 1: For multi-step problems, perform operations in the order they occur in the problem.
Tip 2: For pattern problems, look for consistent differences between terms.
Tip 3: For comparison problems, calculate each quantity separately first.
Tip 4: Always verify your answer by checking if it makes sense in context.
Common errors: Skipping steps, incorrect order of operations, not verifying answers, misreading problems.
Best practices: Document all steps, verify calculations, use systematic approaches, check reasonableness.
Solution Strategy Laws and Rules:

• Problem Understanding: The foundation of successful problem solving

• Sequential Execution: Perform operations in logical order to avoid errors

• Clear Documentation: Show all steps to enable verification and learning

• Verification Requirement: Solutions must be checked for accuracy and reasonableness

• Adaptive Thinking: Adjust approach based on problem type and complexity

Questions & Answers

Question: Why do I need to show all my work? Can't I just write the answer?

Answer: Showing your work is important for several reasons:

  • Tracking Mistakes: If you make an error, you can find where it happened
  • Learning: Writing out steps helps you understand the process
  • Checking: You can review each step to make sure it's correct
  • Teaching: Others can see how you solved the problem
  • Partial Credit: Teachers can see your thinking process

Showing work is an essential part of the worked solution strategy!

Question: How do I know if I've solved a problem correctly?

Answer: Use these verification strategies:

  • Check Reasonableness: Does your answer make sense for the problem?
  • Estimate First: Did your answer come close to your estimate?
  • Reverse Calculation: Can you work backwards from your answer?
  • Unit Check: Do your units make sense?
  • Re-read: Did you answer the question that was asked?

Verification is a crucial step in the worked solution strategy.

Question: What should I do if I get stuck on a step in a multi-step problem?

Answer: Here are strategies for when you're stuck:

  • Re-read: Go back and re-read the problem carefully
  • Identify: Pinpoint exactly what you don't understand
  • Simplify: Try a simpler version of the problem first
  • Sketch: Draw a picture or diagram to visualize
  • Ask: Seek help from a teacher, parent, or classmate

Remember, being stuck is part of learning. Take a break if needed, then try again.