Solved Exercises on Real-Life Subject Matter in Mathematics for Grade 3

Master everyday math: shopping, cooking, time management, and measurements through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping Math
Exercise 1
Sarah went shopping and bought 3 apples at $2 each, 2 loaves of bread at $4 each, and 1 gallon of milk for $3. How much money did Sarah spend in total?
Definition:

Shopping Math: Using math to calculate costs when buying items

Total Cost: The sum of all individual item costs

Shopping Math Method:
  1. List all items and their prices
  2. Calculate the cost for each type of item
  3. Add all individual costs together
  4. Check your answer
Apples
3×$2=$6
Bread
2×$4=$8
Milk
1×$3=$3
Total
$17
Step 1: Calculate apple cost

3 apples × $2 each = $6

Step 2: Calculate bread cost

2 loaves × $4 each = $8

Step 3: Calculate milk cost

1 gallon × $3 each = $3

Step 4: Add all costs

$6 + $8 + $3 = $17

Sarah spent $17 in total
Final answer:

Sarah spent $17 in total

Applied rules:

• Multiplication: Quantity × Price = Cost for that item

• Addition: Sum of all individual costs

• Organized Calculation: Calculate each item separately first

2 Cooking Math
Exercise 2
A recipe calls for 2 cups of flour for 4 servings. How many cups of flour are needed for 12 servings? How many servings can be made with 5 cups of flour?
Definition:

Cooking Ratios: Maintaining proportional relationships when scaling recipes

Proportional Scaling: Increasing or decreasing ingredients proportionally

Original
2c/4s
Scale Factor
12÷4=3
12 Servings
6 cups
5 Cups
10 servings
Step 1: Find the ratio

2 cups of flour for 4 servings means 2÷4 = 0.5 cups per serving

Step 2: Calculate for 12 servings

12 servings × 0.5 cups per serving = 6 cups of flour

Step 3: Calculate servings from 5 cups

5 cups ÷ 0.5 cups per serving = 10 servings

Step 4: Verify the proportions

2c:4s = 6c:12s = 5c:10s (all simplify to 1c:2s)

6 cups for 12 servings, 10 servings from 5 cups
Final answer:

6 cups of flour are needed for 12 servings. 5 cups of flour make 10 servings.

Applied rules:

• Proportional Reasoning: Maintain the same ratio when scaling

• Unit Rate: Find the amount per single unit first

• Multiplication/Division: Scale up or down using the unit rate

3 Time Management
Exercise 3
Emma starts homework at 3:30 PM. She spends 45 minutes on math, 30 minutes on reading, and 20 minutes on science. What time does she finish? If she had started at 4:00 PM instead, what time would she finish?
Definition:

Time Addition: Calculating end time by adding durations to start time

Elapsed Time: The total time that passes during an activity

Start Time
3:30 PM
Total Duration
95 min
Finish Time
5:05 PM
New Start
4:00 PM
New Finish
5:35 PM
Step 1: Calculate total homework time

Math: 45 min + Reading: 30 min + Science: 20 min = 95 minutes total

Step 2: Convert 95 minutes to hours and minutes

95 minutes = 1 hour and 35 minutes

Step 3: Add to start time (3:30 PM)

3:30 PM + 1 hour = 4:30 PM

4:30 PM + 35 minutes = 5:05 PM

Step 4: Calculate for new start time (4:00 PM)

4:00 PM + 1 hour 35 minutes = 5:35 PM

Step 5: Verify the calculation

4:00 PM - 3:30 PM = 30 minutes later start, so finish 30 minutes later: 5:05 PM + 30 min = 5:35 PM ✓

Finishes at 5:05 PM (original) and 5:35 PM (new start)
Final answer:

Emma finishes at 5:05 PM if starting at 3:30 PM, and at 5:35 PM if starting at 4:00 PM.

Applied rules:

• Time Addition: Add durations to find end time

• Unit Conversion: Convert minutes to hours and minutes

• Time Calculation: Handle hour changes when adding minutes

Real-Life Math Rules and Methods
Total Cost = Σ(Quantity × Unit Price)
Shopping Math Formula
Shopping
Cost = Quantity × Price
Individual item cost
Cooking
New Amount = Old Amount × (New Servings/Old Servings)
Scaling recipes
Time
End Time = Start Time + Duration
Time calculation
Key Definitions:

Real-Life Math: Using mathematical concepts to solve everyday problems

Shopping Math: Calculating costs, discounts, and totals when purchasing items

Cooking Math: Scaling recipes, measuring ingredients, and calculating portions

Time Math: Calculating durations, scheduling, and managing time effectively

Measurement Math: Working with units of length, weight, volume, and other quantities

Budgeting Math: Managing money, calculating expenses, and planning spending

Real-Life Problem Solving Methodology:
  1. Read the problem carefully: Identify what is being asked
  2. Identify important information: Note numbers, units, and relationships
  3. Choose the right operation: Decide whether to add, subtract, multiply, or divide
  4. Perform the calculation: Show your work step by step
  5. Check your answer: Make sure it makes sense in the context
Tip 1: Always read the entire problem before starting calculations.
Tip 2: Write down important numbers and what they represent.
Tip 3: Check if your answer is reasonable for the situation.
Tip 4: Draw pictures or make tables to organize information.
Common Applications: Shopping, cooking, time management, budgeting, travel planning, home projects.
Key Skills: Addition, subtraction, multiplication, division, estimation, unit conversion.
Essential Rules:

• Unit Consistency: Make sure all measurements are in the same units

• Order of Operations: Perform calculations in the correct sequence

• Estimation: Check if your answer is reasonable before finalizing

• Context Awareness: Consider the real-world meaning of your answer

Solution: Exercises 4 to 5
4 Measurement Math
Exercise 4
A rectangular garden is 8 feet long and 5 feet wide. What is the perimeter of the garden? What is the area? If a fence costs $3 per foot, how much would it cost to fence the entire garden?
Definition:

Perimeter: The total distance around the outside of a shape

Area: The amount of space inside a shape

Length
8 ft
Width
5 ft
Perimeter
26 ft
Area
40 sq ft
Fence Cost
$78
Step 1: Calculate the perimeter

Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 feet

Step 2: Calculate the area

Area = length × width = 8 × 5 = 40 square feet

Step 3: Calculate fence cost

Fence goes around the perimeter: 26 feet × $3 per foot = $78

Step 4: Verify the calculations

Rectangle has 2 sides of 8ft and 2 sides of 5ft: 8+8+5+5 = 26ft ✓

Perimeter: 26 ft, Area: 40 sq ft, Fence cost: $78
Final answer:

The perimeter is 26 feet, the area is 40 square feet, and the fence would cost $78.

Applied rules:

• Perimeter Formula: P = 2(l + w) for rectangles

• Area Formula: A = l × w for rectangles

• Cost Calculation: Unit cost × Quantity = Total cost

5 Budget Planning
Exercise 5
Alex receives $20 each week as allowance. He spends $5 on snacks, $3 on transportation, and saves the rest. How much does he save each week? How much will he have saved after 8 weeks?
Definition:

Budget Planning: Managing income and expenses to meet financial goals

Savings: Money set aside from income after expenses

Weekly Income
$20
Weekly Expenses
$8
Weekly Savings
$12
8 Weeks Savings
$96
Step 1: Calculate weekly expenses

Snacks: $5 + Transportation: $3 = $8 total expenses

Step 2: Calculate weekly savings

Income - Expenses = $20 - $8 = $12 saved each week

Step 3: Calculate savings after 8 weeks

Weekly savings × Number of weeks = $12 × 8 = $96

Step 4: Verify the calculation

Check: $12 × 8 = $96, and $12 + $8 = $20 (income) ✓

Weekly savings: $12, 8-week savings: $96
Final answer:

Alex saves $12 each week. After 8 weeks, he will have saved $96.

Applied rules:

• Income-Expense Relationship: Savings = Income - Expenses

• Repeated Addition: Total = Single amount × Number of occurrences

• Budget Balance: Income = Expenses + Savings

Comprehensive Guide: Real-Life Math Applications
Real-Life Problem = Information + Operation + Context
Real-Life Math Formula
Key definitions:

Real-Life Math: Applying mathematical concepts to solve everyday problems and make decisions

Word Problems: Mathematical problems presented in real-world contexts

Unit Conversion: Changing measurements from one unit to another

Estimation: Making approximate calculations to check reasonableness

Problem Solving: Systematic approach to finding solutions to mathematical challenges

Mathematical Reasoning: Logical thinking applied to solve problems

Complete problem-solving methodology:
  1. Understand the problem: Read carefully and identify what is being asked
  2. Identify given information: List numbers, units, and relationships provided
  3. Choose the operation: Decide whether to add, subtract, multiply, or divide
  4. Plan the solution: Organize your approach before calculating
  5. Execute the plan: Perform calculations step by step
  6. Check your answer: Verify it makes sense in the context
Tip 1: Always pay attention to units (dollars, feet, minutes, etc.).
Tip 2: Draw diagrams or make tables to organize information visually.
Tip 3: Estimate your answer first to check if your final answer is reasonable.
Tip 4: Always answer the specific question that was asked.
Real-Life Applications: Shopping, cooking, time management, budgeting, travel planning, home improvement, sports statistics, health monitoring.
Common Mistakes: Misreading the problem, calculation errors, incorrect units, not answering the right question.
Essential formulas to remember:

• Rectangle Perimeter: P = 2(l + w)

• Rectangle Area: A = l × w)

• Total Cost: TC = Σ(Quantity × Unit Price)

• Savings: Savings = Income - Expenses

• Unit Rate: Rate = Total ÷ Number of Units

• Time Calculation: End = Start + Duration

Visualizing Real-Life Math Concepts
Exercise 6: Budget Breakdown
Visual breakdown of Alex's weekly budget:
• Income: $20
• Snacks: $5 (25%)
• Transportation: $3 (15%)
• Savings: $12 (60%)

Analysis: The pie chart shows how Alex allocates his weekly allowance.

  • Alex saves 60% of his allowance
  • Expenses account for 40% of his allowance
  • This demonstrates good budgeting habits

Questions & Answers

Question: Why do we need to learn math for real-life situations?

Answer: Math is everywhere in our daily lives! Here are some examples:

• When you go shopping, you need math to count money and make change

• When you cook, you need math to measure ingredients

• When you play games, you use math to keep score

• When you plan your day, you use math to manage time

• When you build with blocks, you use math to measure and count

Learning math helps you solve problems and make good decisions every day!

Question: How can I help my child understand real-life math applications?

Answer: Here are some effective ways to connect math to real life:

• Involve your child in everyday activities that use math:

- Cooking: measuring ingredients, doubling recipes

- Shopping: counting money, comparing prices

- Home projects: measuring, estimating

• Use manipulatives like coins, blocks, or measuring cups

• Create math stories based on your child's interests

• Practice mental math during daily routines

• Encourage your child to explain their thinking

Question: I don't understand word problems. They're too hard!

Answer: Word problems can seem hard at first, but here's a simple way to tackle them:

1. Read the problem slowly and picture what's happening

2. Circle or underline important numbers

3. Cross out words you don't need

4. Ask yourself: "What is the question asking?"

5. Think: "Do I need to add, subtract, multiply, or divide?"

6. Solve step by step

7. Check if your answer makes sense

Practice with simple problems first, then try harder ones!