Solved Exercises on Making Change Practice Problems in Grade 2

Master making change: counting money, calculating change, coin combinations, and word problems through these 5 detailed exercises.

Making Change Rules and Methods
Total Money Given - Cost = Change
Change Calculation Formula
Coin Values
Penny = $0.01
Nickel = $0.05
Dime = $0.10
Quarter = $0.25
Know Your Coins
Bill Values
$1 = 100¢
$5 = 500¢
$10 = 1000¢
Bill Conversions
Change Strategy
Start with largest coins first
Count Down Method
Key definitions:

Change: Money returned when payment exceeds cost

Coin Combination: Different ways to make the same amount

Money Word Problem: Real-life scenario requiring money calculations

Making Change Methodology:
  1. Read the problem: Identify cost and amount paid
  2. Calculate the difference: Subtract cost from payment
  3. Find coin combinations: Start with largest denominations
  4. Verify your answer: Add up to ensure it equals the change needed
Tip 1: Always count change starting with the largest coins first.
Tip 2: Draw pictures of coins to visualize the problem.
Tip 3: Practice counting by 5s, 10s, and 25s for faster coin addition.
Tip 4: Use the "counting up" method: count from cost to payment.
Common errors: Confusing coin values, forgetting to subtract correctly, miscounting change.
Success strategies: Know coin values by heart, practice mental math, check your work.
Essential Money Facts:

• 1 penny = 1 cent = $0.01

• 1 nickel = 5 cents = $0.05

• 1 dime = 10 cents = $0.10

• 1 quarter = 25 cents = $0.25

• 100 cents = $1.00

• Change = Amount Paid - Cost

Solution: Exercises 1 to 3
1 Basic Change Calculation
Exercise 1
Sarah buys a candy bar that costs 75 cents. She gives the cashier $1.00. How much change should she get back?
Definition:

Change: The difference between the amount paid and the cost of the item

Change calculation method:
  1. Convert all amounts to the same unit (cents or dollars)
  2. Subtract the cost from the amount paid
  3. Express the change in coin combinations
Amount Paid:
$1.00 = 100¢
Cost:
75¢
Change:
100¢ - 75¢ = 25¢
Step 1: Convert to same units

$1.00 = 100 cents

Step 2: Subtract to find change

100¢ - 75¢ = 25¢

Step 3: Express as coin combination

25¢ = 1 quarter OR 2 dimes + 1 nickel OR 5 nickels OR 25 pennies

Step 4: Choose most efficient combination

1 quarter is the most efficient way to make 25¢

Sarah should get back 25 cents (1 quarter)
Final answer:

Sarah should receive 25 cents in change, which could be 1 quarter.

Applied rules:

• Subtraction: Change = Amount Paid - Cost

• Unit Conversion: Convert dollars to cents for easier calculation

• Efficiency: Use largest denominations first

Key Tip: When making change, always start with the largest coins first (quarters, then dimes, nickels, then pennies).
2 Multiple Coin Combinations
Exercise 2
Tom bought a toy that costs $1.25. He gave the cashier $2.00. What are all the different ways he can receive his change using quarters, dimes, and nickels?
Definition:

Coin Combination: Different sets of coins that add up to the same total amount

Amount Paid:
$2.00 = 200¢
Cost:
$1.25 = 125¢
Change:
200¢ - 125¢ = 75¢
Coin Type Value Symbol
Quarter 25¢ Q
Dime 10¢ D
Nickel 5¢ N
Step 1: Calculate the change

$2.00 - $1.25 = $0.75 = 75¢

Step 2: Find all possible combinations

Using quarters (25¢), dimes (10¢), and nickels (5¢)

Step 3: Systematic approach - start with largest coin

• 3 quarters = 75¢

• 2 quarters + 2 dimes + 1 nickel = 50¢ + 20¢ + 5¢ = 75¢

• 2 quarters + 1 dime + 3 nickels = 50¢ + 10¢ + 15¢ = 75¢

• 2 quarters + 5 nickels = 50¢ + 25¢ = 75¢

• 1 quarter + 5 dimes = 25¢ + 50¢ = 75¢

• 1 quarter + 4 dimes + 2 nickels = 25¢ + 40¢ + 10¢ = 75¢

• And many more combinations...

Step 4: Most practical combination

3 quarters = 75¢ (most efficient)

Tom's change: 75¢ (3 quarters is most efficient)
Final answer:

Tom should receive 75 cents in change. Possible combinations include 3 quarters, or 2 quarters + 2 dimes + 1 nickel, or 1 quarter + 5 dimes, etc.

Applied rules:

• Multiple Solutions: Same amount can be made with different coin combinations

• Systematic Approach: Start with largest denomination and work down

• Verification: Check that each combination equals the target amount

Key Tip: Organize coin combinations systematically to avoid missing any possibilities.
3 Shopping Scenario
Exercise 3
Lisa has $5.00. She buys a book for $3.40 and a pencil for $0.85. How much money does she have left?
Definition:

Total Cost: Sum of all individual item prices

Remaining Money: Original amount minus total spent

Initial Amount:
$5.00
Book Cost:
$3.40
Pencil Cost:
$0.85
Total Spent:
$3.40 + $0.85 = $4.25
Remaining:
$5.00 - $4.25 = $0.75
Step 1: Calculate total cost

$3.40 + $0.85 = $4.25

Step 2: Subtract total cost from initial amount

$5.00 - $4.25 = $0.75

Step 3: Convert to cents if needed

$0.75 = 75¢

Step 4: Express as coin combination

75¢ = 3 quarters OR 7 dimes + 1 nickel OR 15 nickels, etc.

Lisa has $0.75 remaining
Final answer:

Lisa has $0.75 (75 cents) remaining after her purchases.

Applied rules:

• Addition: Calculate total cost of multiple items

• Subtraction: Remaining money = Starting amount - Total spent

• Multi-step Problems: Break complex problems into simpler steps

Key Tip: When solving multi-step money problems, solve one operation at a time.
Solution: Exercises 4 to 5
4 Counting Up Method
Exercise 4
At the store, a juice box costs $1.65. Emma pays with $2.00. Using the "counting up" method, how much change should she get back?
Definition:

Counting Up Method: Instead of subtracting, count up from the cost to the amount paid

Cost:
$1.65
Amount Paid:
$2.00
Change:
$1.65 → $2.00 = $0.35
Step 1: Start at the cost ($1.65)

We want to count up to $2.00

Step 2: Count up by convenient amounts

$1.65 → $1.70 (add 5¢) → $1.80 (add 10¢) → $1.90 (add 10¢) → $2.00 (add 10¢)

Total added: 5¢ + 10¢ + 10¢ + 10¢ = 35¢

Step 3: Alternative counting up

$1.65 → $1.70 (5¢) → $2.00 (30¢ more) = 5¢ + 30¢ = 35¢

Step 4: Express as coin combination

35¢ = 1 quarter + 1 dime OR 7 nickels OR 3 dimes + 1 nickel, etc.

Emma's change: $0.35 (1 quarter + 1 dime is most efficient)
Final answer:

Emma should receive $0.35 (35 cents) in change. The most efficient combination is 1 quarter and 1 dime.

Applied rules:

• Counting Up: Alternative to subtraction for finding differences

• Flexibility: Multiple ways to count up to the same amount

• Efficiency: Choose the most practical coin combination

Key Tip: The counting up method is often easier than subtraction for young learners.
5 Mixed Currency Challenge
Exercise 5
Max has 3 quarters, 4 dimes, and 2 nickels. He wants to buy a toy that costs $1.20. Does he have enough money? If yes, how much change will he get?
Definition:

Currency Conversion: Calculating the total value of mixed coins and bills

Max's Money:
3 quarters + 4 dimes + 2 nickels
Value Calculation:
(3×25¢) + (4×10¢) + (2×5¢) = 75¢ + 40¢ + 10¢ = 125¢ = $1.25
Toy Cost:
$1.20 = 120¢
Change:
$1.25 - $1.20 = $0.05 = 5¢
Coin Quantity Value Each Total Value
Quarter 3 25¢ 75¢
Dime 4 10¢ 40¢
Nickel 2 5¢ 10¢
Total: 125¢ = $1.25
Step 1: Calculate value of each coin type

Quarters: 3 × 25¢ = 75¢

Dimes: 4 × 10¢ = 40¢

Nickels: 2 × 5¢ = 10¢

Step 2: Add all values together

75¢ + 40¢ + 10¢ = 125¢ = $1.25

Step 3: Compare with cost

$1.25 > $1.20, so Max has enough money

Step 4: Calculate change

$1.25 - $1.20 = $0.05 = 5¢

Yes, Max has enough money. His change: $0.05 (1 nickel)
Final answer:

Yes, Max has enough money. He has $1.25 total, and the toy costs $1.20, so he will receive 5 cents (1 nickel) in change.

Applied rules:

• Individual Calculation: Calculate value of each coin type separately

• Comparison: Compare total money with cost to determine sufficiency

• Change Calculation: Use standard change formula when sufficient funds exist

Key Tip: When working with mixed coins, organize by type and multiply quantity by value.
Money and Making Change Essentials
Payment - Cost = Change
Core Money Formula
Counting Up
Start at cost, count to payment
Easier than subtraction
Largest First
Use biggest coins first
Most efficient method
Multiple Ways
Same amount, different coins
Many combinations possible
Problem-Solving Steps:
  1. Identify: What do you know? What do you need to find?
  2. Plan: Which operation(s) do you need to perform?
  3. Calculate: Perform the necessary calculations
  4. Check: Does your answer make sense?
Tip 1: Practice counting by 5s, 10s, and 25s regularly.
Tip 2: Use real coins at home to practice making different amounts.
Tip 3: Draw circles with coin values to represent physical coins.
Tip 4: Always verify your change calculation by adding it back.
Real-world connection: Making change skills apply to shopping, banking, and budgeting.
Mathematical foundation: Builds number sense and arithmetic skills.
Money Conversion Facts:

• 1 dollar = 100 cents

• 1 quarter = 25 cents = $0.25

• 1 dime = 10 cents = $0.10

• 1 nickel = 5 cents = $0.05

• 1 penny = 1 cent = $0.01

• 4 quarters = 1 dollar

• 10 dimes = 1 dollar

• 20 nickels = 1 dollar

🪙 + 💰 = 🤑
Money Fun Fact

Questions & Answers

Question: I'm confused about making change. When I buy something that costs 85 cents and I pay with $1.00, why do I get 15 cents back? Shouldn't I get 25 cents?

Answer: Great question! Let me explain the math clearly:

  • You paid: $1.00 = 100 cents
  • Item cost: 85 cents
  • Change: 100 cents - 85 cents = 15 cents

Think of it this way: if something costs 85 cents and you give 100 cents, you're giving 15 cents more than needed. That extra 15 cents comes back to you as change.

The confusion might come from thinking about quarters: $1.00 is 4 quarters, and 85 cents is 3 quarters plus 1 dime. So you'd get back 1 quarter minus 1 dime = 15 cents.

Always remember: Change = Money Given - Cost of Item

Question: My child struggles with coin identification. How can I help them memorize which coin is worth what?

Answer: Here are effective strategies to help your child learn coin values:

  • Physical Practice: Use real coins for hands-on learning
  • Mnemonic Devices: "Quarter = Quarter of a dollar = 25 cents", "Dime = Ten cents = 10 cents"
  • Size Doesn't Matter: Remind that a penny is smallest but worth 1 cent, while a nickel is bigger but only worth 5 cents
  • Visual Association: Point out unique features: Lincoln on penny, Jefferson on nickel, Roosevelt on dime, Washington on quarter
  • Regular Practice: Daily counting exercises with different coin combinations

Create games like "Guess the Coin" where you describe the value and let them identify the coin. Also, practice at stores when possible!

Question: What's the best method for teaching children to make change - subtraction or counting up?

Answer: Both methods have their place, but for young learners, I recommend starting with the counting up method:

  • Counting Up: More intuitive for children, especially when the numbers are close together
  • Example: For $1.00 - $0.85, count up: $0.85 → $0.90 (5¢) → $1.00 (10¢ more) = 15¢
  • Subtraction: More abstract, but important for building computational skills

I suggest introducing counting up first, then gradually incorporating subtraction once the concept is solid. Some children may prefer one method over the other, so offering both options is beneficial.

The key is ensuring they understand the relationship between the cost, payment, and change regardless of the method used.