Lesson Plans on Making Change with Money

Master making change with money: counting coins, calculating change, and solving real-world problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Money
Exercise 1
Sarah has 3 quarters, 2 dimes, and 1 nickel. How much money does she have?
Definition:

Coins and their values: Penny = $0.01, Nickel = $0.05, Dime = $0.10, Quarter = $0.25

Counting method:
  1. Identify the value of each type of coin
  2. Multiply the number of each coin by its value
  3. Add all amounts together
Quarters
3 × $0.25 = $0.75
Dimes
2 × $0.10 = $0.20
Nickel
1 × $0.05 = $0.05
Step 1: Calculate value of quarters

3 quarters × $0.25 per quarter = $0.75

Step 2: Calculate value of dimes

2 dimes × $0.10 per dime = $0.20

Step 3: Calculate value of nickels

1 nickel × $0.05 per nickel = $0.05

Step 4: Add all amounts

$0.75 + $0.20 + $0.05 = $1.00

Sarah has $1.00
Final answer:

Sarah has $1.00 total

Applied rules:

• Counting: Multiply quantity by individual value

• Addition: Combine all amounts to find total

• Place Value: Remember decimal places for cents

2 Calculating Change
Exercise 2
Tom buys a toy for $1.25 and pays with $2.00. How much change should he receive?
Definition:

Change calculation: Change = Amount Paid - Cost of Item

Amount Paid
$2.00
Cost of Item
$1.25
Change
$0.75
Step 1: Identify amount paid and cost

Amount paid = $2.00, Cost = $1.25

Step 2: Apply change formula

Change = $2.00 - $1.25

Step 3: Calculate the difference

$2.00 - $1.25 = $0.75

Step 4: Express in coins if needed

$0.75 = 3 quarters OR 7 dimes and 1 nickel

Tom should receive $0.75 in change
Final answer:

Tom receives $0.75 in change

Applied rules:

• Subtraction: Amount paid minus cost equals change

• Regrouping: May need to borrow from dollars to cents

• Multiple representations: Same amount can be made with different coins

3 Real World Problem
Exercise 3
Emma has $3.00. She buys a book for $1.75 and a pencil for $0.45. How much money does she have left?
Definition:

Multi-step money problem: Total remaining = Initial amount - Sum of purchases

Initial Amount
$3.00
Total Purchases
$1.75 + $0.45 = $2.20
Remaining
$3.00 - $2.20 = $0.80
Step 1: Calculate total cost of purchases

Book ($1.75) + Pencil ($0.45) = $2.20

Step 2: Subtract total purchases from initial amount

$3.00 - $2.20 = $0.80

Step 3: Express remaining amount

$0.80 = 8 dimes OR 3 quarters and 1 nickel OR 80 pennies

Step 4: Verify calculation

$2.20 spent + $0.80 remaining = $3.00 initial amount ✓

Emma has $0.80 remaining
Final answer:

Emma has $0.80 left after her purchases

Applied rules:

• Order of operations: Add purchases first, then subtract from initial amount

• Verification: Check that spending + remaining = initial amount

• Equivalent representations: Same amount can be expressed with different coins

Money Values and Making Change Methods

Coin Values

1¢
Penny
5¢
Nickel
10¢
Dime
25¢
Quarter
Change = Paid - Cost
Change Formula
1
Count Money
→
2
Calculate Total Cost
→
3
Find Change
Key definitions:

Money: Currency used to buy goods and services

Change: Money returned when payment exceeds cost

Equivalent amounts: Different combinations of coins with same value

Making Change Methodology:
  1. Count the money: Identify value of each coin/bill
  2. Calculate total cost: Add up prices of items
  3. Subtract to find change: Paid amount minus cost
  4. Express change: In simplest coin combination
Tip 1: Start with the largest coins when making change.
Tip 2: Always check your work by adding change back to cost.
Tip 3: Practice with real coins to build familiarity.
Common errors: Miscounting coins, forgetting to regroup, incorrect subtraction.
Success strategies: Count by fives and tens, verify calculations, use visual aids.
Solution: Exercises 4 to 5
4 Equivalent Amounts
Exercise 4
Show two different ways to make $0.60 using coins.
Definition:

Equivalent amounts: Different combinations of coins that equal the same value

Method 1
2 quarters + 1 dime = $0.60
Method 2
6 dimes = $0.60
Method 3
12 nickels = $0.60
Step 1: Method 1 - Quarters and dimes

2 quarters = 2 × $0.25 = $0.50

1 dime = 1 × $0.10 = $0.10

Total = $0.50 + $0.10 = $0.60

Step 2: Method 2 - All dimes

6 dimes = 6 × $0.10 = $0.60

Step 3: Method 3 - All nickels

12 nickels = 12 × $0.05 = $0.60

Step 4: Additional combinations

1 quarter + 3 dimes + 1 nickel = $0.25 + $0.30 + $0.05 = $0.60

24 nickels = 24 × $0.05 = $1.20 (too much)

Multiple ways to make $0.60: 2 quarters + 1 dime, or 6 dimes
Final answer:

Two ways: 2 quarters + 1 dime OR 6 dimes (many other combinations possible)

Applied rules:

• Equivalence: Different coin combinations can equal the same amount

• Counting: Multiply quantity by value for each coin type

• Verification: Always check that sum equals target amount

5 Shopping Scenario
Exercise 5
At the school store, Jake buys a notebook for $0.85, a pen for $0.35, and stickers for $0.20. He pays with $2.00. How much change should he get back?
Definition:

Multi-purchase scenario: Total cost = sum of all individual item costs

Item Costs
$0.85 + $0.35 + $0.20 = $1.40
Payment
$2.00
Change
$2.00 - $1.40 = $0.60
Step 1: Calculate total cost of all items

Notebook ($0.85) + Pen ($0.35) + Stickers ($0.20) = $1.40

Step 2: Apply change formula

Change = Amount Paid - Total Cost

Change = $2.00 - $1.40 = $0.60

Step 3: Express change in coins

Possible combinations: 2 quarters + 1 dime, or 6 dimes, or 12 nickels

Step 4: Verify the calculation

Spent ($1.40) + Change ($0.60) = $2.00 paid ✓

Jake should receive $0.60 in change
Final answer:

Jake receives $0.60 in change for his purchases

Applied rules:

• Addition: Sum all purchase amounts to find total cost

• Subtraction: Payment minus total cost equals change

• Verification: Spending + change should equal payment

Money Facts, Laws, Methods, and Definitions
Change = Paid - Cost
Making Change Formula
Key definitions:

Coin: Small metal piece used as currency

Bills: Paper money in denominations of $1, $5, $10, $20, etc.

Decimal notation: Money expressed with dollar sign and cents after decimal

Complete Money Methodology:
  1. Identify coin values: Know penny (1¢), nickel (5¢), dime (10¢), quarter (25¢)
  2. Count money: Multiply quantity by value for each coin type
  3. Add amounts: Combine all coin values to find total
  4. Calculate change: Subtract total cost from amount paid
Tip 1: Count by tens using dimes, by fives using nickels.
Tip 2: Start with the largest denomination when making change.
Tip 3: Use subtraction to check if your change is correct.
Tip 4: Practice with real money to develop tactile recognition.
Common errors: Misidentifying coins, incorrect addition/subtraction, forgetting to regroup.
Practice tips: Use play money, create shopping scenarios, count daily allowance.
Money facts to remember:

• 100 pennies = $1.00

• 20 nickels = $1.00

• 10 dimes = $1.00

• 4 quarters = $1.00

• Change = Amount Paid - Total Cost

Questions & Answers

Question: I sometimes get confused about which coin is which. How can I remember the differences between pennies, nickels, dimes, and quarters?

Answer: Great question! Here are memory aids for each coin:

  • Penny (1¢): Smallest value, copper/brown color, Abraham Lincoln on front
  • Nickel (5¢): Silver color, larger than a penny, worth 5 pennies
  • Dime (10¢): Smallest coin physically, silver color, worth 10 pennies
  • Quarter (25¢): Largest coin, silver color, worth 25 pennies

Memory trick: The dime is "tiny" but worth more than a nickel! Also, notice that size doesn't match value - the dime is smaller than the nickel but worth twice as much.

Practice handling real coins frequently to build tactile recognition.

Question: When making change, how do I know which coins to use? Like if I owe someone 60 cents, how do I decide what to give them?

Answer: When making change, use the largest coins first to minimize the total number of coins:

  • Start with quarters (25¢) - how many fit into the amount?
  • Then use dimes (10¢) for the remainder
  • Then nickels (5¢) for what's left
  • Finally pennies (1¢) for the smallest amount

For 60¢: 2 quarters (50¢) + 1 dime (10¢) = 60¢ using just 3 coins

Alternative: 6 dimes = 60¢ using 6 coins

The first option is better because it uses fewer coins!

Question: My child struggles with word problems involving money. What strategies can help them solve these problems more easily?

Answer: Here's a step-by-step strategy for money word problems:

  1. Read carefully: Identify what's being bought and how much each costs
  2. Find the question: What does the problem want to know?
  3. Identify known information: What money was given, what was bought
  4. Plan the solution: Will you add, subtract, or both?
  5. Solve step-by-step: Work through the calculation
  6. Check your answer: Does it make sense in the story?

Encourage drawing pictures or using actual coins to represent the problem. Practice with familiar scenarios like buying snacks or toys.

Always verify that the answer fits the context of the problem!