Making Change

For Elementary Students

What Is Change?

When you buy something and pay with more money than it costs, you get change back!

Think about it like this: If a candy bar costs $2 and you give the store $5, they need to give you back the extra $3. That's your change!

The Simple Formula

Change = Money you paid − Cost of the item

Example: Toy costs $3. You pay with $5.

Change = $5 − $3 = $2

You get $2 back!

Counting Up Method

This is how many cashiers make change — they count up from the price to what you paid!

Example: Item costs $3.25. You pay with $5.

Step 1: Start at $3.25

Step 2: Count up to the next dollar

• Add pennies to get to $3.30: 5 pennies (5¢)
• Add dimes to get to $4.00: 7 dimes (70¢)

Step 3: Count up to $5

• Add dollar bills: 1 dollar

Total change: $1 + 70¢ + 5¢ = $1.75

Another Way: Subtraction

You can also just subtract!

Example: Ice cream costs $4.50. You pay with $10.

  $10.00
−  $4.50
  ______
   $5.50

Your change: $5.50

Breaking Down the Subtraction

Sometimes you need to borrow!

Example: $10.00 − $7.45

Can't do 0 − 5 cents!
Borrow: $10.00 = $9 and 100 cents

  $9.100
− $7. 45
  ______
  $2. 55

Change: $2.55

Buying Multiple Things

Add up all the prices first, THEN find the change!

Example: Buy a book for $5 and a pencil for $1.50. Pay with $10.

Step 1: Total cost

$5.00 + $1.50 = $6.50

Step 2: Find change

$10.00 − $6.50 = $3.50

Your change: $3.50

Do I Have Enough Money?

Before you buy, check if you have enough!

Rule: Your money must be greater than or equal to the price!

Example 1: You have $5. Item costs $4.25.

• $5.00 > $4.25 ✓ You have enough!
• Change: $5.00 − $4.25 = $0.75

Example 2: You have $3. Item costs $3.50.

• $3.00 < $3.50 ✗ Not enough!
• You need $0.50 more

Quick Estimate Trick

Round the prices to check your change!

Example: Item costs $7.89. You pay with $20.

Estimate:

• Round $7.89 to $8
• $20 − $8 = about $12

Actual:

• $20.00 − $7.89 = $12.11

Close to our estimate! ✓

For Junior High Students

Understanding Change

Change is the difference between the amount paid and the total cost of purchased items. It's calculated using subtraction.

Formula: Change = Amount Paid − Total Cost

Real-world application: This concept is fundamental in retail, banking, and personal finance.

Method 1: Direct Subtraction

Calculate change by subtracting the total cost from the amount paid.

Example: Item costs $7.45. Customer pays with $10.

  $10.00
−  $ 7.45
  _______
   $ 2.55

Steps:

1. Align decimal points
2. Subtract cents: 100 − 45 = 55 (borrowing 1 dollar = 100 cents)
3. Subtract dollars: 9 − 7 = 2
4. Result: $2.55

Verification: $7.45 + $2.55 = $10.00 ✓

Method 2: Counting Up (Making Change)

This method counts from the cost up to the amount paid, determining the fewest coins and bills needed.

Example: Item costs $3.67. Customer pays with $5 bill.

Process:

1. Start at $3.67
2. Add 3 pennies → $3.70
3. Add 1 dime → $3.80
4. Add 1 dime → $3.90
5. Add 1 dime → $4.00
6. Add 1 dollar → $5.00

Change: 3 pennies + 3 dimes + 1 dollar = $1.33

Why this method? It minimizes the number of coins/bills given and reduces calculation errors.

Handling Cents and Borrowing

When subtracting money, you often need to borrow from the dollar amount.

Example: $10.00 − $7.45

Problem: Can't subtract 45 cents from 0 cents

Solution: Borrow 1 dollar (= 100 cents)

  $10.00 = $9 + $1.00 = $9 + 100¢

   $9.100
−  $7. 45
   ______
   $2. 55

Alternative approach: Convert entirely to cents

$10.00 = 1,000¢
$7.45 = 745¢

1,000¢ − 745¢ = 255¢ = $2.55

Multiple Items

For multiple purchases, calculate the total cost first, then find change.

Example: Purchases:

• Book: $6.50
• Pen: $1.25
• Notebook: $3.75

Payment: $20 bill

Step 1: Find total cost

  $6.50
  $1.25
+ $3.75
  _____
 $11.50

Step 2: Calculate change

  $20.00
− $11.50
  ______
   $8.50

Change: $8.50

Checking Sufficiency of Funds

Before making a purchase, verify: Amount Available ≥ Total Cost

Example 1: Have $15.50, item costs $12.99

$15.50 ≥ $12.99 ✓
Change = $15.50 − $12.99 = $2.51
Sufficient funds

Example 2: Have $8.25, item costs $9.00

$8.25 < $9.00 ✗
Shortage = $9.00 − $8.25 = $0.75
Need $0.75 more

Estimating Change

Use rounding to quickly estimate expected change and catch errors.

Example: Item costs $17.89, pay with $50

Estimate:

• Round $17.89 to $18
• $50 − $18 = $32 (approximate change)

Actual calculation:

$50.00 − $17.89 = $32.11

Comparison: $32.11 ≈ $32 ✓ (estimate confirms calculation)

Why estimate? Catches major errors (like decimal point mistakes) and builds number sense.

Tax and Tips

In real-world scenarios, sales tax and tips affect the total cost.

Sales tax example: Item price $20, tax rate 8%

Tax = $20 × 0.08 = $1.60
Total cost = $20.00 + $1.60 = $21.60

Pay with $25:
Change = $25.00 − $21.60 = $3.40

Tip example: Restaurant bill $45, leave 20% tip

Tip = $45 × 0.20 = $9.00
Total = $45.00 + $9.00 = $54.00

Pay with $60:
Change = $60.00 − $54.00 = $6.00

Making Change with Specific Denominations

Determine the fewest coins and bills to give as change.

Example: Change needed: $3.47

Break down:

• $3.00 → 3 one-dollar bills (or 1 five, but that's more than needed)
• $0.47 → 1 quarter (25¢) + 2 dimes (20¢) + 2 pennies (2¢)

Total: 3 bills + 5 coins = 8 pieces

Greedy algorithm: Start with largest denominations first for minimum count.

Real-Life Applications

Retail: Cashiers calculate change thousands of times daily

Personal budgeting: Track spending and verify receipts

Currency exchange: Converting between currencies with exchange rates

Banking: Deposit/withdrawal transactions

Food service: Splitting checks, calculating tips

Common Mistakes

Mistake 1: Forgetting to borrow when subtracting

❌ $10.00 − $7.45 = $3.55 (incorrect) ✓ Borrow: $10.00 − $7.45 = $2.55

Mistake 2: Misaligning decimal points

❌

$10.0
− $7.45

✓

$10.00
− $7.45

Mistake 3: Not finding total cost first with multiple items

❌ Calculate change for each item separately ✓ Add all items, then calculate change once

Mistake 4: Giving change larger than amount paid

❌ Paid $5, cost $3, change $8 (illogical!) ✓ Change must be less than amount paid

Tips for Success

Tip 1: Always align decimal points when subtracting

Tip 2: Convert to cents if borrowing is confusing

Tip 3: Estimate to verify your answer makes sense

Tip 4: Practice the counting-up method for mental math

Tip 5: Check: Cost + Change = Amount Paid

Mental Math Strategies

Rounding to nearest dollar:

$8.99 is almost $9
Pay $20: change ≈ $11
Actual: $20 − $8.99 = $11.01 (very close!)

Breaking into parts:

$20 − $7.45
= $20 − $7 − $0.45
= $13 − $0.45
= $12.55

Adding to round numbers:

$7.45 + $0.55 = $8.00
$8.00 + $12.00 = $20.00
Change = $0.55 + $12.00 = $12.55

Practice