Counting money and making change
Counting a mixed group of coins to a total, then working out the change from a purchase
About three lessons of 45 to 55 minutes
Real money, real change
Counting money is one of the few maths skills students use almost every week outside school, at a shop, a market stall, or a school fundraiser. It also quietly practises skip counting, since coins come in different values and counting them well means counting by 25s, 10s, 5s and 1s in the same pile.
This unit teaches two connected skills: counting a mixed group of coins to find a total, and working out how much change is owed when a purchase costs less than the amount paid. Both come down to the same underlying idea, adding and subtracting amounts of money the same way as any other numbers, just with a dollar sign and two decimal places.
- quarter, dime, nickel, penny25¢, 10¢, 5¢, 1¢, the four coins to know in order from biggest to smallest
- count from biggest to smallestcounting quarters first, then dimes, then nickels, then pennies keeps the running total easiest to track
- toy costs $3.75, pay with $4.00change is 25 cents, the amount needed to reach the next dollar
- $ and ¢ are two different unitsdollars and cents are added like whole numbers and cents, not mixed together
What students will be able to do
Students will count a mixed group of coins (pennies, nickels, dimes, quarters) to find a total value, will represent money amounts correctly using dollar and cent symbols, and will work out the change owed when a purchase price is less than the amount paid.
- I can name each coin (penny, nickel, dime, quarter) and its value.
- I can count a mixed group of coins by starting with the biggest value and counting on.
- I can write a money amount correctly using the dollar sign or cent sign.
- I can work out the change from a purchase by counting up from the price to the amount paid.
Standards this unit teaches
- 2.MD.C.8Common Core (US)Money word problems
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using dollar and cent symbols appropriately.
- AC9M2N05Australian Curriculum v9 (ACARA)Model money problems
Model and solve everyday additive problems, including simple money transactions, using calculated or actively counted solutions, and represent the situation using digital tools where appropriate.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Penny
- a coin worth 1 cent
- Nickel
- a coin worth 5 cents
- Dime
- a coin worth 10 cents, the smallest coin in size but worth more than a nickel or penny
- Quarter
- a coin worth 25 cents
- Change
- the money given back when a payment is more than the price of an item
- Cent
- one hundredth of a dollar, shown with the ¢ symbol or as decimal cents after a $ sign
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Know the coins and their values
ConcreteOpen by anchoring each coin's name to its value, since counting coins is meaningless until the values are automatic. Use real or realistic coins so students see and touch the actual size and colour differences.
Teach the four coins in value order from smallest to biggest: penny (1¢), nickel (5¢), dime (10¢), quarter (25¢). Point out that a dime is physically smaller than a nickel or penny, despite being worth more, a common source of confusion.
Practise naming a coin shown and stating its value, and the reverse: given a value, pointing to the matching coin.
Name the coin worth 10 cents.
- Recall the four coin values: penny 1¢, nickel 5¢, dime 10¢, quarter 25¢.
- Match 10 cents to its coin name.
Answer: The dime is worth 10 cents.
- What is a penny worth? A nickel? A dime? A quarter?
- Which coin is physically the smallest, and is it the coin worth the least?
- Put the four coins in order from least to greatest value.
2. Counting a mixed group of coins
PictorialTeach the counting-on strategy: start with the biggest-value coins and count by their value, then move to the next-biggest, ending with pennies counted one at a time. This keeps the running total in the easiest order to track.
Sort coins into groups by type first: all quarters together, then dimes, then nickels, then pennies. Count the quarters by 25s, continue counting on by 10s for the dimes, then by 5s for the nickels, then by 1s for the pennies.
Say the running total aloud at each step (25, 50, 60, 70, 75, 76, 77) so students hear the count build rather than adding silently and losing track.
Count the total value of 1 quarter, 1 dime, 1 nickel and 2 pennies.
- Sort by coin type: 1 quarter, 1 dime, 1 nickel, 2 pennies.
- Count on from the biggest: quarter is 25.
- Add the dime by counting on 10: 25, 35.
- Add the nickel by counting on 5: 35, 40.
- Add the two pennies by counting on 1 at a time: 40, 41, 42.
Answer: The total is 42 cents (42¢). Counting biggest to smallest keeps each step a simple count-on.
- Why do we count the biggest coins first?
- What do you count by once you reach the pennies?
- If you had 2 quarters and 1 dime, what running total would you say at each step?
3. Reading and writing money amounts
AbstractTeach the two correct ways to write a money amount: cents alone with a ¢ sign for amounts under a dollar, or dollars and cents together with a $ sign and two decimal places for a dollar or more.
Amounts under a dollar use the cent sign after the number: 42¢. Amounts of a dollar or more use the dollar sign before the number, with exactly two digits after the decimal point for cents: $1.42, not $1.4 or $1.420.
Practise converting a counted total (like the 42 cents counted in section 2) into both forms where possible, and explain why $0.42 and 42¢ mean the same value written two different ways.
Write 'one dollar and seven cents' using the correct money notation.
- Identify the dollar part: 1 dollar.
- Identify the cent part: 7 cents, which needs a placeholder zero since it is less than 10 cents.
- Write it with the dollar sign and two decimal digits: $1.07.
Answer: $1.07. The zero after the decimal point is required, since cents always needs exactly two digits.
- When do you use the ¢ sign instead of the $ sign?
- Why does $1.07 need a zero after the decimal point?
- Are $0.42 and 42¢ the same amount?
4. Making change
AbstractTeach making change as counting on from the price to the amount paid, the same strategy used for counting coins, just starting from a price instead of zero. Model the count-up-to-the-next-friendly-number approach.
Given a price and the amount paid, count on from the price toward the amount paid, first to the next friendly number (like the next whole dollar), then the rest of the way. The total counted on is the change.
This is genuinely a subtraction problem, amount paid minus price equals change, but counting on is more reliable for students than subtracting money amounts directly, especially with decimals.
A toy costs $3.75. It is paid for with a $4.00 bill. How much change is owed?
- Start at the price: $3.75.
- Count on to the next friendly number, the whole dollar: $3.75 to $4.00 is 25 cents.
- Since $4.00 is exactly what was paid, the counting stops there.
- The total counted on is the change.
Answer: The change is 25 cents ($0.25). Counting on from $3.75 to $4.00 covers the gap in one friendly step of 25 cents.
- What operation is making change actually doing, even though we count on instead?
- Why is counting to the next whole dollar a useful first step?
- If a book costs $2.50 and is paid for with a $5.00 bill, what is the change?
Common misconceptions and how to address them
MisconceptionA bigger coin is always worth more money.
Why it happens: Students judge coin value by physical size and are misled by the dime, which is the smallest coin but worth more than a nickel or a penny.
How to address it: Teach coin values as facts to memorise, separate from size. Compare a dime and a nickel side by side, noting the dime is smaller yet worth double.
MisconceptionYou can count coins in any order and get the right total just as easily.
Why it happens: Students start with whatever coin is on top or nearest, mixing up the count and losing track of the running total.
How to address it: Insist on sorting first: biggest value to smallest, every time. Say the running total aloud at each coin to build the habit.
Misconception$1.4 and $1.40 are different amounts, or $1.4 is how you write one dollar forty cents.
Why it happens: Students transfer whole-number place value habits and do not realise cents always needs exactly two digits.
How to address it: Anchor the rule: cents is always two digits after the decimal point, so $1.4 must be written $1.40. Compare it to always writing two digits on a clock's minutes (3:05, not 3:5).
MisconceptionMaking change means subtracting the smaller number from the larger with the standard written algorithm.
Why it happens: Students attempt column subtraction with decimals and make regrouping errors that counting on avoids entirely.
How to address it: Teach counting on from the price to the amount paid as the default strategy for change, saving written subtraction for when counting on is impractical (a very large gap).
Guided practice (with answers)
1. Count the total value of 2 quarters and 3 pennies.
Answer: 2 quarters is 50 cents, plus 3 pennies is 53 cents (53¢). Count 25, 50, then 51, 52, 53.
2. Write 'sixty cents' using the cent sign, and again using the dollar sign.
Answer: 60¢, or $0.60. Both represent the same amount, sixty cents.
3. A snack costs $1.50 and is paid for with a $2.00 bill. What is the change?
Answer: The change is 50 cents ($0.50). Counting on from $1.50 to $2.00 covers the gap in one step of 50 cents.
4. You have 1 dime, 1 nickel and 4 pennies. What is the total?
Answer: 10 plus 5 plus 4 is 19 cents (19¢). Count 10, 15, then 16, 17, 18, 19.
Independent practice worksheets
Set the matching ChalkBee money worksheets for independent practice, having students count mixed coin groups and work out change from purchases, showing their counting-on steps.
Differentiation
- Start with only one or two coin types at a time (pennies and nickels only) before introducing all four.
- Provide a coin-value reference chart on the desk during independent work.
- Use real or play coins for physical sorting and counting before moving to pictures on a worksheet.
- For change, always count on to the next whole dollar as an explicit first step, rather than jumping straight to the final answer.
- Introduce half-dollar and dollar coins or notes, extending the value range.
- Pose problems with more than one way to make the same total, and ask students to find two different coin combinations.
- Introduce simple money word problems that combine two purchases before finding the total change from a single bill.
- Ask students to find the fewest possible coins that make a given total, a natural extension of coin fluency.
Assessment: exit ticket
A short exit ticket sampling coin counting, money notation, and making change.
1. Count the total: 1 quarter, 2 dimes, 1 penny.
Answer: 25 plus 20 plus 1 is 46 cents (46¢).
2. Write 'two dollars and five cents' correctly.
Answer: $2.05. The zero after the decimal point is required since cents always needs two digits.
3. A pencil costs $0.65. It is paid for with $1.00. What is the change?
Answer: The change is 35 cents ($0.35), counting on from $0.65 to $1.00.
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 knowing the coins and counting mixed groups (sections 1 and 2), Lesson 2 reading and writing money amounts (section 3), Lesson 3 making change plus the exit ticket (section 4 and assessment).
- Language to keep saying: biggest coin first, say the running total, count on to the next dollar. These phrases target the unit's main misconceptions directly.
- This unit deliberately teaches counting on for change rather than written subtraction, since it is more robust for young learners and mirrors how change is actually given in real transactions.
- Curriculum note: the US names money word problems with all four coin types directly at Grade 2 (2.MD.C.8). ACARA v9 folds money into general additive modelling at Year 2 (AC9M2N05) and develops the dollars-and-cents relationship explicitly the following year (AC9M3M04). This unit maps to US Grade 2 and supports the ACARA Year 2 additive-modelling expectations, with the notation work here preparing directly for the Year 3 dollars-and-cents descriptor.
- Present mode and print both work: use Present to model counting coins with the class as a whole, then print the worksheets for independent practice.