Coins, change and shopping maths at home
Few topics in school mathematics have as obvious a purpose as money. Children know that coins buy things, they see adults paying, and many receive pocket money or have a piggy bank. That makes money an ideal context for arithmetic: counting, place value, addition, subtraction, and later decimals and percentages. It is also one of the most useful life skills a child will ever practise. This article suggests how to build understanding of coins and change step by step at home, using real money and real situations.
Written for children aged 6 to 10.
Why money is good mathematics
Money is a practical use of several big ideas at once:
- Counting and skip counting. Counting a handful of coins uses skip counting by 5s, 10s and 25s.
- Place value and exchange. Where pennies are still used (as in the United States), ten pennies are worth one dime; either way, ten dimes are worth a dollar. This is exactly the same "ten of these make one of those" structure behind base-ten numbers.
- Addition and subtraction. Paying and getting change are both addition and subtraction in real life.
- Decimals. Prices such as $3.45 are the first decimals most children meet, and the digits after the decimal point have a meaning they already understand: cents.
(The examples here use dollars and cents, as in Canada and the United States. Canada stopped distributing the penny in 2013 and rounds cash totals to the nearest 5 cents, so penny examples apply to the US or to "when pennies are available". If you live elsewhere, the same ideas work with euros, pounds or any currency.)
Step 1: recognising coins and knowing their values
The first goal is to tell each coin apart and know what it is worth. Place a few of each coin on the table and let your child look and feel: size, colour, edge, pictures and numbers. Note one common surprise: size does not match value. A dime is smaller than a nickel but worth more. This is an excellent opportunity to discuss that a coin's value is not how big it looks, but what it is worth.
Start with one kind of coin at a time and let your child sort a mixed pile. Then play "What is it worth?" holding up a coin and asking the value, and "Which one?" asking them to find a five-cent coin.
Step 2: counting coins
Counting collections of the same coin is skip counting: five dimes is 10, 20, 30, 40, 50. Counting mixed coins is harder and calls for strategy. The best advice: start with the biggest value and work down. Put the quarters together and count by 25s, then add the dimes by tens, then nickels by fives, then any pennies by ones. Sorting by type first removes much of the difficulty.
Games: "Count the piggy bank" (once a week, together), or a treasure chest of coins to be counted by the child. Check by counting a second way: does the total come out the same? Seeing that the total does not depend on the order of counting is a lovely mathematical discovery.
Step 3: making amounts in different ways
A rich activity is making the same amount with different coins. How many ways can you make 25 cents? One quarter, or two dimes and a nickel, or five nickels, or... This builds flexibility and reinforces that the same value can be made up in many ways. It also introduces systematic thinking: how do you know you've found all the ways?
Step 4: shopping and paying
Set up a shop at home. Use real items or toys with price tags (start with prices under a dollar, in whole units of five cents). Your child is the shopkeeper, then the customer. This is wonderful practice because it combines reading prices, adding amounts, choosing coins and checking.
For young children, start with exact payment: "This costs 35 cents. Can you find the coins?" Then move to payment with a larger coin or bill.
Step 5: change
Making change is subtraction, and the best way to learn it is by counting up. If an item costs 65 cents and the customer pays with a dollar, the shopkeeper starts at 65 and counts up to 100: "65, 70 (a nickel), 75 (a nickel), 100 (a quarter)." This "shopkeeper's method" uses coins to count on to the amount paid, and the coins handed over are the change. It is much easier than "100 − 65" for many children, and it is exactly how many cashiers think.
You can show the link between counting up and subtraction when the child is ready: the amount counted up is the difference.
Step 6: prices with decimals
Once your child is comfortable with cents, link to the dollar-and-cents notation. $2.35 means 2 dollars and 35 cents. The decimal point separates dollars from cents. Be explicit that the two digits after the point stand for hundredths of a dollar: 35 cents is 35 out of 100. This is a gentle bridge to decimals and to the idea of tenths and hundredths.
Common error: writing 5 cents as $0.5 instead of $0.05, or thinking $1.5 means one dollar and five cents. Using real coins to show that $1.50 is one dollar and fifty cents helps resolve this.
Real-life activities
Pocket money plan. If your child receives pocket money, use it as a calculation prompt. "You have $4.50. The book costs $6. How much more do you need? How many weeks until you can buy it?" This is mathematics with a real stake.
Grocery trip. Give your child a small amount and a short list. They look for prices, round to the nearest dollar to estimate the total, and check with you at the till.
Comparing prices. Which is the better buy, a pack of six for $3 or a pack of four for $2.50? Encourage "how much each?" thinking, which introduces division and unit price.
Garage sale or lemonade stand. Running a small stand gives practice in pricing, counting money, and making change, all with a real purpose.
Piggy bank maths. Make a chart of savings and watch it grow. This also introduces the idea of data and graphs.
Talking about money
Take care not to make money a source of pressure: keep the games light and let mistakes become learning moments.
Patience and progression
Money skills develop across several years: coins and counting in the early grades, change and decimals in the middle grades, percentages and unit prices later on. There is no hurry. Keep it real, keep it playful, and let your child handle real coins as often as you can. It is hard to think of a more practical, motivating way to build number sense.
Try it in the app
Practise this at the screen too: Count coins, Totals and change within 100, Add, subtract and give change. You may also like our articles on place value and word problems.