Counting money: coins, change and word problems

US and UK coins

In the US, children use four coins every day: the penny (1¢), the nickel (5¢), the dime (10¢) and the quarter (25¢). Size is a trap: a dime is smaller than a penny and a nickel but worth more than both. Half-dollar and dollar coins exist but are rarely seen, and paper bills start at $1. 100 cents make 1 dollar.

In the UK, the coins are 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2, and notes start at £5. 100 pence make 1 pound. Each question in the practice set uses either US or UK money, never both at once, and the method is exactly the same for both.

How to count coins

Start with the coin worth the most. Big steps first means fewer, easier steps: for a quarter and 3 pennies you say 25, 26, 27, 28. Starting with the pennies works too, but then you have to add 25 to 3 in your head, which is harder.

The real skill underneath is skip counting, and switching from one count to another. Picture a number line with big jumps of 25, then medium jumps of 10, then small jumps of 5 and 1. These examples get a little harder each time.

• All the same coin: 6 dimes is 10, 20, 30, 40, 50, 60, so 60¢.
• Two kinds: 3 nickels and 4 pennies is 5, 10, 15, then 16, 17, 18, 19, so 19¢.
• Mixed: 1 quarter, 2 dimes and 2 nickels is 25, 35, 45, 50, 55, so 55¢.
• Past a dollar: 3 quarters and 3 dimes is 25, 50, 75, 85, 95, 105, so 105¢, which is $1.05.
• UK coins: 50p, 20p, 20p, 5p and 2p is 50, 70, 90, 95, 97, so 97p.

Making change by counting up

Change is the amount paid minus the price. The easiest way to find it is to count up from the price, the way a shopkeeper hands back coins. For something costing 63¢ paid with $1: 63 to 65 is 2¢, 65 to 75 is 10¢, and 75 to 100 is 25¢. The change is 2 + 10 + 25 = 37¢. Counting up avoids regrouping across the zeros in 100.

It works the same way with bigger amounts. Buy something for $3.45 and pay with $5: $3.45 to $3.50 is 5¢, $3.50 to $4.00 is 50¢, and $4.00 to $5.00 is $1. The change is $1.55. Some practice questions ask for the change in cents or pence, so $1.55 would be typed as 155.

Money word problems

First decide what the question wants: a total means add, change or a difference means subtract, and enough or not means compare. Then work in one unit, either all cents or dollars and cents.

• Total: a sandwich costs $2.75 and a drink costs $1.40. $2.75 + $1.40 = $4.15.
• Enough or not: Leo has 2 dimes and 3 nickels, which is 35¢. A pencil topper costs 37¢, so he is 2¢ short.
• Fewest coins: to make 41¢, take the biggest coin that fits each time: 25 + 10 + 5 + 1, so 4 coins.
• Fewest coins in pence: 38p is 20p + 10p + 5p + 2p + 1p, so 5 coins.

In an amount like $4.15, the digits after the point are cents: 4 dollars and 15 cents. Always write two digits after the point, so $3.50 and not $3.5. When a practice question says to type the amount like 7.45, type the dollars or pounds, a point, then the cents or pence.

How it is taught in school

In the US, Common Core places money in grade 2: children solve word problems involving dollar bills, quarters, dimes, nickels and pennies, using the $ and ¢ symbols correctly (2.MD.C.8). The grade 1 standards do not include money, so grade 2 is where counting coins is formally taught.

In England, Year 1 pupils recognise and know the value of different coins and notes. In Year 2 they use the £ and p symbols, combine amounts to make a particular value, find different combinations of coins that make the same amount and solve simple problems, including giving change. In Year 3 they add and subtract amounts of money to give change, using both £ and p.

How parents can help

• Empty a purse or a coin jar onto the table and count it together, biggest coins first.
• Play shop with price tags under $1 or £1, and take turns being the shopkeeper who counts up the change.
• Ask how else an amount can be made. 30¢ can be 3 dimes, a quarter and a nickel, or 6 nickels.
• Let your child pay for something small at a real checkout and check the change.
• Print a fresh worksheet, let your child mark it with the answer key, and read the worked steps together for any they missed.