A coin says what it is worth
Every coin has its value on its face. A coin marked 10¢ is worth 10 cents. The sign ¢ stands for cents.
To find how much some coins are worth, count on by each coin's value. Three 10¢ coins count 10, 20, 30, so they are worth 30 cents. They are 3 coins, but they are not 3 cents: each coin is worth 10 cents on its own.
Three 10¢ coins, counted on in tens: 10, 20, 30. They are worth 30¢.
Different coins: biggest first
When the coins are different, add their values together. Start with the coin worth the most, then count on by each smaller coin in turn. For a 25¢ coin, a 10¢ coin and a 5¢ coin: start at 25, count on 10 to 35, then count on 5 to 40. The coins are worth 40 cents.
Any order gives the same total, but starting with the biggest coin makes the steps easy: 25, 35, 40.
Biggest coin first: 25, then 35, then 40. The three coins are worth 40¢.
0¢
Count the coins on, biggest first
Each coin is counted on by what it is worth, biggest first: 25, 35, 45, 50, 55. That is 5 coins and 55¢, two different numbers. The dime is the smallest coin and still worth more than a nickel.
More coins is not always more money
Three 10¢ coins are worth 30¢, and a 25¢, a 10¢ and a 5¢ coin are worth 40¢. Both are 3 coins, but they are worth different amounts, because the coins are worth different amounts.
Four 5¢ coins count 5, 10, 15, 20, so they are worth 20¢. One 25¢ coin on its own is worth more than all four of them. To compare two handfuls of coins, count the value of each handful, not the number of coins in it.
Four 5¢ coins: 5, 10, 15, 20. They are worth 20¢.
One 25¢ coin is worth 25¢, which is more than the four 5¢ coins.
Two slips
The first slip is counting the coins instead of their values: calling three coins 3¢. Read the value on each coin's face and count on by that.
The second slip is missing a coin. Point at each coin once as you count, and keep going until you reach the last one.
Other coins
Coins differ from one country to another. Some countries have 20¢ and 50¢ coins, and they are counted in the same way: count on by the value on each coin.
Worked example: More Coins or More Money
Question Lina has 5 coins: three 20-cent coins and two 5-cent coins. Tom has 3 coins: a 50-cent coin and two 20-cent coins. (a) Who has more money? (b) How much more?
1.Count what Lina has, biggest coin first: 20, 40, 60, then 65, 70. Lina has 70 cents.
Lina has 20, 40, 60, 65, 70 cents. 2.Count what Tom has, biggest coin first: 50, 70, 90. Tom has 90 cents.
Tom has 50, 70, 90 cents. 3.(a) 90 cents is more than 70 cents, so Tom has more money, with fewer coins.
(a) Tom has more money, with fewer coins. 4.(b) Count up from 70 to 90: 70 + 20 = 90. Tom has 20 cents more.
(b) 70 + 20 = 90. Tom has 20 cents more.
Answer: (a) Tom. He has 90 cents and Lina has 70 cents; (b) 20 cents more
Common mistakes
- Saying that Lina has more because she has 5 coins and Tom has 3. The number of coins does not tell what they are worth. One 50-cent coin is worth more than two 20-cent coins.
- Counting every coin as the same amount. A 5-cent coin, a 20-cent coin and a 50-cent coin are worth different amounts, so read the value on each coin.
Worked example: A Handful of Mixed Coins Counted
Question Mei has four coins in her hand: a 20-cent coin, a 5-cent coin, a 50-cent coin and another 20-cent coin. (a) How much money does Mei have? (b) Mei finds one more 5-cent coin. How much money does she have now?
1.Put the coins in order, biggest first: 50 cents, 20 cents, 20 cents, 5 cents.
The four coins, with the biggest value first. 2.Start with the biggest coin and count on: 50, then 50 + 20 = 70, then 70 + 20 = 90.
Count on from the biggest coin: 50, 70, 90. 3.(a) Add the last coin: 90 + 5 = 95. Mei has 95 cents.
(a) 90 + 5 = 95. Mei has 95 cents. 4.(b) One more 5-cent coin makes 95 + 5 = 100 cents. 100 cents is $1.
(b) 95 + 5 = 100 cents, and 100 cents is $1.
Answer: (a) 95 cents; (b) 100 cents, which is $1
Common mistakes
- Counting the coins and saying that Mei has 4 cents. Four is the number of coins. Each coin is worth its own amount, so the amounts are added.
- Starting with the small coins: 5 + 20 + 50 + 20. The total is the same, but the adding is harder. Starting with the biggest coin gives easy steps: 50, 70, 90, 95.