F. Financial Literacy · Counting Money to $200Same Amount, Different CoinsF1.1 A1About 40 minutesLearning goalsI can show the same amount of money in two or more ways using coins.I can trade coins for other coins worth the same amount.I can make an amount using the fewest coins.I can use an organized list to find all the ways to make an amount.Words to knowsame valueWorth the same amount. 2 quarters and 5 dimes have the same value: 50¢.combinationA group of coins (or bills) put together. 1 quarter and 1 nickel is one combination for 30¢.tradeTo swap money for other money that is worth exactly the same.fewestThe smallest number. The fewest coins for 50¢ (without a fifty-cent piece) is 2 quarters.organized listA list made in an order, so you do not miss any ways or repeat any.Let's get started!At the school winter carnival, a cup of hot chocolate costs 50¢. Three friends buy one each.Ari pays with 2 quarters.Bea pays with 5 dimes.Cal pays with 1 quarter, 2 dimes and 1 nickel.They used different coins. Did they all pay the right amount? Let's count!Hot chocolate at a winter carnival. Each cup costs the same, but people can pay with different coins that add up to the same amount. AI-generated imageAri25¢25¢= 50¢Bea10¢10¢10¢10¢10¢= 50¢Cal25¢10¢10¢5¢= 50¢Ari: 25, 50. Bea: 10, 20, 30, 40, 50. Cal: 25, 35, 45, 50. Everyone paid 50¢!They all paid 50¢. There are many ways to make the same amount of money. The coins can look very different, but the value is the same.We can use the equal sign to show this:2 quarters = 5 dimesBoth sides are worth 50¢.Trading coinsWhen you trade, you swap some coins for other coins worth exactly the same. A bank or a store can do this for you. Here are trades worth knowing:These coins......have the same value asCheck2 nickels1 dime5, 105 nickels1 quarter5, 10, 15, 20, 252 dimes and 1 nickel1 quarter10, 20, 254 quarters1 loonie (100¢)25, 50, 75, 10010 dimes1 loonie (100¢)10, 20, 30... 1002 loonies1 toonie (200¢)100, 2008 quarters1 toonie (200¢)25, 50, 75, 100, 125, 150, 175, 200Coin trades. Each row shows two ways to make the same amount.Worked exampleExample 1: Show 75¢ three waysShow 75¢ in three different ways.Way 1: Use quarters. 25, 50, 75. That is 3 quarters.Way 2: Use dimes and a nickel. 10, 20, 30, 40, 50, 60, 70, then 75. That is 7 dimes and 1 nickel.Way 3: Mix them. 25, 50 (2 quarters), 60, 70 (2 dimes), 75 (1 nickel). That is 2 quarters, 2 dimes and 1 nickel.Count each way to check. Each one is 75¢.3 quarters = 7 dimes and 1 nickel = 2 quarters, 2 dimes and 1 nickel. All are 75¢.Worked exampleExample 2: Find ALL the ways to make 25¢How many ways can you make 25¢ with quarters, dimes and nickels?Make an organized list. Start with the biggest coin: 1 quarter. That is one way.Now use no quarters. Try the most dimes that fit: 2 dimes (20¢) and 1 nickel to make 25¢.Use 1 fewer dime: 1 dime (10¢). We need 15¢ more, so add 3 nickels.Use no dimes: 5 nickels.We can't use fewer than 0 dimes, so the list is finished.There are 4 ways to make 25¢.QuartersDimesNickelsTotal10025¢02125¢01325¢00525¢An organized list for 25¢. Each row uses one fewer big coin, so no way is missed.Making an amount with the fewest coinsSometimes we want to carry as few coins as possible. Here is the trick:Start with the biggest coin that is not more than the amount.Use as many of that coin as you can without going over.Move to the next smaller coin for what is left.Keep going until you reach the amount.Worked exampleExample 3: Fewest coins for 140¢Make 140¢ using the fewest coins.The biggest coin that fits is the loonie (100¢). A toonie (200¢) is too much. Now we have 100¢. We need 40¢ more.A quarter fits in 40¢. Now we have 125¢. We need 15¢ more.A second quarter would be too much. A dime fits. Now we have 135¢. We need 5¢ more.A nickel finishes it: 140¢.4 coins: 1 loonie, 1 quarter, 1 dime and 1 nickel.Goal: 140¢ with the fewest coins$1100¢need 40¢25¢125¢need 15¢10¢135¢need 5¢5¢140¢done!Biggest coin that fits first. 4 coins in all.Making 140¢ with the fewest coins: take the biggest coin that fits, then ask how much is still needed. 1 loonie, 1 quarter, 1 dime and 1 nickel.Worked exampleExample 4: Many ways to make 200¢Show 200¢ in four ways.1 toonie (200¢).2 loonies: 100, 200.1 loonie and 4 quarters: 100, 125, 150, 175, 200.8 quarters: 25, 50, 75, 100, 125, 150, 175, 200.1 toonie = 2 loonies = 1 loonie and 4 quarters = 8 quarters. They are all 200¢.Check your workAfter you make an amount, count it again starting with the coin worth the most. If you get the same total, your combination is correct. Two ways are the same value only if their totals match.Just for funRiddle: I am worth 25¢, and there is a caribou on my back. Who am I?A quarter! 🦌Hands-on activityCoin swap shopYou need: real or paper coins, a few small pieces of paper, and a pencil.A grown-up writes amounts on pieces of paper, such as 35¢, 60¢, 100¢, 150¢. Put them face down.Pick one. Make that amount with coins. Count to check.Now trade! Swap some of your coins for others with the same value (for example, swap a quarter for 2 dimes and a nickel). Count again. Is it still the same amount?Make the amount one more time using the fewest coins you can.Draw each way in a table like the one in Example 2.Math talk: "How do you know your two ways are worth the same?"Your turn1Show 30¢ in two different ways.Show answerAnswers will vary. Some ways: 3 dimes; 1 quarter and 1 nickel; 2 dimes and 2 nickels; 1 dime and 4 nickels; 6 nickels. Check that each way counts to 30¢.2How many nickels have the same value as 1 quarter?Show answer5 nickels. 5, 10, 15, 20, 25.3How many quarters have the same value as 1 loonie?Show answer4 quarters. 25, 50, 75, 100.4Fill in the blank: 1 quarter + __ dimes + 1 nickel = 50¢Show answer2 dimes. 1 quarter and 1 nickel make 30¢. We need 20¢ more, and 2 dimes are 20¢.5Show 100¢ using only dimes.Show answer10 dimes. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.6Make 60¢ with the fewest coins (no fifty-cent piece).Show answer3 coins: 2 quarters and 1 dime. 25, 50, 60.7Do these have the same value? Group A: 3 quarters. Group B: 6 dimes and 3 nickels.Show answerYes. Group A: 25, 50, 75. Group B: 10, 20, 30, 40, 50, 60, then 65, 70, 75. Both are 75¢.More practice: warm-up12 nickels have the same value as 1 ____.Show answerdime (10¢).22 loonies have the same value as 1 ____.Show answertoonie ($2, or 200¢).3Show 10¢ in two ways.Show answer1 dime, or 2 nickels.4How many dimes make 50¢?Show answer5 dimes. 10, 20, 30, 40, 50.5True or false: 1 quarter has the same value as 2 dimes.Show answerFalse. 2 dimes are 20¢, but a quarter is 25¢. You would need 2 dimes and a nickel.More practice: on your own1Show 45¢ in three different ways.Show answerAnswers will vary. Some ways: 1 quarter and 2 dimes (25, 35, 45); 4 dimes and 1 nickel (10, 20, 30, 40, 45); 1 quarter, 1 dime and 2 nickels (25, 35, 40, 45); 9 nickels.2Make 85¢ with the fewest coins.Show answer4 coins: 3 quarters and 1 dime. Start with quarters: 25, 50, 75. A 4th quarter would be too much (100¢). We need 10¢ more, so add a dime: 85.3Make 175¢ with the fewest coins.Show answer4 coins: 1 loonie and 3 quarters. Start with the loonie: 100. A toonie is too much. Then quarters: 125, 150, 175.4Mo trades his loonie for quarters. Then he trades one of the quarters for nickels. What coins does he have now? Are they still worth 100¢?Show answer1 loonie = 4 quarters. 1 quarter = 5 nickels. So Mo has 3 quarters and 5 nickels. Count: 25, 50, 75, then 80, 85, 90, 95, 100. Yes, still 100¢. Trading never changes the value.5A muffin costs 120¢. Show two ways to pay exactly.Show answerAnswers will vary. Some ways: 1 loonie and 2 dimes (100, 110, 120); 4 quarters and 2 dimes (25, 50, 75, 100, 110, 120); 1 loonie, 1 dime and 2 nickels.Challenge1Make 50¢ with exactly 4 coins (no fifty-cent piece).Show answer1 quarter, 2 dimes and 1 nickel: 25, 35, 45, 50. Without a quarter, 4 coins can only make 40¢ at most (4 dimes). With 2 quarters you already have 50¢ and can't add 2 more coins. So you need exactly 1 quarter, and the other 3 coins must make 25¢: 2 dimes and 1 nickel.2Make an organized list of all the ways to make 20¢ using dimes and nickels.Show answerThere are 3 ways:2 dimes, 0 nickels1 dime, 2 nickels0 dimes, 4 nickelsStart with the most dimes, then use one fewer dime each time.3Make 150¢ with exactly 6 coins.Show answerAnswers will vary. One way: 6 quarters (25, 50, 75, 100, 125, 150). Another way: 1 loonie, 1 quarter, 1 dime and 3 nickels (100, 125, 135, 140, 145, 150). Count to check that there are 6 coins and the total is 150¢.Check your understandingQuiz1. Which has the same value as 1 dime?2 nickels1 nickel1 quarter2. Which group is worth 75¢?5 dimes7 nickels3 quarters3. Which shows 35¢ with the fewest coins?3 dimes and 1 nickel7 nickels1 quarter and 1 dime4. How many quarters make 200¢?8425. Which is NOT worth 50¢?4 dimes and 1 nickel5 dimes2 quarters6. Jin trades 1 loonie for dimes. How many dimes does he get?100410Mark lesson completeFor parents and teachersWhat your child is learning: that the same amount of money can be made with different combinations of coins (F1.1), and how to trade coins of equal value and make an amount with the fewest coins. Making an organized list builds the mathematical processes of reasoning and representing (A1).Common mistakes:Thinking more coins means more money. 5 dimes and 2 quarters look different, but both are 50¢. Always count to compare.Missing or repeating combinations. Show your child how to start with the most of the biggest coin and use one fewer each time.Going over the amount when finding the fewest coins. Ask, "How much do you still need?" before adding each coin.Forgetting the toonie and loonie are worth cents too. A loonie is 100¢ and a toonie is 200¢.How to help: Use real coins whenever you can. At a store or vending machine, ask, "Can you pay a different way?" Play "bank": your child trades a loonie for quarters, or a quarter for dimes and a nickel, and checks the value stays the same.PreviousCounting Coins up to 200¢NextBills and Coins: Counting Dollars to $200