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Count coins and give change, and read a clock to five minutes with a.m. and p.m.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
In this lesson you count a handful of coins by starting with the ones worth most, work out change from a dollar, and read a clock face to the nearest five minutes. By the end you can say why a dime is worth more than a nickel.
You can add equal groups, count by fives and tens, and subtract a known part from a whole. Money uses those same ideas with different coin values. Today we will count U.S. coins and dollar bills, solve price and change problems, and keep dollar notation separate from clock notation. Our classroom price stories state complete prices; use exactly the amounts given.
| Term | What it means |
|---|---|
| penny | A U.S. coin worth 1 cent. |
| nickel | A U.S. coin worth 5 cents. |
| dime | A U.S. coin worth 10 cents. |
| quarter | A U.S. coin worth 25 cents. |
| dollar | An amount equal to 100 cents. |
| change | The amount returned when payment exceeds the price. |
Two quarters, one dime and three pennies are worth sixty-three cents. Count the quarters as twenty-five and fifty, add ten to reach sixty, then add the three pennies to reach sixty-three. There are six coins but sixty-three cents of value. Counting the objects and counting their value answer different questions. Name the unit in your answer so the reader knows which quantity you found.
Another way: table
| Coin | Value of one | Example group | Group value |
|---|---|---|---|
| Penny | 1 cent | 3 pennies | 3 cents |
| Nickel | 5 cents | 2 nickels | 10 cents |
| Dime | 10 cents | 2 dimes | 20 cents |
| Quarter | 25 cents | 2 quarters | 50 cents |
A coin's value comes from its denomination, not simply its size or color. A dime is smaller than a nickel but is worth ten cents rather than five. Learn the coin names and their values together. In our written tasks the names are supplied, so use the stated values rather than imagining how large a picture might look. A real-coin identification activity should use clear actual coins or accurate pictures with adult guidance.
Sort a mixed group by denomination if that helps you keep track. Count the quarters together, then the dimes, nickels and pennies. Starting with the greatest values often gives convenient landmarks, but another order can still be correct. What matters is adding each coin's value once. Moving a coin into a counted pile can prevent skipping it or counting it twice.
Two nickels have the same value as one dime: five plus five equals ten. Four quarters have the same value as one dollar: twenty-five plus twenty-five plus twenty-five plus twenty-five equals one hundred cents. These exchanges preserve value while changing the number of coins. A collection with more coins does not necessarily contain more money.
For example, five pennies are worth five cents, while one quarter is worth twenty-five cents. If asked which collection has more coins, choose the pennies. If asked which has greater value, choose the quarter. Say what the comparison is about before calculating. The coin count can be useful for packing or sorting, but it is not a substitute for the total value.
For three dimes, two nickels and four pennies, count ten, twenty, thirty for the dimes. Continue thirty-five and forty for the nickels, then forty-one, forty-two, forty-three and forty-four for the pennies. The running total changes its step size when the denomination changes. Do not keep counting by tens after you move to the nickels.
A subtotal record offers another method. Three dimes contribute thirty cents, two nickels contribute ten cents, and four pennies contribute four cents. Then add 30 + 10 + 4 = 44 cents. This is especially useful when a group contains many coins. Check that the subtotals include every denomination in the original list.
A total can pass one dollar. Three quarters and four dimes are seventy-five plus forty cents, or one hundred fifteen cents. That is one dollar and fifteen cents. The money has not changed value when you rename it. One hundred of the cents form a dollar, leaving fifteen cents. Keep the whole-cent total available when a task asks for its answer in cents.
When checking a sum, look for common omissions. If the result is short by the number of pennies, the pennies may have been left out. If it is close to the number of coins rather than their value, the denominations may have been ignored. Recount one group at a time and explain which part needed repair. A specific check is more useful than repeatedly recounting the same way without locating the error.
The cent symbol is ¢, so forty-five cents can be written 45¢. The dollar symbol is $, so three dollars can be written $3 or $3.00. In dollar notation, the two digits to the right of the decimal point record cents. One dollar and five cents is $1.05. One dollar and fifty cents is $1.50. The zero in $1.05 keeps five cents from being read as fifty cents.
Use one consistent notation for a single amount. Writing 45¢ or $0.45 gives the same value. Writing $45¢ mixes the two unit markers and is unclear. For our calculations, it is often easiest to express all amounts as whole cents first. Add or subtract those whole numbers, then rename the result in dollars and cents if requested.
Dollar bills have values too. Two one-dollar bills are two dollars, or two hundred cents. A five-dollar bill and three one-dollar bills total eight dollars. If all amounts are whole dollars, keep dollars as the unit. If a story mixes a one-dollar bill with coins, converting the bill to one hundred cents lets all the parts use a common unit.
Do not add one dollar and twenty-five cents as though they were the bare numbers one and twenty-five. One plus twenty-five equals twenty-six, but twenty-six cents is not the mixed amount. Use 100 + 25 = 125 cents, or state one dollar and twenty-five cents. The relationship one dollar equals one hundred cents explains the conversion, just as one hundred ones make one hundred in place value.
Change is the part of a payment that remains after the price has been paid. If an item costs sixty-five cents and the payment is one dollar, subtract sixty-five from one hundred. The change is thirty-five cents. The price and change together must equal the payment: 65 + 35 = 100. This relationship gives a check for every change problem.
You can count up from the price instead of subtracting in columns. From sixty-five, add five to reach seventy, then thirty to reach one hundred. The added amounts total thirty-five cents. The final landing one hundred is the payment, not the change; the change is the combined distance counted up. Labeling the jumps helps keep those quantities separate.
If two items are bought with one payment, first combine their prices. A pencil costs twenty-eight cents and an eraser costs thirty-seven cents. Their total is sixty-five cents. Paying one dollar leaves thirty-five cents. Subtracting just one item's price would give too much change because the other item still has to be paid for. Record the combined price before calculating the returned amount.
Check whether the payment is enough. If the total price is one hundred ten cents and the payment is one dollar, there is no change to return. Ten more cents are needed. In these lessons we describe that shortfall directly rather than writing a negative change amount. Compare payment and price before deciding whether to calculate change or additional money needed.
Several coin collections can make the same amount. Thirty cents can be a quarter and a nickel, three dimes, or six nickels. If a task asks for any collection worth thirty cents, all three are valid. If it asks for the fewest coins among these choices, the quarter and nickel use only two. If it limits which denominations are available, check that condition before selecting a collection.
To build a payment using a specified recipe, track the remainder. Suppose you must use one quarter and then dimes and pennies to make forty-eight cents. After the quarter, twenty-three cents remain. Two dimes leave three cents, so use three pennies. The check is 25 + 10 + 10 + 1 + 1 + 1 = 48. A different collection may have the same value but fail a rule such as exactly one quarter.
Money notation can look like time notation, but the units are different. The amount $1.25 means one dollar and twenty-five cents. The time 1:25 means twenty-five minutes after one o'clock. A dollar contains one hundred cents, while an hour contains sixty minutes. Do not use a hundred-based money calculation to read a clock or use a colon in a price.
A classroom sale might open at 3:25 p.m. and charge twenty-five cents for a card. The matching number twenty-five does not make those quantities interchangeable. The clock's long hand points to five because five groups of five minutes have passed since the hour. The price is counted with coin values. For a schedule, the short hand tells the hour already begun and p.m. identifies the afternoon. For the purchase, the price and payment determine change. State the unit before choosing the calculation.
When recording a solution, include the original prices, the payment and the returned or missing amount. Read the question once more to decide which result to report. A coin total, a purchase total and a change amount are all legitimate numbers, but they answer different questions. A clear sentence such as The change is thirty-five cents shows that the calculation has been interpreted, not just completed.
In a classroom role-play, a learner buys a twenty-eight-cent pencil and a thirty-seven-cent eraser with one dollar. The seller records sixty-five cents as the combined price and returns thirty-five cents, perhaps as a quarter and a dime. A partner checks the transaction by adding the two prices and the returned coins to make one hundred cents. If the seller returns seventy-two cents, the check reveals that only the pencil price was removed. The eraser was omitted. The written record of both purchases helps locate that error. These are invented classroom prices supplied for the exercise, so the calculation uses them directly without assuming anything about a real store.
A class plans a pretend sale that opens at 3:25 p.m. A card costs forty-eight cents. One learner records the opening time with a colon and p.m.; another constructs a payment with one quarter, two dimes and three pennies. The payment totals forty-eight cents, while the clock time is read using five-minute intervals and the hour already begun. Keeping these records in separately labeled columns prevents a price from being mistaken for a time. If a buyer pays one dollar for the card, the change is fifty-two cents. Checking 48 + 52 = 100 connects the payment to the price; the opening time does not enter that arithmetic.
More coins do not necessarily mean more money, and physical coin size is not a reliable value rule. Convert a dollar to one hundred cents before mixing it with cent amounts. Change is the gap between payment and total price, not the price itself. Keep decimal money notation separate from the colon used in a clock time.
Identify each denomination.
2 quarters, 1 dime and 3 pennies.
Coin names determine the values.
Count the quarters.
25 + 25 = 50 cents.
Each quarter contributes twenty-five.
Include the dime.
50 + 10 = 60 cents.
The running total now includes three coins.
Include the pennies.
60 + 1 + 1 + 1 = 63 cents.
Every remaining coin contributes one cent.
Check count versus value.
6 coins are worth 63 cents.
The two quantities use different units.
Read the price.
The card costs 65 cents.
This is the part kept by the seller.
Rename the payment.
1 dollar = 100 cents.
Both amounts must use the same unit.
Count to the next ten.
65 + 5 = 70.
Five cents is the first part of the change.
Count to the payment.
70 + 30 = 100.
Thirty cents completes the gap.
Combine the change parts.
5 + 30 = 35 cents.
The jumps together equal the returned amount.
Check the payment.
65 + 35 = 100 cents.
Price and change account for the dollar.
Read both prices.
A pencil costs 28 cents and an eraser 37 cents.
Both purchases must be included.
Find the combined price.
28 + 37 = 65 cents.
One payment covers both items.
Rename the payment.
A one-dollar bill is 100 cents.
The calculation needs a common unit.
Calculate the change.
100 - 65 = 35 cents.
The unused part of the payment returns to the buyer.
Choose a first change coin.
A quarter supplies 25 cents.
Ten cents remain after that coin.
Complete the change collection.
A dime supplies the remaining 10 cents.
25 + 10 = 35.
Check the whole transaction.
28 + 37 + 25 + 10 = 100 cents.
Prices and returned coins account for the entire payment.
Read the target and rule.
Make 46 cents with one quarter, dimes and pennies.
The quarter count is fixed.
Subtract the quarter's value.
46 - 25 = 21 cents remain.
The remaining coins must make that gap.
Use whole dimes and pennies.
Verify the payment.
A quarter is 25 cents, a dime is 10 cents, a nickel is 5 cents and a penny is 1 cent. How many cents are 3 quarters, 4 dimes, 2 nickels and 3 pennies worth altogether?
Answer:
Two classroom items cost 25 cents and 12 cents. You pay one dollar. Find the change.
Combine both prices.
25 + 12 = 37 cents.
Both purchases belong to the transaction.
Use a common payment unit.
100 - 37 = change cents.
One dollar is one hundred cents.
Check the returned amount.
The price and change together must total 100 cents.
All of the payment must be accounted for.
A toy costs 90 cents. You pay with a dollar, which is 100 cents. How much change do you get?
Answer:
A quarter is 25 cents, a dime is 10 cents, a nickel is 5 cents and a penny is 1 cent. How many cents are 3 quarters, 4 dimes, 3 nickels and 4 pennies worth altogether?
Answer:
A toy costs 35 cents. You pay with a dollar, which is 100 cents. How much change do you get?
Answer:
Match each handful of coins to whether it makes exactly 60 cents.
| makes exactly 60 cents | does not make 60 cents | |
|---|---|---|
| two quarters and a dime | ||
| two quarters and a nickel | ||
| four dimes |
A notebook costs 57 cents. Lee offers one quarter, 2 dimes, and 4 pennies. The payment is short. Record the value offered and how many more cents Lee must add to pay exactly.
| Offered value in cents | Additional cents needed | |
|---|---|---|
| Payment repair |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A pretend-shop item costs 77 cents. Construct exact payment using exactly one quarter, as many dimes as possible, no nickels, and pennies for the rest. Record the dime and penny counts. Also record the change if you paid one dollar instead.
| Dimes | Pennies | Change from $1 (cents) | |
|---|---|---|---|
| Payment record |
You can count mixed coins, find the change from a dollar, read a clock to five minutes, and say whether a time is a.m. or p.m.
16. Check a coin payment, step 3
2 dimes and 1 penny make 21 cents.
Dimes contribute ten each and the penny supplies one.
16. Check a coin payment, step 4
25 + 10 + 10 + 1 = 46 cents.
The values and the one-quarter condition both match.