Money Foundations

Identifying Pennies and Nickels

Money helps us buy things. Today we will learn about two coins: the penny and the nickel.

We will learn how to tell them apart by looking at their color, size, and value.

What is a penny?

A penny is a coin worth 1 cent.

We can write that as \(1\text{¢}\).

• A penny is copper-colored, or brown.
• A penny is the smallest common coin.
• On the front, you can see a person's face.

When you see a small brown coin, it is probably a penny.

What is a nickel?

A nickel is a coin worth 5 cents.

We can write that as \(5\text{¢}\).

• A nickel is silver-colored.
• A nickel is bigger than a penny.
• On the front, you can see a person's face.

When you see a bigger silver coin, it may be a nickel.

How are pennies and nickels different?

• A penny is brown and worth 1 cent.
• A nickel is silver and worth 5 cents.
• A penny is smaller.
• A nickel is larger.

Let’s compare them:

$$1\text{ penny} = 1\text{¢}$$

$$1\text{ nickel} = 5\text{¢}$$

This means a nickel is worth more than a penny.

Remember it like this:

• Penny = small, brown, \(1\text{¢}\)
• Nickel = bigger, silver, \(5\text{¢}\)

Look carefully at the coin

When you try to name a coin, ask yourself:

1. What color is it?
2. Is it small or bigger?
3. Is it worth \(1\text{¢}\) or \(5\text{¢}\)?

This can help you choose the right coin.

Worked Example 1

You see a small brown coin. What coin is it?

Step 1: Small and brown matches a penny.

Answer: It is a penny.

Value: \(1\text{¢}\)

Worked Example 2

You see a bigger silver coin. What coin is it?

Step 1: Bigger and silver matches a nickel.

Answer: It is a nickel.

Value: \(5\text{¢}\)

Worked Example 3

Which coin is worth more: a penny or a nickel?

A penny is worth \(1\text{¢}\).

A nickel is worth \(5\text{¢}\).

Since \(5\text{¢} > 1\text{¢}\), the nickel is worth more.

Answer: The nickel is worth more.

Worked Example 4

You have one penny and one nickel. Name each coin and say its value.

• Penny = \(1\text{¢}\)
• Nickel = \(5\text{¢}\)

Answer: The penny is worth \(1\text{¢}\), and the nickel is worth \(5\text{¢}\).

Tips to help you remember

• Penny starts with P. Think: Penny, Plain brown, Pays \(1\text{¢}\).
• Nickel starts with N. Think: Nickel, Not brown, worth \(5\text{¢}\).

Let’s practice thinking

• If the coin is brown, it is a penny.
• If the coin is silver and bigger than a penny, it is a nickel.
• If the coin is worth \(1\text{¢}\), it is a penny.
• If the coin is worth \(5\text{¢}\), it is a nickel.

Summary

A penny is a small brown coin worth 1 cent.

A nickel is a bigger silver coin worth 5 cents.

If you remember color, size, and value, you can tell a penny and a nickel apart.

Identifying Dimes and Quarters

Money helps us buy things. Today we will learn about two coins: the dime and the quarter.

It is important to know what these coins look like and how much they are worth. A dime is worth 10 cents. A quarter is worth 25 cents.

We can write their values like this:

$$\text{dime} = 10\text{ cents}$$

$$\text{quarter} = 25\text{ cents}$$

How to identify a dime

• A dime is a small coin.
• It is silver-colored.
• It is worth 10 cents.
• The front shows a person.
• The back may show a torch with branches.

Remember: the dime is small, but it is still worth 10 cents.

How to identify a quarter

• A quarter is a bigger coin than a dime.
• It is silver-colored.
• It is worth 25 cents.
• The front shows a person.
• The back may show different pictures, but it is still a quarter.

Remember: the quarter is usually bigger than the dime and is worth 25 cents.

Dime or quarter?

Sometimes both coins look alike because they are both silver-colored. That is why we look carefully at the size and remember the value.

• Dime = smaller coin = \(10\) cents
• Quarter = bigger coin = \(25\) cents

A helpful way to remember

• Dime, D for 10 cents.
• Quarter, think of 25 cents.

You do not need to count by ones to know these coins. You can learn their values by memory.

Worked Example 1

You see a small silver coin. It is smaller than a quarter. What coin is it?

Step 1: Think about the size. It is small.

Step 2: A small silver coin is a dime.

Answer: It is a dime, and it is worth 10 cents.

Worked Example 2

You see a bigger silver coin. What coin could it be: a dime or a quarter?

Step 1: Compare the size. It is bigger.

Step 2: The bigger coin is a quarter.

Answer: It is a quarter, and it is worth 25 cents.

Worked Example 3

Which coin is worth more: a dime or a quarter?

We know:

• Dime = \(10\) cents
• Quarter = \(25\) cents

Since \(25 > 10\), the quarter is worth more.

Answer: A quarter is worth more than a dime.

Worked Example 4

Mia has one dime and one quarter. What are the coins, and what are they worth?

Step 1: Name the coins.

• One coin is a dime.
• One coin is a quarter.

Step 2: Tell the value of each coin.

• Dime = \(10\) cents
• Quarter = \(25\) cents

Answer: The dime is worth 10 cents, and the quarter is worth 25 cents.

Let’s practice what to say

• “This is a dime. It is worth 10 cents.”
• “This is a quarter. It is worth 25 cents.”

Tips for remembering

• The dime is smaller.
• The quarter is bigger.
• A dime is worth \(10\) cents.
• A quarter is worth \(25\) cents.

Summary

A dime and a quarter are both silver-colored coins. A dime is the smaller coin and is worth 10 cents. A quarter is the bigger coin and is worth 25 cents. When you look at the coin’s size and remember its value, you can tell them apart.

Identifying Dollar Bills

Money helps us buy things. Some money is made of paper. Paper money in the United States is called a bill.

In this lesson, we will learn how to पहचान? No—let’s say it simply: we will learn how to identify the one-dollar bill. A one-dollar bill is worth 1 dollar.

You may also see this written as $1. The $ sign means dollars.

So:

$$1\text{ dollar} = \$1$$

What does a one-dollar bill look like?

A one-dollar bill is usually green and has the number 1 on it.

When you look at a one-dollar bill, you can look for these clues:

• It is a paper bill, not a coin.
• It has the number 1 on it.
• It is worth one dollar.
• We can write its value as $1.

How is a dollar bill different from coins?

Coins are small, round, and made of metal. A dollar bill is flat, made of paper, and shaped like a rectangle.

If you are asked to find the dollar bill, look for the paper money with 1 on it.

Value of a one-dollar bill

One one-dollar bill is worth 1 dollar.

$$\$1 = 1\text{ dollar}$$

If you have more than one one-dollar bill, you can count by ones:

• 1 bill = $1
• 2 bills = $2
• 3 bills = $3
• 4 bills = $4

Each one-dollar bill adds 1 more dollar.

Worked Example 1

You see one paper bill with a 1 on it. What is it?

It is a one-dollar bill.

Its value is $1.

Worked Example 2

You have 2 one-dollar bills. How much money do you have?

Count the bills:

$$1 + 1 = 2$$

So, you have $2.

Worked Example 3

Which is the dollar bill?

• A round metal coin
• A paper bill with the number 1

The correct answer is the paper bill with the number 1.

That is the one-dollar bill.

Worked Example 4

You have 3 one-dollar bills. How much money do you have?

Count by ones:

$$1 + 1 + 1 = 3$$

So, 3 one-dollar bills = $3.

Tips to help you remember

• Bill means paper money.
• The number 1 helps you find the one-dollar bill.
• One one-dollar bill is worth $1.
• More one-dollar bills can be counted by ones.

Let’s practice thinking

1. If you see a paper bill with a 1, it is a one-dollar bill.
2. If you have 1 one-dollar bill, you have $1.
3. If you have 2 one-dollar bills, you have $2.
4. If you have 4 one-dollar bills, you have $4.

Summary

A one-dollar bill is US paper money worth 1 dollar. It has the number 1 on it, and we write its value as $1. To find a dollar bill, look for the paper bill with 1 on it. If you have more than one, count by ones to find the total.

Counting Collections of Same Coins

Today we will learn how to find the total value of a group of coins when all the coins are the same.

We will practice with pennies, nickels, and dimes. When all the coins match, we can use skip counting to count faster.

This helps us count money the easy way.

First, let's remember the value of each coin.

• A penny is worth 1 cent.
• A nickel is worth 5 cents.
• A dime is worth 10 cents.

We write cents with the cent sign, like this: ¢.

How do we count a group of same coins?

Look at the coin. Ask, “How much is one coin worth?” Then count by that number for each coin.

• For pennies, count by 1s.
• For nickels, count by 5s.
• For dimes, count by 10s.

Pennies

Each penny is worth 1 cent. So if you have pennies, you count by 1s.

If you have 4 pennies, you count:

\(1, 2, 3, 4\)

So 4 pennies are worth 4¢.

Nickels

Each nickel is worth 5 cents. So if you have nickels, you count by 5s.

The skip-counting pattern for nickels is:

\(5, 10, 15, 20, 25, 30\)

Each number tells the total value so far.

Dimes

Each dime is worth 10 cents. So if you have dimes, you count by 10s.

The skip-counting pattern for dimes is:

\(10, 20, 30, 40, 50, 60\)

Each number tells the total value so far.

Steps to count same coins

1. Look at the coin name.
2. Remember its value.
3. Count how many coins there are.
4. Skip count by the coin's value.
5. Say the total in cents.

Worked Example 1

Find the value of 6 pennies.

Each penny is worth 1 cent.

Count by 1s six times:

\(1, 2, 3, 4, 5, 6\)

So, 6 pennies = 6¢.

We can show it like this:

Worked Example 2

Find the value of 4 nickels.

Each nickel is worth 5 cents.

Count by 5s four times:

\(5, 10, 15, 20\)

So, 4 nickels = 20¢.

We can show it like this:

Worked Example 3

Find the value of 3 dimes.

Each dime is worth 10 cents.

Count by 10s three times:

\(10, 20, 30\)

So, 3 dimes = 30¢.

We can show it like this:

Worked Example 4

Find the value of 7 nickels.

Each nickel is worth 5 cents.

Count by 5s seven times:

\(5, 10, 15, 20, 25, 30, 35\)

So, 7 nickels = 35¢.

Helpful idea

As you point to each coin, say the next skip-count number. This helps you keep track and not count a coin two times.

For example, with 5 dimes, point and count:

\(10, 20, 30, 40, 50\)

So 5 dimes = 50¢.

Watch out!

• Do not count nickels by 1s. Count nickels by 5s.
• Do not count dimes by 1s. Count dimes by 10s.
• Make sure all the coins are the same kind.

Try to remember

• Penny = 1¢
• Nickel = 5¢
• Dime = 10¢

If the coins are all pennies, count by 1s.

If the coins are all nickels, count by 5s.

If the coins are all dimes, count by 10s.

Summary

Counting collections of same coins is easy when you know each coin's value.

Use skip counting to find the total:

• Pennies: count by 1s
• Nickels: count by 5s
• Dimes: count by 10s

When all the coins are the same, skip counting helps you find the total value quickly and correctly.

Counting Mixed Coins: Dimes and Pennies

We can use coins to count money. Today we will learn how to count dimes and pennies together.

A penny is worth 1 cent. We write that as \(1\text{¢}\).

A dime is worth 10 cents. We write that as \(10\text{¢}\).

This means a dime is the same as 10 pennies.

When we count mixed coins, we can use what we know about tens and ones.

• Dimes are the tens.
• Pennies are the ones.

So we count the dimes first, then add the pennies.

How to count dimes and pennies

1. Count how many dimes there are.
2. Count by tens: \(10, 20, 30, \dots\)
3. Count how many pennies there are.
4. Add the pennies one by one.

You can think: dimes first, pennies next.

Here is a helpful way to remember:

• 1 dime = \(10\text{¢}\)
• 2 dimes = \(20\text{¢}\)
• 3 dimes = \(30\text{¢}\)
• 4 dimes = \(40\text{¢}\)
• 5 dimes = \(50\text{¢}\)

Then add the pennies:

• \(20\text{¢} + 3\text{¢} = 23\text{¢}\)
• \(40\text{¢} + 2\text{¢} = 42\text{¢}\)

Worked Example 1

Count 1 dime and 2 pennies.

Start with the dime. 1 dime = \(10\text{¢}\).

Now add 2 pennies. Count on: \(11\text{¢}, 12\text{¢}\).

So the total is:

Answer: 12¢

Worked Example 2

Count 2 dimes and 4 pennies.

First count the dimes: \(10\text{¢}, 20\text{¢}\).

2 dimes = \(20\text{¢}\).

Now add 4 pennies: \(21\text{¢}, 22\text{¢}, 23\text{¢}, 24\text{¢}\).

So the total is:

Answer: 24¢

Worked Example 3

Count 3 dimes and 6 pennies.

First count the dimes: \(10\text{¢}, 20\text{¢}, 30\text{¢}\).

3 dimes = \(30\text{¢}\).

Now add 6 pennies: \(31\text{¢}, 32\text{¢}, 33\text{¢}, 34\text{¢}, 35\text{¢}, 36\text{¢}\).

So the total is:

Answer: 36¢

Worked Example 4

Count 4 dimes and 9 pennies.

First count the dimes: \(10\text{¢}, 20\text{¢}, 30\text{¢}, 40\text{¢}\).

4 dimes = \(40\text{¢}\).

Now add 9 pennies: \(41\text{¢}, 42\text{¢}, 43\text{¢}, 44\text{¢}, 45\text{¢}, 46\text{¢}, 47\text{¢}, 48\text{¢}, 49\text{¢}\).

So the total is:

Answer: 49¢

A place value trick

Dimes tell us the tens number. Pennies tell us the ones number.

If you have 2 dimes and 5 pennies, that is 2 tens and 5 ones.

So 2 dimes and 5 pennies = 25¢.

If you have 4 dimes and 3 pennies, that is 4 tens and 3 ones.

So 4 dimes and 3 pennies = 43¢.

Things to watch out for

• Do not count a dime as 1. A dime is 10 cents.
• Count all the dimes first.
• Then count the pennies.
• The cent sign ¢ means cents.

Try thinking like this:

• 3 dimes = \(30\text{¢}\)
• 3 dimes and 2 pennies = \(32\text{¢}\)
• 5 dimes and 1 penny = \(51\text{¢}\)

Summary

A penny is worth \(1\text{¢}\), and a dime is worth \(10\text{¢}\).

To count mixed coins, count the dimes by tens first, then add the pennies by ones.

Dimes are like tens, and pennies are like ones. This helps you find the total amount quickly and correctly.

Equivalent Coin Combinations

Today we will learn that different groups of coins can have the same value.

This means you can make the same amount of money in more than one way. For example, 1 dime, 2 nickels, and 10 pennies are different coin groups, but they are all worth the same amount.

First, let’s remember coin values.

• Penny = \(1\) cent
• Nickel = \(5\) cents
• Dime = \(10\) cents
• Quarter = \(25\) cents

When two coin groups have the same value, we call them equivalent. That is a big word that means equal in value.

So if one group is worth \(10\) cents and another group is also worth \(10\) cents, the two groups are equivalent.

How do we check if coin groups are equivalent?

1. Look at the first group of coins.
2. Count its total value.
3. Look at the second group of coins.
4. Count its total value.
5. If both totals are the same, the groups are equivalent.

Let’s practice counting coin values.

We can count pennies by ones:

$$1+1+1+1+1=5$$

So 5 pennies are worth \(5\) cents.

We can count nickels by fives:

$$5+5=10$$

So 2 nickels are worth \(10\) cents.

We can remember that 1 dime is worth \(10\) cents.

Worked Example 1

Are 1 nickel and 5 pennies equivalent?

Count the value of 1 nickel:

$$5$$

Count the value of 5 pennies:

$$1+1+1+1+1=5$$

Both groups are worth \(5\) cents.

Yes! 1 nickel and 5 pennies are equivalent.

Worked Example 2

Are 1 dime and 2 nickels equivalent?

Count the value of 1 dime:

$$10$$

Count the value of 2 nickels:

$$5+5=10$$

Both groups are worth \(10\) cents.

Yes! 1 dime and 2 nickels are equivalent.

Worked Example 3

Are 1 dime and 10 pennies equivalent?

Count the value of 1 dime:

$$10$$

Count the value of 10 pennies:

$$1+1+1+1+1+1+1+1+1+1=10$$

Both groups are worth \(10\) cents.

Yes! 1 dime and 10 pennies are equivalent.

Worked Example 4

Are 1 quarter and 2 dimes equivalent?

Count the value of 1 quarter:

$$25$$

Count the value of 2 dimes:

$$10+10=20$$

The totals are not the same.

No. They are not equivalent.

Here are some equivalent coin combinations to remember.

• 1 nickel = 5 pennies
• 2 nickels = 1 dime
• 1 dime = 10 pennies
• 2 dimes + 1 nickel = 25 cents
• 1 quarter = 25 pennies

We can write some of these like this:

$$1\text{ nickel}=5\text{ pennies}$$

$$1\text{ dime}=2\text{ nickels}=10\text{ pennies}$$

$$1\text{ quarter}=2\text{ dimes}+1\text{ nickel}$$

Tips for success

• Count pennies by ones.
• Count nickels by fives.
• Count dimes by tens.
• Always compare the total values, not just the number of coins.

That last tip is very important.

Sometimes one group has more coins, but it is still worth the same amount as a group with fewer coins. For example, 1 dime is only 1 coin, but it has the same value as 10 pennies.

Try thinking about these:

• Which is worth the same as 1 nickel? 5 pennies.
• Which is worth the same as 1 dime? 2 nickels or 10 pennies.
• Which is worth the same as 1 quarter? 2 dimes and 1 nickel.

Summary

Equivalent coin combinations are different groups of coins that have the same value.

To check, count the value of each group and compare the totals.

Remember:

• 1 nickel = 5 pennies
• 1 dime = 2 nickels = 10 pennies
• 1 quarter = 2 dimes + 1 nickel

Great job! Now you know that money can be made in different ways while still being equal in value.

Solving Money Word Problems means using what we know about coins, bills, adding, and taking away to answer real-life questions.

Money word problems often tell a little story. We listen for the important parts: How much money is there? How much is spent? How much is left?

In this lesson, we will practice finding the total amount, paying for something, and figuring out how much money is left.

First, let’s remember the value of common U.S. money.

• Penny = \(1\) cent
• Nickel = \(5\) cents
• Dime = \(10\) cents
• Quarter = \(25\) cents
• 1 dollar bill = \(100\) cents

When we solve money problems, it helps to work in cents. Cents are smaller numbers that are easy to add and subtract.

How to solve a money word problem:

1. Read the story carefully.
2. Find the money amounts.
3. Decide what to do: add or subtract.
4. Solve.
5. Check if the answer makes sense.

When do we add?

• When we put money together
• When we find the total amount

When do we subtract?

• When money is spent
• When we want to know how much is left
• When we want to know the change

Example 1: Putting money together

Lia has 1 dime and 3 pennies. How much money does she have?

First, find each coin’s value.

• 1 dime = \(10\) cents
• 3 pennies = \(3\) cents

Now add.

Lia has 13 cents.

Why did we add? We added because Lia put all her money together to find the total.

Example 2: Buying something

Ben has 15 cents. He buys a sticker for 5 cents. How much money is left?

Ben starts with \(15\) cents. He spends \(5\) cents.

When money is spent, we subtract.

Ben has 10 cents left.

Why did we subtract? The cost of the sticker was taken away from Ben’s money.

Example 3: A coin word problem

Sara has 1 nickel and 1 dime. She wants to buy a toy eraser that costs 12 cents. Does she have enough money?

First, find how much money Sara has.

• 1 nickel = \(5\) cents
• 1 dime = \(10\) cents

Add the coins.

Sara has \(15\) cents.

The eraser costs \(12\) cents. Sara has \(15\) cents, so yes, she has enough money.

Now we can find how much money will be left.

Sara will have 3 cents left.

Example 4: Paying with a dollar

Leo has 1 dollar. He buys juice for 30 cents. How much money is left?

Remember: \(1\) dollar = \(100\) cents.

Now subtract the cost.

Leo has 70 cents left.

Helpful clues in word problems

• in all or altogether usually means add
• left usually means subtract
• spent usually means subtract
• enough means compare the money you have to the cost

Let’s practice thinking.

If a problem says, “Mia has 2 nickels,” we can count:

\(5 + 5 = 10\). Mia has 10 cents.

If a problem says, “Mia buys something for 4 cents,” then we take away:

Mia has 6 cents left.

Tips for solving money word problems

• Count each coin carefully.
• Say the coin values out loud.
• Add to find the total.
• Subtract when money is used.
• Write your answer with cents or dollars.

Check your work

Ask yourself:

• Did I use the right coin values?
• Did I add or subtract?
• Does my answer make sense?

For example, if you had \(10\) cents and spent \(3\) cents, your answer should be less than \(10\) cents. If it is bigger, something is wrong.

Summary

Money word problems tell a story about coins, bills, buying, and money left over. We add to find how much money there is in all. We subtract when money is spent or when we find how much is left. Always count coin values carefully and check that your answer makes sense.