problem solving coin worksheets

Money Worksheets

Welcome to the money worksheets page at Math-Drills.com where you will not be short-changed! This page includes Money worksheets for counting coins and for operations with Dollars, Euros, and Pounds.

Students encounter money early on, and they must be able to manage it themselves in their everyday lives and into adulthood. There are many activities that you can do related to counting, adding, and subtracting money, so save some coins or purchase some play money to complete some of the activities on the money math worksheets below.

The policies of the United States Mint and the European Central Bank allow us to use their coin images on our worksheets. The Canadian coin images are used with permission from the Royal Canadian Mint. Permission to use Australian currency coin designs was obtained from the Royal Australian Mint.

Most Popular Money Worksheets this Week

Counting Coins Worksheets

This is a great place to start with younger students as they are likely to encounter coins before they encounter too many bills. Including children in money transactions helps them to develop important money management skills and has benefits in other math topics such as fractions.

Until everyone starts paying with their smart phones and microchips in their fingers, coins are still a thing. The U.S. Mint still makes billions of coins every year and children will probably encounter them very early on in their life. Knowing how much money you have in coins can be accomplished with a coin counting machine, or it can be accomplished with some mental math.

• Counting U.S. Coins Counting U.S. Coins Counting U.S. Coins including Half and One Dollar Coins Counting Small Collections of U.S. Coins Counting Small Collections of U.S. Coins including Half and One Dollar Coins
• Counting Sorted U.S. Coins Counting Sorted U.S. Coins Counting Small Collections of Sorted U.S. Coins
• Counting Canadian Coins Counting Canadian Coins Counting Canadian Coins (No $) Counting Small Collections of Canadian Coins Counting Small Collections of Can. Coins (No $) Counting Canadian Coins Including 50 Cent Pieces
• Counting Sorted Canadian Coins Counting Sorted Canadian Coins Counting Sorted Canadian Coins (No $) Counting Small Collections of Sorted Canadian Coins Counting Small Collections of Sorted Canadian Coins (No $)

No one likes their coins better than the U.K. With pockets full of eight different coin values, reinforced stitching on trouser pockets and handbags is common place. Learning to count all of these coins is a feat in itself, but the worksheets in this category should help.

• Counting British Coins Counting British Coins Counting British Coins - No Pound Coins Counting Small Collections of British Coins Counting Small Collections of British Coins (No Pound Coins)
• Counting Australian Coins Counting Australian Coins Counting Australian Coins (No Dollars) Counting Small Collections of Australian Coins Counting Small Collections of Australian Coins (No Dollars)
• Counting Sorted Australian Coins Counting Sorted Australian Coins Counting Sorted Australian Coins (No Dollars) Counting Small Collections of Sorted Australian Coins Counting Small Collections of Sorted Australian Coins (No Dollars)
• Counting Euro Coins Counting Euro Coins Counting Euro Coins (No 1 or 2 Cents) Counting Euro Coins (No 1 or 2 Euro Coins) Counting Euro Coins (Only 5, 10, 20 and 50 Cent Coins) Counting Small Collections of Euro Coins Counting Small Collections of Euro Coins (No 1 or 2 Cents) Counting Small Collections of Euro Coins (No 1 or 2 Euro coins) Counting Small Collections of Euro Coins (Only 5, 10, 20 and 50 Cent Coins)
• Counting Sorted Euro Coins Counting Sorted Euro Coins Counting Sorted Euro Coins (No 1 or 2 Cents) Counting Sorted Euro Coins (No 1 or 2 Euro coins) Counting Small Collections of Sorted Euro Coins Counting Small Collections of Sorted Euro Coins (No 1 or 2 Cents) Counting Small Collections of Sorted Euro Coins (No 1 or 2 Euro coins)
• Counting New Zealand Coins Counting New Zealand Coins (No Dollars) Counting New Zealand Coins Counting Small Collections of New Zealand Coins (No Dollars) Counting Small Collections of New Zealand Coins

Rounding Money Amounts

The next dollar up is a skill for young students who are not yet able to make change, but can determine how many dollars it will take to cover an amount. For example, if something is $5.45 in a store, then they would need to give $6 to cover that amount since the next dollar up from $5.45 is $6. Students should understand that any amount above zero after the decimal means they need to add another dollar to the number before the decimal in order to have enough to pay for the item. The rest of the worksheets in this section are general rounding questions involving dollar amounts.

• Next Dollar Up (U.S. Version) Next Dollar Up (Amounts to $5 ) (U.S. Version) Next Dollar Up (Amounts to $10 ) (U.S. Version)
• Next Dollar Up (Canadian Version) Next Dollar Up (Amounts to $5 ) ( Canadian Version) Next Dollar Up (Amounts to $10 ) ( Canadian Version)
• Next Dollar Up (Australian Version) Next Dollar Up (Amounts to $5 ) ( Australian Version) Next Dollar Up (Amounts to $10 ) ( Australian Version)
• Next Pound Up (U.K. Version) Next Pound Up (Amounts to £5 ) Next Pound Up (Amounts to £10 )
• Rounding Dollar Amounts Rounding Dollar Amounts to the Nearest 5 Cents Rounding Dollar Amounts to the Nearest 10 Cents Rounding Dollar Amounts to the Nearest 20 Cents Rounding Dollar Amounts to the Nearest 25 Cents Rounding Dollar Amounts to the Nearest 50 Cents Rounding Dollar Amounts to the Nearest 1 Dollar Rounding Dollar Amounts to the Nearest 2 Dollars Rounding Dollar Amounts to the Nearest 5 Dollars
• Rounding British Pound Amounts Rounding British Pound Amounts to the Nearest 5 Pence Rounding British Pound Amounts to the Nearest 10 Pence Rounding British Pound Amounts to the Nearest 20 Pence Rounding British Pound Amounts to the Nearest 25 Pence Rounding British Pound Amounts to the Nearest 50 Pence Rounding British Pound Amounts to the Nearest 1 Pound Rounding British Pound Amounts to the Nearest 2 Pounds Rounding British Pound Amounts to the Nearest 5 Pounds
• Rounding Euro Amounts Rounding Euro Amounts to the Nearest 5 Cents Rounding Euro Amounts to the Nearest 10 Cents Rounding Euro Amounts to the Nearest 20 Cents Rounding Euro Amounts to the Nearest 25 Cents Rounding Euro Amounts to the Nearest 50 Cents Rounding Euro Amounts to the Nearest 1 Euro Rounding Euro Amounts to the Nearest 2 Euros Rounding Euro Amounts to the Nearest 5 Euros

Adding and Subtracting Money

Adding money amounts is a nice way to gently move students into thinking about decimals and what a great opportunity to use some manipulatives. Students generally perform better with math that has meaning. Decimal numbers to hundredths have most likely been in students' lives since very early on as stores display prices, parents comment about the prices to help develop critical thinking in their children, so if there is one decimal that students understand well, it is money. They sometimes have trouble relating it to paper and pencil which is why manipulatives come in handy. Play money is a little cheaper than real money and doesn't disappear quite as quickly.

• Adding Money Amounts with Increments Specifically for U.S. Canadian Currencies Adding With Amounts up to $10 Adding With Amounts up to $100 Adding in Increments of 50 Cents ($) Adding in Increments of 25 Cents ($) Adding in Increments of 10 Cents ($) Adding in Increments of 5 Cents ($)
• Adding Money Amounts with Increments Specifically for British Currency Adding With Amounts up to £10 Adding With Amounts up to £100 Adding Increments of 50 Pence (£) Adding Increments of 20 Pence (£) Adding Increments of 10 Pence (£) Adding Increments of 5 Pence (£) Adding Increments of 2 Pence (£)
• Adding Money Amounts with Increments Specifically for Australian and New Zealand Currencies Adding With Amounts up to $10 Adding With Amounts up to $100 Adding Increments of 50 Cents ($) Adding Increments of 20 Cents ($) Adding Increments of 10 Cents ($) Adding Increments of 5 Cents ($)
• Adding Money Amounts with Increments Specifically for Euro Currency Adding With Amounts up to €10 Adding With Amounts up to €100 Adding Increments of 50 Euro Cents Adding Increments of 20 Euro Cents Adding Increments of 10 Euro Cents Adding Increments of 5 Euro Cents Adding Increments of 2 Euro Cents

The strategy of choice for subtracting money is the counting up strategy. It works especially well for giving change from whole dollar/Pound/Euro amounts. Following is an example of how it works. Let's say the bill at the grocery store came out to $13.46 and the cashier was presented with a $20.00 bill and for some odd reason, the monitor on his cash machine had a crack in it that obscured the amount of change to give. What would he do?! The first thing to do is to take four cents out of the drawer because he needs to add the $13.46 to an unknown amount to make $20, and four cents will bring the $13.46 up to $13.50 which makes things rounder and, for most, a little easier. Next, he needs to pull out two quarters to bring the amount up to $14 even. He can then remove a dollar bill to make the amount $15, and finally pull out a $5 bill to count up to $20. Now, if he wanted to know how much change he gave, he just needs to think back to what he pulled out of the drawer: $5 + $1 + $0.50 + $0.04 = $6.54.

• Subtracting Money Amounts with Increments Specifically for U.S. and Canadian Currencies Subtracting With Amounts up to $10 Subtracting With Amounts up to $100 Subtracting in Increments of 50 Cents ($) Subtracting in Increments of 25 Cents ($) Subtracting in Increments of 10 Cents ($) Subtracting in Increments of 5 Cents ($)
• Subtracting Money Amounts with Increments Specifically for British Currency Subtracting With Amounts up to £10 Subtracting With Amounts up to £100 Subtracting Increments of 50 Pence (£) Subtracting Increments of 20 Pence (£) Subtracting Increments of 10 Pence (£) Subtracting Increments of 5 Pence (£) Subtracting Increments of 2 Pence (£)
• Subtracting Money Amounts with Increments Specifically for Australian and New Zealand Currencies Subtracting With Amounts up to $10 Subtracting With Amounts up to $100 Subtracting Increments of 50 Cents ($) Subtracting Increments of 20 Cents ($) Subtracting Increments of 10 Cents ($) Subtracting Increments of 5 Cents ($)
• Subtracting Money Amounts with Increments Specifically for Euro Currency Subtracting With Amounts up to 10 € Subtracting With Amounts up to 100 € Subtracting Increments of 50 Euro Cents (€) Subtracting Increments of 20 Euro Cents (€) Subtracting Increments of 10 Euro Cents (€) Subtracting Increments of 5 Euro Cents (€) Subtracting Increments of 2 Euro Cents (€)
• Adding and Subtracting Money Amounts with Increments Specifically for U.S. and Canadian Currencies Adding & Subtracting With Amounts up to $10 Adding & Subtracting With Amounts up to $100 Adding & Subtracting in Increments of 50 Cents ($) Adding & Subtracting in Increments of 25 Cents ($) Adding & Subtracting in Increments of 20 Cents ($) Adding & Subtracting in Increments of 10 Cents ($) Adding & Subtracting in Increments of 5 Cents ($)
• Adding and Subtracting Money Amounts with Increments Specifically for British Currency Adding & Subtracting With Amounts up to £10 Adding & Subtracting With Amounts up to £100 Adding & Subtracting Increments of 50 Pence (£) Adding & Subtracting Increments of 20 Pence (£) Adding & Subtracting Increments of 10 Pence (£) Adding & Subtracting Increments of 5 Pence (£) Adding & Subtracting Increments of 2 Pence (£)
• Adding and Subtracting Money Amounts with Increments Specifically for Australian and New Zealand Currencies Adding & Subtracting With Amounts up to $10 Adding & Subtracting With Amounts up to $100 Adding & Subtracting in Increments of 50 Cents ($) Adding & Subtracting in Increments of 20 Cents ($) Adding & Subtracting in Increments of 10 Cents ($) Adding & Subtracting in Increments of 5 Cents ($)
• Adding and Subtracting Money Amounts with Increments Specifically for European Currency Adding & Subtracting With Amounts up to 10 € Adding & Subtracting With Amounts up to 100 € Adding & Subtracting Increments of 50 Euro Cents (€) Adding & Subtracting Increments of 20 Euro Cents (€) Adding & Subtracting Increments of 10 Euro Cents (€) Adding & Subtracting Increments of 5 Euro Cents (€) Adding & Subtracting Increments of 2 Euro Cents (€)

Making change from bills and notes worksheets.

• Making Change from U.S. Bills Making Change from U.S. $1 Bills Making Change from U.S. $5 Bills Making Change from U.S. $10 Bills Making Change from U.S. $20 Bills Making Change from U.S. $50 Bills Making Change from U.S. $100 Bills
• Making Change from Mixed U.S. Bills Making Change from U.S. Bills up to $5 Making Change from U.S. Bills up to $10 Making Change from U.S. Bills up to $20 Making Change from U.S. Bills up to $50 Making Change from U.S. Bills up to $100
• Making Change from Canadian Bills Making Change from Canadian $5 Bills Making Change from Canadian $10 Bills Making Change from Canadian $20 Bills Making Change from Canadian $50 Bills Making Change from Canadian $100 Bills
• Making Change from Mixed Canadian Bills Making Change from Canadian Bills up to $10 Making Change from Canadian Bills up to $20 Making Change from Canadian Bills up to $50 Making Change from Canadian Bills up to $100
• Making Change from Euro Notes Making Change from Euro €5 Notes Making Change from Euro €10 Notes Making Change from Euro €20 Notes Making Change from Euro €50 Notes Making Change from Euro €100 Notes Making Change from Euro €200 Notes
• Making Change from Mixed Euro Notes Making Change from Euro Notes up to €10 Making Change from Euro Notes up to €20 Making Change from Euro Notes up to €50 Making Change from Euro Notes up to €100 Making Change from Euro Notes up to €200

Further worksheets will be released as soon as the Reserve Bank of New Zealand releases more banknotes from Series 7.

• Making Change from New Zealand Banknotes Making Change from New Zealand $5 Banknotes Making Change from New Zealand $10 Banknotes
• Making Change from Mixed New Zealand Banknotes Making Change from New Zealand Banknotes up to $10

The Bank of England sent us this response regarding our request for images: "Please note that the Bank of England does not provide images of notes." Therefore, we are unable to create making change math worksheets using Bank of England banknotes.

Multiplying and Dividing Money

It would be nice if our own money could multiply quite as nicely in our bank accounts as it does on these worksheets. Alas, we will have to settle with low interest rates multiplying our money over the span of decades. These multiplying money worksheets would go well with some money manipulatives. Simply make several piles of the same amount (the same number of piles as the multiplier), combine it all into one pile, regroup as much as possible (e.g. five ones into a five), and count up the results.

• Multiplying Dollar Amounts by 1-Digit Multipliers (U.S. and Canada Version) Multiplying Dollar Amounts in Increments of 1 Cent by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 5 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 10 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 25 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 50 Cents by One-Digit Multipliers
• Multiplying Dollar Amounts by 2-Digit Multipliers (U.S. and Canada Version) Multiplying Dollar Amounts in Increments of 1 Cent by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 5 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 10 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 25 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 50 Cents by Two-Digit Multipliers
• Multiplying Pound Sterling Amounts by 1-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 1 Penny by One-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 2 Pence by One-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 5 Pence by One-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 10 Pence by One-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 20 Pence by One-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 50 Pence by One-Digit Multipliers
• Multiplying Pound Sterling Amounts by 2-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 1 Penny by Two-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 2 Pence by Two-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 5 Pence by Two-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 10 Pence by Two-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 20 Pence by Two-Digit Multipliers Multiplying Pound Sterling Amounts in Increments of 50 Pence by Two-Digit Multipliers
• Multiplying Dollar Amounts by 1-Digit Multipliers (Australia and New Zealand Version) Multiplying Dollar Amounts in Increments of 1 Cent by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 5 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 10 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 20 Cents by One-Digit Multipliers Multiplying Dollar Amounts in Increments of 50 Cents by One-Digit Multipliers
• Multiplying Dollar Amounts by 2-Digit Multipliers (Australia and New Zealand Version) Multiplying Dollar Amounts in Increments of 1 Cent by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 5 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 10 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 20 Cents by Two-Digit Multipliers Multiplying Dollar Amounts in Increments of 50 Cents by Two-Digit Multipliers
• Multiplying Euro Amounts by 1-Digit Multipliers Multiplying Euro Amounts in Increments of 1 Cent by One-Digit Multipliers Multiplying Euro Amounts in Increments of 2 Cents by One-Digit Multipliers Multiplying Euro Amounts in Increments of 5 Cents by One-Digit Multipliers Multiplying Euro Amounts in Increments of 10 Cents by One-Digit Multipliers Multiplying Euro Amounts in Increments of 20 Cents by One-Digit Multipliers Multiplying Euro Amounts in Increments of 50 Cents by One-Digit Multipliers
• Multiplying Euro Amounts by 2-Digit Multipliers Multiplying Euro Amounts in Increments of 1 Cent by Two-Digit Multipliers Multiplying Euro Amounts in Increments of 2 Cents by Two-Digit Multipliers Multiplying Euro Amounts in Increments of 5 Cents by Two-Digit Multipliers Multiplying Euro Amounts in Increments of 10 Cents by Two-Digit Multipliers Multiplying Euro Amounts in Increments of 20 Cents by Two-Digit Multipliers Multiplying Euro Amounts in Increments of 50 Cents by Two-Digit Multipliers

Dividing money amounts by whole numbers worksheets.

• Dividing Dollar Amounts by 1-Digit Multipliers (U.S. and Canada Version) Dividing Dollar Amounts in Increments of 1 Cent by One-Digit Divisors Dividing Dollar Amounts in Increments of 5 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 10 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 20 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 25 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 50 Cents by One-Digit Divisors
• Dividing Dollar Amounts by 2-Digit Multipliers (U.S. and Canada Version) Dividing Dollar Amounts in Increments of 1 Cent by Two-Digit Divisors Dividing Dollar Amounts in Increments of 5 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 10 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 20 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 25 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 50 Cents by Two-Digit Divisors
• Dividing Pound Sterling Amounts by 1-Digit Multipliers Dividing Pound Sterling Amounts in Increments of 1 Penny by One-Digit Divisors Dividing Pound Sterling Amounts in Increments of 2 Pence by One-Digit Divisors Dividing Pound Sterling Amounts in Increments of 5 Pence by One-Digit Divisors Dividing Pound Sterling Amounts in Increments of 10 Pence by One-Digit Divisors Dividing Pound Sterling Amounts in Increments of 20 Pence by One-Digit Divisors Dividing Pound Sterling Amounts in Increments of 50 Pence by One-Digit Divisors
• Dividing Pound Sterling Amounts by 2-Digit Multipliers Dividing Pound Sterling Amounts in Increments of 1 Penny by Two-Digit Divisors Dividing Pound Sterling Amounts in Increments of 2 Pence by Two-Digit Divisors Dividing Pound Sterling Amounts in Increments of 5 Pence by Two-Digit Divisors Dividing Pound Sterling Amounts in Increments of 10 Pence by Two-Digit Divisors Dividing Pound Sterling Amounts in Increments of 20 Pence by Two-Digit Divisors Dividing Pound Sterling Amounts in Increments of 50 Pence by Two-Digit Divisors
• Dividing Dollar Amounts by 1-Digit Multipliers (Australia and New Zealand Version) Dividing Dollar Amounts in Increments of 1 Cent by One-Digit Divisors Dividing Dollar Amounts in Increments of 5 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 10 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 20 Cents by One-Digit Divisors Dividing Dollar Amounts in Increments of 50 Cents by One-Digit Divisors
• Dividing Dollar Amounts by 2-Digit Multipliers (Australia and New Zealand Version) Dividing Dollar Amounts in Increments of 1 Cent by Two-Digit Divisors Dividing Dollar Amounts in Increments of 5 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 10 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 20 Cents by Two-Digit Divisors Dividing Dollar Amounts in Increments of 50 Cents by Two-Digit Divisors
• Dividing Euro Amounts by 1-Digit Multipliers Dividing Euro Amounts in Increments of 1 Cent by One-Digit Divisors Dividing Euro Amounts in Increments of 2 Cents by One-Digit Divisors Dividing Euro Amounts in Increments of 5 Cents by One-Digit Divisors Dividing Euro Amounts in Increments of 10 Cents by One-Digit Divisors Dividing Euro Amounts in Increments of 20 Cents by One-Digit Divisors Dividing Euro Amounts in Increments of 50 Cents by One-Digit Divisors
• Dividing Euro Amounts by 2-Digit Multipliers Dividing Euro Amounts in Increments of 1 Cent by Two-Digit Divisors Dividing Euro Amounts in Increments of 2 Cents by Two-Digit Divisors Dividing Euro Amounts in Increments of 5 Cents by Two-Digit Divisors Dividing Euro Amounts in Increments of 10 Cents by Two-Digit Divisors Dividing Euro Amounts in Increments of 20 Cents by Two-Digit Divisors Dividing Euro Amounts in Increments of 50 Cents by Two-Digit Divisors

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These money word problems worksheets engage students with real world problems and applications of math skills. The problems are grouped by addition and subtraction (appropriate for second or third grade students), or multiplication and division (appropriate for fourth or fifth grade students who have mastered decimal division), or combinations of all four operations. Click one of the buttons below to view the individual worksheets in each set.

Addition and Subtraction

28 money word problems worksheets.

Addition and subtraction word problems for money.

Multiplication and Division

20 money word problems worksheets.

Introductory word problems for multiplication and division.

Mixed Operation Money Word Problems

16 money word problems worksheets.

Mixed operation word problems with money.

Addition and Subtraction with Extra Facts

Addition and subtraction word problems for money with extra unused facts in the problem.

Multiplication and Division with Extra Facts

Word problems for money multiplication and division with extra unused facts in the problem.

Mixed Operation Money Word Problems with Extra Facts

Mixed operation word problems with money with extra unused facts in the problem.

Word Problems to Introduce Money Skills

Money is a powerful and familiar application of basic math operations, and the money story problem worksheets on this page are perfect for grade school age children to start putting their basic arithmetic skills to work.

The worksheets start with sets that have exactly the information needed to solve particular money word problems, but an important skill is to learn to identify excess or unused facts in the problem description. Because money problems in the real world appear in the context of lots of information you may not need to solve a problem, recognizing what information is important is often as critical a skill as being able to do the basic arithmetic. The money word problems worksheets marked as having 'extra facts' on this page are appropriate for 3rd or 4th grade students who can confidently solve other problems.

The word problems are grouped into sets focusing on addition and subtraction, or multiplication and division, or combinations of all four operations. If you are learning basic math facts, worksheets appropriate to the operations you are working on may help solidify concepts and can be used alongside math fact practice for extra support. Because these are all money story problems, they typically involve both dollars and cents, so students will need some familiarity with decimal arithmetic to solve them.

For a visual introduction to money, check out the Money Worksheets page, which includes Making Change and a really nice set of Printable Play Money that can be a great manipulative aid when solving money word problems and more!

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Use the worksheets below to help teach counting coins , counting dollars and cents , and making change . We also have resources on operations with money and money place value . we also have our international section featuring Canadian, British, and Australian currencies.

Counting Money: USA

Learn to identify coins, coin names, and their values. This page has worksheets, task cards, as well as cut-and-glue activities. example: What coin is this? Quarter.

This page will have students counting sets of pennies only, nickels only, dimes only, and/or quarters only. These basic-level activities are designed primarily for students in Kindergarten and 1st grades. example: Three nickels. How much money is shown? 15 cents.

Print worksheets and games on counting mixed coins. This page features basic level activities best suited for students in 1st and 2nd grade. example: 1 nickel and 3 pennies. How much money is shown? 8 cents.

Here are some more advanced worksheets on counting mixed coins. These were designed for students in 2nd through 4th grades. example: 2 quarters, 5 dimes, six nickels, and two pennies. How much money is shown? $1.62

This page has worksheets split up into 3 groups: counting money up to $4.00, counting money up to $12.00, and counting money up to $50.00. example: 2 twenty dollar bills, 6 quarters, and 7 nickels. How much money is shown? $41.85

Making Change

With these worksheets, students can practice making change. Includes task cards, word problems, and other printables.

Operations with Money

Practice adding money amounts with these printable worksheets, task cards, and games.

Print out these files to supplement your lessons on subtracting money and using subtraction to make change. Includes worksheets, a 'magic digits' game, and task cards.

Multiply money amounts by 1-digit numbers. THis page has a worksheet generator tool, as well as pre-made worksheets, puzzles, and task cards.

Money Place Value & Rounding

Use the mathematical symbols for greater than , less than , and equal to to compare money amounts.

With these activities, students will learn to round money amounts to the nearest dollar or the nearest ten cents.

Unlike regular rounding, on these worksheets students will always round up to the next dollar to determine how many bills are needed. For example, a t-shirt costs $6.29. You'd round up and give the cashier $7.

Counting Money: International

These printable worksheets and games have Australian coins and banknotes on them.

This page will have students counting Canadian toonies, loonies, quarters, dimes, and nickels. Most worksheets do not include pennies.

Count British pounds. Banknotes and coins include £2, £1, 50p, 20p, 10p, 5p, 2p, and 1p coins. Includes task cards, worksheets, and class games.

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Year 3 Money Challenges Solving Money Problems

Welcome to our Year 3 Money Challenges page. Here you will find our selection of printable money problem worksheets to help your child learn to use their money skills to solve a range of problems.

These challenges are a great resource as an extension for more able pupils, or to consolidate and extend learning.

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Year 3 Money Learning

Knowing how to handle and calculate with money is a very important life-skill.

During Year 3, children build on their knowledge and skills they have achieved during Year 2.

By the time children reach the end of Year 3, they should be able to:-

• use decimal notation for amounts of money, e.g. £3.27
• change amounts in £ to amounts in pence and back;
• count money up to £10;
• calculate change for amounts of money up to £1 mentally;
• solve simple problems involving money;
• use informal methods to add and subtract money amounts in £ and pence.

Our worksheets will support your child with these objectives.

Year 3 Money Challenges Information

The following worksheets involve solving challenges involving money amounts. They are a great way to consolidate and extend money learning once children are confident with counting money amounts.

The challenges start off at a fairly easy level with problems that involve lower value coins and smaller money amounts. The challenges later on involve more complex problems with larger values to calculate.

If you are teaching a class or group of children, then these sheets should give you some great differentiated learning activities with a money theme.

An answer sheet is available for each challenge provided.

The money challenges in each section are carefully graded, allowing you to introduce concepts at an easier level before introducing harder work, or differentiate within your class.

Using the sheets in this section will help your child to:

• count money in coins up to £1;
• develop their reasoning and thinking skills;
• solve problems involving money.

All the money worksheets in this section will help your child to become more confident with money, and develop better problem solving skills.

Year 3 Money Challenges Worksheets

There are 3 challenges - Tyger's Money Square Challenge, Row of Coins Challenge and How Much Money Challenge.

Each main challenge has several versions which start with the easiest level and progress onto harder levels of challenge.

Row of Coins Challenges

• Row of Coins Challenge 1
• PDF version
• Row of Coins Challenge 2
• Row of Coins Challenge 3
• Row of Coins Challenge 4

Tyger's Money Square Challenges

• Tyger's Money Square Challenge 1
• Tyger's Money Square Challenge 2
• Tyger's Money Square Challenge 3
• Tyger's Money Square Challenge 4

How Much Money Challenges

• How Much Money Challenge 1
• How Much Money Challenge 2
• How Much Money Challenge 3

Extension Activity Ideas

If you are looking for a way to extend learning with the How Much Money challenge, why not...

Try playing 'How Much Money' in pairs.

One person chooses 2 or 3 coins and the other person has to ask questions which involve 'yes' or 'no' answers.

To make the game more interesting, have a maximum of 5 questions before you make a guess!

Looking for some more UK money worksheets?

We also have some counting money worksheets with amounts up to £1 or £5.

The sheets are at a more basic level than those on this page.

• Free UK Money Worksheets Coins up to £1
• Year 3 Money Worksheets Coins up to £5
• Year 4 Money Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Money Riddles

These puzzles are a great money starter activity to get children thinking and puzzling out which the correct answer is out of a set number of choices. They are great for partner work too.

UK Money Riddles

If you are looking for some fun learning puzzles involving money, then look no further.

The puzzle sheets in this section are designed primarily for children in Years 3 and 4 who need to develop their problem solving skills and mathematical language.

Using these challenges will help your child to:

• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.
• Money Riddles for Kids (UK coins)

Money Column Addition Worksheets

Here you will find a selection of Column Addition Money sheets designed to help your child add different amounts of money.

Using these sheets will help your child to:

• add up a range of money amounts involving decimals.

The worksheets in this section are aimed at children in Years 4 and 5.

• Column Addition Money Worksheets (UK)

Money Column Subtraction Worksheets

Here you will find a selection of Column Subtraction Money sheets designed to help your child subtract different amounts of money.

• subtract a range of money amounts involving decimals.
• Column Subtraction Money Worksheets (UK)
• Counting Money Games

Here is our collection of counting money games for kids.

All of these games are suitable for kids aged from 1st grade and upwards.

Playing games is a great way to practice math skills in a fun way. Games also help to develop reasoning, thinking and memory.

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11 Free Worksheets on Counting Mixed Coins

These worksheets on counting mixed coins will help to visualize and understand mixed coins and money systems. 1st-5th grade students will learn basic mixed counting methods and can improve their basic counting skills with our free printable worksheets.

Table of Contents

11 Exciting Counting Mixed Coins Worksheets

Please download the following counting mixed coins worksheets and practice.

Counting Mixed Coins

International Coins

Complete Bonds

Circle Correct Hand

Different Coin Combination

Fewest Possible Coins

Coin Riddles

Comparing Coins

Word Problems

In this first method, you’ll learn how to count mixed coins in various ways . The following methods are essential for learning to count coins.

Counting Mixed Coins without Dollar Bills

To count mixed coins without dollar bills, follow these steps:

• Sort coins by denomination (pennies, nickels, dimes, and quarters).
• Count each pile of coins, grouping them in manageable batches.
• Assign values: pennies (one cent), nickels (five cents), dimes (ten cents), and quarters (twenty-five cents).
• Add up the total values for an accurate count of mixed coins.

Counting Mixed Coins with Dollar Bills up to $4

Now, count the mixed coins with dollar bills up to $4. Carefully read all the questions and add the mixed coins and money.  

Counting Mixed Coins with Dollar Bills up to $12

This worksheet for counting is up to $12. Carefully add the mixed coins. 

Counting Mixed Coins: International Money

This worksheet is all about international money.

The money categories and their values are displayed in the following worksheets.

Take a look first and remember them for later activities related to comparing money worksheets.

Counting Australian Coins

The following worksheet is for counting Australian coins.

Count and remember the Australian coins.

Counting Canadian Coins

The following worksheet is for counting Canadian coins. Count and recognize Canadian coins.

Counting UK Coins

The worksheet that follows can be used to count UK coins. Count and remember the UK coins.

Completing Money Bonds with Mixed Coins and Bills

This money worksheet will generate problems using coins and bills that are chosen at random.

Add the notes and coins before recording their findings.

Circling the Hand with the Correct Amount of Money

Worksheets for circling the correct amount of money include coins and bills.

After reading the amount of money on hand, circle the appropriate coins or bills that make up that sum.

Drawing Coins to Show Certain Amounts of Money

Worksheets for drawing coins to show a certain amount of money include coins and bills. After reading the amount of money, draw the appropriate coins or bills that make up that sum.

Showing the Same Amount of Money with Different Coins

Worksheets for showing the same amount of money with several coins, using different coins.

Draw the appropriate coins that make up the sum after reading the amount of money.

Showing Different Coin Combinations

Worksheets for showing an amount of money with several different coins.

Draw the appropriate coins that make up the sum after reading the given amount of money.

Showing Fewest Possible Coins

Worksheets for displaying a sum of money with the fewest number of coins. After reading the amount of money, draw the appropriate coins that make up the total. 

Solving Mixed Coin Riddles

It’s time to solve some mixed coin riddles. Each of the riddles has some clues. See the clues carefully, and find the answers to the riddles like a pro.

Comparing Mixed Coin Sets

Three types of symbols are used to compare the mixed coins .

The greater than sign ( < )

The less than sign ( > )

The equal sign ( = )

A worksheet related to this activity is attached below.

Coins are given on both sides in the following worksheet. Find the appropriate sign and write it in the box. For your better understanding, I’ve written the first one.

Solving Counting Mixed Coin Word Problems

This attached worksheet is about the word problem of mixed coins. Read carefully and solve them.

Download Free Worksheet PDF

So today, we’ve discussed how to count mixed coins using the concepts of counting mixed coins, counting international money, completing, circling, and drawing mixed coins, showing mixed coins, comparing mixed coins, and some interactive word problems. Download our free worksheets, and after practicing these worksheets, students will surely improve their money skills and have a better understanding of mixed coins.

Hello! Welcome to my profile. I have done my graduation from Ahsanullah University Of Science and Technology in Electrical and Electronic Engineering. Currently, I have started working as a Content Developer for “You’ve got this math” at SOFTEKO. As an Electric engineer, I always try to achieve innovative knowledge. I have an interest in research articles on different ideas. Also, I really like to solve innovative and mathematical problems. I really hope I’ll do better in the future as an Engineer.

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• Counting U.S. Money

Counting Coins and Bills | U.S. Money Worksheets

Money is an integral part of our life. Hence, teaching kids of grade 3, grade 4, and grade 5 to manage money is a vital math topic. This compilation of money worksheets on counting U.S. bills and coins is sure to impart an in-depth knowledge in managing money as kids practice counting coins like pennies, nickels, dimes, quarters, and $1, $5, $10, $100 bills. Find practice PDFs to count and check if there's enough money to buy items you need, and learn the most important aspect of saving money as well. Kick-start your practice with our free worksheets!

Penny, Nickel, Dime and Quarter Worksheets

This assortment of penny, nickel, dime and quarters worksheets consist of topics like matching coins to value, counting and ordering U.S. coins, cut-paste activity, equivalent coins, American coin combinations and more.

(60 Worksheets)

Counting Coins and $1 Bill

Familiarize 3rd grade and 4th grade kids with the American currency coins like pennies, nickels, dimes, quarters, half-dollars and one-dollar bills in this array of printable worksheets. Direct kids to count the bills and coins and write the amount in the space provided.

• Download the set

Counting Coins and Bills ($1, $5, $10)

Bolster skills in counting U.S. coins and bills featuring all the coins and dollar bills ranging up to $10. Compute the amount in each money problem and write the value.

Counting U.S. Bills and Coins

Count the money in each question, look for the matching price tags in the shopping catalog and map the letter on the item to the correct amount. The easy level has items worth ≤ $100 while the moderate level has items worth ≥ $100.

Matching U.S. Money to Value

This unit of printable U.S. money worksheets present the bills and coins on one side and the value on the other. Instruct 4th grade and 5th grade kids to count the money and match it to its equivalent value.

Matching Money to Money

This stock of pdf exercises is very helpful in testing the conceptual knowledge as kids count the bills and coins on either side. They identify the equal amounts and connect the matching sets.

Counting U.S. Money | MCQ

Determine the total amount of bills and coins in each set and choose the correct amount in this MCQ section of money worksheets. Best serves as a recapitulation exercise.

U.S. Money | Cut and Paste Activity

Enumerate the bills and coins in each purse and figure out the item that matches the amount in the purse. Cut the items and glue them below the appropriate purse to complete the pdf worksheets.

Is there enough Money?

This batch of printable worksheets will give grade 4 kids a real-time shopping experience. They need to read each real-life scenario carefully, count the amount in each wallet and write if there is enough money in the wallet to buy the item.

Saving Money

Examine the piggy banks, count the U.S. bills and coins in each piggy bank. Then answer the questions on saving based on your observation and comprehension.

Related Worksheets

» Money Charts and Activities

» Making Change

» Comparing and Ordering Money

» Adding Money

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Money word problems

Counting money word problem worksheets.

These money word problems involving the counting of coins. Students are given stories in which they are asked to count their coins and decide, who has more money, whether they have enough money to buy an item, and similar. 

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How to Solve Your Company’s Toughest Problems

A conversation with Harvard Business School professor Frances Frei on how to solve any problem in five clear steps.

• Apple Podcasts

You’ve likely heard the phrase, “Move fast and break things.” But Harvard Business School professor Frances Frei says speed and experimentation are not enough on their own. Instead, she argues that you should move fast and fix things. (That’s also the topic and title of the book she coauthored with Anne Morriss .)

In this episode, Frei explains how you can solve any problem in five clear steps. First, she says, start by identifying the real problem holding you back. Then move on to building trust and relationships, followed by a narrative for your solution — before you begin implementing it.

Key episode topics include: leadership, strategy execution, managing people, collaboration and teams, trustworthiness, organizational culture.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

• Learn more about HBR’s “ Future of Business” virtual conference (November 2023)
• Find more Harvard Business Review live events
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Maybe you’ve heard the phrase, “move fast and break things.” It refers to a certain approach for rapid innovation that was popularized in Silicon Valley and invoked by many tech firms. But Harvard Business School professor Frances Frei says that speed and experimentation are not enough on their own. Instead, Frei argues that you should “move fast and fix things.” That’s the topic and title of the book she co-authored with Anne Morriss.

In this episode, Harvard Business Review’s editorial audience director Nicole Smith sits down with Frei to discuss how you can solve any problem in five quick steps. You’ll learn how to start by uncovering your true problem. Then, move on to build trust, relationships, and a narrative for your solution before you dive in on the actual work of implementing your fix.

This conversation was originally part of HBR’s “Future of Business” virtual conference in November 2023. Here it is.

FRANCES FREI: So, I would love to talk to you about how to move fast and fix things. And I’ll tell you the reason that Anne and I wrote this book – and it’s really a quest we’ve been on – is that Mark Zuckerberg, in his IPO for Facebook, famously said, “we’re going to move fast and break things.” And the problem with that is that it gave the world a false trade-off. It convinced so many of us that you could either move fast and break things or you could take care of people, one or the other. And we have found that there is a third, much better way. And that is, we can move even faster if we fix things along the way. And so, that’s what I’d love to talk to you about right now. And the way that we think about this is that if you want to move fast and fix things, we have to do it on a foundation of trust. And so, the first thing to do is to experience high trust. And we’re going to talk about how to build trust. But the way we see the world can be described in this grid. And in the presence of trust, we can move really fast. That’s how we move fast and fix things. We call it accelerating excellence. It’s only when we’re in the presence of low trust that we move fast and break things, or what we call being reckless disruption. And as I said, so many organizations are afraid of reckless disruption that they actually end up in this state of responsible stewardship, which is really just going slowly. And so, we wrote the book to get those that are in responsible stewardship to realize that we could go across the way to accelerating excellence. And we didn’t have to go down to reckless disruption. So, the way that we think about this, and it’s the way we wrote the book, is that there’s a five-step plan to do it. We organized the book for days of the week. We think that the metabolic rate of organizations can be improved significantly and that many, many hard problems can be solved in just one week. So, we wrote the book in the structure of a week. Step one is we have to find our real problem, that if we’re… for far too many of us, we’re addressing the symptom and not the cause. At any problem, there’s going to be trust broken at the bottom of it. And we’re going to solve for trust. We’re then going to learn how to get more perspectives to make our plans even better. Learn how to tell a narrative that works. And then, and only then, on Friday, do we get to go as fast as we can. And what typically happens in the move fast and break things is that we move Friday too forward in the week. So, our goal is to put ourselves in a position to move fast. And you have to wait till Friday to do that. So, what do I mean by finding the real problem? Most of us, a problem gets presented as a symptom. So, I’ll give you a recent example that got presented to me and Anne. We got called by a company. And they said, we’re having a gender problem. Will you come in and help us? And we’ve been able to help many organizations solve gender problems. So, we go in there. And we just wanted to make sure that they really did have a gender problem. The symptoms were super clear. There were no women at the top of the organization. Not very many women were coming into the organization. And great women were leaving the organization. So, they had… it looked like a gender problem. But it took, I don’t know, an hour. It took 60 minutes, certainly not even all of Monday, to uncover that their actual problem was not a gender problem. Their actual problem was a communication problem. And if we did all of the things that we know exist in our gender tool kit on how to fix gender, that would have all been wasted effort. But instead, what we found out is that the founders of this organization, and they were two cofounders, and they were very similar to each other, and they’d worked together and known each other for decades. They had a really uncomfortably and aggressively direct communication style. That communication style repelled all women and most men. So yes, the symptoms were gender. But oh, my goodness, the cause was that the two founders were succumbing to a problem many of us succumb to, which is, we were treating others as we like to be treated. They loved to be treated with aggressively direct communication. But nobody else loved it. And when we simply confronted them with that and taught them that instead of treating others as you want to be treated, now it’s a puzzle. Find out how they want to be treated, and treat them that way. Gets fixed. And all of a sudden, women and lots of other men are flowing to the organization. So, Monday… and we take a whole day for this. Let’s make sure we’re solving the real problem. And symptoms are rarely the cause. So, we just want to do some due diligence, some due diligence there. Once we know we’re solving for the real problem, there’s going to be trust broken down somewhere in the… amidst the problem. Well, very fortunately, we now understand trust super well. If I’m going to earn your trust, you will have an involuntary reaction of trusting me if you experience my authenticity, logic, and empathy all at the same time. When these three things are present, you will trust me. But if any one of these three is missing, you will not trust me. And here’s the catch. If trust is broken, and we know it’s only ever broken for one of these three reasons, we need to know which of the three, because the prescriptions to solve a broken authenticity pillar versus logic pillar versus empathy pillar, they’re entirely different from one another. So, you can think about rebuilding trust. It’s just a matching game. Know which one is at stake. And then bring in the curated prescription for that. There is a myth about trust that it takes a lifetime to build and a moment to destroy. And then you can never rebuild it. None of those things are true, that we can actually build trust very quickly when we understand the architecture of it. We can rebuild it quickly and just as strong as it was before. So, this notion that trust is a Faberge egg, it’s catchy and not true. Trust is being rebuilt all the time. But we want to do it with a deep understanding of the stable architecture. So, Tuesday takes all day. We solve for trust. On Wednesday, we call Wednesday making new friends. And what we mean by that is whichever collection of people you bring to the table who are the people that maybe are on your senior team or the people that you bring to the table to solve problems. And here, I’ve represented a table. And there’s eight check marks for eight seats. I encourage you to bring four extra chairs to that table. If you have eight seats, bring four extra chairs. Point to the extra chairs and ask yourself, who’s not here? Who has a stake in our problem who’s not represented at the table? I was recently in a conversation with our senior colleagues at the Harvard Business School. And we were talking about how to do junior faculty development. And we came up with what we thought were great ideas. And then we looked around and we were like, Oh, my goodness, there’s no junior faculty here. How on Earth do we know if these are good ideas? So, we got the empty seats. We invited people in. And sure enough, the junior faculty helped improve our plans dramatically. The equivalent of that always happens. So, on Wednesday, we want to make new friends. So, one is inviting them into the room. But then the second part is, how do you make sure that their voices are heard? And what we need to do is that when someone comes to the room, they’re going to be awfully tempted to say things that they think we want to hear. They’re going to be awfully tempted to conform to what we’re already saying. So, what we need to do is learn how to be inclusive of their unique voices. And the way we do that is by going through this four-step progressive process, which is, first, we have to make sure they feel safe and that they feel… they’re going to feel physically and emotionally safe, I’m sure, but that they feel psychologically safe. And that’s a shout-out to Amy Edmondson and all of her beautiful work there. But we have to make sure that we feel safe. Once we feel safe, then it’s our job to make sure that the new voices feel welcome. You can think of that as table stakes. Then when we’re doing is we’re really trying to move people up the inclusion dial. And here, this is when it really starts to make a big difference. And now what we want to do is make sure that they feel celebrated for their unique contribution. And so, what we’re doing is moving them up the inclusion dial. Now, here’s why that’s kind of hard. Most of us tend to celebrate sameness. And here, I’m asking you to celebrate uniqueness. And what I mean by celebrating sameness is that for the most part, like, when I watch my students in class, if one student says something, and then another student was going to say that, after class, they go and seek out the first person. And they’re like, you’re awesome. You said what I was going to say. They didn’t realize this. They’re celebrating sameness. They’re encouraging sameness. So, what I do is I advise my students to not share that verbal treat, that what we playfully refer to as a Scooby snack. Don’t share that Scooby snack for when somebody says something you were going to say. Share it for when somebody says something you could never have said on your own, and that it comes from their lived experience and learned experience, and how they metabolize successes and failures, and their ambition, if they’re lucky enough to have neurodiversity, their worldview, all of that. It’s a beautiful cocktail. Wait till they say something that comes uniquely from all of that. Celebrate that. When we celebrate uniqueness, that’s when we get the blossoming of the perspectives. And what we want to do to make somebody really feel included is we celebrate them when they are in our presence. But if you really want somebody to feel included, and we bring folks into the room for this, make sure that you champion them when they’re in the absence. So, let’s not just ask the junior faculty to come along. Or if it’s a senior team, and it’s mostly men, and the board of directors is coming in, and we’re like, oh, goodness. Let’s make sure we can show some women too. So, we bring some women along. We celebrate them in our presence. Let’s make sure that we champion them in our absence as well, which is celebrate their uniqueness in our presence and champion them in rooms that they’re not yet allowed into in their absence. So that’s Wednesday. Let’s make new friends. Let’s include their voices. Let’s champion those new voices in their absence. Thursday, we tell a good story. And stories have three parts to it: past, present, and future. It is really important – if you’re going to change something, if you’re going to fix something, it is critical to honor the past. People that were here before us, if they don’t feel like we see the past, we see them, we’re honoring the past, I promise you, they’re going to hold us back. And they’re going to be like The Godfather movie and keep pulling us back. So, we have to honor the past with clear eyes, both the good part of the past and the bad part of the past. Then we have to answer the question, why should we change now? Like, why shouldn’t we change maybe next week, maybe the week after, maybe the month after, maybe next year? So, it’s really important that we give a clear and compelling change mandate that answers the question, why now? Why not in a little while? I find that if you’re a retailer, and you have the metaphor of Walmart just opened up next door, clear, compelling. We have to… that should be our metaphor. How can we be, with as crisp of a language, clear and compelling about why now? And then we’ve honored the past. We have a clear and compelling change mandate. You want people to follow us in the improved future, we have to have a super rigorous and a super optimistic way forward. We have seen so many people be optimistic without rigor. Nobody’s going to follow. And similarly, rigor without optimism, also, nobody’s going to follow. So, it’s our job to keep refining and refining and refining until we can be both rigorous and optimistic. Now, how do we know when our plan is working? Well, here are the four parts of storytelling that we know. Our job is to understand this plan so deeply that we can describe it simply. When we describe it, we want to make sure if I describe it to you, and you describe it to the next person, that the next person understands it as if I described it to them. So, our job is to understand so deeply that we can describe simply that it’s understood in our absence. And the ultimate test is it’s understood when they go home and share it with their family. They have the same understanding we want. We find this to be the four-stage litmus test to make sure we have been effective in our communication. And when people understand it this well, then they can act on it in our absence. And that’s when we’re now in the position to go as fast as we can. And when all of that infrastructure is in place, well, then we can go super fast. And there are all kinds of clever ways that we can do that. So, I look forward to opening this up and having a conversation with you.

NICOLE SMITH: That was excellent. Professor, we got several questions. I want to just dive right into it. Tessa asked, what tools, practices, and skills do you use to uncover the underlying superficial problems? It sounded like you talked a lot about questions and asking questions.

FRANCES FREI: Yeah, it’s right. So, the Toyota production system would famously refer to the five whys. And they had… and that was root cause analysis, which we all know. But essentially, what they found is that it’s about five… why does this exist? Well, why does that exist? Well, why does that exist? Like, if you ask why five times, they found that that’s how you got to the root cause. We find, in practice, the answer is closer to three. It’s rarely one. So, it would be, the symptom and the cause are usually a few layers. And you want to keep asking why. So, that’s the first thing I would say, is that we want to have… make sure that you’re doing root cause analysis. But the second thing on a specific tool, the tool that we like the most, we call the indignities list. And what you do is that… and the way we found out the symptom is we went to women in this company, because that’s what… they said they were having a gender problem. And we asked the women, is there anything that’s going on at work that just… it feels like it’s just nicking your dignity? And it occurs for… is it happening to you, or you observe it happening to other women? So, you go in search of the indignities list. Every time we do this, you’ll get a list of issues. Often, they will sound trivial. When you start to get convergence on those indignities, we then ask you to convert those indignities to the dignity list. And in this case, it was the communication style. And you know what the awesome thing about that was? It was free.

NICOLE SMITH: Wow.

FRANCES FREI: You can’t beat free.

NICOLE SMITH: Monique asks, can you speak more about how to amplify others’ ideas and perspectives, especially when they’re from underrepresented stakeholders?

FRANCES FREI: Oh, I love that question. Thank you very much. And so, I’m going to go to… here is my favorite visual on the amplification part, which is the team I’ve drawn in the middle, it’s a three-person team. And each circle represents a person on the team. And I’m showing that there’s three circles in the middle, that those folks are very similar to one another. And then on either side, we have a team where there’s difference among us. And this is where the underrepresented might come in. If we’re not careful, when we have underrepresented voices, we’re only going to be seeking from them the parts that overlap with us. So, this is when we’ve invited them to the table, but we’re not inclusive of their voices. What we want to do is make sure that everybody feels comfortable bringing all of their richness to the table, not just the part that overlaps. And so, what we find we need to do is be very solicitous about… and same with questions. From your perspective, how does this sound to you? What else are we missing? What I’m trying to do is get you off the scent of saying what you think I want to say or even asking you to say what I want to say because it makes me feel better. But I want to be inclusive of all of the gorgeous uniqueness. And this, of course, ties to diversity, equity, and inclusion, which I know has gotten a rocky go of things in the press. But what I’ll tell you is, if I got to rewrite diversity, equity, and inclusion, I would have written it as inclusion, equity, and diversity, because I have seen teams bring… I have seen organizations bring in diverse and underrepresented talent and not get the benefit from it.

NICOLE SMITH: Yeah.

FRANCES FREI: So, diversity may or may not beget inclusion. But I have never, ever seen an organization that was inclusive that didn’t beget gorgeous diversity.

NICOLE SMITH: Right.

FRANCES FREI: So, be inclusive first.

NICOLE SMITH: I appreciate you saying that, not just sitting at the table, but actually including and giving lift to people’s voices. I also want to talk about this friends thing you keep talking about, making new friends. First of all, how do I identify who’s a friend?

FRANCES FREI: Yeah. So, in this case, I want the friend to be someone who is as different from you as possible. So, the new friends. Like, who’s worthy of friendship? Not someone who you’re already attracted to, not somebody who you’re already hanging out with. So, here’s the thing about humans. We really like people who are really like us. It doesn’t make us bad people. But it just makes us human. And so, what I want you to do is seek difference. Find people from different perspectives. And that will be demographic difference, different lived experience, different learned experience. And so, if we’re senior faculty, let’s invite in junior faculty. If we’re all women, let’s invite in a man. If we’re all engineers, let’s make sure we’re bringing in the perspective of marketing. So, what I would say is my guiding principle is seek difference. Those are your potential new friends.

NICOLE SMITH: OK, so Steve wants to hone in on Friday, right? And Steve asks, can you paint a quick sketch of what’s going fast after this being slower – a slower, more thoughtful process?

FRANCES FREI: I sure can. Thank you, Steve. And so, here’s how I would think about Friday. We need ruthless prioritization. And what I mean by that is that for the most part, organizations have… that we work equally on everything. We think everything is equally important. But what we know is that organizations that win, they have ruthless prioritization. And they know, this is what I’m designed to be great at. And this is what I’m designed to be bad at. Not bad for sport, bad in the service of great. And if an organization can’t discern between these two, they’re going to end up with exhausted mediocrity. And so, what we have to do for our employees and the rest of the organization is, here’s what we’re going to optimize on. That’s half the story. And here’s what we’re not. So, I’ll give you an example of this. And the example is from Steve Jobs. And if those of you that are a bit techie, and you remember 20 years ago, when Steve Jobs walked out on that Worldwide Developer Conference stage with a manila envelope, and it had a MacBook Air in it. And he slid out that MacBook Air. And the crowd and the world went crazy, because it was the lightest-weight laptop in the world. Well, he very, very openly said, we are best in class at weight because we are worst in class at physical features. We could have been best in class at physical features. But then we would have been worst in class at weight. Or we could have chosen to be average at both. But then we would have had to rename our company. And then he made fun of another company that I won’t say here. So, we will end up… if we aren’t deliberate, we’re going to end up with exhausted mediocrity, constantly getting better at the things we’re bad at, which, without realizing it, means we’re getting worse at the things we’re good at. So, the most important thing we can do on Friday is to articulate, this is what we want to be disproportionately good at. And thus, this is what we want to be disproportionately bad at. And there’s a whole other series of things. But that’s the most important one.

NICOLE SMITH: Mm-hmm. Speaking of Steve Jobs, we have a question where they ask, do you think that the culture in Silicon Valley is changing from break things to fix things, particularly as it pertains to not only their own companies, but broader societal problems?

FRANCES FREI: Yeah, so I – not in all of Silicon Valley. So, I think we can famously see, it’s not clear to me that Twitter is moving fast and fixing things. But what I will say is that, look at Uber today. And I had the pleasure of going and working with Uber back in 2017, when they were going to move fast and break things. They are moving fast and fixing things now, and going at a catapulting speed. Or ServiceNow didn’t ever even go through move fast and break things. It’s just moving fast and fixing things. Stripe is doing the same thing. Airbnb is now moving fast and fixing things. So, what I would say is that Silicon Valley can now choose to move fast and fix things, whereas, in the past, I think they only thought they had the choice of going slow or moving fast and breaking things. Today, we have the choice. And more and more companies are making that choice.

NICOLE SMITH: Mm-hmm. And so, Bill asked, which one of these steps do you find the most commonly in need of… that companies need the most help with? So, you laid out Monday through Friday. Is there something that sticks out often?

FRANCES FREI: Well, I’ll tell you that if companies are really pressed for time, they skip Thursday. And that’s to their peril, because if we skip Thursday, that means we have to be present. And we’re a bottleneck for everything. That means people need us to translate why this is important. So, I would say that Thursday is the one that’s most often skipped. And I encourage you not to. And then I would say that Tuesday is the one that’s most often misunderstood because of all of the myths I mentioned that we have about trust. And we just think, oh, if trust is broken, we have to work around it, as opposed to going right through it and rebuilding trust.

NICOLE SMITH: So, Thursday, that’s the storytelling, honoring the past, describing it simply, right? So why do we struggle to describe things simply?

FRANCES FREI: Oh, I don’t know what your inbox looks like on your email. But you tell me how many long emails you have.

NICOLE SMITH: I refuse to deal with my inbox. I’ll deal with it later.

FRANCES FREI: So, Mark Twain was right. I apologize for sending you a long letter. I didn’t have the time to send you a short letter. It’s the metaphor for all of this, that when we understand something in a complicated way, we want to benefit people from the entirety of our knowledge. And we just throw up all of it on people, as opposed to realizing the beautiful curation and skill that’s required to go from understanding it deeply to understanding it elegantly in its simplicity. So, I think it takes time. It’s also… it takes skill. Like, this is… there are professional communicators for a reason. They’re really good at it. But if you’re on your second draft of something, you have no chance of describing it simply. So, I would say, unless you’re on your 10th draft, you’re probably describing it in too complicated of a way.

NICOLE SMITH: Yeah. So, can I ask you a little bit more of a personal question, Professor?

FRANCES FREI: Yeah, anything.

NICOLE SMITH: So, Abby asks, how do you apply the essential steps to moving fast and fixing things in your own consulting role? So, Uber and all the places that you go.

FRANCES FREI: Yeah. Yeah, so I’ll tell you, when we’ve been successful, it’s when organizations come to us, and they say, here’s our problem. Will you help us? When we’ve been unsuccessful is when we go to the organizations, and we’re like, we think you’re having a problem. So, pull works. Push doesn’t. So, the only thing we can’t provide is the desire to change. And so, I would say personally, make sure there’s an opening. And then you can be super helpful in fixing a problem. And I also would say that all of this applies to yourself. I mean, that ruthless prioritization – so many of us are trying to be good at as many things as possible – at work, at home, daughter, sister, cousin, parent, friend – as opposed to, I’m going to kill it at work, kill it at home. And I am not going to be good… not now. I’m not going to be as good at all of these other things. So, you can either choose exhausted mediocrity, or you can have the nobility of excellence. These things are choices. So, I think all of this applies to ourselves.

NICOLE SMITH: So, let’s go back to Tuesday, where you drew that triangle with logic, and empathy, and authenticity. So, Hung asks, between logic and empathy, which one would you say an individual should develop first? And Hung really describes just having a left foot and right foot and not knowing which one to go forward.

FRANCES FREI: Yeah. So, here’s what I would say, Hung, is, ask yourself… I bet you’re trusted most of the time, which means people are experiencing your authenticity, logic, and empathy most of the time. But ask yourself, the last time, or the most recent times you had a skeptic, you had someone who was doubting you, who they were wobbling on your trust, ask yourself, what is it that they doubted about you? And if it’s that they doubted your logic, double click there. If they doubted your empathy, double click there. And that is, each of us has what we call a wobble. Each one of us has a pattern where the distribution of these is higher for one or the other. That’s the sequence I would go in. There’s not some generic sequence that is better. All three of these pillars are equally important. But I bet, for each one of us, one tends to be more shaky than the other. And that’s what I would go after. Now, I will just tell you the distribution in the world. The vast majority of us have empathy wobbles, then logic wobbles, then authenticity wobbles. But that doesn’t help any of us specifically. It just tells us we have lots of company.

NICOLE SMITH: OK. So, we got a lot more questions and a little time. I want to get as many as I can in, but…

FRANCES FREI: OK, I’ll go super quick. Yeah.

NICOLE SMITH: No, take your time. But I just want to let you know, you’re pretty popular in this conversation. Rock star, as Allison said. Tara asks, how can company leadership make sure that their messaging is actually heard and understood? I feel like you touched on this a bit with simplicity.

FRANCES FREI: Yeah. Yeah, and I think that the way to do it is, talk to people about your message that didn’t hear it directly from you. And see how well they understood. That tells you whether or not it’s reaching. So, don’t ask the people that were in the room. Ask the people that were spoken to by other people in the room. That will tell you how well it’s there. And if it took you a long time to describe it, I promise you, it’s not going to be heard.

NICOLE SMITH: Mm. Oh, wow. Yeah, thinking about it, probably need to shorten my own stories a little bit here. So, Karen asks you, how do you handle employees who are not willing to accept others’ points of view and be open minded? I mean, you described this uniqueness and diversity. But there are people who are holdouts that don’t see the advantage of that.

FRANCES FREI: So, I often find those folks are an education away, because if I can let you know that if I get to benefit from everyone’s point of view, and you only get to benefit from some people’s point of view, I will competitively thump you. So, let’s say you don’t have the moral imperative wanting to do it. Well, the performance imperative… we have found that organizations that are inclusive get a 200% to 500% boost on employee engagement and team performance with no new people, no new technology, simply the act of being inclusive. So, the person who doesn’t want to be inclusive, I’m going to ask them, can they afford… can their career afford performing so suboptimally?

NICOLE SMITH: Mm. And so, we have a question. The person didn’t leave their name, so I don’t have a name. But how much time do you spend on each stage? Some folks like to spend more time on stages than others. Does the team not move forward until everyone’s satisfied with the current step? What do you do when you hit a roadblock on each stage, and not everyone is in agreement?

FRANCES FREI: Yeah. Well, I don’t like consensus, so I’ll just… I’ll say there. And so, what I try to do is work on momentum, which is that I want to make sure that everybody’s voices have been heard. But then you have to leave the decision to someone else. So, we want to do is make sure everybody’s voices are heard, and they had a chance to do it. But we don’t hold out until the very last person. We move forward. And then we can retrace and see if the momentum can bring people forward. So, not consensus. I would consider it not consensus, and we have to make sure that everybody gets to air out what their problems are.

NICOLE SMITH: OK. Well, Christopher asks our last question. How does transparency fit into this model, specifically this trust, authenticity, logic model? Does it have a place?

FRANCES FREI: Yeah. It sure does. And I find that the most important part for transparency is on the logic side. So, if you’re going to say… if you’re going to inspect whether or not I have good rigor, and I have a good plan, I could say, oh, just have faith. I did all of this hard work. Or I could give you a glimpse inside so that you can see the inner workings. Now, I often call it a window of transparency, because there’s actually a cost of full transparency that I’m not always willing to take. But a window of transparency, I think we always need. So, to me, the transparency part is, let’s be transparent about our logic so people can see it for themselves, and they don’t have to do it in too much of a faith-based way.

NICOLE SMITH: Professor, that was all dynamic. And thank you for the illustrations. You made it simple with the illustrations.

FRANCES FREI: Yeah, all right. Awesome. Thanks so much.

NICOLE SMITH: Thank you for your time.

FRANCES FREI: OK.

HANNAH BATES: That was Harvard Business School professor Frances Frei in conversation with HBR’s editorial audience director Nicole Smith at the “Future of Business” virtual conference in November 2023.

We’ll be back next Wednesday with another hand-picked conversation about leadership from Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

When you’re ready for more podcasts, articles, case studies, books, and videos with the world’s top business and management experts, you’ll find it all at HBR.org.

This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Dave Di Iulio, Terry Cole, and Maureen Hoch, Erica Truxler, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener. See you next week.

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The Vapes of Wrath

Alexi Horowitz-Ghazi

Leon Neyfakh

Emma Peaslee

When the vape brand Juul first hit the market back in 2015, e-cigarettes were in a kind of regulatory limbo. At the time, the rules that governed tobacco cigarettes did not explicitly apply to e-cigarettes. Then Juul blew up, fueled a public health crisis over teen vaping, and inspired a regulatory crackdown. But when the government finally stepped in to solve the problem of youth vaping, it may have actually made things worse.

Today's episode is a collaboration with the new podcast series "Backfired: the Vaping Wars." You can listen to the full series at audible.com/Backfired .

This episode was hosted by Alexi Horowitz-Ghazi and Leon Neyfakh. It was produced by Emma Peaslee and edited by Jess Jiang with help from Annie Brown. It was fact checked by Sofia Shchukina and engineered by Cena Loffredo. Alex Goldmark is Planet Money 's executive producer.

Help support Planet Money and hear our bonus episodes by subscribing to Planet Money + in Apple Podcasts or at plus.npr.org/planetmoney .

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Music: NPR Source Audio - "Comin Back For More," "Sorry I Kept You," and "Eku Oja Meta"

Throwing money at plunging birth rates won't solve the issue, demography experts say

• By 2100, 97% of countries are expected to have fertility rates below replacement levels.
• Demography experts told BI that countries offering financial incentives won't solve this.
• Promoting gender equality might help, but it's unlikely to reverse population decline, they said.

The world is facing a fertility rate crisis, and experts warn that giving financial incentives to would-be parents isn't going to come close to solving it.

A Lancet study forecasts that by 2100, over 97% of countries will have fertility rates below the population replacement level .

Some countries, fearing shrinking populations, have invested heavily in policies in the hopes of reversing the decline.

In Tokyo, the rates are so low that the government is launching a dating app to help citizens find love and get married.

The Japanese government has also tried to boost fertility rates by offering up to a year of parental leave and even cash incentives.

In South Korea, the least fertile country in the world, Seoul is offering people money to reverse their vasectomies or untie their tubes.

That's on top of South Korean companies offering employees up to $75,000 to have children, and a government allowance system that gives all parents with newborns $750 a month until their baby turns one.

However, according to Trent MacNamara, a Texas A&M professor whose work has focused on fertility rates, throwing money at the problem can only do so much.

"Theoretically, it's possible to produce higher fertility with traditional policy," he told Business Insider. "If a government transferred new parents about 5% of the costs of raising a child, we could expect a roughly 5% bump in fertility."

But he noted that such measures come with "backbreaking costs" that governments are hesitant to bear, especially given the strain aging populations place on social welfare systems.

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MacNamara said that even in countries like South Korea, which has invested billions, the impact of the policies is still inconclusive.

While governments are scrambling for solutions, none have discovered the holy grail — an affordable, practical policy leading to sustained fertility rate rises, he said.

Sarah Harper, a professor of gerontology and the director of the Oxford Institute of Population Ageing, says that cash incentives have a limited long-term effect.

"It encourages a mini-baby boom, followed by a baby crash, as those women who would have spread their childbearing across several years all go at the same time to get the cash bonus," she told BI.

Harper said that instead of throwing money at the issue, the biggest chance for success is through promoting gender equity.

She said that countries that promote "positive parenting, ensuring that mothers, as well as fathers, can continue their careers through acceptance in the workplace," have the best chance of maintaining birth rates.

However, she added that even this is unlikely to return levels to above-replacement.

Philip N. Cohen, a family demographer at the University of Maryland, said it's a "fool's errand" trying to solve the fertility crisis.

He said that most policy ideas have failed, and besides, "human history in the period of modernity, the last few hundred years, is the history of declining birth rates."

A few unique, ambitious policy ideas could, in theory, make an impact — like a social welfare fund for single mothers and mass immigration from poorer countries—but, Cohen said, they're unlikely to be implemented in most countries.

"That's politically fraught, even if the math of it makes perfect sense," he said.

As for the overall trend, "there's no way I think we can turn that around," he said.

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