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25 Money Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma Johnson

Word problems with money are first introduced in the Maths Curriculum in Year 2. At this stage, children learn to recognise the different coins and the symbols for pounds and pence; find different combinations of coins and begin to solve simple addition and subtraction word problems.

As pupils progress through primary, they continue to encounter money and word problems involving money, right through to upper Key Stage 2. By Year 6 money is no longer specifically identified in the curriculum. However, pupils continue to be exposed to money word problems, through a range of mathematical concepts and word problems including: addition and subtraction word problems , division word problems , multiplication word problems decimals, fractions, percentages, ratio and algebra.

Money word problems in Year 2

Money word problems in year 3, money word problems in year 4, money word problems in year 5, money word problems in year 6.

• Why are word problems important for children’s understanding of money

How to teach money word problem solving in primary school

Money word problems for year 2, money word problems for year 3, money word problems for year 4, money word problems for year 5, money word problems for year 6, more word problems resources.

When children are first introduced to money problems, it is important for them to physically have the money to hold and manipulate, to help solve the problems. As students progress through the school, there is less of a need to have the money physically in their hands. Once they have built confidence in using written calculation methods, they are able to solve more complex problems involving money.

All Kinds of Word Problems

Download this free pack of word problems covering a wide range of maths topics. Perfect for developing your class' problem solving skills!

Children benefit from regular exposure to word problems, alongside any fluency work they are doing. To help you with this, we have put together a collection of 25 money word problems, which can be used with pupils from Year 2 to Year 6.

Children are also exposed to money word problems in Third Space Learning’s online one-to-one tutoring programmes. Adapted to the needs of each individual students, our programmes help to build maths skills and grow confidence in our young mathematicians.

Money word problems in the national curriculum

In Year 2, pupils are introduced to the different coins; learn the symbols for pounds and pence and combine amounts to make a particular value. They work on simple problems in a practical context involving addition word problems , and subtraction word problems of money of the same unit, including giving change.

Pupils in Year 3 continue to build on their understanding of money and its use in a practical context. They progress from adding and subtracting money of the same unit, to working with both pounds and pence; adding and subtracting amounts and giving change. Pupils in Year 3 start to solve simple 2-step calculations, by finding totals and working out how much change would be given.

In Year 4, the curriculum no longer mentions money under measures, but pupils continue to work with money through fractions and decimals. At this stage, pupils are expected to solve simple measures and money problems involving fractions and decimals to two decimal places.

Pupils in Year 5 are becoming more confident with the formal written methods for the four operations and are exposed to money word problems involving all four. They also continue to build on the knowledge of fractions and decimals and are first introduced to percentages through a range of word problems.

By Year 6, money is no longer explicitly mentioned in the curriculum, however pupils are exposed to word problems across a range of concepts, including: the four operations, fractions, decimals and percentage word problems , ratio word problems and algebra.

Why are word problems important for children’s understanding of money

Word problems are essential to children’s understanding of money, because they enable students to use money in a range of contexts they will be using in real-life. Confidence with money is a key life skill and it is important children have plenty of exposure to using it in a wide range of contexts. Money problems give children the opportunity to utilise the skills they have learnt in the maths lessons and put them into context, in a situation they understand and can relate to.

Pupils need to be taught the skills needed to solve word problems. It is essential they understand the importance of reading questions carefully, making sure they fully understand what is being asked. They then need to identify which calculation is required and whether there are any concrete resources or pictorial representations they can use to help them, alongside the coins, such as place value counters and bar models.

Here is an example:

An adult’s ticket to the water park costs £15.50, whilst a children’s ticket cost £9.50.

How much would it cost for 2 adults and 2 children to visit the water park and how much change would they get from £100?

How to solve:

What do you already know?

• We know that an adult ticket costs £15.50 and a child ticket costs £9.50.
• To calculate the cost of both adults, we are going to need to multiply the £15.50 by 2, or add £15.50 and £15.50.
• We will also need to do the same with the child’s ticket, costing £9.50.
• Once we have calculated the total cost of both adults and both children, we’ll need to add these answers together, to establish the total cost for the whole family.
• To calculate the amount of money from £100, we will need to subtract the total cost for the family from £100.

How can this be represented pictorially?

• We can draw bar models to represent the cost of the adult tickets, child tickets and the total for the family.
• We can then use the answer from the third bar model to represent finding how much change from £100.
• We can see from these bar models that there would be £50 left once the family had paid to enter the waterpark.

Money word problems in Year 2 require students to recognise coins and use the symbols for pounds and pence. Children solve real world problems –  finding totals and calculating change when working with the same unit (pounds or pence). 

Mason buys a pen for 14p and a rubber for 8p. How much does he spend altogether?

Answer: 22p

14 + 8 = 22

Maisie gets 20p from the tooth fairy. She already had 16p.

How much does she have now?

Answer: 36p

20 + 16 = 36

Maisie has 3 coins.

She has 16p in total.

Which 3 coins must she have?

Answer: 10p, 5p and 1p

10 + 5 + 1 = 16

Maryam spends 28p on a bag of sweets.

She gets 12p change.

How much did she pay for the bag of sweets?

Answer: 40p

28 + 12 = 40p

Hamza has two 20p coins.

He buys a chocolate bar for 30p.

How much change does he get?

Answer: 10p change

20 + 20 = 40

40 – 30 = 10

Word problems for year 3 build upon the knowledge from year 2,  solving word problems involving both pounds and pence together and calculating change. At this stage, children should be using decimal notation for amounts of money and using both formal and informal methods to add and subtract money amounts in pounds and pence.

(Pictures of 1p, 5p, 10p, 20p, 50p and £1 coins here)

Jamie has the coins above in his wallet. If he takes out 3 coins, what is the highest amount he could take out of his wallet?

Answer: £1.70

£1 + 50p + 20p

Noah buys 2 chocolate bars for £1.35 each and a packet of crisps for 45p.

How much does he spend altogether?

Answer: £3.15

1.35 x 2 = 2.70

2.70 + 45 = 315

Tickets for the school fair are £1.50 for children and £2.50 for adults.

How much will it cost for family of 2 adults and 2 children to go to the fair?

1.50 x 2 = 3

2.50 x 2 = 5

Jackson buys 4 apples for 30p each and 2 bananas for 25p each.

30 x 4 = 120

25 x 2 = 50

120 + 50 = 170

Amaya had £10 to spend at a carboot sale.

She bought 2 books for £1.20 each and a pack of pens for £1.50,

How much money did she have left at the end?

Answer: £6.10

Children should be able to solve each part mentally, by adding the pounds and then the pence.

1.20 +1.20 = 2.40

2.40 + 1.50 = 3.90

To work out how much change Amaya would get, children can count up from £3.90 to £10.00. They will find this easier than subtracting £3.90 from £10.00.

10.00 – 3.90 = 6.10

With word problems for year 4 , pupils need to be able to order amounts of money, using rounding to estimate and calculate using the four operations. They also encounter money maths problems through other concepts, such as fractions.

Sam bought a T-shirt for £18.50 and a hoodie for £24.99. How much did he spend in total?

Answer: £43.49

Show as column method: 18.50 + 24.99 = 43.49

• Pizza: £2.99
• Burger: £2.50
• Hot dog: £1.80
• Fries: 1.25

Chloe took her best friend out to celebrate her birthday.

She bought a pizza, a burger and 2 portions of fries.

How much did she spend altogether?

Answer: £7.99

Show as column method:

2.99 + 2.50 = 5.49

1.25 x 2 = 2.50

5.59 + 2.50 = 7.99

Mason won £500 in a competition.

He decided to give ⅕ of the prize to his sister, ⅕ to his brother and ⅕ to his parents.

How much money did he keep for himself?

⅕ of 500 = 100

He gave ⅗ away and kept ⅖ for himself. ⅖ of 500 = 200

A school paid 4p for every worksheet printed out on the photocopier

Teachers printed out 560 maths worksheets in one week.

How much did the school spend, printing out the worksheets?

Answer: £22.40

560 x 4 = 2240

2240p = £22.40

Sara had £100 to spend on clothes. 

She bought a pair of jeans for £44.50 and a top for £35.99

How much money did Sara have left?

Answer: £19.51

44.50 + 35.99 = 80.49

100 – 80.49 = 19.51

Word problems for year 5 include the four operations, but with larger numbers than pupils were working with in Lower Key Stage 2. They are also presented to students through fraction word problems , decimal and percentages topics 

Mr Smith spends £5,999 on a car and £3,899 on a caravan.

Answer: £9,898

Show as column addition:

5999 + 3899 = 9898

Oliver is saving to buy a laptop costing £1250.

He has saved ⅖ of the money he needs. How much more does he need to save to buy the laptop?

Answer: £750

⅕ = 1250 ÷ 5 = £250

Mason saves £9 every week, from carrying out jobs around the house.

He is saving to buy a new phone, costing £370.

How many weeks will it take him to save enough money to buy the phone?

Answer: Mason will need to save for 42 weeks

Show as bus stop division: 370 ÷ 9  =   41 r1

Amber is at the fun fair.

Her favourite ride costs £2.75. She goes on that 5 times and buys a packet of doughnuts for £1.80.

If she had £20 to spend, how much money does she have left at the end?

Answer: £4.45

2.75 x 5 = 13.75

13.75 + 1.80 = £15.55

20.00 – 15.55 = 4.45

Jemma is calculating how much it will cost her to buy party bags for all the friends who come to her party.

Each party bag costs £3.75 and she has 9 friends coming to her party.

How much will she need to pay for the 9 party bags in total?

Answer: £33.75

Show as column multiplication: 3.75 x 9 = 33.75

With word problems for year 6 , pupils encounter multi-step word problems and those involving larger amounts of money and cover a range of concepts, including: the 4 operations, fractions, decimals, percentages, ratio and algebra. Money word problems are often included in the KS2 reasoning SATs papers.

Mr and Mrs Jackson are buying a new house. 

The house costs £425,999 to buy and they have a deposit of £84,000 from the sale of their last house.

How much more will they have to borrow, to be able to buy the house?

Answer: £341,999

425,999 – 84,000 = 341,999

The cost for all 90 Year 6 pupils to visit the outward bounds centre for the day is £2,430

How much does it cost per child?

Answer: £27

Show as long division:

2430 ÷ 90 = 27

A car decreases in value by 23% in one year. If it was worth £10,000 when it was bought. How much is it worth now?

Answer: £7,700

10% of 10,000 = £1,000

20% of £10,000 = £2000

1% of £10,000 = 100

3% of £10,000 = 300

10,000 – 2300 = 7,700

Mr Lampard was budgeting for the month,

He needed to pay: 

• £240 council tax
• £150 for gas and electricity
• £45 for water
• £38 for internet and phone line
• £125 petrol

After tax he earns £3200 per month.

How much does he have left over for food, social activities and saving.

Answer: £1802

Total spent:

800 + 240 + 150 + 45 + 38 + 125 = 1398

3200 – 1398 = 1802

£60 is shared between Abbie, Ben and Carly, as a ratio of 2:3:7

How much does each person get?

Answer: Abbie: £10, Ben: £15, Carly: £35

60 ÷ 12 = 5

Looking for more word problems on a range of topics? Take a look at our collection of time word problems .

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Free Printable Money Math Worksheets for 6th Year

Money Math: Discover a comprehensive collection of free printable math worksheets for Year 6 students, designed to enhance their understanding of money-related concepts and problem-solving skills.

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Explore printable Money Math worksheets for 6th Year

Money Math worksheets for Year 6 are an essential tool for teachers looking to enhance their students' understanding of financial concepts and mathematical skills. These worksheets provide a wide range of engaging and challenging problems that cover topics such as calculating percentages, understanding simple and compound interest, and working with decimals and fractions. By incorporating these worksheets into their lesson plans, teachers can ensure that their Year 6 students develop a strong foundation in money management and math, preparing them for more advanced concepts in the future. With a variety of formats and difficulty levels, Money Math worksheets for Year 6 cater to the diverse learning needs of students, making them an invaluable resource for teachers.

Quizizz offers an extensive collection of interactive worksheets, including Money Math worksheets for Year 6, that can be easily integrated into a teacher's curriculum. This platform not only provides a vast array of worksheets but also allows teachers to create their own quizzes and assessments to further engage their students and track their progress. In addition to Money Math worksheets, Quizizz offers resources for various other subjects, such as science, social studies, and language arts, making it a one-stop solution for teachers looking to diversify their teaching materials. By utilizing Quizizz, teachers can ensure that their Year 6 students receive a well-rounded education, while also making learning fun and interactive.

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Resources tagged with: Money

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Solving Problems - Money (Year 6)

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In KS2 Maths, Year Six kids become money masters! They learn to use addition, subtraction, multiplication, and division like superheroes. They can work out change, find costs, deal with percentages, and even switch between currencies. Now, they tackle bigger money challenges!

Money problems mean using addition for total costs, subtraction for change, and division/multiplication for saving secrets. Imagine saving £1.50 each week – how long to get £10? Ready for a fun quiz to test your money skills? Let's dive in!

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• 6th Grade Math

Fun and educational money math worksheets for 6th Grade learners

Understanding and using money math skills is vital for 6 th Grade learners as it prepares them for solving real-world money problems and some advanced math topics. Hence, if you are looking for resources to teach your students how to solve their financial transactions confidently, you are in the right place. This article has prepared some fun and educational money math worksheets for 6th-Grade learners to practice and confidently apply their money skills to many real-life scenarios.

6th Grade money math worksheets: How they can help your kids develop essential skills for the Future

As one of our primary objectives in this article, we will introduce you to Mathskills4kids.com , an outstanding website with remarkable 6th Grade money math worksheets . You may be wondering how these worksheets will help your kids develop essential skills for the future . Worry less. Just try them out and see how your 6 th Grade math students can make smart financial decisions now and in the future.

Money math is an important topic for 6th graders to learn and practice because it helps them develop essential skills for managing their finances, such as budgeting, saving, and investing.

It also prepares them for more advanced math topics, such as algebra and geometry, that involve money and decimals.

In this article, however, we will review some basic money concepts, introduce money math skills for 6th grade, and provide fun and engaging money math activities and worksheets for 6th graders to try at home or in the classroom.

BROWSE THE WEBSITE

Download free worksheets, grade 6 math topics.

• Whole numbers

Multiplication

• Exponents and square roots
• Number theory
• Add & subtract decimals
• Multiply & divide decimals
• Fractions & mixed numbers
• Add & subtract fractions
• Multiply fractions
• Divide fractions
• Operations with integers
• Mixed operations
• Rational numbers
• Problems solving
• Ratio & proportions
• Percentages
• Measuring units
• Consumer math
• Telling time
• Coordinate graph
• Algebraic expressions
• One step equations
• Solve & graph inequalities
• Two-step equations
• 2D Geometry
• Symmetry & transformation
• Geometry measurement
• Data and Graphs
• Probability

Start practice on Sixth Grade here

Why money math matters for 6th graders.

Money math matters for 6th graders because it helps them understand the value of money and how to use it wisely. Money math teaches them how to compare prices, calculate discounts, sales tax, and interest, and make intelligent decisions about spending and saving.

Money math also helps them develop critical thinking and problem-solving skills useful for many other subjects and situations. By learning money math, 6th graders can become more confident and responsible with their money and prepare for their future financial goals.

Review of basic money concepts: coins, bills, and decimal notation

Before diving into money math skills for 6th grade, let's review some basic money concepts that 6th graders should already know. These include:

• The names and values of coins and bills in the U.S. currency system
• How to count, add, subtract, multiply, and divide money amounts using coins and bills
• How to write money amounts using decimal notation (e.g., $3.25)
• How to compare and order money amounts using decimal notation (e.g., $3.25 < $4.50)
• How to round money amounts to the nearest cent, dime, or dollar using decimal notation (e.g., $3.27 ≈ $3.30)

Also, if your 6th grader needs a refresher on these concepts, you can download the following fun and educational money math worksheets from Mathskills4kids.com and give them to practice:

• Coin Recognition Worksheets : These worksheets help students identify and count coins by their names and values.
• Money Addition Worksheets : These worksheets help students practice adding money amounts using coins and bills.
• Money Subtraction Worksheets : These worksheets help students practice subtracting money amounts using coins and bills.
• Money Multiplication Worksheets : These worksheets help students practice multiplying money amounts by whole numbers or decimals.
• Money Division Worksheets : These worksheets help students practice dividing money amounts by whole numbers or decimals.
• Money Decimal Worksheets : These worksheets help students practice writing, comparing, ordering, and rounding money amounts using decimal notation.

Money Math Skills for 6th Grade learners: Calculating Discounts, Sales Tax, and Interest

Now that we have reviewed some basic money concepts, let's move on to some money math skills specific to 6th-grade learners . These money mathskills4kids’ skills include:

• How to calculate discounts using percentages (e.g., 20% off)
• How to calculate sales tax using percentages (e.g., 8% sales tax)
• How to calculate simple interest using the formula I = Prt (where I is the interest amount, P is the principal amount, r is the annual interest rate, and t is the time in years)
• How to apply these skills to real-world scenarios involving shopping, banking, and investing

These skills are essential for 6th graders because they help them understand how money changes over time due to various factors. They also help them evaluate different options and make informed choices when buying or selling goods or services or borrowing or lending money.

To help your 6th grader master these skills, you can download the following fun and educational money math worksheets from Mathskills4kids.com to help them practice:

• Discount Worksheets : These worksheets help students practice calculating discounts using percentages.
• Sales Tax Worksheets : These worksheets help students practice calculating sales tax using percentages.
• Simple Interest Worksheets : These worksheets help students practice calculating simple interest using the formula I = Prt.
• Money Word Problems Worksheets : These worksheets help students apply their money math skills to real-world scenarios involving shopping, banking, and investing.

Money math activities for 6th Grade: Budgeting, Saving, and Investing

Another way to help your 6th Grade students learn and enjoy money math is to engage them in fun and interactive money math activities involving budgeting, saving, and investing .

These activities can help your 6th grader develop essential life skills such as planning ahead, setting goals, tracking expenses, making trade-offs, saving for the future, and growing their wealth.

Some examples of these activities are:

They will also adjust their budget according to unexpected events such as emergencies or windfalls. This activity helps students learn how to manage their money and live within their means.

They also have to consider different saving options such as bank accounts, certificates of deposit, or bonds. This activity helps students learn how to save for their future and appreciate the power of compound interest.

They also have to monitor the performance of their portfolio and calculate their profits or losses. This activity helps students learn how to invest in the stock market and understand the risks and rewards of investing.

How to help your 6th Grader master money math

As a parent or teacher, you can play a vital role in helping your 6th grader master money math . Here are some tips on how you can support your 6th grader's money math learning:

• Encourage your 6th grader to practice money math regularly using the resources provided in this article or other online or offline sources.
• Make money math fun and relevant by connecting it to your 6th grader's interests, hobbies, or aspirations. For example, you can use money math to plan a family vacation, buy a gift for a friend, or start a business.
• Involve your 6th grader in real-life money situations such as shopping, banking, or investing. For example, you can let your 6th grader compare prices, calculate discounts or sales tax, or choose a saving or investing option.
• Praise your 6th grader's efforts and achievements in money math and celebrate their progress and improvement. For example, you can reward your 6th grader with a certificate, a sticker, or a treat for completing a money math worksheet or activity.

Bonus: More money math resources for sixth-Graders practice

If you want to give your 6th grader more practice and fun with money math, here are some web links with descriptions of online games, videos, and worksheets that you can use.

• Math Playground : Money Games . This website has a variety of interactive games that let your 6th grader practice money skills such as counting change, making change, comparing prices, calculating discounts, and more. Some of the games are also available as apps for mobile devices. https://www.mathplayground.com/index_money.html .
• Khan Academy : Money . This website has videos and exercises covering money topics such as decimal notation, place value, rounding, adding and subtracting decimals, multiplying and dividing decimals, and converting between fractions and decimals. The videos are clear and engaging, and the exercises provide instant feedback and hints. https://www.khanacademy.org/math/arithmetic/arith-decimals .
• Math Goodies: Percent and Proportions Worksheets . This website has a collection of printable worksheets that help your 6th grader practice calculating percentages, proportions, discounts, sales tax, interest, and more. The worksheets have answer keys and worked-out solutions. https://www.mathgoodies.com/worksheets/percent-and-proportions-wks .
• Practical Money Skills : Financial Literacy for Kids . This website has a wealth of resources that teach your 6th grader about financial literacy concepts such as budgeting, saving, investing, credit, debt, and more. The resources include games, videos, comics, articles, quizzes, calculators, and lesson plans. https://www.practicalmoneyskills.com/learn/financial_literacy/kids .
• Math Blaster : Money Math Problems . This website has a fun and challenging game that tests your 6th grader's money math skills. The game involves solving money problems using addition, subtraction, multiplication, division, fractions, decimals, and percentages. The game has different difficulty levels and rewards your 6th grader with coins that can be used to buy items for their virtual space station. https://www.mathblaster.com/parents/math-games/money-math-problems .

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Money math is an essential skill for 6th graders to learn and master. It helps them understand the value of money, make smart financial decisions, and prepare for the real world.

By reviewing the basic money concepts, learning the money math skills for 6th grade, doing the money math activities and worksheets for 6th grade, and using the bonus money math resources for sixth-graders practice, you can help your 6th grader become a money math whiz!

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Money - levelled sats questions - KS2

Subject: Mathematics

Age range: 7-11

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11 October 2014

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Money Problems — Rounding to 2 d.p. (Year 6)

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Children can use their calculators to solve these monetary problems, but they will need to remember to round their answers to 2 decimal places. If they are really up for a challenge, see how many they can solve without using a calculator!

An answer sheet is included.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Decimals
• Topic Group: Fractions, Decimals and Percentages
• Year(s): Year 6
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 24/10/2023
• Resource Code: M2WAT705
• Curriculum Point(s): Solve problems which require answers to be rounded to specified degrees of accuracy.

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Year 6 Maths Worksheets UK Hub Page

Welcome to our Year 6 Maths Worksheets area.

Here you will find a wide range of free printable Year 6 Maths Worksheets for your child to enjoy.

Come and take a look at our rounding decimal pages, or maybe some of our adding and subtracting fractions worksheets. Perhaps you are looking for some worksheets about finding angles in a triangle, or need some ratio problem worksheets to help your child learn about ratio?

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 6 Maths Learning

Here are some of the key learning objectives for the end of Year 6:

• know and use Place value up to 10 million
• Counting on and back in steps of powers of 10 from any number up to 10 million
• Round numbers to any given degree of accuracy.
• Count forwards and backwards through zero with positive and negative numbers.
• Read Roman numerals to 1000 and recognise years written in Roman numerals
• solve multi-step problems using addition and subtraction in a range of contexts
• identify multiples and factors including common factors
• multiply and divide up to 4-digit numbers by up to 2 digits
• Use their knowledge of the order of operations to carry out calculations involving the four operations.
• Identify common factors, common multiples and prime numbers.
• solve problems involving addition, subtraction, multiplication and division
• simplify fractions
• compare and order fractions including mixed numbers
• add and subtract fractions with different denominators including mixed numbers
• multiply simple fractions together and simplify the answer
• divide proper fractions by whole numbers
• recall and use equivalence between simple fractions, decimals and percentages.
• Multiply and divide whole numbers and decimals up to 3dp by 10, 100 or 1000
• read, write, order and compare numbers up to 3dp
• round decimals with up to 3dp to the nearest whole
• solve problems with numbers up to 3dp
• work out percentages of different amounts
• solve problems using percentages
• use simple formulae
• express missing number problems using algebra
• find pairs of numbers that satisfy equations with two variables
• solve problems involving simple ratios
• solve problems involving similar shapes where the scale factor is known
• use, read, write and convert between standard units of measure
• measure, compare and calculate using different measures
• know that shapes with the same area can have different perimeters
• find the area of parallelograms and right triangles
• find the volume of cubes and cuboids
• convert between miles and km
• name and understand the parts of circles - radius, diameter and circumference
• draw 2D shapes accurately using dimensions and angles
• compate and classify 2D shapes by a range of properties
• find missing angles in triangles, quadrilaterals and regular shapes
• use coordinates in all 4 quadrants
• draw and translate simple shapes in all 4 quadrants
• interpret and construct pie charts and line graphs
• calculate the mean as an average

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 6 is generally equivalent to 5th Grade in the US.

On this page you will find link to our range of math worksheets for Year 6.

Quicklinks to Year 6 ...

• Place Value Zone
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Word Problems Zone

Fractions percents ratio zone.

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Geometry Zone

Data analysis zone.

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Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 6 number worksheets.

Here you will find a range of Free Printable Year 6 Number Worksheets.

Using these Year 6 maths worksheets will help your child to:

• use place value with numbers up to 10 million;
• use place value with up to 3 decimal places;
• understand how to use exponents (powers) of a number;
• understand and use parentheses (brackets);
• understand and use multiples and factors;
• extend their knowledge of prime and composite (non-prime) numbers up to 100;
• know and be able to use the PEMDAS (or PEDMAS) rule.
• Place Value Worksheets to 10 million
• Place Value to 3dp
• Ordering Decimals Worksheets
• PEMDAS Rule Support Page
• PEMDAS Problems Worksheets
• Balancing Math Equations
• Roman Numerals worksheets

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places and also large numbers up to 100 million.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

• Ordering Large Numbers up to 100 million
• Ordering Decimals to 3dp

Rounding Decimals

• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Year 6 Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• count on and back into negative numbers.
• Counting By Decimals

Year 6 Mental Maths Zone

Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 6 Mental Maths Tests

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Year 6 Addition Worksheets

• add decimals including tenths and hundredths mentally;
• add a columns of multi-digit numbers, including decimals.
• Decimal Addition Fact Worksheets
• 5th Grade Addition Worksheets BIG Numbers
• Decimal Column Addition Worksheets
• Money Worksheets (randomly generated)

Year 6 Subtraction Worksheets

Using these sheets will help your child to:

• subtract decimals including tenths and hundredths mentally;
• subtract multi-digit numbers, including decimals using column subtraction.
• Subtracting Decimals Worksheets (mental)
• Subtraction Worksheets up to Billions (columns)
• Column Subtraction with Decimals

Year 6 Multiplication Worksheets

• extend their knowlege of multiplication to decimals;
• use their multiplication tables to answer related facts, including decimals;
• multiply a range of decimals with up to 2 decimal places (2dp) by a whole number;
• multiply different money amounts by a whole number.
• Multiplying Decimals by 10 and 100
• Multiplication Fact Sheet Decimals
• Decimal Multiplication Worksheets to 1dp
• Decimal Multiplication Worksheets to 2dp
• Free Multiplication Worksheets (randomly generated)
• Multiply and Divide by 10 100 (decimals)
• Multiplication & Division Worksheets (randomly generated)
• Multiplication Word Problems

Division Worksheets 5th Grade

Using these Year 6 maths worksheets will help your child learn to:

• divide any whole number up to 10000 by a two digit number;
• express any division with a remainder in the form of a mixed number (a number with a fraction part).
• Long Division Worksheets (whole numbers)
• Long Division of Decimal Numbers
• Decimal Division Facts
• Division Facts Worksheets (randomly generated)

Year 6 Maths Problems

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

These sheets involve solving one or two more challenging longer problems.

• Year 6 Math Problems (5th Grade)

These sheets involve solving many 'real-life' problems involving data.

• Year 6 Math Word Problems (5th Grade)

These sheets involve solving a range of ratio problems.

Year 6 Fraction Worksheets

Year 6 percentage worksheets, year 6 ratio worksheets.

• compare and order fractions;
• add and subtract fractions and mixed numbers;
• understand how to multiply fractions by a whole number;
• understand how to multiply two fractions together, including mixed fractions;
• understand the relationship between fractions and division;
• know how to divide fractions and mixed fractions;
• convert decimals to fractions.
• Comparing Fractions Worksheet page
• Adding Fractions Worksheets
• Adding Improper Fractions
• Subtracting Fractions Worksheets
• Adding Subtracting Fractions Worksheets
• Improper Fraction Worksheets
• Converting Decimals to Fractions Worksheets
• Fractions Decimals Percents Worksheets
• Multiplying Fractions Worksheets
• Dividing Fractions by Whole numbers
• Divide Whole numbers by Fractions
• Simplifying Fractions Worksheets
• Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• Percentage Word Problems

These Year 6 Ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets

Year 6 Geometry Worksheets

• know how to find missing angles in a range of situations;
• learn the number of degrees in a right angle, straight line, around a point and in a triangle;
• know how to calculate the area of a triangle;
• know how to calculate the area of a range of quadrilaterals.
• learn the formulas to calculate the area of triangles and some quadrilaterals;
• write and plot coordinates in all 4 quadrants.
• (5th Grade) Geometry - Angles
• Area of Quadrilaterals
• 5th Grade Volume Worksheets
• Coordinate Worksheets (1st Quadrant)
• Coordinate Plane Worksheets (All 4 Quadrants)
• Parts of a Circle Worksheets

Measurement Zone, including Time & Money

Year 6 measurement worksheets.

Using these sheets will help your child understand how to:

• learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
• learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
• learn how to estimate a measurement of length, weight or liquid;
• convert temperatures in Celsius and Fahrenheit.
• (5th Grade) Measurement Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

• Time Word Problems Worksheets - Riddles (harder)

Using these sheets will help you to:

• find the mean of up to 5 numbers;
• find a missing data point when the mean is given.
• Mean Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 6 maths games.

• Year 6 Math Games (5th Grade)

Year 6 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

• Printable Math Puzzles

Math Salamanders Year 6 Maths Games Ebook

Our Year 6 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 6 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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Five things to know as the tax deadline looms

Scott Horsley

About a third of all taxpayers are expected to file their returns in the last two weeks before the April 15th deadline. Scott Olson/Getty Images hide caption

About a third of all taxpayers are expected to file their returns in the last two weeks before the April 15th deadline.

With less than a week to go before the April 15th deadline, most taxpayers can breathe easy. About two-thirds have already filed their returns. And 68% of those got refunds. The average refund so far in 2024 is $3050 — 4.8% bigger than last year. Here are five things to know about this year's tax filing season.

How to file your tax returns: 6 things you should know this year

Procrastination rate holds steady.

This year's filing season began a week later than last year's. But as of March 29 , the total number of returns filed with the IRS was roughly even with last year. The agency had received more than 90 million tax returns by the end of last month. The vast majority of people (96.7%) filed electronically — which the IRS prefers and which greatly speeds processing. Of those electronic returns, 53% were completed by tax professionals while 47% were done by do-it-yourselfers. The IRS expects to receive about 50 million more returns during the final two weeks of the filing season. (Because of state holidays, taxpayers in Massachusetts and Maine have until April 17th to file this year.)

If you need more time

If you can't get your taxes done by next week's deadline, you can always file for an extension . That buys you another six months, until October 15. Postponing the filing deadline doesn't postpone the tax bill, though. You should still go ahead and pay any taxes you think you owe now, to avoid facing penalties and interest for a late payment.

This year, colleges must choose between fast financial aid offers, or accurate ones

Some people filed for free this year using a new irs website.

A small group of people sidestepped the commercial tax prep industry and filed electronic returns directly with the government for free this year. They were part of a new, IRS pilot program called "Direct File." It's only available in 12 states , and only for people with relatively simple tax returns . The IRS estimates that about 100,000 people might experiment with the program this year. If successful, Direct File could be expanded to more states and more taxpayers in future years.

If you don't qualify for the new Direct File program, you still might be able to file your taxes for free, so long as your adjusted gross income is under $79,000. You can check out free tax-filing options at the IRS Free File website . Some of the options include a free state tax return as well.

Crafters, re-sellers, and ticket scalpers avoid a paperwork headache for now

Under the American Rescue Plan, companies like eBay, Etsy, Depop and StubHub were supposed to start sending 1099-K tax forms this year to anyone who sold or re-sold items for as little as $600 in 2023. Those sales were also to be reported to the IRS, to make sure anyone who earned a profit on them paid the appropriate income tax. After complaints that would create a paperwork nightmare for a lot of small-time sellers ("What's my cost basis for that used guitar I just sold?"), the IRS postponed enforcement of the new rule . For the 2023 tax year, the agency will stick with its old reporting threshold, which only requires 1099-Ks for people who made at least $20,000 in sales and had more than 200 transactions.

Small sellers aren't completely off the hook, though. For the current tax year (the one you'll report on next year), the IRS plans to require 1099-Ks for sales of $5000 rather than $20,000. And unless Congress changes the law before then, the $600 threshold is set to kick in the following year. None of these reporting requirements change anyone's tax liability — just the government's ability to track the sales.

Biden unveils a budget that would cut costs for families and hike taxes for the rich

Rising wages and 'bracket creep'.

Workers' incomes have generally been rising. Average wages rose 4.1% for the 12 months ending in March. Because the federal income tax is "progressive" — meaning higher incomes are subject to higher tax rates — rising incomes could push people into higher tax brackets — a phenomenon known as "bracket creep." The IRS guards against this by adjusting tax brackets upwards each year, in line with inflation. If your income rises more slowly than inflation, you could actually find yourself in a lower tax bracket.

Other provisions of the tax code are also indexed for inflation, so things like the standard deduction and the maximum contribution to tax-advantaged retirement savings typically go up every year. In periods of higher inflation, these annual increases can be significant. The standard deduction for a married couple filing jointly this year rose by $1800.

There are many different measures of inflation. The yardstick the IRS uses to index tax brackets is called " chained CPI ." It typically shows prices climbing a little more slowly than the inflation measure used to calculate things like the Social Security cost of living adjustment . In 2023, for example, Social Security benefits jumped by 8.7%, but tax brackets rose just 6.9%.

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A.I.’s Original Sin

A times investigation found that tech giants altered their own rules to train their newest artificial intelligence systems..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

[MUSIC PLAYING]

Today, a “Times” investigation shows how as the country’s biggest technology companies race to build powerful new artificial intelligence systems, they bent and broke the rules from the start.

My colleague Cade Metz on what he uncovered.

It’s Tuesday, April 16th.

Cade, when we think about all the artificial intelligence products released over the past couple of years, including, of course, these chatbots we’ve talked a lot about on the show, we so frequently talk about their future their future capabilities, their influence on society, jobs, our lives. But you recently decided to go back in time to AI’s past, to its origins to understand the decisions that were made, basically, at the birth of this technology. So why did you decide to do that?

Because if you’re thinking about the future of these chatbots, that is defined by their past. The thing you have to realize is that these chatbots learn their skills by analyzing enormous amounts of digital data.

So what my colleagues and I wanted to do with our investigation was really focus on that effort to gather more data. We wanted to look at the type of data these companies were collecting, how they were gathering it, and how they were feeding it into their systems.

And when you all undertake this line of reporting, what do you end up finding?

We found that three major players in this race OpenAI, Google, and Meta as they were locked into this competition to develop better and better artificial intelligence, they were willing to do almost anything to get their hands on this data, including ignoring, and in some cases, violating corporate rules and wading into a legal gray area as they gathered this data.

Basically, cutting corners.

Cutting corners left and right.

OK, let’s start with OpenAI, the flashiest player of all.

The most interesting thing we’ve found, is that in late 2021, as OpenAI, the startup in San Francisco that built ChatGPT, as they were pulling together the fundamental technology that would power that chatbot, they ran out of data, essentially.

They had used just about all the respectable English language text on the internet to build this system. And just let that sink in for a bit.

I mean, I’m trying to let that sink in. They basically, like a Pac-Man on a old game, just consumed almost all the English words on the internet, which is kind of unfathomable.

Wikipedia articles by the thousands, news articles, Reddit threads, digital books by the millions. We’re talking about hundreds of billions, even trillions of words.

So by the end of 2021, OpenAI had no more English language texts that they could feed into these systems, but their ambitions are such that they wanted even more.

So here, we should remember that if you’re gathering up all the English language text on the internet, a large portion of that is going to be copyrighted.

So if you’re one of these companies gathering data at that scale, you are absolutely gathering copyrighted data, as well.

Which suggests that, from the very beginning, these companies, a company like OpenAI with ChatGPT, is starting to break, bend the rules.

Yes, they are determined to build this technology thus they are willing to venture into what is a legal gray area.

So given that, what does OpenAI do once it, as you had said, runs out of English language words to mop up and feed into this system?

So they get together, and they say, all right, so what are other options here? And they say, well, what about all the audio and video on the internet? We could transcribe all the audio and video, turn it into text, and feed that into their systems.

Interesting.

So a small team at OpenAI, which included its president and co-founder Greg Brockman, built a speech-recognition technology called Whisper, which could transcribe audio files into text with high accuracy.

And then they gathered up all sorts of audio files, from across the internet, including audio books, podcasts —

— and most importantly, YouTube videos.

Hmm, of which there’s a seemingly endless supply, right? Fair to say maybe tens of millions of videos.

According to my reporting, we’re talking about at least 1,000,000 hours of YouTube videos were scraped off of that video sharing site, fed into this speech recognition system in order to produce new text for training OpenAI’s chatbot. And YouTube’s terms of service do not allow a company like OpenAI to do this. YouTube, which is owned by Google, explicitly says you are not allowed to, in internet parlance, scrape videos en masse from across YouTube and use those videos to build a new application.

That is exactly what OpenAI did. According to my reporting, employees at the company knew that it broke YouTube terms of service, but they resolved to do it anyway.

So, Cade, this makes me want to understand what’s going on over at Google, which as we have talked about in the past on the show, is itself, thinking about and developing its own artificial intelligence model and product.

Well, as OpenAI scrapes up all these YouTube videos and starts to use them to build their chatbot, according to my reporting, some employees at Google, at the very least, are aware that this is happening.

Yes, now when we went to the company about this, a Google spokesman said it did not know that OpenAI was scraping YouTube content and said the company takes legal action over this kind of thing when there’s a clear reason to do so. But according to my reporting, at least some Google employees turned a blind eye to OpenAI’s activities because Google was also using YouTube content to train its AI.

So if they raise a stink about what OpenAI is doing, they end up shining a spotlight on themselves. And they don’t want to do that.

I guess I want to understand what Google’s relationship is to YouTube. Because of course, Google owns YouTube. So what is it allowed or not allowed to do when it comes to feeding YouTube data into Google’s AI models?

It’s an important distinction. Because Google owns YouTube, it defines what can be done with that data. And Google argues that it has a right to that data, that its terms of service allow it to use that data. However, because of that copyright issue, because the copyright to those videos belong to you and I, lawyers who I’ve spoken to say, people could take Google to court and try to determine whether or not those terms of service really allow Google to do this. There’s another legal gray area here where, although Google argues that it’s OK, others may argue it’s not.

Of course, what makes this all so interesting is, you essentially have one tech company Google, keeping another tech company OpenAI’s dirty little secret about basically stealing from YouTube because it doesn’t want people to know that it too is taking from YouTube. And so these companies are essentially enabling each other as they simultaneously seem to be bending or breaking the rules.

What this shows is that there is this belief, and it has been there for years within these companies, among their researchers, that they have a right to this data because they’re on a larger mission to build a technology that they believe will transform the world.

And if you really want to understand this attitude, you can look at our reporting from inside Meta.

And so what does Meta end up doing, according to your reporting?

Well, like Google and other companies, Meta had to scramble to build artificial intelligence that could compete with OpenAI. Mark Zuckerberg is calling engineers and executives at all hours pushing them to acquire this data that is needed to improve the chatbot.

And at one point, my colleagues and I got hold of recordings of these Meta executives and engineers discussing this problem. How they could get their hands on more data where they should try to find it? And they explored all sorts of options.

They talked about licensing books, one by one, at $10 a pop and feeding those into the model.

They even discussed acquiring the book publisher Simon & Schuster and feeding its entire library into their AI model. But ultimately, they decided all that was just too cumbersome, too time consuming, and on the recordings of these meetings, you can hear executives talk about how they were willing to run roughshod over copyright law and ignore the legal concerns and go ahead and scrape the internet and feed this stuff into their models.

They acknowledged that they might be sued over this. But they talked about how OpenAI had done this before them. That they, Meta were just following what they saw as a market precedent.

Interesting, so they go from having conversations like, should we buy a publisher that has tons of copyrighted material suggesting that they’re very conscious of the kind of legal terrain and what’s right and what’s wrong. And instead say, nah, let’s just follow the OpenAI model, that blueprint and just do what we want to do, do what we think we have a right to do, which is to kind of just gobble up all this material across the internet.

It’s a snapshot of that Silicon Valley attitude that we talked about. Because they believe they are building this transformative technology, because they are in this intensely competitive situation where money and power is at stake, they are willing to go there.

But what that means is that there is, at the birth of this technology, a kind of original sin that can’t really be erased.

It can’t be erased, and people are beginning to notice. And they are beginning to sue these companies over it. These companies have to have this copyrighted data to build their systems. It is fundamental to their creation. If a lawsuit bars them from using that copyrighted data, that could bring down this technology.

We’ll be right back.

So Cade, walk us through these lawsuits that are being filed against these AI companies based on the decisions they made early on to use technology as they did and the chances that it could result in these companies not being able to get the data they so desperately say they need.

These suits are coming from a wide range of places. They’re coming from computer programmers who are concerned that their computer programs have been fed into these systems. They’re coming from book authors who have seen their books being used. They’re coming from publishing companies. They’re coming from news corporations like, “The New York Times,” incidentally, which has filed a lawsuit against OpenAI and Microsoft.

News organizations that are concerned over their news articles being used to build these systems.

And here, I think it’s important to say as a matter of transparency, Cade, that your reporting is separate from that lawsuit. That lawsuit was filed by the business side of “The New York Times” by people who are not involved in your reporting or in this “Daily” episode, just to get that out of the way.

I’m assuming that you have spoken to many lawyers about this, and I wonder if there’s some insight that you can shed on the basic legal terrain? I mean, do the companies seem to have a strong case that they have a right to this information, or do companies like the “Times,” who are suing them, seem to have a pretty strong case that, no, that decision violates their copyrighted materials.

Like so many legal questions, this is incredibly complicated. It comes down to what’s called fair use, which is a part of copyright law that determines whether companies can use copyrighted data to build new things. And there are many factors that go into this. There are good arguments on the OpenAI side. There are good arguments on “The New York Times” side.

Copyright law says that can’t take my work and reproduce it and sell it to someone. That’s not allowed. But what’s called fair use does allow companies and individuals to use copyrighted works in part. They can take snippets of it. They can take the copyrighted works and transform it into something new. That is what OpenAI and others are arguing they’re doing.

But there are other things to consider. Does that transformative work compete with the individuals and companies that supplied the data that owned the copyrights?

And here, the suit between “The New York Times” company and OpenAI is illustrative. If “The New York Times” creates articles that are then used to build a chatbot, does that chatbot end up competing with “The New York Times?” Do people end up going to that chatbot for their information, rather than going to the “Times” website and actually reading the article? That is one of the questions that will end up deciding this case and cases like it.

So what would it mean for these AI companies for some, or even all of these lawsuits to succeed?

Well, if these tech companies are required to license the copyrighted data that goes into their systems, if they’re required to pay for it, that becomes a problem for these companies. We’re talking about digital data the size of the entire internet.

Licensing all that copyrighted data is not necessarily feasible. We quote the venture capital firm Andreessen Horowitz in our story where one of their lawyers says that it does not work for these companies to license that data. It’s too expensive. It’s on too large a scale.

Hmm, it would essentially make this technology economically impractical.

Exactly, so a jury or a judge or a law ruling against OpenAI, could fundamentally change the way this technology is built. The extreme case is these companies are no longer allowed to use copyrighted material in building these chatbots. And that means they have to start from scratch. They have to rebuild everything they’ve built. So this is something that, not only imperils what they have today, it imperils what they want to build in the future.

And conversely, what happens if the courts rule in favor of these companies and say, you know what, this is fair use. You were fine to have scraped this material and to keep borrowing this material into the future free of charge?

Well, one significant roadblock drops for these companies. And they can continue to gather up all that extra data, including images and sounds and videos and build increasingly powerful systems. But the thing is, even if they can access as much copyrighted material as they want, these companies may still run into a problem.

Pretty soon they’re going to run out of digital data on the internet.

That human-created data they rely on is going to dry up. They’re using up this data faster than humans create it. One research organization estimates that by 2026, these companies will run out of viable data on the internet.

Wow. Well, in that case, what would these tech companies do? I mean, where are they going to go if they’ve already scraped YouTube, if they’ve already scraped podcasts, if they’ve already gobbled up the internet and that altogether is not sufficient?

What many people inside these companies will tell you, including Sam Altman, the chief executive of OpenAI, they’ll tell you that what they will turn to is what’s called synthetic data.

And what is that?

That Is data generated by an AI model that is then used to build a better AI model. It’s AI helping to build better AI. That is the vision, ultimately, they have for the future that they won’t need all this human generated text. They’ll just have the AI build the text that will feed future versions of AI.

So they will feed the AI systems the material that the AI systems themselves create. But is that really a workable solid plan? Is that considered high-quality data? Is that good enough?

If you do this on a large scale, you quickly run into problems. As we all know, as we’ve discussed on this podcast, these systems make mistakes. They hallucinate . They make stuff up. They show biases that they’ve learned from internet data. And if you start using the data generated by the AI to build new AI, those mistakes start to reinforce themselves.

The systems start to get trapped in these cul-de-sacs where they end up not getting better but getting worse.

What you’re really saying is, these AI machines need the unique perfection of the human creative mind.

Well, as it stands today, that is absolutely the case. But these companies have grand visions for where this will go. And they feel, and they’re already starting to experiment with this, that if you have an AI system that is sufficiently powerful, if you make a copy of it, if you have two of these AI models, one can produce new data, and the other one can judge that data.

It can curate that data as a human would. It can provide the human judgment, So. To speak. So as one model produces the data, the other one can judge it, discard the bad data, and keep the good data. And that’s how they ultimately see these systems creating viable synthetic data. But that has not happened yet, and it’s unclear whether it will work.

It feels like the real lesson of your investigation is that if you have to allegedly steal data to feed your AI model and make it economically feasible, then maybe you have a pretty broken model. And that if you need to create fake data, as a result, which as you just said, kind of undermines AI’s goal of mimicking human thinking and language, then maybe you really have a broken model.

And so that makes me wonder if the folks you talk to, the companies that we’re focused on here, ever ask themselves the question, could we do this differently? Could we create an AI model that just needs a lot less data?

They have thought about other models for decades. The thing to realize here, is that is much easier said than done. We’re talking about creating systems that can mimic the human brain. That is an incredibly ambitious task. And after struggling with that for decades, these companies have finally stumbled on something that they feel works that is a path to that incredibly ambitious goal.

And they’re going to continue to push in that direction. Yes, they’re exploring other options, but those other options aren’t working.

What works is more data and more data and more data. And because they see a path there, they’re going to continue down that path. And if there are roadblocks there, and they think they can knock them down, they’re going to knock them down.

But what if the tech companies never get enough or make enough data to get where they think they want to go, even as they’re knocking down walls along the way? That does seem like a real possibility.

If these companies can’t get their hands on more data, then these technologies, as they’re built today, stop improving.

We will see their limitations. We will see how difficult it really is to build a system that can match, let alone surpass the human brain.

These companies will be forced to look for other options, technically. And we will see the limitations of these grandiose visions that they have for the future of artificial intelligence.

OK, thank you very much. We appreciate it.

Glad to be here.

Here’s what else you need to know today. Israeli leaders spent Monday debating whether and how to retaliate against Iran’s missile and drone attack over the weekend. Herzi Halevi, Israel’s Military Chief of Staff, declared that the attack will be responded to.

In Washington, a spokesman for the US State Department, Matthew Miller reiterated American calls for restraint —

^MATTHEW MILLER^ Of course, we continue to make clear to everyone that we talked to that we want to see de-escalation that we don’t want to see a wider regional war. That’s something that’s been —

— but emphasized that a final call about retaliation was up to Israel. ^MATTHEW MILLER^ Israel is a sovereign country. They have to make their own decisions about how best to defend themselves. What we always try to do —

And the first criminal trial of a former US President officially got underway on Monday in a Manhattan courtroom. Donald Trump, on trial for allegedly falsifying documents to cover up a sex scandal involving a porn star, watched as jury selection began.

The initial pool of 96 jurors quickly dwindled. More than half of them were dismissed after indicating that they did not believe that they could be impartial. The day ended without a single juror being chosen.

Today’s episode was produced by Stella Tan, Michael Simon Johnson, Muge Zaidi, and Rikki Novetsky. It was edited by Marc Georges and Liz O. Baylen, contains original music by Diane Wong, Dan Powell, and Pat McCusker, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

• April 17, 2024   •   24:52 Are ‘Forever Chemicals’ a Forever Problem?
• April 16, 2024   •   29:29 A.I.’s Original Sin
• April 15, 2024   •   24:07 Iran’s Unprecedented Attack on Israel
• April 14, 2024   •   46:17 The Sunday Read: ‘What I Saw Working at The National Enquirer During Donald Trump’s Rise’
• April 12, 2024   •   34:23 How One Family Lost $900,000 in a Timeshare Scam
• April 11, 2024   •   28:39 The Staggering Success of Trump’s Trial Delay Tactics
• April 10, 2024   •   22:49 Trump’s Abortion Dilemma
• April 9, 2024   •   30:48 How Tesla Planted the Seeds for Its Own Potential Downfall
• April 8, 2024   •   30:28 The Eclipse Chaser
• April 7, 2024 The Sunday Read: ‘What Deathbed Visions Teach Us About Living’
• April 5, 2024   •   29:11 An Engineering Experiment to Cool the Earth
• April 4, 2024   •   32:37 Israel’s Deadly Airstrike on the World Central Kitchen

Hosted by Michael Barbaro

Featuring Cade Metz

Produced by Stella Tan ,  Michael Simon Johnson ,  Mooj Zadie and Rikki Novetsky

Edited by Marc Georges and Liz O. Baylen

Original music by Diane Wong ,  Dan Powell and Pat McCusker

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

A Times investigation shows how the country’s biggest technology companies, as they raced to build powerful new artificial intelligence systems, bent and broke the rules from the start.

Cade Metz, a technology reporter for The Times, explains what he uncovered.

On today’s episode

Cade Metz , a technology reporter for The New York Times.

Background reading

How tech giants cut corners to harvest data for A.I.

What to know about tech companies using A.I. to teach their own A.I.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Cade Metz writes about artificial intelligence, driverless cars, robotics, virtual reality and other emerging areas of technology. More about Cade Metz

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