problem solving maths year 4

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Year 4 Maths Worksheets UK Hub Page

Welcome to our Year 4 Maths Worksheets Hub page.

Here you will find our selection of printable maths worksheets for Year 4 children, for your child will enjoy.

Take a look at our times table colouring pages, or maybe some of our fraction of shapes worksheets. Perhaps you would prefer our time worksheets, or learning about line or block symmetry?

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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 4 Maths Learning

Here are some of the key learning objectives for the end of Year 4:

• know and use Place value up to 4 digits
• Compare and order numbers up to 10,000
• Counting on and back in 1s, 10s, 100s and 1,000s from different starting points
• Position numbers on a number line up to 10,000
• Round numbers to the nearest 10, 100 or 1000.
• Count backwards through zero and use negative numbers.
• add and subtract with up to 4 digits in columns
• add or subtract 1s, 10s, 100s or 1000s from a 4-digit number
• solve 2-step problems using addition and subtraction
• recall and use multiplication and division facts up to 12x12
• recognise and use factor pairs
• multiply 2-digit and 3-digit numbers by a 1-digit number
• solve problems using multiplication and division
• count up and down in hundredths
• recognise and use equivalent fractions
• add and subtract fractions with the same denominator
• solve fraction problems including with non-unit fractions
• write common fractions such halves and quarters as decimals;
• understand tenths and hundredths as decimals
• round decimals with 1dp to the nearest whole
• compare numbers with up to 2dp
• solve simple money and measure problems
• measure, compare and calculate using different measures
• find the area and perimeter of squares and rectangles
• convert between 12- and 24-hour clock
• convert between different units of measure
• identify and order acute and obtuse angles
• compare and classify 2D and 3D shapes according to their properties
• identify lines of symmetry in 2D shapes
• use coordinates in the first quadrant
• translate shapes up, down, left and right
• interpret and present data in bar graphs, pictograms and tabels
• solve 1-step and 2-step problems using data in tables, pictograms and graphs

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 4 is generally equivalent to 3rd Grade in the US.

On this page you will find link to our range of math worksheets for Year 4 pupils.

Quicklinks to Year 4 ...

• Online 3rd Grade Practice
• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions zone.

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

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 4 numbers & place value worksheets.

Using these Year 4 maths worksheets will help your child to:

• learn their place value with 4 digit numbers;
• use place value models to understand how to combine thousands, hundreds, tens and ones;
• understand the value of each digit in a 4 digit number;
• learn to use standard and expanded form with 4 digit numbers.
• learn to read and write Roman numerals
• Place Value Models 4 Digits
• Place Value 4 Digit Numbers Worksheets (conversion)
• Ordering 4-Digit Numbers
• Ordering Negative Numbers -10 to 10
• Roman Numerals worksheets

Year 4 Counting & Sequences Worksheets

Each worksheets consists of a sequence which has been partially filled in. The rest of each sequence must be completed.

At this grade, the focus is on counting on and back in constant steps of a digit.

• Counting on and back by digits

Rounding, Inequalities, Multiples and Balancing Equations

Using these Year 4 Maths worksheets will help your child to:

• round a number to the nearest 10, 100 or 1000;
• use the > and < symbols correctly for inequalities;
• use multiples and apply them to solve problems.
• learn to balance math equations
• Rounding to the nearest 10 Worksheets
• Rounding to the nearest 100 worksheets
• Rounding to the nearest 1000 worksheets
• Rounding Inequalities Multiples Worksheets
• Balancing Math Equations

Year 4 Mental Math Zone

Here you will find a range of printable Year 4 mental maths quizzes for your child to enjoy.

Each quiz 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 4 Mental Maths Test sheets

Number Bonds Worksheets

The worksheets on this page will help to develop children's knowledge of numbers bonds to 20, 50 and 100.

There are a range of matching and wordsearches for children to enjoy whilst developing their number bond knowledge.

• Number Bonds to 50 and 100

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Year 4 Addition Worksheets

• learn to add numbers mentally to 100;
• add on 1, 10, 100 and 1000 to different numbers;
• learn to add 4 digit numbers in columns;
• Addition Facts Worksheets to 100+100
• 4-Digit Addition Worksheets
• Money Addition Worksheets (£ )

Year 4 Subtraction Worksheets (3rd Grade)

Using these subtraction worksheets will help your child to:

• learn to subtract numbers mentally to 100;
• learn to do 4 Digit column subtraction.
• Third Grade Subtraction Worksheets to 100
• 4 Digit Subtraction Worksheets
• Money Subtraction Worksheets UK (£ )

Year 4 Multiplication Worksheets

• learn their multiplication tables up to 12 x 12;
• understand and use different models of multiplication;
• solve a range of Year 4 Multiplication problems.

Online Times Table Practice

• Times Tables Practice Zone

Understanding Multiplication

• Understanding Multiplication Facts Worksheets to 10x10

Multiplication Table Worksheets

• Multiplication Table Worksheets - 2 3 4 5 10
• Multiplication Drill Sheets 6 7 8 9
• Fun Multiplication Worksheets to 10x10
• Times Table Worksheets Circles 1 to 12 tables
• Multiplying (integers) by 10 and 100 Worksheets
• Multiplying by Multiples of 10 and 100

2-Digit Multiplication

• 2 Digit Multiplication Worksheets

Multiplication Word Problems

• Year 4 Multiplication Word Problem Worksheets (3rd Grade)

Randomly Generated Multiplication Worksheets

Using our random worksheet generator, you can:

• Choose the tables you want to test;
• Choose how big you want the numbers to go - up to 5 times, 10 times or bigger!
• Choose how many questions per page.
• Times Tables Worksheets (randomly generated)
• Free Multiplication Worksheets (randomly generated)
• Single Digit Multiplication Worksheets Generator
• Multiplication & Division Worksheets (randomly generated)

Year 4 Division Worksheets

Using these Year 4 Maths worksheets will help your child learn to:

• understand how division and multiplication relate to one another;
• know their division facts to 10x10;
• begin to learn 2-digit by 1-digit long division.
• Division Facts to 10x10 Worksheets
• Divding by Multiples of 10 and 100 Worksheets
• Year 4 Long Division Worksheets (3rd grade)
• Division Facts Worksheets (randomly generated)

Using the 3rd Grade Math worksheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• develop their knowledge of fractions;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

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

• Year 4 Math Problems (3rd Grade)

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

• Year 4 Math Word Problems for kids (3rd Grade)

These sheets involve solving 3-digit and 4-digit addition word problems.

• Addition Word Problems 3rd Grade (3- and 4-digits)

These sheets involve solving 3-digit and 4-digit subtraction problems.

• Subtraction Word Problems 3rd Grade

These sheets involve solving a range of multiplciation problems.

These sheets involve solving a range of division problems.

• Division Worksheets Grade 3 Word Problems

Year 4 Fraction Worksheets

Using these sheets will help your child to:

• understand what fractions are;
• relate fractions to everyday objects and quantities;
• place different fractions on a number line;
• shade in different fractions of a shapes;
• work out unit fractions of numbers.

• What is a Mixed Number Support page
• Finding Fractions - Fraction Spotting
• Fractions of Shapes Worksheets
• Unit Fraction of Numbers
• Halves and Quarters (up to 100)
• Fraction Number Line Sheets
• Adding Fractions with Like Denominators
• Subtracting Fractions with like denominators
• Fraction Riddles for kids (easier)

Year 4 Geometry Worksheets

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Use reflective symmetry to reflect shapes in a mirror line.
• recognise and identify right angles and lines of symmetry;
• recognise and identify parallel lines;
• identify the faces, edges, vertices and nets of 3d shapes;
• Year 4 Free Printable Geometry Worksheets
• Block Symmetry Worksheet
• Line Symmetry Worksheets
• Symmetry Activities
• Geometry Nets Information and Worksheets

Measurement Zone, including Time & Money

Year 4 measurement worksheets.

• Year 4 Measurement Worksheets - reading scales
• Metric Conversion Worksheets

Year 4 Money Worksheets

Using challenges is a great way to get kids to use their thinking skills and extend learning by applying the knowledge they have.

• count a range of coins up to £10
• compare money amounts
• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.
• Year 4 Money Challenges
• Column Addition Money Worksheets (UK)
• Column Subtraction Money Worksheets (UK)

Area and Perimeter Worksheets

• understand area and perimeter;
• learn how to find the area and perimeter of rectangles.
• Area Worksheets
• Perimeter Worksheets

Time Worksheets

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

• tell the time to the nearest 5 minutes;
• become familiar with both digital and analogue times;
• use the words 'past' and 'to' to describe the time correctly.
• add and subtract time intervals from times and work out time intervals.
• Add and Subtract Time Worksheets
• Elapsed Time Worksheets
• Printable Time Worksheets - Time Puzzles (easier)
• 24 Hour Clock Conversion Worksheets

On this page there are a selection of bar and picture graphs, including bar graphs with real-life data such as tree heights.

• Year 4 Bar Graph Worksheets (3rd grade)
• Year 4 Venn Diagram Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 4 maths games.

The following games involve different Year 4 Maths activities which you and your child can enjoy together.

• Year 4 / Third Grade Math Games

Year 4 Math Puzzles

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

• Year 4 Math Puzzle Worksheets (3rd Grade)

Math Salamanders Year 4 Maths Games Ebook

Our Year 4 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 4 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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20 Word Problems For Year 4: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 4 play an important role in Year 4 maths. In Year 4, the main focus is to ensure that pupils are becoming more fluent with whole numbers and the four operations. Students work to develop efficient written methods and to be accurate with their calculations. Pupils in Year 4 are exposed to a wider range of problem-solving questions and progress from one to two-step problems.

It is important that all children are given regular opportunities to access reasoning and word problem style questions. Fluency, reasoning and problem solving should be intertwined through every lesson, with all children having the opportunity to tackle each of these question types. 

All Kinds of Word Problems Multiplication

Strengthen your students' problem solving and multiplication skills with this pack of multiplication word problems

Place value 

Addition and subtraction , multiplication and division, fractions, decimals and percentages, measurement, why are word problems important in year 4 maths, how to teach problem solving in year 4, addition word problems for year 4, subtraction word problems for year 4, multiplication word problems for year 4, division word problems for year 4, fraction and decimal word problems in year 4, time word problems in year 4, multi-step word problems in year 4., more primary word problems resources.

There can sometimes be a tendency for reasoning and problem solving questions to be treated as extension activities for only the higher attaining pupils to attempt, but children of all abilities need to be accessing them on a regular basis.

To help you with this, we have put together a collection of 20 word problems aimed at Year 4 pupils. For more Year 4 maths resources, take a look at our collection of Year 4 maths worksheets .

Year 4 Maths Word Problems in the National Curriculum

In Year 4, pupils progress from solving one-step problems, to also being exposed to two-step problems across a range of topics, as set out in the National Curriculum.

Solve word problems involving counting in multiples of 6,7,9, 25 and 100; finding 1000 more or less than a given number; counting backwards through 0 to include negative numbers; ordering and comparing numbers beyond 1000 and rounding numbers to the nearest 10. 100 and 1000

Solve addition and subtraction word problems with up to 4 digits, including two-step word problems, deciding which operations and methods to use and why.

Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems.

Solve problems involving increasingly harder fractions word problems to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Also Solve simple measure and money problems involving fractions and decimals to 2 decimal places.

Solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days.

Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Word problems are increasingly important as pupils move through Key Stage 2. As they become more confident with some of the core concepts pupils need to be applying this knowledge to a range of situations. By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 times table and should be showing precision and fluency in their work.

Word problems in Year 4 should be fun and engaging for students. There are many ways to do this, including:

• acting out the problem;
• using manipulatives and visual images to help children understand the maths within the problem;
• use of talk partners to encourage children to discuss the question and share strategies for reaching a solution;
• using relatable problem solving situations.

Children need to be encouraged to read word problem questions carefully, to ensure they have identified the key information needed to be able to solve the problem. Pupils need to think about what they already know and how that information can help them to answer the question. They should also be encouraged to draw pictures and visual images, where appropriate, to help them to understand what the question is asking.

Here is an example:

A shop has an 8m roll of fabric.

The first customer buys 125cm of fabric and the second customer buys 3m from the same roll.

How much fabric is left on the roll, once the two customers have taken theirs?

How to solve:

What do you already know?

• The amount the first customer buys is given in cm, the amount the second customer buys is given in m. These needed to be converted to the same unit.
• Pupils in Year 4 need to be able to convert cm to m and vice versa. In this question, both the cm can be given as m or the m changed to cm to solve it.
• Once the units are the same, the two amounts need to be added together, to work out the total amount bought by the two customers.
• We can see this is a two-step question. To calculate how much fabric is left on the roll, the total amount bought by the two customers needs to be subtracted from the initial amount of fabric on the roll.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the total amount of fabric bought, we need the units to be the same. We can either calculate in cm (300cm + 125cm = 425cm) or in m (3m + 1.25m = 4.25m)
• The amount of material bought needs to be subtracted from the original amount. This can again be solved in m or cm. Either in m: 8m – 4.25m = 3.75m or in cm: 800cm – 425cm = 375cm
• The total amount of material left is 3.75m or 375cm

In Year 4, addition word problems involve questions up to 4-digit numbers. They can include one and two-step addition and incorporate a range of concepts, such as measures and money word problems  

Addition question 1

It is 4164 miles to travel from London to Doha and 3266 miles to travel from Doha to Bangkok.

How far is it to travel from London to Bangkok, if the flight stops in Doha first?

Answer (1 mark): 7430 miles

Addition question 2

Fill in the missing numbers in this calculation.

Answer (1 mark): 6840

Addition question 3

On Saturday, 5486 fans attended a football game and 3748 fans attended a rugby game.

How many fans watched the two games in total?

Answer (1 mark): 9234

Subtraction word problems in Year 4, also involve numbers up to 4-digits, including both one and two-step problems, covering a range of concepts. By this stage, children should be confident in estimating and using the inverse, to check calculations.

Subtraction question 1

3241 people visited the zoo on Saturday.

On Sunday 2876 people visited.

How many more people visited the lake on Saturday than on Sunday?

Answer (1 mark): 365

 3241 – 2876 = 365

Subtraction question 2

 A teacher prints out 1242 worksheets in a term.

If 435 were maths worksheets, how many did she print out for the other subjects?

Answer (1 mark): 807

Subtraction question 3

The temperature in Toronto dropped to minus 15 degrees celcius in December. 

In July the temperature was 47 degrees celsius warmer than it was in December. What was the temperature in July? 

Answer (1 mark): 32 degrees warmer

47 – 15 degrees = 32 degrees celsius

Counting on 47 degrees from minus 15 degrees  = 32 degrees celsius

In Year 4, multiplication word problems can include recalling facts for times tables up to 12 x 12 and multiplying two and three-digit numbers by a 1-digit number, using formal written layout.  

Multiplication question 1

All the pupils in Year 4 complete a mental maths test.

27 pupils score 9 marks out of 10.

What is the total number of marks scored by the 27 pupils?

Answer (1 mark): 243

27 x 9 = 243

Multiplication question 2

Year 3 and 4 children from a local primary school go on a school trip. 

Six mini buses are used to transport the children.

 There are 17 children on each minibus.

How many children go on the school trip?

Answer (1 mark): 102

17 x 6 = 102 children

Multiplication question 3

Biscuits come in packs of 18.

Mrs Smith buys 8 packs for the parents at the Y4 maths workshop.

How many biscuits does she buy altogether?

Answer (1 mark): 144 biscuits

Division word problems in year 4 require pupils to be able to recall division facts for multiplication tables up to 12 x 12. Formal written method of division isn’t a requirement until Year 5 however, many schools choose to teach the formal method in Year 4. Pupils need to understand the concept of grouping and sharing and to understand the link between multiplication & division.

Division question 1

Sam has 28 friends coming to his birthday party.

Each child will receive a cupcake, which come in packs of 4.

How many packs of cupcakes will Sam need to buy?

Answer (1 mark): 7 packs

28 ÷ 4 = 7 

Division question 2

4 children raised £96 between them on a sponsored walk.

If they split the money evenly between the four of them, how much did each pupil raise?

Answer (1 mark): £24 each

96 ÷ 4 = 24

Division question 3

Ahmed is thinking of a number

He says, ‘when I divide my number by 12, the answer is 108.

What number was Ahmed thinking of?

Answer (1 mark): 9

108 ÷ 12 = 9

In Year 4, decimal and fraction problems involve increasingly harder fractions to calculate quantities and fractions to divide quantities, including non-unit fractions, where the answer is a whole number. Decimal word problems include measure and money problems involving fractions and decimals up to 2 decimal places.

Fraction and decimal question 1

Jamie has 18 sweets. 

He gives \frac{1}{6} of the sweets to his friend and keeps the rest himself.

How many sweets does Jamie have now?

Answer (1 mark): 15 sweets

\frac{1}{6} of 18 = 3

18 – 3 = 15

Fraction and decimal question 2

Jaxon collected 36 conkers. 

\frac{1}{4} of the conkers fell out of a hole in his bag, when he was walking home.

How many conkers did Jaxon have left, when he got home?

\frac{1}{4} of 36 = 9

36 – 9 = 37      or      \frac{3}{4} of 36 = 29 (3 x 9)

Fraction and decimal question 3

Sara ate \frac{3}{12} of a chocolate bar and gave \frac{2}{12} to her friend.

What fraction of the chocolate bar did she have left? 

 Answer (1 mark): \frac{7}{12}

In Year 4, time word problems include: converting from hours to minutes, minutes to seconds, years to months and weeks to days.

Time question 1 

A cake was put in the oven at 4:35pm and taken out at 4:57pm.

How long was the cake in the oven?

Answer (1 mark): 22 minutes

57-35 = 22 minutes

Using an number line: 

Time question 2

It took Evie 25 minutes to complete a page of number problems. 

If she started at 2:45pm. What time did she finish?

Answer (1 mark): 3:10pm

In Year 4, children are introduced to multi-step word problems requiring up to two steps. These problems cover a range of concepts, including the four operations, fractions, decimals and measures.

Third Space Learning’s online one-to-one tutoring frequently incorporates multi-step questions to test students’ knowledge and problem solving skills. Our personalised tutoring programme works to identify gaps in students’ learning, fill those gaps, reinforce students’ knowledge and build confidence.

Multi-step question 1

There are 6 handwriting pens in each pack.

A class has 30 children and each child needs 2 handwriting pens.

How many packs will the teacher need to buy?

Answer (2 marks): 10 packs of handwriting pens.

30 x 2 = 60

Multi-step question 2

 Sophie has £4.50.

She buy 3 books at a carboot sale, costing 50p, 65p and £1.20.

How much money does she have left?

Answer (2 marks): £2.15 left

Multi-step question 3

Abullah is thinking of a number.

He doubles the number and adds 7.

He gets an answer of 25. 

What was his original number?

Answer (2 marks): 9

Third Space Learning offers word problems for all primary year groups. Take a look at our word problems for year 3 , word problems for year 5 and word problems for year 6 . Our word problems span a range of topics such as ratio word problems and percentage word problems .

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Multiplication & division in Year 4 (age 8–9)

In Year 4, children will be expected to be able to use formal written methods of short multiplication and short division confidently. This includes:

• knowing and using multiplication and division facts for all times tables up to 12 × 12
• multiplying three-digit by one-digit numbers
• multiplying three numbers together.

Fractions & decimals in Year 4 (age 8–9)

In Year 4, children will be expected to explore the link between fractions and multiplication/division and begin to learn about decimals. This includes:

• solve simple measure and money problems involving fractions and decimals
• recognising and writing tenths and hundredths as decimals
• rounding decimal numbers with one decimal place to the nearest whole number.

Geometry in Year 4 (age 8–9)

In Year 4, children will be expected to extend their knowledge of properties of shapes and be able to describe the position of shapes on a coordinate grid. This includes:

• comparing shapes such as quadrilaterals and triangles based on their properties and sizes
• drawing mirror images of shapes in lines of symmetry
• plotting points and describing how shapes move up/down/left/right on a coordinate grid.

Measurement in Year 4 (age 8–9)

In Year 4, children will be expected to be able convert between some units of measurement, such as kilometres to metres and calculate measurements in relation to shapes. This includes:

• working out the perimeter and area of rectilinear shapes
• solving problems involving converting units of time
• adding, subtracting, multiplying and dividing measurements including money.

Statistics in Year 4 (age 8–9)

In Year 4, children will interpret and present data in bar charts, pictograms, tables, and other graphs. They will begin to understand how data can show changes over time. This includes:

• interpreting and presenting discrete and continuous data using graphs
• interpreting and making time graphs (a type of line graph)
• solving problems by comparing, adding, and subtracting data from tables, charts, and graphs.
• Age 3–4 (Early Years)
• Age 4–5 (Reception)
• Age 5–6 (Year 1)
• Age 6–7 (Year 2)
• Age 7–8 (Year 3)
• Age 8–9 (Year 4)
• Age 9–10 (Year 5)
• Age 10–11 (Year 6)
• Year 1 (age 5–6)
• Year 2 (age 6–7)
• Year 3 (age 7–8)
• Year 4 (age 8–9)
• Year 5 (age 9–10)
• Year 6 (age 10–11)
• Help with times tables
• Ratio & proportion
• Learning to tell the time
• Numicon parent guide
• MyMaths parent guide
• Maths activity books

Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)

This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.

Problem solving: finding the missing digits in 4-digit numbers. Tricky!

Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!

Reasoning about numbers on a number line and rounding numbers.

More reasoning about number and place value.

Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.

More written explanations on which operation to use and whether the question should be done mentally or on paper.

Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.

Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.

Solving problems

A selection of problem solving activities and word problems.

Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer

Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.

5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!

A range of number and money problems, typical of those found in KS2 test papers.

More number and money problems, typical of those found in KS2 test papers.

Tricky word problems involving time and money.

More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.

Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.

Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.

Number patterns, remainders, number machines and much more in this mixed selection of problems.

Working out the missing value.

More working out missing values.

Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?

Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?

Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?

An addition challenge suitable for year 4 on.

The fish are all called numbers. Can you work out their names by solving the clues?

Investigations

More open ended activities where children choose the approach to the task.

Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.

How many different three course meals can Sam choose?

Investigate patterns made by placing consecutive numbers in a number square.

A great little investigation which has plenty of extension possibilities.

Fun addition investigation using the date: 22.02.2022.

Some thoughts on how important this area of maths is.

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Problem-solving maths investigations for year 4.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 4 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 4 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 4:

• Individually, they are incorporated into every unit in our Year 4 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 4 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

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Problem-Solving Booklet: Year 4

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This Problem-Solving Booklet is a great resource for your students to practise utilising problem-solving skills.

This booklet has 18 pages of questions, having students apply addition, subtraction, division, and multiplication operations to answer the problem. Each page has the students identify the operation needed and the problem-solving strategy they will use, then record the number sentence to solve the problem. Some problems have multiple steps to extend students. It also contains two cover pages as it may be suitable to use with other year grades.

This would work well in small group activities, extension work, or as an independent task.

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Year 4/5 word problems all 4 operations

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Year 4 tasks

Thanks for visiting NZMaths. We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.  

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

To solve maths problems at year 4 it is very important for your child to be able to instantly recall addition and subtraction facts up to 20, and multiplication and division facts for their 2, 3, 4, 5 and 10 times tables to solve problems.

e-ako maths provides free online basic fact learning tools which will help your child learn their basic facts, as well as a collection of games to improve their speed and accuracy. If you think this would benefit your child, click to read how to access this resource  (show instructions).

• To access e-ako maths, your child will need an account. You can make a new account for free, but check first whether they already have one that they use at school. If they do, they can use the same username and password to use e-ako maths at home.
• You can log in to e-ako maths or register a new account from the e-ako maths home page . If you are registering a new account to use at home you will need to click the "No join code? Click here." button and then "I am learning at home".

• The two large green boxes at the top are 'Learning tools' which will test the basic facts your child knows, and then help them learn the ones they don't already know.
• The blue buttons below are a collection of games designed to practise basic facts to improve speed and accuracy. 
• In Year 3 your child should mostly be concentrating on learning and practising their addition and subtraction facts, the buttons on the left.

Click to read about the purpose of the tasks below  (show purpose).

The tasks in this section are intended:

• for students in year 4 
• to complement similar class tasks
• to be a selection only of enjoyable learning opportunities for your child (and for you) 
• to generate useful explanations and discussions between you and your child.

The tasks in this section are NOT: 

• intended to be comprehensive in their coverage of all maths at year 4
• drill and practice exercises.

These Year 4 tasks recognise that students:

• are mostly working at level 2 of the NZ Curriculum, growing in their understanding of number, algebra, geometry, measurement and statistics
• are all different, and some find parts of maths easier or harder than others
• are learning a range of approaches to solving problems that may involve several steps
• learn from and appreciate tasks presented in a variety of ways
• respond well to supportive questions from adults, such as, ‘What is the question asking you to do?’, or ‘What do you already know that might help you (solve the problem)?’
• enjoy exploring open tasks for which there can be a range of appropriate approaches and solutions (accordingly, set answers are not included for a number of these tasks).

We suggest that you ask your child what they are learning in maths at school, and select a task from this menu.

Click for  versions with Māori content .

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Mathematical Problem Solving in the Early Years

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Group-worthy tasks and their potential to support children to develop independent problem-solving skills

Developing the classroom culture: using the Dotty Six Activity as a springboard for investigation

The questions Year 8 maths pupils are expected to answer correctly

School children are expected to be able to read, write and compare fractions, add and subtract decimals, solve linear equations, and find the perimeter and areas of shapes by the time they reach Year 8.

According to the Refreshed New Zealand Curriculum, students should know how to recognise, read, write, represent, compare, order, and convert between fractions, decimals, and percentages.

Students should also be able to add and subtract decimals to three places, add and subtract fractions with related denominators and write fractions in their simplest form.

The curriculum also states students should know how to solve linear equations through trial and error as well as be able to find the perimeter and area of shapes composed of triangles and rectangles, show these findings and describe how they reached these results.

University of Auckland mathematics education senior lecturer Lisa Darragh told the Herald there were broadly six content areas in mathematics education for Year 8 students: “numbers, algebra, geometry, measurements, statistics and probability”.

“Interwoven with that, you have a greater or lesser emphasis on processes - things like problem-solving, logic and reasoning or communicating your mathematical thinking,” she said.

Prime Minister Christopher Luxon said he rushed through plans to fast-track changes to the maths curriculum after seeing “appalling” results last week that showed four out of five Year 8 students were behind in their learning.

The move to introduce structural maths for year 0-8 students from term one in 2025 – a year earlier than planned – was the big announcement in Luxon’s speech to the National Party conference on Sunday.

Luxon revealed afterwards the announcement was pulled together in a few days, prompted by the new achievement data from the Curriculum Insights and Progress Study (Cips) that slightly over a fifth of Year 8 students in New Zealand had reached the benchmark for mathematics.

That study showed 22% were at or above the curriculum level, 15% were less than one year below the level and a 63% were more than one year below it.

Among Māori students, 12% were where they should be, 10% were less than a year behind and 77% were more than a year behind.

Luxon – who has frequently said education was a big priority for him – said it would make it harder to hit National’s target for 80% of students to be at or above their curriculum levels by 2030.

Could you answer these questions?

a) 1/2 +1/4 = ?

b) Explain why you think this.

Question 2 - The shaded circle task

Question 3 - The chocolate bar task

Question 4 - The fractions task

Question 5 - Coloured counters

There are some coloured counters in a bowl.

1/4 are black.

1/5 are green.

1. a) Are there more black or more green counters in the bowl?

More Black / More Green (Tick response)

b) Show how you got your answer. You can use words and pictures.

Question 6 - Closest to 3/5

a) Which of these is closest to 3/5

b) Explain why you think this. You can use words and pictures.

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Breaking’s Olympic Debut

A sport’s journey from the streets of new york all the way to the paris games..

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 Sabrina Tavernise. And this is “The Daily.”

So my name is Gabriel “Kwikstep” Dionisio.

Rokafella, R-O-K-A-F-E-L-L-A.

I go by Kid Glyde. I represent Dynamic Rockers. I’m from Queens, New York.

This year at the Olympic Games, there’s one sport that’s on stage for the first time — breakdancing.

I’m excited that people are going to be exposed to it on that kind of stage.

They’re going to see breaking. They’re going to see hip-hop. They’re going to feel it. They’re going to — you know what I’m saying? So it’s going to be an experience.

Today, my colleague, Jonathan Abrams, tells the story of how it went from the streets of New York all the way to the Paris games.

But I’m also concerned that it’s not being represented at its fullest cultural capacity.

People are clueless to what this even is. And people are going to be really surprised.

And the debate that journey has inspired about whether treating breakdancing as just another sport might be a mistake.

This comes from a culture that had to go through so much just to exist. So are you going to do right by us?

[MUSIC PLAYING]

It’s Friday, August 9. Jonathan, welcome to the show.

Thank you so much, Sabrina.

So, Jonathan, we’re going to talk today about the Olympics. And I think something that catches people’s attention is when the Olympics adds new sports. The Olympics is this ancient thing. So, I find that kind of surprising when new things pop up. And you’ve been writing specifically about the new event that is debuting this year in Paris, and that is breakdancing.

Yeah, a lot of people in the community refer to it as “breaking.” Breakdancing is kind of a term that they have said was created by mainstream media and not a term that they use. So it’s almost frowned upon.

Ah. OK, breaking. Got it.

So it’s been a little bit of a journey these last few years to get it to the Olympics. And this is such a special watershed moment. It’s kind of crazy to think that breakdancers are going to be at the Olympic Games. They’re going to be mixing along with LeBron James, with Kevin Durant, with Simone Biles, all these athletes you historically think of being involved and intertwined with the games. You’re going to have a component of hip-hop right there alongside with them.

And it’s joining a class of new sports recently added to the Olympics, like skateboarding and rock climbing and surfing. And if you look at these sports, what they all have in common is that they’re trying to get a younger audience to watch the games.

And what the International Olympic Committee — they’ve been frank about what they’re trying to do — is that they’re trying to go for that younger audience because viewership has been way, way down. And so these ancient games are trying to modernize themselves by changing the rules and welcoming these new events to have a newer, younger, more diverse viewership.

OK, so breakdancing — oh, sorry, breaking — is here to try to breathe some new life into the Olympic Games — expand the audience, as you say. But I don’t really think of breaking as a sport, I mean, never mind a competitive Olympic sport.

Lots of people make that argument, Sabrina, but competition has been part of breaking since its inception in the Bronx in the 1970s. At that time, New York City is basically in this state of disrepair. The construction of the Cross Bronx Expressway cuts through the heart of the South Bronx, and it displaces thousands of residents. Crime levels rise, unemployment increases. These large buildings are sitting vacant because of white flight. And property owners, some are facing default, and they start burning their buildings in order to cash in on the insurance value. And people, especially the Black and Brown people in the Bronx, they’re feeling this sense of utter hopelessness. And the culture of hip hop grows out of that despair. It was a way for these marginalized communities to take something back and to have something for themselves.

And breaking is a key component of hip-hop, because when hip-hop first formed and came along, it was presented as this vivacious, multifaceted gem, where you had four distinct tenants and components. One was lyricism, the artists words going along a track of music. One is turntablism, or being a DJ, and that’s scratching records. The other one is graffiti, or writing. And then the last one is breaking. And that’s the physical expression of hip-hop, dancing to the music.

And so these latchkey kids in the Bronx would throw these massive parties where breaking was born. And people, they came together, and they formed crews. And they competed against one another. And they danced to make a name for themselves. They danced to earn respect in their street, in their neighborhood, and in their city. And that was how they cultivated self-esteem and made something of themselves when they really had nothing else.

OK, so in these poor neighborhoods in the Bronx, in this very turbulent time, kids were finding themselves finding inspiration in breaking. Why exactly did they call it breaking? Why that word?

Breaking comes from these pioneering DJs being able to figure out how to extend the breaks for songs. So say there’s a drum break in a famous song where it’s a snippet, and then the song will continue.

And they were the most popular parts of the songs, where kids would dance for 10, 15 seconds and then stop.

DJ’s like DJ Kool Herc and Grandmaster Flash. They were innovators and engineers because they figured out how to extend those breaks.

And once they were able to loop them endlessly, then kids were able to extend their dances and be able to dance and be creative with it and form the circles. And that’s where breaking came from.

So what did it actually look like?

There is no way I can accurately describe breaking just through words. I can try to say that it’s graceful or powerful or athletic, and all those words seem to fall flat. Breaking is a call and response. It’s a back and forth conversation. It’s almost like trumped up jazz.

Picture this. You’re going into a crowded party. There’s people everywhere. Music is thumping. If you’re walking to the cypher, which is the circle where breakers perform and compete in, you finally get to the front and what you see is people doing these most amazing moves, moves that you don’t think are possible with the human body.

They’re spinning, contorting their bodies into pretzels, stopping on a dime, bending backwards, and doing windmills and airflares. And then the next person is going to come in and challenge them. And what breaking is, it’s attitude. It’s an expression of yourself. It’s energy balled up.

And when did breaking go beyond the streets of the Bronx and really kind of emerge as a sport?

Well, before it got to that level, it had to become part of the mainstream culture. And breaking started to hit that level around the early to mid 1980s. And at this point, people may know “Rapper’s Delight.” They can maybe say “a hip hop, the hippie to hippie, hip hop.” Everybody knows that song by then.

But these movies, like “Flashdance” and “Wild Style,” are also starting to come out, and they’re starting to capture hip-hop’s infancy. And one of the main ones that comes out in 1984 is “Beat Street,” and that’s pivotal.

Bronx rockers. Gino, hey, come on.

Yo. Let’s serve.

There’s a scene of the movie with these crews coming together in a club.

And there’s anticipation. There is adrenaline. It looks like they may fight. But no, instead of fighting, a dance battle breaks out.

And if you’ve never seen this, like I said earlier, about words and being able to describe it, if somebody described breakdancing to you and you had never seen it in person, you wouldn’t have a good clue as to what it was.

But now, for the first time, in movie theaters from LA to New York, you can actually see what it is. And then you have these pioneering groups, like Rock Steady Crew and Dynamic Rockers, Zulu Kings, New York City Breakers, they all start to be in these movies and do these demonstrations globally. And that inspires a whole generation of kids to get into breakdancing.

This is the newest craze. It’s called breakdancing.

So as the popularity of breakdancing continues, experts say it’s OK to dance, as long as you just watch your step.

It’s the Big Breakdance Contest from the Roxy, with host Leslie —

And at this point, we’re starting to see judges and prizes be introduced into breaking. Then in 1990, a German breaker set up a breakdance competition in Germany known as Battle of the Year. And 2001 was a pivotal year because it’s the first year that Red Bull has its Lord of the Floors competition.

History in the making, y’all.

And that, again, convened all the best breakers to be able to compete against one another to measure themselves up. But there’s also the carrot at the end of the stick.

The runner-up of the 2001 Red Bull Lords of the Floor is —

There’s a multi-thousand dollar cash prize that’s awarded to the top talent.

The winners, Los Angeles Breakers. Come and get your checks.

So you start to see the trappings of this thing that was created in New York City in the Bronx in the 1970s start to leave its beginnings a little bit and become more of a competition and more of a sport through Red Bull and these other entities that are sponsoring it.

Y’all loving it or what? Give a big round of applause to all the contestants.

We’d like to thank Jaimeson Keegan and the whole Red Bull crew.

OK, so breaking is going mainstream in a very big way. But in my mind, there’s a big difference between a Red Bull event and the Olympics. So how do we get from here to there?

It’s actually a bit of a wild story. So nearly three decades ago, this global governing body of dance, International Dance Sport, is recognized by the International Olympic Committee, and they want to bring dance to the Olympics. So they want to have ballroom dancing. And they suggest that, and they get rebuffed.

So they eventually rebrand themselves as World Dance Sport Federation, and they find out that it’s not foxtrot or salsa or ballroom that the Olympic thinks could have a shot. It’s breaking. Breaking is highly watchable, easily viewable on social media. And it comes along as the Olympics is reevaluating what they’re going to use as a sport to try and gain that younger audience.

There was a testing period in 2018.

Winter Olympic Games just got a little more exciting. Breakdancing will now be part of the Youth Olympic Games. And there’s still a search for —

They debuted breaking at the Youth Olympics in Buenos Aires.

3, 2, 1! It’s battle time!

And what happens is that it exceeds almost every expectation by every metric possible. There was more than 50,000 people who attended the two-day event in 2018. There was over 2.5 million social media impressions, according to the International Olympic Committee. I mean, it seems like it aligns itself perfectly with the Olympics mission of trying to skewer to a younger audience. And once you see those numbers, that pretty much locked up breaking for the 2024 Olympic Games in Paris.

The Olympic Games are changing, and the future of breaking is coming.

We’ll be right back.

OK, so now we’re at the Games. Everybody’s watching how this is going to go, which must be pretty exciting for breakers.

You would think so. But there’s a lot of skepticism and tension from many of these veterans and pioneers and purists of breaking.

And what do they say? Why do they not feel excited about this?

Well, I think anytime you take something and strip it away from its roots — and let’s be honest, Paris 2024 is very, very, very far away from Bronx 1970s.

[LAUGHS]: That is true.

It is not going to be the same thing or presented in the same thing. I think that’s what the purists and the pioneers are afraid of.

But Jonathan, couldn’t you also make the case that skateboarding is also a specific kind of culture and that it also has all of its own peculiarities and is also potentially hard to judge by a bunch of Olympic judges?

To some extent, yeah. But breaking, it’s just different in a lot of ways. The pioneers and the purists, the ones who invented this thing will argue that it’s more than just a hobby or even a sport. It’s a lifestyle. It’s the product of a culture. It’s something that was born from Black and Brown people’s struggles in a deeply turbulent time in American history and is a way for people to express themselves, to tell their stories, to build self-confidence.

And on top of that, there’s a lot of breakers who just aren’t happy with how this arrived at the Olympics in the first place. It arrived in the hands of the World Dance Sport Federation. And remember, that’s an organization that wasn’t even associated with breaking. They were trying to put ballroom dancing into the Olympics way before they ever thought about breaking.

So back in 2017, a bunch of breakers, they got together and they signed a petition essentially protesting this organization. And they were saying, you don’t represent us. You’re not from our community, but you’re taking our art form and using it to advance your own goals. And all of this has left a lot of breakers really worried and concerned about what exactly this weekend is going to look like for breaking.

OK, let’s dig into that. What will breaking look like on stage in Paris? What can we expect?

Right, so there’s a lot of questions about how it’s going to actually look. In Paris, you’re going to have some of the crucial components of breaking. You’re going to have attitude. You’re going to have breakers. They’re going to be challenging each other. There’s going to be athleticism. [MUSIC PLAYING]

But there’s also going to be judges. A breaker is going to go get a score. Then the next breaker is going to go and get a score. So you can kind of see those seeds of the origin of this thing that was born in New York in the 1970s. But it’s definitely something different, and it’s more sterile and sanitized.

There’s going to be 16 men and 16 women who will go across two days of competition. There’s going to be nine judges, and they’re going to score the breakers based on five criteria — vocabulary, technique, execution, originality, and lastly, musicality.

And break those down for me. What do they actually mean?

The vocabulary is not how many words somebody can say. It’s the array of moves that a breaker deploys. And technique covers the breaker’s body control and their use of space. Execution consists of the cleanliness of one’s moves.

Then originality is improvising during their rounds, being able to react to what their opponent is doing. And then musicality is staying on beat with the music. They’re not going to know the music beforehand, so they’re going to have to really tune their moves to what’s going on to the beat.

OK, so this is how the judges are actually going to do it. But what about kind of what we know about breaking, the spirit of competition, the kind of outdoing each other, the attitude it brings, like the showboating? Is that taken into account in how it’s going to go with the Olympics?

Yeah, I can guarantee you this, Sabrina, that this is going to be the only Olympic sport with the misbehavior button.

What’s that?

The judges will be able to hit a misbehavior button if competitiveness crosses into crassness, if they deem that to be the case.

What’s an example of something that would get a misbehavior button?

Say if you finish off a move with the freeze and stick up your middle finger at your opponent.

[LAUGHS]: OK, fair enough. Got it. OK, misbehavior button. So this sport, of course, started here in the US. I have to ask, who are the Americans competing this year? Tell me about them.

Yeah, somebody that I’ve talked to a lot leading up to the Games is Sunny Choi, who was the first American woman to qualify for the Games.

All right, switching it up, all the way to USA, first entry, Sunny.

She’s Korean-American. She’s from Tennessee. She’s ironically the only New Yorker — she now lives in New York — who is competing in Paris at the Games.

All right, Sunny slay. Oh, you started as a gymnast? Is that true?

Yeah, so I actually, I watched the Olympics growing up.

She has a background in gymnastics, and she was working at Estée Lauder when she decided to go into breaking full-time.

Some people have been like, you’re a very unlikely Olympian. And I’m like, yeah, kind of. I had always envisioned myself going to the Olympics as a gymnast, and then I never thought I would have the chance again. And so it coming back full circle is amazing.

Woo! Victor.

OK, Victor.

What you got?

On the men’s side, you have Victor Montalvo, who goes by “B-Boy Victor.” And he’s a two-time Red Bull World One champion. He’s from Florida.

So my dad and his twin brother used to break back in Mexico. And they actually taught me, my brother, and my cousin.

His father was a pioneer in the Mexican breaking scene.

I was introduced into breaking at the age of six years old. And I took it serious at the age of 10.

Oh, my gosh.

Yeah, yeah.

So breaking is really in Victor’s blood. And he’s definitely a favorite to medal on the men’s side.

Heavy round.

Still go where the action is.

Victor, what you got?

Victor with the eye contact, going straight into it. He’s like, I see you, and I got you.

OK, so I’m assuming these Americans are poised to win this fundamentally American sport.

Eh, not necessarily, Sabrina.

Breaking is such a global entity now that I feel like America has really fallen behind some of these other countries and when it’s more popular and when people do it more often. So you look at this field and there’s breakers from Japan, from the Netherlands, from France, from Kazakhstan, from all over the world. On the women’s side, there’s B-Girl Nika from Lithuania.

And last year, she won the 2023 world title at the age of 16.

Wow, amazing. A Lithuanian girl has the world title, actually.

Yeah, and she’s an amazing story. And I think she’s emblematic of breaking and its evolution because she discovered breaking on YouTube at the age of five and within just about a decade is one of the world’s best breakers in the world and will be heavily favored to win a gold medal at the first Olympic breaking competition.

Just to go back to the tension around breaking in the Olympics that we started with, Jonathan, and the question of it leaving its roots, becoming detached from the place and the culture it sprung from, is there an argument that that’s already happened, that as people are kind of wanting to pull it back toward where it came from, it’s already gone. It already went out there. Is there any going back?

Yeah, that’s a great question. And I think we’re at this crossroads where you have breaking’s authenticity at stake. And breaking is about that expression from the heart. It’s about being able to show your attitude, your charisma, who you are as a person through your dance. And the pioneers and the purists are going to be watching this to see what part of the soul and the struggle exists as this thing that they invented, nurtured, and cultivated reaches its biggest stage ever.

But it is out there. And for somebody to be able to be in a foreign country and just study the art form on YouTube and be able to become world class leaders in it, it says something, one, about the art form and how wide-ranging and impactful it can be. And it also just says that this isn’t just New York’s anymore. This is global.

And perhaps the people performing on that stage are what breakdancing is now, right, in some ways?

Yeah, and we’re going to see people, men and women from different countries all over the world represented in Paris. And in some ways, it’s very, very far away from what was invented in New York in the 1970s.

But at the same time, seeing people from different countries and men and women be the best at breaking that they can possibly be is also exposing breaking to a whole new generation. And exposing breaking at the Olympics could be the vessel that keeps it alive for the next generation.

Jonathan, thank you.

Sabrina, anytime.

Here’s what else you should know today. On Thursday, former President Donald Trump held a news conference at Mar-a-Lago. It was his first public appearance since Vice President Kamala Harris became the Democratic presidential nominee.

And I look forward to the debates because I think we have to set the record straight.

In his remarks, Trump proposed three dates in September for debates with the vice president.

I haven’t recalibrated strategy at all. It’s the same policies — open borders, weak on crime.

Trump insisted that little had shifted in the contest, despite polling showing a tightening race.

Listen, I had 107,000 people in New Jersey. You didn’t report it. I’m so glad you asked. What did she have yesterday? 2,000 people? If I ever had 2,000 people, you’d say my campaign is finished.

It was an effort by the former President to recapture some political momentum, as the new Democratic ticket has continued to dominate the news coverage. During his remarks, ABC confirmed that it would host the two candidates for a debate on September 10th.

A quick reminder to catch a new episode of “The Interview” right here tomorrow. This week, Lulu Garcia-Navarro talks with Republican Senator James Lankford, including about Republicans who turned on him when he tried to pass bipartisan immigration reforms.

I did have several folks saying, I’ll destroy you if you do this, because although I like you, I like President Trump better. And he’s got to be elected for the future of the country. And you can’t take this issue off the table.

Today’s episode was produced by Sydney Harper and Luke Vander Ploeg, with help from Shannon Lin and Will Reid. It was edited by Lexie Diao and MJ Davis Lin, with help from Ben Calhoun, contains original music by Dan Powell, Marion Lozano, and Diane Wong, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Sabrina Tavernise. See you on Monday.

• Apple Podcasts
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Hosted by Sabrina Tavernise

Featuring Jonathan Abrams

Produced by Sydney Harper Luke Vander Ploeg Shannon M. Lin and Will Reid

Edited by Lexie Diao MJ Davis Lin and Ben Calhoun

Original music by Dan Powell Marion Lozano and Diane Wong

Engineered by Alyssa Moxley

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

More than 50 years after its inception, “breaking” — not “break dancing,” a term coined by the media and disdained by practitioners — will debut as an Olympic sport.

Jonathan Abrams, who writes about the intersection of sports and culture, explains how breaking’s big moment came about.

On today’s episode

Jonathan Abrams , a Times reporter covering national culture news.

Background reading

The Olympic battles in breaking will be a watershed moment for a dance form conceived and cultivated by Black and Hispanic youth in the Bronx during the 1970s.

Breakers are grappling with hip-hop’s Olympic moment. Will their art translate into sport?

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, Michael 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, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, 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, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

Jonathan Abrams writes about the intersections of sports and culture and the changing cultural scenes in the South. More about Jonathan Abrams

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