problem solving 3rd class

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Class 3 NCERT Solutions

NCERT Solutions for Class 3 Maths

Just practising questions is not enough; you need to make sure that the answers are correct. So, while your kid is solving the questions in the NCERT textbook, they need a reference for the solutions. Here, we bring to you 100% accurate NCERT Solutions for Class 3 Maths.

All these solutions have been designed by our subject-matter experts with full diligence to provide you with the most accurate answers. To make sure that your little one is able to grasp the NCERT solutions well, the language has been kept as simple as possible.

Kids can practise the questions on various topics of CBSE Class 3 Maths and check their answers. We offer you detailed explanations of all the questions in the NCERT textbook of Maths. You can also download the PDF of the solutions.

Class 3 Maths NCERT Solutions

Below are the chapter-wise links to the CBSE Maths Solutions for Class 3:

Chapter-wise NCERT Solutions for Class 3 Maths

Ncert solutions for class 3 maths chapter 1 where to look from.

This chapter deals with the introduction to various types of views of an object – the top view and the side view. Kids are explained how the same thing can look different from different sides. The lesson also talks about mirror images of various objects, dividing images of objects into two equal halves, etc.

NCERT Solutions for Class 3 Maths Chapter 2 Fun with Numbers

The chapter Fun with Numbers covers the concept of counting numbers in a very interesting way. It discusses counting numbers above 100, word problems on numbers, and solving word problems using addition and subtraction. It also explains the concept of units, tens and hundreds.

NCERT Solutions for Class 3 Maths Chapter 3 Give and Take

Through this chapter, kids get introduced to a wider view of the addition of numbers. The chapter has short techniques that kids can follow to get the sum of numbers quickly. The chapter has word problems as well as direct questions on the addition of numbers.

NCERT Solutions for Class 3 Maths Chapter 4 Long and Short

This chapter introduces kids to the concept of measurement. The chapter has various exercises and questions to make the students understand the units of length – centimetres, metres and kilometres.

NCERT Solutions for Class 3 Maths Chapter 5 Shapes and Designs

Shapes are one of the most interesting concepts which kids love to learn in their formative years. This chapter teaches kids about various shapes, edges and corners in a shape, etc. The chapter also helps young minds understand and recognise patterns around them.

NCERT Solutions for Class 3 Maths Chapter 6 Fun with Give and Take

This chapter elaborates on the concept of addition and subtraction. The lesson uses various word problems and questions to explain to kids addition and subtraction in a faster way. It takes a deeper dive into the same concept through numbers having more digits. It explains addition and subtraction using the unit’s place, ten’s place and hundred’s place.

NCERT Solutions for Class 3 Maths Chapter 7 Time Goes on

The importance of time is not something new we hear about. Kids, too, must be made aware of the various aspects of time. This lesson talks about the concept of time. It makes kids ponder about the things/activities that happen in a few minutes, a few hours, a few days and even further. Then it introduces the students to calendars – weeks, months, years, dates, days, etc.

NCERT Solutions for Class 3 Maths Chapter 8 Who Is Heavier?

Do things which look heavier necessarily have to be actually heavier? This chapter discusses the concept of weight and balance. The lesson uses various stories and puzzles to make kids understand these concepts easily.

NCERT Solutions for Class 3 Maths Chapter 9 How Many Times?

Multiplication is nothing but multiple additions. This chapter explains how multiplication and addition are linked to each other and how instead of adding the same number multiple times, you can simply use multiplication. The chapter also teaches kids multiplication tables through interesting pictures, questions and puzzles.

NCERT Solutions for Class 3 Maths Chapter 10 Play with Patterns

Recognising patterns is one of the most important topics of mental ability. In this chapter, kids get more comprehension of patterns and sequences. The students are taught these concepts through numerous exciting questions and puzzles.

NCERT Solutions for Class 3 Maths Chapter 11 Jugs and Mugs

This chapter lets kids get a broader view of measurements. Kids need to guess the amount of an entity which can fill another entity. It also delves deeper into word problems and interesting puzzles, which make it precise for kids’ understanding.

NCERT Solutions for Class 3 Maths Chapter 12 Can We Share?

The division is one of the most important arithmetic operations. This chapter introduces kids to the concept of division. Sharing anything equally utilises division. This lesson covers the concept of distribution and division through brain-tickling word problems and puzzles. It also establishes the link between multiplication and division.

NCERT Solutions for Class 3 Maths Chapter 13 Smart Charts

Charts and graphs make it easier to depict any piece of information. This chapter deals with smart charts and how data can be easily represented through charts and tables.

NCERT Solutions for Class 3 Maths Chapter 14 Rupees and Paise

This chapter introduces kids to the world of money. In India, money is used in terms of rupees and paise. This chapter explains how to get the sum of money where the money is in the form of notes of 500, 100, 50, 10, 20, 2, 1, and coins of 10, 5, 2 and 1. The chapter also includes word problems on the creation of cash memos, finding the price of tickets for covering a certain distance and other real-time problems.

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Third Grade Problem-Solving Activities and Exercises

It's important for kids to learn problem-solving skills because they'll use them in various school subjects, as well as in life in general. Keep reading for sample activities and exercises that you and your child can do at home to improve his or her problem-solving skills.

What Types of Activities Promote Third Grade Problem-Solving Skills?

Giving your child genuine problems to solve can help him or her to see how schoolwork applies to real life. For example, if you're planning a party, you might have your child use his newly developed skills in multiplication and division to figure out the logistics, such as how many tables and chairs will be needed, based on the number of anticipated guests.

Your child also can apply his or her third-grade math skills during everyday events, like visiting the grocery store. While shopping, you can have your child calculate the price of the items you're purchasing to determine if you're staying within a budget. For instance, would it bust your $18 budget if you bought five boxes of cereal that were priced at $4 a box? Your child could practice his or her multiplication skills by determining that $4 x 5 = $20 and then his or her problem-solving skills by noting that this would, indeed, put you over budget.

Additionally, you might challenge your child to complete fun experiments. For example, you could work with your child to design a container that will protect an egg that's dropping from the top of your house. Your child will have to use creative thinking in order to create a safe container.

Problem-Solving Exercises and Solutions

1. A room has an area of 400 feet. What are some possible dimensions for this room?

2. Ken has to be at work by 8:30 am. His office is 30 minutes away, and he wants to stop for coffee, which typically takes 10 minutes. What time should Ken leave his house in the morning?

3. There are too many guests at Karla's party. There are 44 people present, but Karla only has 22 pieces of cake. How can Karla give each of her guests a piece of cake?

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35 math problems for 3 rd graders

In 3rd grade, students are introduced to important math concepts that become the building blocks for future mathematical learning. Let’s practice those concepts with this list of math problems for 3rd graders.

Author Katie Wickliff

Published September 25, 2023

Key takeaways
In 3rd grade math, students develop a deeper understanding of multiplication and division, fractions, and measurements.
Word problems for 3rd graders require more advanced comprehension skills.
Place Value: Understanding place value helps us read and write numbers correctly and compare their values.
Look for opportunities for your child to practice their math at home–worksheets, math games , or a math practice app will help strengthen new mathematical knowledge. While consistency is key, math practice for 3rd graders should be engaging and fun.

Table of contents

Subtraction
Multiplication
Measurement
Multi-step word problems

Answer sheet

In addition to reviewing and strengthening the skills learned in previous years, 3rd graders learn multiplication and division, explore fractions, calculate measurements, and more. Also, word problems for 3rd graders are often multi-step, requiring students to understand what operations to perform and how to perform them correctly.

This list of 3rd grade math problems is intended to reinforce concepts students have already been taught. The list is divided into sections: addition, subtraction, multiplication, division, fractions, measurement, and multi-step problems. These sections allow students to specifically focus their practice, but feel free to skip around and choose the 3rd grade math practice problems that best suit your child’s needs.

35 Third Grade Math Problems

Section 1: addition.

At the school carnival, Hattie won 25 tickets at ring toss and 40 tickets at balloon darts. How many tickets did she win altogether?

There are 15 baby chicks at the barn. 12 more chicks are born. How many baby chicks are at the barn now?

How can you represent the number line with an equation?

$problem solving 3rd class$

Using the number line, solve 7+ _ = 22

$problem solving 3rd class$

Amir practices basketball three days a week. On Tuesday, he practices basketball for 60 minutes. On Wednesday, he practices for 37 minutes. On Thursday, he practices for 15 minutes. Which expression shows how to find the total number of minutes Amir practiced? Circle the correct answer

Section 2: Subtraction

Using the number line, solve 17-6=

$problem solving 3rd class$

There are 224 Lions fans and 212 Tigers fans at the football game. How many more Lions fans than Tigers fans are at the game?

An animal shelter has 27 kittens available for adoption. On Friday, 8 kittens are adopted. How many kittens are left at the shelter?

Gemma has 130 beads for bracelets. She gives 75 beads to Piper and 6 beads to Claire. Which expression shows how to find the total number of beads Gemma has left? Circle the correct answer.

Using the number line, solve 30- _ = 14

$problem solving 3rd class$

Section 3: Multiplication

Using the picture below, write a multiplication equation to find the number of shapes

$problem solving 3rd class$

Francis and Jane are playing a card game. Francis has 7 cards. Jane has 3 times as many cards as Francis. How many cards does Jane have?

$problem solving 3rd class$

Using the number line to show hops, complete the multiplication sentence

$problem solving 3rd class$

Solve the equation

$problem solving 3rd class$

Mariela has 8 pages of math homework. There are 4 problems on each page. How many total problems does Mariela have for math homework?

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Section 4: Division

Connor has 80 crayons that he will put into crayon boxes. Each crayon box can hold 8 crayons. How many crayon boxes does he need?

Using the number line to show hops, complete the division sentence

$problem solving 3rd class$

Natalie divided 12 marbles into equal groups of 3. Draw a representation to show equal grouping.

Craig’s mom brought 12 cookies to the soccer game. She shared them equally among Craig and 3 teammates. Which expression will solve the problem correctly? Circle the answer.

Section 5: Fractions

Using the number line, work out what A, B and C represent.

$problem solving 3rd class$

Plot ¼ on this number line:

$problem solving 3rd class$

A cheese pizza has 8 slices. Marco ate 2 of the slices. His dad at the rest. What fraction of the pizza did Marco eat? What fraction of the pizza did his dad eat?

There are 15 flowers in a garden. 10 flowers are yellow and the rest are red. What is the fraction of red flowers in the garden?

Using the number line, find the value of K and L. Which is bigger?

$problem solving 3rd class$

Section 6: Measurement

A school bus is 12 feet long and a car is 4 feet shorter than the bus. How long is the car?

John is 64 inches tall, Mabel is 59 inches tall, and Phoebe is 57 inches tall. How much taller is John than Phoebe?

Use the ruler provided to measure to the nearest ¼ inch:

$problem solving 3rd class$

Find the area of the square below

$problem solving 3rd class$

Find the perimeter of the rectangle below

$problem solving 3rd class$

Section 7: Multi-step word problems

Sarah has two $10 bills. Her sister has one $5 bill. They combine their money to buy a game that costs $22 dollars. How much change will they receive?

Dad baked 36 cookies for the bake sale. Jonas baked 24 cookies for the bake sale. His brother ate 5 cookies before the bake sale started. How many cookies do they have left to sell?

The school bus seats 75 students in all. On Friday, the school bus was full. At the first stop, 7 students got off. At the second stop, 15 students got off. How many children were left on the bus?

George has 25 water balloons. He wants to divide the water balloons equally between himself and 2 friends. How many water balloons will each get? Will there be any water balloons left over?

On Monday, 5 inches of snow fell. On Tuesday, 3 inches of snow fell. On Wednesday, 7 inches of snow fell. The school will have a snow day if it snows 21 inches or more. How many more inches would it have to snow for the school to have a snow day?

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Addition answers

25+40= 65. Hattie won 65 tickets

15+12= 27. 27 baby chicks are at the barn

7+ 15= 22. This should be represented by 15 “hops” on the number line

Subtraction answers

17-6=11. This should be represented by 11 “hops” on the number line

224-212= 12. There are 12 more Lions fans than Tiger fans

27-8= 19. There are 19 kittens left at the shelter.

Multiplication answers

2×3=6; 3×2=6

7×3=21. Jane has 21 cards.

$problem solving 3rd class$

8×4= 32

Division answers

$problem solving 3rd class$

40÷8= 5. It will take Max 5 days to pay Bennett.

Drawing should show 3 groups of 4 marbles each.

Fractions answers

The ¼ should be plotted on the point between 0 and ½

Marco ate 2/8 (or ¼) of the pizza. His dad ate 6/8 (or ¾) of the pizza

5/15 (or ⅓)

K= ⅜, L= 6/8 (or ¾). L is larger.

Measurement answers

12-4=8. The car is 8 feet long.

64-57=7. John is 7 inches taller than Phoebe

8×8=64. The area is 64 yd2

8+8+2+2=20 cm

Multi-step word answer answers

$10+$10= $20.

$20+$5=$25.

$25-$22= $3

Sarah and her sister will receive $3 in change

They have 55 cookies left to sell

53 students are left on the bus

George and his friends each get 6 water balloons, with one left over.

5 in+ 3 in+ 7 in= 15 in

21 in- 15 in= 6 in

It must snow 6 more inches to get a snow day.

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

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3rd Grade Addition and Subtraction

Word problems.

Welcome to our 3rd Grade Addition and Subtraction Word Problems page. Here is our selection of free addition and subtraction word problem worksheets, which will help your child practice solving a range of addition and subtraction problems using 3-digit and 4-digit numbers.

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3 Digit Addition & Subtraction Word Problems
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Addition & Subtraction Word Problems up to 1000 Online Quiz

3-digit and 4-digit Word Problems

Each sheet consists of a range of 5 addition and subtraction word problems with numbers up to thousands.

There is a space on each sheet for working out, so that your child can write out the problem and solve it.

We have split the worksheets up into 3-digit word problems and 4-digit word problems.

Using these sheets will help your child to:

add and subtract numbers with 3-digit and 4-digit numbers;
solve addition and subtraction word problems with and without regrouping.
recognise the language used in addition and subtraction - sum, total, difference, how many more, etc.
solve problems involving more than 1 step.

3rd Grade Addition and Subtraction Word Problems

3-digit addition and subtraction word problems.

There are two versions of each sheet.

The first version (version A) contains problems where no regrouping is needed.

The second version (version B) contains similar problems but regrouping is needed to solve them.

Answers have been provided with each sheet, along with the calculation needed to solve the problem.

The following sheets are all 1-step addition or subtraction word problems.

3-Digit Addition and Subtraction Word Problems Sheet 1A (no regrouping)
PDF version
3-Digit Addition and Subtraction Word Problems Sheet 1B
3-Digit Addition and Subtraction Word Problems Sheet 2A (no regrouping)
3-Digit Addition and Subtraction Word Problems Sheet 2B

4-digit Addition and Subtraction Word Problems

The word problems all involve either addition or subtraction (both with and without regrouping).

4-Digit Addition and Subtraction Word Problems Sheet 1
4-Digit Addition and Subtraction Word Problems Sheet 2

Harder 2-Step Addition and Subtraction Word Problems

These problems are trickier than those above.

Each problem involved two steps to solve, and may involve just addition, just subtraction or both operators.

There are 4 problems on each sheet, and more space to work out the solutions.

2-Step Addition Subtraction Problems up to 3-digits Sheet 1
2-Step Addition Subtraction Problems up to 4-digits Sheet 1

Looking for some easier worksheets?

Take a look at our Subtraction word problems for first graders.

On this page, your child will learn to work out basic subtraction word problems with numbers to 20.

2nd Grade Addition and Subtraction Word Problems (up to 100)

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Addition Subtraction Fact Worksheets (randomly generated)
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Addition and Subtraction Word Problems to 1000 Online Quiz

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NCERT Solutions For class 3 Maths
NCERT Solutions

NCERT Solutions for Class 3 Maths - Free PDF Download

Mathematics is a fundamental subject that introduces a student to the world of logic and reasoning. The skills developed are of prime importance. NCERT Solutions for Class 3 Maths is best described and compiled by our subject-matter experts, who are specialists in this field. NCERT Solutions for 3rd Class Maths is a great platform that provides the fundamentals of all the chapters and accurate answers to complex numerical Maths Sums for Class 3.

NCERT Solutions Maths for Class 3 is what a student requires to conquer their exams. Students are free to explore and visualize the concepts by using NCERT Solutions for Class 3th Maths.

If you feel, that practising questions is not enough, then you are wro ng. To make sure the questions you are solving during examinations are correct, practice is a must. And while you solve the NCERT question, you might need a reference for the solutions. Here, we bring to you the NCERT Solutions for Class 3 Maths in pdf format on this page. All these solutions to each question covered in NCERT Class 3 Maths have been designed by subject-matter experts at Vedantu after a thorough understanding of the topic to provide you with the most accurate answers.

So, you can easily practice the questions on various topics of NCERT Class 3 Maths and verify your answers. The subject experts at Vedantu also offered detailed explanations of all the questions in the NCERT textbook of Math.

Detailed Overview of Class 3 Maths NCERT Solutions

Significance of ncert solutions class 3 maths.

The syllabus of Class 3 Mathematics consists of 14 chapters in total. Students will be introduced to different concepts of Numbers, Subtraction, Addition, Shapes, Designs, Time, and much more. They will get to learn how to measure the weight of objects, recognize patterns, etc. The chapters also include topics of Money, Sharing, Length, and so much more. These chapters are extremely interesting to study and students will get a lot of help in covering their syllabus before the exams from the NCERT Maths Book Class 3 Solutions PDF Free Download .

Students need to properly organize their study schedules properly in order to give attention to all the chapters of Class 3 Mathematics. With their overall development, students can ensure a good score on the final exams. Mathematics is one of the most important subjects in Class 3, introducing the students to a wide variety of new and advanced concepts. The students can easily gain a lot of knowledge about the concepts with the help of NCERT Class 3 Maths Solutions offered by Vedantu. These solutions have been composed by mathematics experts and hence students can have the best content for their preparation. These solutions will allow the students to clear their concepts and learn more about Mathematics in the best way. The solutions have been explained in a step-by-step format using graphs, tables, images, and various other elements to make learning easy and fun for the students.

NCERT Solutions for Class 3 Maths | Chapter-wise List

Given below are the chapter-wise NCERT Solutions for Class 3 Maths . These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

NCERT Solutions for Class 3 Maths

Class 3 Maths NCERT Solutions - Free PDF Download

Downloading the NCERT Solutions for Class 3 Maths PDF from the Vedantu website and app is simple and easy. The methodical approach to laying the foundations of the subject guarantees the success of any student in their final exams. NCERT Solutions for 3rd Class Maths PDF download provides solutions to mastering the concepts, applying general logic, and solving numerical problems curated by our subject experts.

A student can breeze through their revision with ease. The solutions for Class 3 NCERT Solutions provide a step-by-step guide to a student of any calibre and helps to develop a passion for the subject.

Vedantu’s NCERT Solutions for 3rd Class Maths have been created by our subject-matter experts who can help you obtain a better score in your final exam. All the solutions provided in our NCERT Solutions for 3rd Standard Maths have been created in accordance with the guidelines provided by CBSE . We have provided the solutions with a detailed explanation. The questions have step-by-step solutions given in an easy-to-understand language. Once you use this as your reference, you will be able to get a higher grade in your exam.

On this page, you will find the solutions in a step-by-step manner. Studying these solutions will help the students understand how they can solve the problems in a way that helps them score well in their exams. You will be able to grasp the concepts faster and better. This guide is the perfect reference for you to score well in the CBSE exam. Download the chapter-wise solutions, and you will be ready for your exam.

Simply practising Maths Sums for Class 3 for your exam is not enough. It is important to ensure that you are solving them using the right method and getting accurate answers. When you are solving the questions from your NCERT textbooks, occasionally, you might need a reference with all the solutions. That is why Vedantu has created NCERT Solutions for 3rd Standard Maths that are 100% accurate. All the chapter-wise solutions on Vedantu have been created by our subject matter experts with complete diligence so that you have access to the most accurate answers.

The language used in these solutions has been kept as simple as possible so that you are able to grasp all the solutions well. You can practice the questions on all the topics given in your CBSE Class 3 Maths textbook and check your answers. All the Maths Sums for Class 3 are accompanied by detailed explanations. You can download the solutions in PDF format so that you can study anytime and anywhere.

If you find it difficult to solve problems from your NCERT textbook or are not able to understand how you should approach a problem, NCERT Solutions for 3rd Class Maths can be of great help. Available for free, Vedantu’s NCERT Solutions for Class 3 Maths can be an invaluable tool for you that helps you do your homework and prepare for your exam. These solutions are created as per the guidelines provided by the CBSE to help you with your exam preparation and daily learning. These are well-researched solutions created by top experts in the field. The answers correspond to the NCERT textbooks. You will be able to find the solution to all the exercise problems from each chapter in these solution guides.

We have ensured that all the answers are provided in an easy to understand and clear language. They are also supplemented with illustrations and graphics so that you have a better understanding of the concept. You can use these for quick correction between your tests and exams.

NCERT Solutions for Class 3 Maths Chapters

Chapters summary.

NCERT Maths Class 3 textbook follows the prescription of the CBSE board and is part of the CBSE NCERT Mathematics Class 3 curriculum. It is the primary source for this topic. The terminology, formulas, and analogy of the chapters are explained in a neat and simplified format.

Additionally, the student is provided with wonderful illustrations, diagrams, and different schematics to understand its applications and purpose in our world. The numerical problems are written in a simple step-by-step format to establish a strong foundation of the topic. Our subject experts have meticulously curated these NCERT Solutions for 3rd Class Maths to provide an overall knowledge base for the chapter.

Class 3 Maths Chapter-Wise Marks Weightage

This Class 3th Maths has a weightage of 50 marks. This subject is highly important from an exam point-of-view and to achieve your final grade. Basic questions on reasoning, current applications, and simple numerical keep repeating in exams from this subject, for which preparing from these study materials makes students score better.

If you are looking for NCERT Solutions for Class 3 Maths, it is recommended that you bookmark this page. This is a practical solution for your exam preparation. Since they are easy to understand, you will be able to finish your homework faster and prepare for your exam. These are 100% accurate and are explained in a step-by-step manner to help you understand them better.

As you are going through the page, you can find the chapter you want. Whether you are preparing for your final exams or just a random test for your class, you should use these solutions to get a better score.

NCERT Solutions for Class 3 Maths Chapter 1 - Where to Look From?

This chapter covers how you view an object from different sides, like from the top or the side. If you want to get a thorough understanding of this concept, you have to practice as many questions as you can.

NCERT Solutions for Class 3 Maths Chapter 2 Fun with Numbers

The ‘Fun with Numbers’ section covers counting numbers. The Maths Sums for Class 3 include word problems on addition and subtraction, number, and units.

NCERT Solutions for Class 3 Maths Chapter 3 Give and Take

This chapter covers the very important concept of addition. You will learn some techniques through which you can calculate the sum easily and quickly. Make sure that you solve all the problems as it will help you develop your skills.

NCERT Solutions for Class 3 Maths Chapter 4 Long and Short

The ‘Long and Short’ chapter covers the different length units, including centimetres, meters, and kilometres. By practising all the Maths Sums for Class 3 that are given in this chapter, you will have improved knowledge of the concept, which will come in handy in your higher classes as well as your daily life.

NCERT Solutions for Class 3 Maths Chapter 5 Shapes and Designs

In the ‘Shapes and Designs’ chapter, you will be learning about shapes, edges, and corners. The concepts that you learn in this chapter will not only help you with your exam but also improve your mental aptitude.

NCERT Solutions for Class 3 Maths Chapter 6 Fun with Give and Take

This chapter is all about addition and subtraction. There are a lot of Maths Sums for Class 3 that will help you understand the concept better and improve your accuracy and speed.

NCERT Solutions for Class 3 Maths Chapter 7 Time Goes on

As the name of the chapter suggests, this chapter is all about time. You will be learning about seconds, minutes, and hours. This chapter also covers the concept of a calendar which includes days, weeks, months, and years.

NCERT Solutions for Class 3 Maths Chapter 8 Who is Heavier?

The ‘Who is Heavier’ chapter is about weights and balance. There are solved examples, stories, puzzles, and Maths Sums for Class 3 that you can use for practising.

NCERT Solutions for Class 3 Maths Chapter 9 How Many Times?

The ‘How many times?’ The chapter covers multiplication. You will be learning about the connection between multiplication and addition through puzzles and Maths Sums for Class 3. It is a fun chapter that will form the foundation for advanced concepts in higher classes.

NCERT Solutions for Class 3 Maths Chapter 10 Play with Patterns

In the ‘Play with Patterns’ chapter, you will be learning about patterns and sequences. Through Maths Sums for Class 3 and puzzles, you will be able to develop the important mental skill of recognizing patterns.

NCERT Solutions for Class 3 Maths Chapter 11 Jugs and Mugs

This chapter is all about measurements. To help you get a broader understanding of the concept, the exercises cover word problems as well as puzzles.

NCERT Solutions for Class 3 Maths Chapter 12 Can We Share?

This is the chapter that will cover division. Apart from the introduction, it also includes some word problems and puzzles that will be fun to solve. Lastly, you will be learning about how multiplication and division are connected to each other.

NCERT Solutions for Class 3 Maths Chapter 13 Smart Charts

The Smart Charts chapter is all about representing data visually. You will be learning about what are smart smarts and how you can use them to depict any form of data.

NCERT Solutions for Class 3 Maths Chapter 14 Rupees and Paise

This chapter covers currency. Indian currency is rupees and paise. You will be learning about the different types of notes and coins that are available in the country. The exercises given in this chapter will cover some word problems on the same.

Importance of NCERT Solutions for Class 3 Maths

NCERT (National Council of Educational Research and Training) was created to standardize India’s education system. Vedantu’s NCERT Solutions for Class 3 Maths can be helpful in providing you with an in-depth and detailed understanding of all the concepts and questions given in NCERT textbooks. Apart from this, there are several benefits of referring to the NCERT Solutions for 3rd Class Maths:

Every Concept is Explained in Detail

The NCERT Solutions for 3rd Standard Maths has a detailed explanation of all the concepts. Our subject matter experts have explained the concepts in an easy language so that you are able to understand the concepts better and score better in your exams.

Accurate Solutions

Our subject matter experts who have designed the NCERT solutions for Class 3 Maths have years of experience as teachers. They review all the solutions so that you have an accurate guide for NCERT Solutions and are not misguided by the study materials.

Learn Offline

Vedantu’s NCERT Solutions for 3rd Standard Maths for all the chapters are available in PDF format so that you can download them and learn the subject offline. You will be able to access these solutions anytime and anywhere. You can even share the links of PDFs with your classmates.

Clear Your Doubts

If you have any confusion regarding any topic in Class 3 Maths, you can use Vedantu’s NCERT Solutions for Class 3 Maths to clear them. All the solutions have been explained in an easy language so that you can clear your concepts and doubts easily.

Created By The Best Experts

Vedantu’s NCERT Solutions for 3rd Class Maths are designed by a top expert math teacher who has years of experience teaching the subject. This is high-quality study material that will help you score better in your exam. The solutions are created after extensive research on the subject. Once you have your concepts cleared, you will be able to solve a wide range of problems.

Revise Topics Easily

If you want to score well in the exams, it is important to have a good command over the Maths chapters. So, these solutions have been crafted by the experts to ensure your proper revision before exam time. Students don’t have to go through the entire textbook as they can solve the given questions and complete the syllabus in time.

Understand the Exam Pattern

The experts at Vedantu have crafted the solutions according to the CBSE guidelines. Thus, students can refer to these solutions and figure out the exam pattern and answering format easily. They can devise a proper answering strategy to score good marks in the exams.

Rectify Any Mistakes

In case you have made any mistakes while answering the questions, you can now compare your answers to the NCERT solutions and rectify the mistakes. You can find out the topics in the chapters where you might make mistakes and improve your learning experience.

How Can Parents Help Their Kids With Their Studies?

Assisting your kid with their studying can be tough, especially if you are not sure where to start. Here are a few suggestions that will help you assist your child and inculcate healthy study habits in your child.

Know When to Reassess

If you want your kids to get an understanding of the concepts, you need to make them engage actively with the material. This includes questioning and discussing their learning and helping them relate what they are learning in their classroom to the outside leaves. When your kid is studying at home, they should be the one doing the heavy lifting involving studying and recalling and not you. If you feel like you are doing more than your kid, it might be time to reassess their studying habits and assess.

Rereading Doesn’t Always Work

Rereading has certain benefits. However, it is possible that your child can spend this time doing something better, especially if they are reading the same paragraph repeatedly. It might have happened to you as well when you are trying to read a paragraph but end up realizing that you don’t have any idea about what you read. The same can happen with your child as well, especially if there are distractions around like phones.

Limit the Distractions

It is your job as a parent, especially to a kid in Class 3, that there are no distractions around them. After they have finished studying without getting distracted, you can offer them small rewards. Keep in mind that no one can multitask effectively. If they are paying attention to their favourite song or show or answering a text, they are not paying attention to your studies.

Ask Questions

You have to quiz your child on the material while providing a few hints as you can. It will help them realize the concepts they know and what they don’t. It will also eliminate the false sense of knowledge accompanied by guessing correctly. Even though guessing isn’t bad, you don’t want your child to have a false sense of mastery. In fact, when they answer a question, question the reasoning behind it. Before having on, have them answer correctly several times.

Discuss Stumbling Blocks

Make your child write down all the major concepts related to the material, followed by making them explain their understanding of the concepts without heavily relying on the notes. If they are stumbling, especially after being given a small hint, it means that they haven’t mastered the concept yet. Ask them calmly to explain what confuses them. Discussing the concepts will help them recover and move on. In case this tactic doesn’t work, ask them to write down everything they know about the subject. It helps jog their comprehension.

When Possible, Ask Recall Questions

There are three forms of recognition questions - multiple-choice, fill-in-the-blank, and matching questions. In Maths Sums for Class 3, students have a corresponding word bank from which they have to recognize the right answer. Even though working on these kinds of questions every now and then is fine, you shouldn’t focus on them. You have to focus on recall Maths Sums for Class 3 as they involve no hints and are more challenging. You can even transform a recognition question into a recall question by asking the question to your child without providing them with the option. If your kid flounders, ask them to explain anything that they can recall about the concept. More often than not, they will recall the correct response along with other important details.

If you are unable to help your child, you can still remind them to quiz themselves, remove distractions, and take short breaks, especially during long study sessions. By using the above-mentioned tips, your child will have more effective and efficient study habits which would mean more learning, better marks, and a more motivated student.

Why Are Vedantu's Solutions Best?

The NCERT Solutions for 3rd Class Maths are great when you want something for your last day's preparation. It comes with solutions to the questions as well as an explanation of the concept. To get the most of your practice time, you can solve all the subject-related questions in one go without getting stuck on any one question. The solutions include chapter-by-chapter solutions and simplified points that are in line with the CBSE curriculum. These solutions are very useful for you because of the fact that they contain detailed answers to every single problem given in your textbook. It is the perfect way to have a fun learning experience.

After you are done with your lessons and homework, you can refer to these solutions to know whether or not you solved them correctly. It is important to note that you don’t have to finish your NCERT Maths textbook before you start using the NCERT Solutions for Class 3 Maths . You can read the book line by line and understand the concepts better.

If you want to score well in your exam, having a good command of your NCERT textbook will be enough. You need to go through all the examples and the questions from the exercises. First, try solving the Maths Sums for Class 3 all by yourself.

In order to ensure that your concepts are crystal clear, Vedantu’s NCERT Solutions for 3rd Standard Maths have a structure that clarifies all the Mathematical concepts to you. Vedantu has made sure that all the answers and facts in their solutions are not unnecessarily stretched.

The information that you obtain from the solutions will help you become aware of what you should know and what you should expect while preparing for your final exams. Once you become familiar with the structure of the exam and practice the questions from Vedantu’s NCERT Solutions for 3rd Class Maths, your confidence level will increase which will have an impact on your exam performance. This will, in turn, lead to better results. It is important to note that the support and benefits of this module does not end with your exam.

Not everyone has the required language skills to understand the concepts without wasting any time. With NCERT Solutions for Class 3 Maths , you will have a guide for preparation, practicing, and revision. You will be able to score well in your final exam. If you are having any difficulty in solving Maths Sums for Class 3 from your NCERT textbooks or are not able to approach the problem, Vedantu’s NCERT Solutions are available to you for free.

Download Chapter Wise List of Class 3 Maths Solutions For Better Results

The NCERT Solutions provided for Class 3 Maths are extremely valuable to students who want to prepare for their exams in the best way. These solutions come with detailed explanations and steps to ensure that students get a proper explanation of the different mathematical concepts. To make the most out of your practice, download the Class 3rd Maths Book Answers from the official website of Vedantu. After you have completed studying the chapters in the textbook, practice with the solutions to make sure that your preparation is properly done for the final exams.

Important Related Links for NCERT Class 3 Maths

NCERT Books for CBSE Class 3 Maths

CBSE Worksheet for Class 3 Maths

CBSE Class 3 Syllabus for Maths

FAQs on NCERT Solutions For class 3 Maths

1. What Do NCERT Solutions for 3rd Class Maths Teach Students?

Mathematics plays a key role in our world. Our world uses the subject of Maths to help us measure, read time, and weigh objects. A student is required to learn how to calculate and measure accurately. Class 3 Maths for NCERT solutions provides a strong base on the core concepts of the subject and gears a student to face the world. Learning and practising these concepts helps a student grow confident in their abilities and understanding of the subject.

2. What is the Important Chapter to be Focused on in NCERT Class 3 Maths?

A student at a young age must strengthen their basics. The mind is the most skilled and vast possession’ in terms of using logic. Class 3 Maths helps a student harness the power of logic and guides them to learn extremely valuable skills that could guide their career to greater heights. All chapters prescribed for Class 3 Maths are basic foundation chapters of prime importance. Chapters dealing with money, measurement, and time are the key components utilized in our daily lives.

3. How can you use NCERT Solutions for 3rd Class Maths?

In order to use Class 3 Maths NCERT Solutions effectively, you need to make sure that you have an in-depth understanding of the concepts used for solving the problems. This way, when you are consulting these solutions, you will be able to comprehend these concepts in a better way and retain what you have learned efficiently.

4. Should I make notes while referring to NCERT Solutions for 3rd Standard Maths?

Yes, these notes will become a simplified guide you can use for building an in-depth understanding of the concepts or while revising before the exam. It will also help you recall and retain concepts when required. That is why it is important that you make notes while referring to NCERT Solutions for Class 3 Maths in order to expedite your learning process.

5. What is the best way to learn the concepts that are covered in NCERT Solutions for Class 3 Maths?

The best way to learn concepts covered in the NCERT Solutions for Class 3 Maths is to practice these solutions constantly. If you find any concept difficult and are not able to proceed further while attempting a question, you can clarify your doubts immediately to ensure that you don’t have any learning gap.

6. Can you use other methods for solving problems other than the one used in NCERT Solutions for Class 3 Maths?

Yes, you can use the method that is given in NCERT Solutions for Class 3 Maths . However, you have to make sure that the approach we use and the answer you get is universally recognized. You should not use any tricks in solving the problems as they are not standardized techniques. You won’t be able to score full marks by using such tricks.

7. Why choose Vedantu for NCERT Solutions for 3rd Class Maths?

Vedantu is one of the best websites you can use for Class 3 Maths NCERT Solutions . These solutions have been created by the top subject matter experts with years of experience in the field. They are precise, reliable, and provide the best techniques you can use to solve any problem. We also provide some tips you can use for solving sums with accuracy and speed.

8. How many chapters are there in NCERT Solutions for 3rd Standard Maths?

There are a total of 14 chapters in Class 3 Maths NCERT Solutions . All the problems covered in this can be used to improve your understanding of all the concepts. You will get an in-depth analysis of all the problems.

9. Do you have to practice all the questions given in the NCERT Solutions for Class 3 Maths?

All the solutions that are provided in Vedantu’s NCERT Solutions for Class 3 Maths are based on the curriculum. If you want to get good marks, you have to be well-versed with every question that is given in the Class 3 Maths NCERT textbook. If you practice regularly using these solutions, you will be able to score well in your exam.

10. Are NCERT Solutions for Class 3 Maths enough for CBSE exams?

Vedantu’s NCERT Solutions for Class 3 Maths are enough for the CBSE exam. The school teachers usually set the paper that includes Maths Sums for Class 3 from the NCERT books. There might be some difference in the values or language. However, the approach to solving these problems will be more or less the same. If you have a robust knowledge of all the chapters, you will be able to solve the problems and clear the examination successfully.

11. Where can I find chapter-wise solutions for NCERT Solutions for 3rd Standard Maths?

You can use the links given on this page to access the chapter-wise solutions for NCERT Class 3 Maths . All the chapters have exercise-wise solutions pdf that you can download for free. These pdfs are in a scrollable format and compatible with mobile screens which will make it easy for you to use them.

12. What is the syllabus of Maths of Class 3?

The syllabus of class 3 Maths comprises basic foundational concepts like addition, subtraction, multiplication, and division. For gaining more insights on this chapter, students are advised to download the NCERT Solutions and prepare for their exams. By practising regularly students will get well versed in each chapter. With the help of these solutions, students will be able to clarify all their doubts and prepare themselves to secure a perfect score in the exams.

13. What does Class 3 Addition cover?

Class 3 addition covers the fundamental concept of adding two or more numbers. For example - 10+5 gives 15. The NCERT Solutions that Vedantu provides help the students understand the concepts better. These solutions are created by the subject experts to help the students clarify their doubts and prepare for the exams well. Download the pdf for free of cost on the Vedantu website as it will help the kids master these basic concepts and ace their exams at their own pace.

14. What is a fraction in Maths for Class 3?

A fraction represents a portion or a part of the whole. A fraction consists of a numerator and a denominator. 3/9 forms a fraction. 3 here is the numerator and 9 is the denominator. Learning about fractions might be tricky and Vedantu provides simplified instructions and numerous examples to make the learning fun. These solutions are carefully crafted by a qualified group of subject experts to help the score well in the exam. Students can download the PDF of the NCERT Solutions on Vedantu’s website for free of cost.

15. How many chapters are there in NCERT Solution for Class 3 in Maths?

There are eight Chapters in Class 3 Maths, NCERT Solutions. To learn all the chapters and the basic concepts, students are advised to download the NCERT solution provided by Vedantu. Vedantu is one of the most trusted online learning spaces that help students ace their exams. These solutions are carefully created by the experts for the students to prepare for their exams. With constant practice, students can excel in all these concepts. The solutions are also available on Vedantu’s website(vedantu.com) the Vedantu Mobile app at free of cost.

16. How do the NCERT solutions for maths help the students of Class 3?

NCERT Solutions for Maths contain all important questions that will help the students practice all the detailed solutions created by the subject experts. Since these questions are created following the CBSE syllabus, students can practice all the questions at their own pace. NCERT solutions come with sample question papers to help the students get well versed in all the chapters and ace their exams.

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5 Problem-Solving Activities for the Classroom

Problem-solving skills are necessary in all areas of life, and classroom problem solving activities can be a great way to get students prepped and ready to solve real problems in real life scenarios. Whether in school, work or in their social relationships, the ability to critically analyze a problem, map out all its elements and then prepare a workable solution is one of the most valuable skills one can acquire in life.

Educating your students about problem solving skills from an early age in school can be facilitated through classroom problem solving activities. Such endeavors encourage cognitive as well as social development, and can equip students with the tools they’ll need to address and solve problems throughout the rest of their lives. Here are five classroom problem solving activities your students are sure to benefit from as well as enjoy doing:

1. Brainstorm bonanza

Having your students create lists related to whatever you are currently studying can be a great way to help them to enrich their understanding of a topic while learning to problem-solve. For example, if you are studying a historical, current or fictional event that did not turn out favorably, have your students brainstorm ways that the protagonist or participants could have created a different, more positive outcome. They can brainstorm on paper individually or on a chalkboard or white board in front of the class.

2. Problem-solving as a group

Have your students create and decorate a medium-sized box with a slot in the top. Label the box “The Problem-Solving Box.” Invite students to anonymously write down and submit any problem or issue they might be having at school or at home, ones that they can’t seem to figure out on their own. Once or twice a week, have a student draw one of the items from the box and read it aloud. Then have the class as a group figure out the ideal way the student can address the issue and hopefully solve it.

3. Clue me in

This fun detective game encourages problem-solving, critical thinking and cognitive development. Collect a number of items that are associated with a specific profession, social trend, place, public figure, historical event, animal, etc. Assemble actual items (or pictures of items) that are commonly associated with the target answer. Place them all in a bag (five-10 clues should be sufficient.) Then have a student reach into the bag and one by one pull out clues. Choose a minimum number of clues they must draw out before making their first guess (two- three). After this, the student must venture a guess after each clue pulled until they guess correctly. See how quickly the student is able to solve the riddle.

4. Survivor scenarios

Create a pretend scenario for students that requires them to think creatively to make it through. An example might be getting stranded on an island, knowing that help will not arrive for three days. The group has a limited amount of food and water and must create shelter from items around the island. Encourage working together as a group and hearing out every child that has an idea about how to make it through the three days as safely and comfortably as possible.

5. Moral dilemma

Create a number of possible moral dilemmas your students might encounter in life, write them down, and place each item folded up in a bowl or bag. Some of the items might include things like, “I saw a good friend of mine shoplifting. What should I do?” or “The cashier gave me an extra $1.50 in change after I bought candy at the store. What should I do?” Have each student draw an item from the bag one by one, read it aloud, then tell the class their answer on the spot as to how they would handle the situation.

Classroom problem solving activities need not be dull and routine. Ideally, the problem solving activities you give your students will engage their senses and be genuinely fun to do. The activities and lessons learned will leave an impression on each child, increasing the likelihood that they will take the lesson forward into their everyday lives.

My Problem-Solving Journal 3rd Class

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'Third Millennium Thinking': How to use scientific tools to solve everyday problems

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Emiko Tamagawa

The cover of "Third Millennium Thinking" and author Saul Perlmutter. (Courtesy of Little, brown & Company and Jon Schainker)

Life is full of decisions. “ Third Millennium Thinking: Creating Sense in a World of Knowledge ” outlines methods of making choices rationally using scientific methods.

Nobel Prize-winning physicist Saul Perlmutter , philosophy professor John Campbell , and social psychologist Robert MacCoun turned their course at the University of California Berkeley on using scientific tools to approach everyday problems into a book.

Perlmutter says it's easy to fall into mental traps or fool ourselves when making a choice. But when people assess all the variables that could influence them and the potential outcomes, they approach questions more thoughtfully, he says.

“There is so much of what is the scientific approach to the world that is never taught anywhere,” Perlmutter says. “It seemed like this was a time for us to be trying to figure out how can we teach this in ways that don't require having to become a scientist in order to do it.”

Book excerpt: 'Third Millennium Thinking: Creating Sense in a World of Nonsense'

By Saul Perlmutter, John Campbell and Robert MacCoun

INTRODUCTION

In just the past few decades, those of us who live in the internet-connected world have obtained access to a nearly unfathomable amount of information. We can click a link and instantly gain insight into whatever we’re curious about, whether it’s treatment options for a particular health condition, how to build a solar generator, or the political history of Malta. On the other hand, sometimes there is so much information we don’t know how to sort or evaluate it. The social science database ProQuest, for example, boasts of “a growing content collection that now encompasses . . . 6 billion digital pages and spans six centuries.” And that’s just old-school, print information! The Internet Archive’s Wayback Machine, an archive of websites and other digital artifacts dating back to 1996, hosts almost a trillion pages of digital content, tens of millions of books and audios, and nearly a million software programs.

More and more often, it can be hard to determine what to focus on, let alone how to distinguish what’s revelatory and enlightening, in and among all the highly technical, specialized, contradictory, incomplete, out‑of‑date, biased, or deliberately untrue information we can now access. Was that drug study funded by a pharmaceutical company? Did an AI system invent all those supposedly authentic product reviews? What do those statistics leave out? What does that article even mean ? It is also increasingly tricky to identify whom to trust for expert guidance in interpreting this information. There are all sorts of people out there who claim expertise — and perhaps your favorite experts aren’t my favorite experts. Experts disagree, or have ulterior motives, or perhaps don’t understand the world or “real life” beyond their own narrow perspective. How do we find an expert we can safely trust?

To make a sound decision, take a meaningful action, or solve a problem — whether as individuals, in groups, or as a society — we need first to understand reality. But when reality is not easy to discern, and we’re not sure which experts to trust to clarify the matter, we adopt other strategies for navigating the clutter. We “go with our gut”; decide what we “believe” and look for evidence to reaffirm whatever that is; adopt positions based on our affiliations with people we know; even find reassurance in belittling the people who disagree with us. We choose to consult experts who tell us what we like to hear; or bond in shared mistrust of people providing or communicating the information that confuses us, whether they are scientists, scholars, journalists, community leaders, policymakers, or other experts. These coping strategies may help us get by in our personal or professional lives; they may provide a consoling sense of identity or belonging. But they do not actually help us see clearly or make good decisions. And resorting to them can have dangerous social and political consequences.

How can we navigate better — as individuals, and as a society — in this age of informational overwhelm? How do we ward off confusion, avoid mental traps, and sift sense out of nonsense? How do we make decisions and solve problems collaboratively with people who interpret information differently or have different values than we do?

The three of us — a physicist (Saul), a philosopher ( John), and a psychologist (Rob) — have been working closely together for nearly a decade on a project to help our students learn to think about big problems and make effective decisions in this “too much information” age. We began our collaboration in 2011, in response to what was already a worrying trend toward no‑think, politics-driven decision-making. An issue like raising the national debt ceiling, for example, was being debated that summer as if it were a religious schism, rather than a simple, practical, probably even testable question of what economic approach would work best to improve the country’s economic well-being. Most of the arguments both yea and nay betrayed equal disregard for, or ignorance of, the most basic principles of scientific thought. We began to wonder whether it might be possible to first articulate and then teach the principles that would lead to clearer thinking, more rational arguments, and a more fruitful collaborative decision-making process.

The result was a team-taught, multidisciplinary Big Ideas course at UC Berkeley, intended to teach students the whole gamut of ideas, tools, and approaches that natural and social scientists use to understand the world. We also designed the course to show how useful these approaches can be for everybody in day‑to‑day life, whether working individually or collaboratively, in making reasoned decisions and solving the full range of problems that face us. To our great satisfaction, the course has been both popular and successful, and has since been replicated and adapted by other teachers at a growing number of other universities.1 Our students appear to rethink their worlds and emerge energized with new ways to approach both personal decision-making and our society’s problems. They are better able to investigate their questions, evaluate information and expertise, and work together as members of a group or a society. Inspired by their enthusiasm, we began to think about new ways to share these tools — and this new way of thinking and working together — beyond the classroom, with students and citizens of all ages.

We have become ever more concerned that our society is losing its way, causing suffering — and missing great opportunities — simply because we don’t have the tools that could help us make sense of the extraordinary amount of complex, often contradictory information now available to us. Practical problem-solving can come to a standstill when we cannot ascertain the facts of the problems, or, when those problems require communal or political solutions, even agree with others on what those facts are. We humans, who can figure out rocket science and fly to the moon, can’t always figure out how to navigate uncertainty and conflicting points of view to make a simple reasonable decision when we need to.

Part of the problem is that science itself is often a major source of the highly technical, opaque, inconsistent, and contradictory information that has overwhelmed, perplexed, and even angered people. Trust in science has eroded in the recent past.2 The achievements of science cannot live up to all the utopian expectations those successes have generated. Some scientific achievements have also come with negative social, political, or environmental side effects. For these and other reasons, science has become one of the totems of polarization in political discussions. In short, as science became harder to understand, was connected to undesirable side effects, and subjected to politically partisan critiques, many people lost their trust in scientists and in “science” itself.3

But science also has a phenomenal record of providing insight into — if not answers to — the most confounding questions humans have thought to ask. It has helped us to solve puzzles, address problems, and make better lives over millennia. It is a culture of inquiry rooted in the dawn of humankind, with centuries of practice in evaluating conflicting information in a baffling world, and in distinguishing what we know from what we don’t. Along the way, scientists have learned from both successes and mistakes, breakthroughs and blunders, to refine the tools with which to address new questions and solve new problems.

Over the past few years, we have all become aware of the shocking degree of polarization in our society, and the surprising interaction between this polarization and our society’s often-problematic relationship to science and scientific expertise. If we are to have any hope of finding the practical common plans and common understandings that can move our society ahead together, we need to learn to accept the possibility of errors in our own thinking, and our need for opposing views that help us see where we are going wrong. And we need to understand the source of the disenchantment with and backlash against scientific progress that arose during the end of the Second Millennium and seek to repair it.

No one book and no single approach can heal the rifts. Not all of our polarized disagreements will vanish. But we have to start somewhere. And we believe that one of our more promising starting points is with the culture of science — if we begin to borrow its tools, ideas, and processes, and make a Third Millennium shift in our own thinking.

Adapted from "Third Millenium Thinking" by Saul Perlmutter, John Campbell, and Robert MacCoun. Copyright © 2024 by Saul Perlmutter, John Campbell, and Robert MacCoun. Used with permission of Little, Brown Spark, an imprint of Little, Brown and Company. New York, NY. All rights reserved.

Emiko Tamagawa produced and edited this interview for broadcast with Todd Mundt . Grace Griffin adapted it for the web.

This article was originally published on March 26, 2024.

This segment aired on March 26, 2024.

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Solving the ‘3 Body Problem’

Unpacking netflix’s new hit with the times’s cosmic affairs correspondent..

Produced by Alex Barron

Edited by Lynn Levy

Engineered by Efim Shapiro

Featuring Dennis Overbye

The show “3 Body Problem” premiered on March 21 and quickly became one of Netflix’s most-watched titles. It is an adventure story about a group of scientists contending with an extraterrestrial threat. But despite its science fiction trappings, the show is often based in real — and complex — scientific concepts, whether string theory or nanomaterials. In this episode, Dennis Overbye, The Times’s cosmic affairs correspondent, breaks down some of the more brain-bending science behind “3 Body Problem.”

On today’s episode

Dennis Overbye is the cosmic affairs correspondent for The Times, covering physics and astronomy.

The New York Times Audio app is home to journalism and storytelling, and provides news, depth and serendipity. If you haven’t already, download it here — available to Times news subscribers on iOS — and sign up for our weekly newsletter.

Dennis Overbye is the cosmic affairs correspondent for The Times, covering physics and astronomy. More about Dennis Overbye

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Aliens attack science in '3 Body Problem,' a new adaptation of a Chinese sci-fi novel

Eric Deggans

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem. Maria Heras/Netflix hide caption

The new Netflix series brings to life a sprawling, successful Chinese novel outlining a new kind of alien invasion. Above, Zine Tseng in 3 Body Problem.

My favorite kind of science fiction involves stories rooted in real science — much as I love a good lightsaber or phaser fight, there is something special about seeing characters wrestle with concepts closer to our current understanding of how the universe works.

That's why I enjoy so much of what happens in Netflix's 3 Body Problem , the TV series which brings to life a sprawling, successful Chinese novel rooted in science, outlining a new kind of alien invasion.

Book Reviews

'three-body problem' asks a classic sci-fi question, in chinese.

3 Body Problem actually starts with two problems. First, we meet investigators tackling a string of unexplained suicides by scientists, including one who had a bizarre countdown written on the walls of his home in blood with his eyes gouged out. (Fortunately, viewers only see the horrific aftermath.) Benedict Wong plays one of those investigators, continually lightening the show's ominous vibe with his spot-on portrayal of a world-weary gumshoe tracking the world's biggest mystery with a healthy dose of gallows humor.

Benedict Wong plays Da Shi in 3 Body Problem. Ed Miller/Netflix hide caption

Benedict Wong plays Da Shi in 3 Body Problem.

"One of the betting sites had him picked as a favorite for the next Nobel Prize in physics," Wong's assistant tells him of the scientist who died.

"You can bet on that?" Wong's character replies, looking over the gruesome scene.

Tracking why science is broken

The other problem which surfaces immediately is that science seems to have stopped working. Researchers are reporting results from experiments in supercolliders that make no sense, putting the lie to all our accepted theories of physics. Saul Durand — played by Jovan Adepo, Durand is one among a group of brilliant, young scientist friends at the center of the story — notes simply, "science is broken."

Jovan Adepo and Jin Cheng in 3 Body Problem. Ed Miller/Netflix hide caption

Jovan Adepo and Jin Cheng in 3 Body Problem.

This all adds up to a unique attack on humanity's scientific progress. But who – or what – is behind these bizarre occurrences, involving events which don't seem possible in the modern world?

Netflix's show takes its time unveiling the full scope of the story and answering these questions, which leads to the third problem here. It takes a while for the series' narrative to really gain momentum – my advice is to hang on through the first three episodes (yes, I also hate streaming shows which ask this of beleaguered viewers; but in this case, it's worth it).

The pacing may not be a surprise, given that two of the series' three creators are David Benioff and D.B. Weiss, former showrunners of HBO's Game of Thrones , which had its own problems with narrative flow at times (the third creator is former True Blood writer/executive producer Alexander Woo). Once the show does find its groove, the series builds into an epic science fiction tale with eye-popping special effects – the tragic destruction of a huge ship packed with people is one that stuck with me long after viewing — and a timeline stretching from China's 1960s-era cultural revolution to the present day.

Bringing a Chinese sci fi-literary triumph to TV

Netflix's 3 Body Problem is based on a 2008 novel from Chinese engineer and science fiction writer Liu Cixin; the original novel became a book series touted by big names like Barack Obama. It managed the neat trick of popularizing Chinese science fiction internationally while delivering compelling observations on the nature of humanity's societal and technological progress, some of which actually find their way into the TV show.

Cultural Revolution-Meets-Aliens: Chinese Writer Takes On Sci-Fi

It makes sense that a story like this — which crosses between Western and Chinese culture to tell the story of a planet under threat – would be cracked by Netflix. The streaming service has educated a generation of American customers to appreciate smart, entertaining TV from South Korea, Latin America, Europe and elsewhere across the globe.

So kicking off 3 Body Problem with a scene showing a young Chinese scientist watching an angry mob murder her father – who is also a scientist – during the purges of China's cultural revolution feels daring and entirely on brand. Later on, that younger scientist, fueled by hate and loss, will make a decision that puts the entire planet at risk, showing how disappointment in humanity's missteps can lead to desperate, misguided solutions.

Fans of the books will find some tweaks here to make for better television, amping up the thriller elements of the story to ask a compelling question: How to fight an alien enemy targeting the world's scientific progress?

As the characters in 3 Body Problem lurch toward answers, we all get to bask in an ambitious narrative fueling an ultimately impressive tale. Just remember to be patient as the series sets the stage early on.

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A high-order B-spline collocation method for solving a class of nonlinear singular boundary value problems

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Published: 26 March 2024

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Pradip Roul 1

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A high-order numerical scheme based on collocation of a quintic B-spline over finite element is proposed for the numerical solution of a class of nonlinear singular boundary value problems (SBVPs) arising in various physical models in engineering and applied sciences. Five illustrative examples are presented to illustrate the applicability and accuracy of the method. In order to justify the advantage of the proposed numerical scheme, the computed results are compared with the results obtained by two other fourth-order numerical methods, namely the finite difference method (Chawla et al. in BIT 28(1):88–97, 1988) and B-spline collocation method (Goh et al. in Comput Math Appl 64:115–120, 2012).

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An optimal computational method for a general class of nonlinear boundary value problems

Pradip Roul, V. M. K. Prasad Goura & Ravi Agarwal

A fast numerical scheme for solving singular boundary value problems arising in various physical models

Pradip Roul & V. M. K. Prasad Goura

A high-order numerical method for solving nonlinear derivative-dependent singular boundary value problems using trigonometric B-spline basis function

Mohammad Prawesh Alam & Arshad Khan

Data availability

No datasets were generated or analysed during the current study.

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The 3-body problem is real, and it’s really unsolvable

Oh god don’t make me explain math

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Rosalind Chao as Ye Wenjie standing in the middle of three overlapping circles

Everybody seems to be talking about 3 Body Problem , the new Netflix series based on Cixin Liu’s Remembrance of Earth’s Past book trilogy . Fewer people are talking about the two series’ namesake: The unsolvable physics problem of the same name.

This makes sense, because it’s confusing . In physics, the three-body problem attempts to find a way to predict the movements of three objects whose gravity interacts with each of the others — like three stars that are close together in space. Sounds simple enough, right? Yet I myself recently pulled up the Wikipedia article on the three-body problem and closed the tab in the same manner that a person might stagger away from a bright light. Apparently the Earth, sun, and moon are a three-body system? Are you telling me we don’t know how the moon moves ? Scientists have published multiple solutions for the three-body problem? Are you telling me Cixin Liu’s books are out of date?

All I’d wanted to know was why the problem was considered unsolvable, and now memories of my one semester of high school physics were swimming before my eyes like so many glowing doom numbers. However, despite my pains, I have readied several ways that we non-physicists can be confident that the three-body problem is, in fact, unsolvable.

Reason 1: This is a special definition of ‘unsolvable’

Jin Cheng (Jess Hong) holds up an apple in a medieval hall in 3 Body Problem.

The three-body problem is extra confusing, because scientists are seemingly constantly finding new solutions to the three-body problem! They just don’t mean a one-solution-for-all solution. Such a formula does exist for a two-body system, and apparently Isaac Newton figured it out in 1687 . But systems with more than two bodies are, according to physicists, too chaotic (i.e., not in the sense of a child’s messy bedroom, but in the sense of “chaos theory”) to be corralled by a single solution.

When physicists say they have a new solution to the three-body problem, they mean that they’ve found a specific solution for three-body systems that have certain theoretical parameters. Don’t ask me to explain those parameters, because they’re all things like “the three masses are collinear at each instant” or “a zero angular momentum solution with three equal masses moving around a figure-eight shape.” But basically: By narrowing the focus of the problem to certain arrangements of three-body systems, physicists have been able to derive formulas that predict the movements of some of them, like in our solar system. The mass of the Earth and the sun create a “ restricted three-body problem ,” where a less-big body (in this case, the moon) moves under the influence of two massive ones (the Earth and the sun).

What physicists mean when they say the three-body problem has no solution is simply that there isn’t a one-formula-fits-all solution to every way that the gravity of three objects might cause those objects to move — which is exactly what Three-Body Problem bases its whole premise on.

Reason 2: 3 Body Problem picked an unsolved three-body system on purpose

A woman floating in front of three celestial bodies (ahem) in 3 Body Problem

Henri Poincaré’s research into a general solution to the three-body problem formed the basis of what would become known as chaos theory (you might know it from its co-starring role in Jurassic Park ). And 3 Body Problem itself isn’t about any old three-body system. It’s specifically about an extremely chaotic three-body system, the exact kind of arrangement of bodies that Poincaré was focused on when he showed that the problem is “unsolvable.”

[ Ed. note: The rest of this section includes some spoilers for 3 Body Problem .]

In both Liu’s books and Netflix’s 3 Body Problem , humanity faces an invasion by aliens (called Trisolarans in the English translation of the books, and San-Ti in the TV series) whose home solar system features three suns in a chaotic three-body relationship. It is a world where, unlike ours, the heavens are fundamentally unpredictable. Periods of icy cold give way to searing heat that give way to swings in gravity that turn into temporary reprieves that can never be trusted. The unpredictable nature of the San-Ti environment is the source of every detail of their physicality, their philosophy, and their desire to claim Earth for their own.

In other words, 3 Body Problem ’s three-body problem is unsolvable because Liu wanted to write a story with an unsolvable three-body system, so he chose one of the three-body systems for which we have not discovered a solution, and might never.

Reason 3: Scientists are still working on the three-body problem

Perhaps the best reason I can give you to believe that the three-body problem is real, and is really unsolvable, is that some scientists published a whole set of new solutions for specific three-body systems very recently .

If physicists are still working on the three-body problem, we can safely assume that it has not been solved. Scientists, after all, are the real experts. And I am definitely not.

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If you want to engage them, maths questions for 3rd class and 4th class students need to do two things. Firstly, they need to show how they relate to everyday life. As we said, maths is all about problem-solving, and your 3rd and 4th class students need to understand that. Secondly, you need to make the problems and activities fun to engage ...
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Flexible schedule. In this Super Mario class, students will discover the many tips & tricks of learning their multiplication facts (numbers 0 - 12). Students will learn & engage with peers, solidify their comprehension with Nearpod activities & board games!
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Simple division word problems. After reading the word problem and understanding the 'real world scenario', the student must formulate the division equation to solve the problem. Only simple division is required. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.
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Class 3
Class 3. 7 units · 59 skills. Unit 1. Numbers from 1 to 1000. Unit 2. ... Test your knowledge of the skills in this course. Start Course challenge. Math; Class 3. 5,700 possible mastery points. Mastered. Proficient. Familiar. Attempted. Not started. Quiz. Unit test. ... Break apart 3-digit subtraction problems; Add on a number line; Subtract ...
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A high-order numerical scheme based on collocation of a quintic B-spline over finite element is proposed for the numerical solution of a class of nonlinear singular boundary value problems (SBVPs) arising in various physical models in engineering and applied sciences. Five illustrative examples are presented to illustrate the applicability and accuracy of the method. In order to justify the ...
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Math Message Boards FAQ & Community Help
Japan mathematical olympiad finals 2006, problem 3. Kunihiko_Chikaya 27. N Mar 25, 2024 by solasky. Find all functions defined on real numbers and taking real values such that for all real numbers. H. Increasing Subsequence Length. oVlad 6. N Mar 25, 2024 by mathhotspot. Source: KöMaL A. 759.

NCERT Solutions for Class 3 Maths

Class 3 Maths NCERT Solutions

Chapter-wise NCERT Solutions for Class 3 Maths

NCERT Solutions for Class 3 Maths Chapter 2 Fun with Numbers

NCERT Solutions for Class 3 Maths Chapter 3 Give and Take

NCERT Solutions for Class 3 Maths Chapter 4 Long and Short

NCERT Solutions for Class 3 Maths Chapter 5 Shapes and Designs

NCERT Solutions for Class 3 Maths Chapter 6 Fun with Give and Take

NCERT Solutions for Class 3 Maths Chapter 7 Time Goes on

NCERT Solutions for Class 3 Maths Chapter 8 Who Is Heavier?

NCERT Solutions for Class 3 Maths Chapter 9 How Many Times?

NCERT Solutions for Class 3 Maths Chapter 10 Play with Patterns

NCERT Solutions for Class 3 Maths Chapter 11 Jugs and Mugs

NCERT Solutions for Class 3 Maths Chapter 12 Can We Share?

NCERT Solutions for Class 3 Maths Chapter 13 Smart Charts

NCERT Solutions for Class 3 Maths Chapter 14 Rupees and Paise

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35 math problems for 3 rd graders

Answer sheet

35 Third Grade Math Problems

Section 2: Subtraction

Section 3: Multiplication

Practice 3rd grade math with DoodleMath

Section 4: Division

Section 5: Fractions

Section 6: Measurement

Section 7: Multi-step word problems

Addition answers

Subtraction answers

Multiplication answers

Division answers

Fractions answers

Measurement answers

Multi-step word answer answers

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Maths information pack

Information pack

3rd Grade Addition and Subtraction

3-digit and 4-digit Word Problems

3rd Grade Addition and Subtraction Word Problems

4-digit Addition and Subtraction Word Problems

Harder 2-Step Addition and Subtraction Word Problems

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NCERT Solutions for Class 3 Maths - Free PDF Download

Detailed Overview of Class 3 Maths NCERT Solutions

NCERT Solutions for Class 3 Maths | Chapter-wise List

NCERT Solutions for Class 3 Maths

Class 3 Maths NCERT Solutions - Free PDF Download

NCERT Solutions for Class 3 Maths Chapters

Class 3 Maths Chapter-Wise Marks Weightage

NCERT Solutions for Class 3 Maths Chapter 1 - Where to Look From?

NCERT Solutions for Class 3 Maths Chapter 2 Fun with Numbers

NCERT Solutions for Class 3 Maths Chapter 3 Give and Take

NCERT Solutions for Class 3 Maths Chapter 4 Long and Short

NCERT Solutions for Class 3 Maths Chapter 5 Shapes and Designs

NCERT Solutions for Class 3 Maths Chapter 6 Fun with Give and Take

NCERT Solutions for Class 3 Maths Chapter 7 Time Goes on

NCERT Solutions for Class 3 Maths Chapter 8 Who is Heavier?

NCERT Solutions for Class 3 Maths Chapter 9 How Many Times?

NCERT Solutions for Class 3 Maths Chapter 10 Play with Patterns

NCERT Solutions for Class 3 Maths Chapter 11 Jugs and Mugs

NCERT Solutions for Class 3 Maths Chapter 12 Can We Share?