division assignment for class 3

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3rd Grade Math Worksheets: Division

Free division worksheets.

Our 3rd grade division worksheets include i) simple division worksheets to help kids with their division facts and mental division skills and ii) an introduction to long division including simple division with remainder questions .  Practice dividing by tens and hundreds is also emphasized.

Sample Grade 3 Division Worksheet

More division worksheets

Explore all of our division worksheets , from simple division facts to long division of large numbers.

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Division Worksheets Grade 3 Solving Division Problems

Welcome to our Division Worksheets Grade 3 page.

Here you will find a wide range of free 3rd Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

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Division Worksheets Grade 3

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 3rd grade to the end.

The first two sheets involve drawing out different amounts in groups and solving simple problems which do not require any reasoning skills.

Sheets 3 to 5 involve understanding and working out division word problems that require a little more reasoning and thinking about.

Sheets 6 and 7 are the most complicated and involve division problems with remainders. In order to solve the word problem, the remainder needs to be rounded up or down, depending on the context.

Division Worksheets Grade 3 - Worksheets

Simple division worksheets problems.

• Division Problems Sheet 3.1
• PDF version
• Division Problems Sheet 3.2

Medium Level Division Word Problems

• Division Problems Sheet 3.3
• Division Problems Sheet 3.4
• Division Problems Sheet 3.5

Harder Division Problems (interpreting remainders)

• Division Problems Sheet 3.6
• Division Problems Sheet 3.7

Looking for some harder Division worksheets

Our 4th grade division worksheets are similar to those on this page but at a more challenging level.

The links below will take you to our division worksheets for 4th grade.

These sheets involve solving a range of division problems.

• Division Worksheets Grade 4 Word Problems
• Divding by Multiples of 10 and 100 Worksheets
• 4th Grade Long Division Worksheets

More Recommended Math Worksheets

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

More Division Worksheets

• Divide a 2 digit number by a single digit;
• Use remainders when dividing;
• Calculate division facts related to multiplication facts.
• Division Facts to 10x10 Worksheets
• Long Division Worksheets 3rd Grade
• Division Facts Worksheets (randomly generated)

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Division worksheet for class 3 | 3rd grade division worksheets

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In the third grade, division is often associated with multiplication, being its logical inverse as an arithmetic operation. Additionally, since the topic of division is invariably taught after multiplication, it’s likely that your child will encounter an easier time with mastering its concept. That is, by no means, an excuse for them to slouch on figuring out the intricacies of division. This page contains several division worksheets for class 3 that you can read, download and print for your child’s next math activities. Whether you’re a parent homeschooling your little learner or a teacher, having our worksheets available can save you some much-coveted time and energy for your other obligations. A child that regularly practices solving a wide variety of division problems will become quite proficient over time. They’ll benefit from having worksheets that are neat and organized, and which have a bounty of different division items for them to flex their mathematical muscle. Their math worksheet should also ideally be in a large, legible font to make them easy to read. If they’re still starting to learn about dividing, it can also be quite valuable to have worksheets which contain a set of illustrations accompanying the problems, to better represent the concept of division through real-world analogies. Unlike all of the preceding arithmetic operations, the process of solving division equations can look a little unfamiliar. As a consequence, it’s important for third grade students to identify which numbers in the equation constitute the divisor and dividend. Additionally, they’ll need to interpret which numbers are the quotients and remainders. On a related note, answering division problems in the third grade usually have the student solve for the remainder, or otherwise keep it intact. This will change in later years, when kids learn more about decimals and remainders have to be eliminated in full from the solution. Dividing things properly is a skill that your child will regularly employ in their actual lives – from delegating different tasks to groups of people, or equally distributing school supplies or other resources in their classroom, to managing their allowance in a proper fashion, the applications to division are virtually inexhaustible. To that end, there are plenty of ways for you to help them master division through real-world activities. You can approach division through challenging them to count the number of grapes or orange slices in a bowl and sharing an equal number to their friends. If they enjoy reading books, you can also ask them to find out how many pages their latest novel has. Let them consider how many pages they usually read in a single day, then have them solve the numbers of days they’ll need to finish the entire book. You’re welcome to peruse and download our 3rd grade division worksheets to help you equip your kids or students with enough experience in handling division problems. Combined with proper rest, recreation and encouragement, you might be pleasantly surprised at how easily your learners will breeze through the third grade and beyond.

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Free Printable Division Worksheets for 3rd Class

Math Division worksheets for Class 3 students: Discover a collection of free printable resources to help teachers effectively teach division concepts and enhance students' learning experience.

Recommended Topics for you

• Divisibility Rules
• Division Facts
• Long Division
• Division Strategies

Explore Division Worksheets by Grades

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Explore printable Division worksheets for 3rd Class

Division worksheets for Class 3 are an essential tool for teachers looking to help their students build a strong foundation in mathematics. These worksheets provide a variety of problems that challenge students to apply their understanding of division concepts, such as equal sharing, repeated subtraction, and the relationship between multiplication and division. With a range of difficulty levels, these worksheets cater to the diverse needs of students in Class 3, allowing teachers to differentiate instruction and ensure that every learner is appropriately challenged. By incorporating division worksheets for Class 3 into their lesson plans, teachers can effectively assess student progress and identify areas where additional support may be needed, ultimately setting their students up for long-term success in math.

Quizizz, a popular online platform for creating and sharing interactive quizzes, offers a wide range of resources for teachers, including division worksheets for Class 3. In addition to these worksheets, Quizizz also provides teachers with access to thousands of pre-made quizzes and games that can be easily customized to align with specific learning objectives. This extensive library of resources allows teachers to engage their students in a variety of ways, from individual practice to whole-class competitions, all while tracking student progress and performance in real-time. By incorporating Quizizz into their teaching strategies, educators can create a dynamic and engaging learning environment that supports the development of critical math skills for Class 3 students.

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Class iii math, class 3 division, class ii recap, division by a one digit number without remainder, division by a one digit number with remainder, division by 10 and 100, division by two digit number, division by three digit number, story time division, division test, division worksheet, answer sheet.

In class II, we have learnt that division is nothing but repeated subtraction. In other word, we can say division is a process by which equal amount of distribution can be done among a group. Few examples are given below.

Example 1. 48 ÷ 6 = __________ Solution. We must recall the 6 tables and find out where 48 comes. That is 6 × 8 = 48. So, the answer will be 8.

Example 2. 36 ÷ 18 = _________ Solution. We must recall 18 tables and find out where 36 comes. That is 18 × 2 = 36. So, the answer will be 2.

Some of the basic Division properties are given below.

1. When a number is divided by itself then the quotient will be 1. That means, 7 ÷ 7 = 1 2. When a number is divided by 1 then the quotient will be the number itself.That means, 9 ÷ 1 = 9 3. When 0 is divided by any number then the quotient will be 0 itself. That means, 0 ÷ 5 = 0

We have learnt division of 3 digit numbers by 1 digit number. We will use same method for division of 4 or 5 digit numbers by 1 digit numbers without remainder. Few examples are given below.

Let's take some example where first digit on the left most of the dividend is not divisible by the divisor.

Let's assume we have 6 chocolates and we must divide it among 5 children equally. If we give one chocolate to each child, then 5 chocolates will be over, and 1 chocolate will remain with us. Let's go through some examples given below.

Rules to verify the division 1. Division without remainder    Dividend = Quotient × Divisor 2. Division with remainder    Dividend = (Quotient × Divisor) + Remainder

When we divide a number by 10, the digit at the ones place of the dividend is the remainder. The number formed by the digits after removing the ones place digit of the dividend is the quotient. Let's see some examples.

When we divide a number by 100, the number formed by tens and ones place of the dividend is the reminder. The number formed by remaining digits of dividend is quotient. Let's go through some of the examples.

All the rules that we have learnt earlier will be used in this kind of division. Here, we will have 2 digits divisor. Let's see some examples.

All the rules that we have learnt earlier will be used in this kind of division. Here, we will have 3 digits divisor. Let's see some examples.

In our day to day life we use concept of multiplication in many ways, few examples are shown below.

Division Test - 1

Division Test - 2

Division Worksheet - 1

Division Worksheet - 2

Division Worksheet - 3

Division-Answer Download the pdf

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Unit 7: Division

Intro to division.

• The idea of division (Opens a modal)
• Division as equal groups (Opens a modal)
• Visualizing division with arrays (Opens a modal)
• Division with groups of objects Get 5 of 7 questions to level up!
• Division with arrays Get 5 of 7 questions to level up!
• Divide with visuals Get 5 of 7 questions to level up!

Intro to remainders

• Intro to remainders (Opens a modal)
• Divide with remainders (2-digit by 1-digit) Get 3 of 4 questions to level up!

Class 3 NCERT (CBSE and ICSE) Division

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Division Assignment - 1 Class 3 Worksheet PDF for Maths (Free Download)

The Division Assignment - 1 Class 3 Worksheet contains numerous questions that help students to practice several questions to develop a better understanding of this topic. Along with the questions to practice, the worksheets of Division Assignment - 1 Maths for class 3 allow students to be thorough with the short cut methods and variety of answering methods to easily solve a maths question.

The Division Assignment - 1 Class 3 Worksheet is beneficial for the students as it allows them to enhance their accuracy in writing the answers of Division Assignment - 1. Our Maths experts have prepared the worksheet and answers of Division Assignment - 1 worksheet so that children can use them to improve their knowledge in basic Maths.

Division Assignment - 1 Class 3 Worksheet PDF

For the convenience, our experts have binded the whole questions of Division Assignment - 1 Class 3 Worksheet into PDF. Now, as a guardian, you can guide your kids to solve the Division Assignment - 1 Class 3 Worksheet PDF so that they can have better exam preparation as well as a better understanding of the topic.

The PDF is absolutely free of cost and it can be downloaded from Selfstudys. The Worksheet of Division Assignment - 1 PDF is ideal for all those students who are studying in Class 3 and NCERT Class 3 Maths Book has been prescribed to them.

Worksheets of Division Assignment - 1 Maths for Class 3 with Answers

Since, the worksheet is solved by the students while they do Self-study at their comfort; our experts have prepared the Worksheets of Division Assignment - 1 Maths for Class 3 with Answers. Referring to this PDF will help the students to get instant help whenever they will face difficulty in answering the worksheet questions of Division Assignment - 1.

The answers are highly accurate and in a step by step method. Apart from getting instant help, the worksheets of Division Assignment - 1 Maths for class 3 with answers are good study resources for cross-checking the written answers.

The answers of Class 3 Division Assignment - 1 are also useful for clearing any kind of confusion or doubts in the topic.

Why Division Assignment - 1 Class 3 Worksheet is Important?

The class 3 NCERT Maths worksheet give and take has a great impact on a class 3 student. Because it allows students to explore a variety of practices. Solving several questions from a single chapter helps students to develop a deeper understanding of the topic. 

Those who refer to the worksheet on class 3 Maths NCERT Division Assignment - 1 can revise their learnings from the chapter as well. A good revision and practice of questions from Division Assignment - 1 can help students to score good marks in Class 3 Maths.

How to Download Division Assignment - 1 Worksheet Class 3?

The Division Assignment - 1 Class 3 Worksheet can be downloaded from the given steps below:

• Visit Selfstudys website
• Click on CBSE from the Navigation bar/button
• Once, it will expand, click on “ KVS NCERT CBSE Worksheets ”
• A new page will load where you have to select class “3rd”
• Now, either search the Subject name Mathematics or click from the given options to download the Class 3 Worksheet Division Assignment - 1 .

What is the benefit of using Class 3 NCERT Maths Worksheet Division Assignment - 1?

Referring to the Division Assignment - 1 Class 3 Worksheet assists students to solve some additional questions from the chapter as well as develop a strong grip on the topic. The worksheet provides benefits in following ways-

• Getting instant help:- No matter at which question a student is stuck, the Worksheets of Division Assignment - 1 Maths for Class 3 with Answers can help them to clear all doubts and understand the proper terminology to write the answers of chapter Division Assignment - 1.
• A thorough revision to the topic Division Assignment - 1: - Revision is important in all the subjects including Class 3 Maths. Therefore, to revise the topic of class 3 Math-Magic Division Assignment - 1, students can refer to the Class 3 Worksheet. 
• A complete package to utilise the time:- During the holidays, kids often try to avoid studying and waste their time on useless things all day. However, the great benefit of the Division Assignment - 1 worksheet class 3 is that it allows students to practice some extra questions during the holidays. As a result, they can keep their study continuous.

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CBSE Class 3 Maths Division with Remainder Worksheets

CBSE Class 3 Maths Division with Remainder Worksheets – Worksheets have become an integral part and are the most engaging study materials for kids these days. The Standard 3 Maths Division with Remainder Worksheets will help your younger one to practice what they have learned in class. Division with Remainder Worksheets for Grade 3 will develop a curiosity in your kid to learn.

Maths Worksheets for Class 3 are a perfect combination of fun and learning. Find the most interesting and relevant puzzle activities for your kids here. In the Mathematics Grade 3 Division with Remainder Worksheets Puzzles will be in the form of crosswords, true or false, pictures, mazes, fill-ups, MCQs, objectives, questions and answers, and so on.

Download Free Printable Class 3 Maths Division with Remainder Worksheets

Mathematics Worksheets for Class 3 on Division with Remainder will help your kid remember what he/ she learned in school for a long time. Your Grade 3 kid will love to solve these engaging exercises and interesting collections of Puzzles.

FAQs on Maths Division with Remainder Class 3 Worksheets

1. How does a child learn Mathematics Division with Remainder at Class 3 Level?

A child can learn Maths Division with Remainder at Class 3 Level through the worksheets prevailing on our page.

2. What are the topics in Maths Class 3?

Mathematics Class 3 will have topics like Division with Remainder etc.

3. Where can I get Mathematics Worksheets for Class 3 Division with Remainder for free?

You can get Maths Division with Remainder Worksheets Class 3 free of cost from our Worksheetsbuddy.com page. You can use them for your kid to get practice.

4. Are the CBSE Class 3 Division with Remainder Worksheets over here printable?

Yes, the CBSE Class 3 Division with Remainder Worksheets here are printable and you can download them easily.

We Hope the information prevailing on our page regarding CBSE Class 3 Mathematics Division with Remainder Worksheets has been useful to you. For more info feel free to reach us and we will assist you at the easiest possible. Keep in touch with our site for more information on Class Wise Worksheets for various subjects.

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Division Word Problems Worksheets for 3rd Graders

These fun division word problems worksheets for 3rd graders online are all you need to help your child strengthen their knowledge and skills. Make the activity of learning something to look forward to by using these interactive division word problems worksheets. Get started now to add fun to your 3rd grader's routine!

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Use Multiplication to Solve Division Word Problems Worksheet

Boost your ability to use multiplication to solve division word problems by printing this worksheet.

Solving Problems on Division Worksheet

Put your skills to the test by practicing to solve problems on division.

Model the Division Situations Worksheet

Learners must model division situations to enhance their math skills.

Model the Division Scenarios Worksheet

Combine math learning with adventure by modeling the division scenarios.

Word Problems on Comparing Division Expression Worksheet

Boost your ability to solve word problems on comparing division expressions in this worksheet.

Solving Real-Life Problems on Division Worksheet

This downloadable worksheet is designed for solving real-life problems on division.

Solving Word Problems on Division Worksheet

In this worksheet, learners will get to solve word problems on division.

Real World Problems on Division Worksheet

Focus on core math skills with this fun worksheet by solving real world problems on division.

Solve Real World Problems on Division Worksheet

This downloadable worksheet is designed to solve real world problems on division.

Real Life Problems on Division Worksheet

Focus on core math skills with this fun worksheet by solving real life problems on division.

Estimate the Answer of the Division Word Problems Worksheet

Make math practice a joyride by solving to estimate the answer of the given division word problems.

Divide 2-digit Numbers by 1-digit Numbers: Summer Word Problems Worksheet

A summer-themed worksheet for students to practice dividing 2-digit numbers by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Halloween Word Problems Worksheet

Halloween-themed worksheet to enhance skills in dividing 2-digit numbers by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Christmas Word Problems Worksheet

Christmas-themed worksheet to practice dividing 2-digit numbers by 1-digit numbers through word problems.

Divide 2-digit Numbers by 1-digit Numbers: Shopping Word Problems Worksheet

Interactive worksheet for solving shopping themed division problems with 2-digit by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Travel Word Problems Worksheet

This worksheet involves solving travel-themed word problems by dividing 2-digit numbers by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Sports Word Problems Worksheet

Sports-themed worksheet to practice dividing 2-digit numbers by 1-digit through word problems.

Divide 2-digit Numbers by 1-digit Numbers: Cooking Word Problems Worksheet

This worksheet blends cooking themes with math, guiding students to divide 2-digit by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Winter Word Problems Worksheet

Winter-themed worksheet to practice dividing 2-digit numbers by 1-digit numbers through word problems.

Divide 2-digit Numbers by 1-digit Numbers: Easter Word Problems Worksheet

An Easter-themed worksheet for students to practice dividing 2-digit numbers by 1-digit numbers.

Divide 2-digit Numbers by 1-digit Numbers: Thanksgiving Word Problems Worksheet

Thanksgiving-themed worksheet with word problems to practice dividing 2-digit by 1-digit numbers.

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• Long Division for Class 3

Introduction to Long Division

Long division is a method in Mathematics for dividing big numbers into steps or parts, breaking the division questions into smaller stages. It is the most commonly used approach for dividing problems and makes it easier for kids to learn about the division better. Examine the following long division to find the divisor , dividend , quotient , and remainder. Before executing it, we must be aware of the crucial aspects of long division.

Long Division with Single-Digit Divisor

Long division is done like simple division. When the divisor is a single digit, it is easy to divide the dividend. You can learn and practice the steps that need to be followed while long division is given.

Step One: Check the first unit of the dividend whether it is divisible by the divisor or not.

Step Two: If the first unit is less than the divisor, take the second digit into account.

Step Three: Then, find the suitable multiple and subtract the numbers. After subtraction brings down the next digit and then again repeat the above steps till you get the remainder as 0 or a number that further cannot be divided.

Example of Long Division With Single Digit Divisor

Long Division with Two-Digit Divisor

The long division with a two-digit divisor can be done using the same steps that are mentioned above. In this, the only change is that in the dividend we take the first two digits of the number to subtract it from the multiple of the divisor. And the rest of the steps are the same.

Example of Long Division of Two- Digit Divisor

Long Division with Remainders

The long division ends when there is a remainder left that cannot be further divided by the divisor or the value of the number is less than the divisor itself. Like in the above-mentioned 435 divided by 4 sample questions, after taking down the last digit 5 to be subtracted we are left with 3. As 3 is less than the divisor 4 so we will now conclude the long division as there are no more digits present in the dividend, which can be used to reduce it. So, we are left with 3 as the remainder.

Long Division without Remainders

Long division without remainders means that the remainder is 0 or the last number to be subtracted by the multiple of the divisor was the same giving us the remainder 0. In an example of a division of 126 by 2, we will get 63 as the quotient. As the last digit 6 is completely divisible by 2 we get the remainder as 0 making it a long division without remainder.

The long division is similar to the standard division. The division consists of dividend, divisor, quotient, and the remainder where the divisor can be single-digit, double-digit, or triple-digit. The remainder can be zero or a number that is less than the divisor. If the dividend does not get divided fully or does not have a remainder as 0, then the division can continue further by using a decimal point . The divisor can be single-digit, two-digit, or three-digit.

Long Division Worksheets

1. Divide 432 by 15.

Explanation: In this, we will take the first two digits of the dividend as our divisor is two digits. A multiple of 15 which is less than or equal to 43 is found and then it is subtracted. The remainder along with the next digit of the dividend is then evaluated and subtracted again.

Solution of the division of 432 by 15

2. Divide 1850 by 12 using long division.

Explanation: Step one: As 18 is a little greater than the divisor itself so we will subtract it by 12. We get 6 as the remainder.

Step Two: Bring down 5 and the new number becomes 65 which can be subtracted from 60 which is a multiple of 12.

Step Three: Now bring down 0 and subtract it with the multiple of 12. There is a remainder left as 2. We get our answer as 154 the quotient.

Solution of Division of 1850 by 12

3. What is the value of the remainder when the division ends without any remainder left?

not defined

none of the above

FAQs on Long Division for Class 3

1. What is the polynomial long division?

Ans: Long division of polynomials is a method in algebra that divides a polynomial by another polynomial of the same or lower degree.

2. How do you do long division with decimals?

Ans: Long division with decimals is done in the same way as regular division. It is done in the following order:

Fill in the blanks with the normal form of the division.

To begin, divide the whole number component by the divisor.

Place the quotient's decimal point above the dividend's decimal point.

Bring down the numerals to the tenth place, that is, the digit after the decimal.

Divide and bring down the next digit in order.

Divide until all of the dividend digits are used up and the remainder has a value smaller than the divisor or 0.

3. What is a division used for?

Ans: Long division is used to find an answer to the numbers which need to be shared. In a case where you want to distribute 80 chocolates equally among your 8 friends, so you would use division in such a case. 

4. State if the statement true or untrue. When a long division is used, the remainder is always less than the divisor.

Ans: True, in the case of long division, the remainder is always less than the divisor.

5. How is a long division better than a short division?

Ans: The shorter division method is used to divide large complex numbers by a single digit number, whereas the long division method is used to divide complex numbers by two or three-digit numbers. 

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Grade 3 - Operations and Algebraic Thinking

Standard 3.OA.A.2 - Practice division word problems with numbers up to 10.

Included Skills:

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

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40 Creative Ways To Make Teaching Division Easier (and More Fun!)

It’s time to divide and conquer!

Teaching division can be tough, especially when you start tackling larger numbers and long division. These division activities make the process easier. They help kids conceptualize and visualize, driving the concepts home. Plus, they’re a lot of fun!

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1. Introduce division as sharing

When it comes down to it, isn’t division really just sharing? Play this simple game where kids roll dice and share out pom-pom cherries as equally as possible. It’s a great start to teaching division.

Learn more: JDaniel4’s Mom

2. Continue teaching division by reading a book or two

Kids are never too old for story time. These clever books are the perfect jumping-off point for teaching division, especially if you have kids use counters like pom-poms to act out the story  as you go.

• Divide and Ride (Murphy/Ulrich)
• The Doorbell Rang (Hutchins)
• The Multiplying Menace Divides (Calvert/Geehan)
• A Remainder of One (Pinczes/MacKain)
• Bean Thirteen (McElligott)

3. Make a model

Understanding division is much easier when you lay it out as a model first. Kids break numbers into even groups, then write out the number sentence they represent.

Learn more: Tunstall’s Teaching Tidbits

4. Make division anchor charts to support learning

Keep anchor charts handy while you’re teaching division to give students an easy reference when they struggle. Use these charts for inspiration:

• Tricks to Learn Division Vocabulary, The Owl Teacher
• Divisibility Rules, My Math Resources
• Long Division with Sticky Notes, Caffeine Queen Teacher
• Division Strategies, Room 330 Anchor Charts

5. Teach the Divisibility Rules

These tricks make dividing bigger numbers so much easier. Grab a free printable to share with students at the link.

Learn more: Homeschool Giveaways

6. Turn Guess Who? into Guess What?

Pick up an old Guess Who? game at the thrift store and repurpose it to make a totally fun way to practice division facts!

Learn more: Life Between Summers

7. Practice division facts with Wrap-Ups

This division game is a fun alternative to flashcards. Kids wrap yarn around the cards from the problem on the left to the answer on the right. Then they flip over the card to see if they’re right. Buy Learning Wrap Ups Division Keys here.

8. Try teaching division with LEGO bricks

Check out this video for an easy way to introduce division concepts to your students using perennially popular LEGO bricks. (Get more LEGO math ideas here.)

9. Sort jelly beans into an egg carton

As you pave the way for understanding division, try activities where kids divide large groups of objects into smaller equal groups. Sorting jelly beans into an egg carton is one great way to do this.

Learn more: Homeschool Blog

10. Learn with licorice strings and Skittles

Kids always love math games that you can eat at the end! Pass out licorice strings and a bowlful of Skittles, and use them for a lesson on division.

Learn more: Tales from Outside the Classroom

11. Work on different division strategies

For kids who really struggle with the concept, try teaching division strategies using this free printable mat. It gives them a variety of ways to tackle division problems.

Learn more: Teaching With Jennifer Findley

12. Batter up for division facts

Calling all sports fans! Grab this free printable baseball division game and roll the dice as you compete to see who can hit a home run.

Learn more: 123Homeschool4Me/Baseball Division Game

13. Make division flower learning aids

An important part of learning to divide is mastering the basic division facts. These cute flowers give kids a colorful way to quiz themselves.

Learn more: Ofamily Learning Together

14. Put together Popsicle puzzles

Snag these free printable Popsicle puzzles at the link below to give kids another fun way to practice their division facts. ( Plus, find more ways to use wood craft sticks in the classroom here. )

Learn more: 123Homeschool4Me/Popsicle Puzzles

15. Go Fish for division facts

Give “Go Fish” a division spin! Instead of looking for matching pairs, players compete to find pairs of cards that divide evenly into each other. For instance, in the hand shown, the player could lay down the 8 and the 2, because they divide to make 4.

Learn more: Cuppa Cocoa

16. Win the division facts race

If you’ve got a bin full of toy cars, this division practice game is for you. Grab the free printables and learn how to play at the link.

Learn more: Deceptively Educational

17. Assemble division star puzzles

These pretty star puzzles are deceptively tricky! Think of them as dominoes for division . Get a free full printable set at the link.

Learn more: Hojo’s Teaching Adventures

18. Fight the division dragon

Sharpen your sword and get ready to complete The Knight’s Quest! This free printable game is another engaging way to practice your division facts.

Learn more: 123Homeschool4Me/Division Dragon

19. Take a turn at Jenga

It’s so fun to use Jenga in the classroom! Create a set of division facts flashcards using colored paper that matches the Jenga block colors. Kids choose a card, answer the question, and then try to remove a block of that color from the stack.

20. Play a monster board game

Grab this free printable board to give your students practice dividing by threes. If you like it, the rest are available for purchase.

Learn more: Teacher’s Takeout

21. Roll and write number sentences

Dice are a terrific tool for teaching division number sentences. Kids simply roll two dice, then write the multiplication and division  number sentences for them. (Tip: Try using dice-in-dice to up the fun factor. Here are other fun dice-in-dice activities too!)

Learn more: Math Geek Mama/Number Sentences

22. Write the room to practice division facts

Write the room activities get kids up and moving, which is terrific for learning. Hang these free printable cards around the room, then give kids a clipboard and answer sheet and send them off to find and solve the division facts.

Learn more: The Applicious Teacher

23. Solve a division puzzle square

These puzzling squares challenge kids to fill in the correct numbers as they try to create a division problem that works in every direction. Grab the printable at the link.

Learn more: Education.com/Puzzle Squares

24. Spin and divide

These free printables offer another way to practice division facts. Use a pencil and paperclip to make the spinner.

Learn more: 3 Dinosaurs

25. Draw Equation Maker games

In the first block, write a series of dividends. Write divisors in the second block and quotients in the third. Kids use markers to cover the numbers that make up a correct equation.

Learn more: Fun Games 4 Learning

26. Solve using the Does McDonald’s Serve Burgers? method

As you start to tackle long division, there are a variety of methods you can use. One popular option is this one, which gives kids a way to remember the steps: divide, multiply, subtract, and bring down.

Learn more: Brittany Noll-Cooper/Pinterest

27. Keep things in line with graph paper

This is such an easy accommodation you can make for kids who have difficulty keeping their columns straight. Simply have them lay the problems out on graph paper. (No graph paper? Turn a sheet of notebook paper sideways and use the lines to make columns.)

Learn more: Caffeine Queen Teacher/Graph Paper

28. Lay out playing cards for long division

Here’s a fun, hands-on long division game that uses a deck of playing cards. You can start out with equations that don’t require remainders, then get more complicated as kids progress.

Learn more: Middle School Math Man

29. Work on division facts with triangle cards

Triangle flashcards are a simple tool for teaching division and multiplication. You cover one corner with your hand, then divide if the colors don’t match or multiply if they’re the same. You can make a set of your own, or buy them on Amazon here .

30. Go on a treasure hunt

Everything is a little more fun with a treasure map! Students solve the equations and cross off the answers until only one number is left—X marks the spot!

Learn more: Education.com/Treasure Hunt

31. Use the Herding Game for teaching division with remainders

Just when kids think they have division all figured out, along come remainders! Teaching division with remainders can be one of the trickiest tasks, so start by playing this fun and active game. For each round, the teacher calls out different groups of animals for students to form (“Form herds of 5 elephants!”). Any leftover students who don’t fit into the group go into the “holding pen,” introducing the idea of remainders.

Learn more: The Teacher Studio/The Herding Game

32. See remainders in real life with cookies

Buy a couple of bags of cookies and ask your class to find the best way to divide them up fairly. Consider whether remainder cookies can be divided to add fractions into the mix. Now that’s some delicious math!

Learn more:  The Teacher Studio/Division Cookies

33. Turn remainders into a good thing

Make teaching remainders more fun with this game that turns them into the most wanted! The goal for each round is to wind up with the highest reminder. You’ll need dice, counters, and the free printable game sheets you can find at the link.

Learn more: Teacher Scout Mom

34. Learn to play Damult Dice Division

Grab three dice and a pencil and paper for this strategy game, named after the teacher who invented it. Roll three dice, and determine the division problem that gives you the highest possible quotient (rounded to the nearest whole number). You get 10 bonus points if there’s no remainder!

Learn more: Math for Love

35. Check your work

This might seem obvious, but teach your kids to check their work by multiplying it back out again. Add in remainders at the end, and you should get the same numbers all over again.

Learn more: Stress-Free Teaching

36. Create a division house

This is such a creative way of teaching division! Kids answer a series of questions to determine the specifications of their “division house.” For instance, to determine the number of windows in the house, students must divide the day of the month they were born by the number of kids in their family. When they’re done with the math, it’s time to draw their house!

Learn more: Teaching With a Mountain View

37. Batter up for long division baseball

This long division game requires a little strategy, as kids roll dice and try to create problems that give them the highest possible quotient on each turn. Wrong answers count as a strike, so be careful! Learn how to play and get the free printables at the link.

Learn More: You’ve Got This Math

38. Adopt and care for pets

Add this super cute game to your rainy-day closet, and kids will learn and practice division without even realizing it! Get it from Amazon here.

39. Pass out play money to make teaching division meaningful

Money activities always grab kids’ attention because they know they can use them someday in the real world. Pull out your stack of play money and learn how to use it for teaching division at the link.

Learn more: Shut the Door and Teach

40. Use Bingo for teaching division as fractions

Division and fractions go hand in hand. This free printable Bingo game helps kids understand the connection between the two.

Learn more: Math Geek Mama/Division Bingo

Love these division activities? You’ll want to check out our roundup of multiplication activities too.

Plus, find out how other teachers tackle multiplication and ask for advice on the weareteachers helpline group on facebook ..

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50 Fun Hands-On Activities and Games To Teach Multiplication

Making it fun makes it stick! Continue Reading

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We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 3 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 3th. Our expert faculty have covered Class 3 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 3 Mathematics and CBSE Assignments for Mathematics Class 3 will be really helpful for standard 3th students to prepare for the class tests and school examinations. Class 3th students can easily free download in Pdf all printable practice worksheets given below.

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Assignments For Class 3 Mathematics

Class 3 Maths Assignment PDF have been developed for Standard 3 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 3 Mathematics from our website as we have provided all topic-wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 3 Mathematics. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics book and get good marks in class 3 exams.

Assignments for Class 3 Mathematics as per CBSE NCERT pattern

All students studying in Grade 3 Mathematics should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics exam for standard 3. We have made sure that all topics given in your textbook for Mathematics which is suggested in Class 3 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school-level tests and examinations. It’s easy to take print of these assignments as all are available in PDF format.

Some important features of our free Class 3 Maths Assignment PDF

Class 3 Maths Assignment pdf –  These worksheets include learning with ten frames, addition and subtraction, place value and fact families, geometry, size comparison, and more. Greater than less than worksheets, making 5 math worksheets, Sorting pumpkins and fall leaves by size, practice the fact families up to 10, Length comparison cut & paste activity.

SHAPES WORKSHEETS –  Shape book to learn and recognize eight basic shapes with a fun tracing and coloring book, Spot and dot shapes, Reindeer shapes worksheets which helps in shapes recognition practice, rainbow shapes color by number, 2D shapes 3D shapes worksheets, children will sort 2d and 3d shapes, as well as work on 3d shapes characteristics and tracing shapes worksheet.

ADDITION AND SUBTRACTION WORKSHEETS –  Ten frame addition to 10 worksheets, Addition and subtraction word problems, Word problems for addition and subtraction from 10, Dot marker addition to 10, Addition and subtraction within 5 fast facts, Dot marker subtraction within 10 worksheets.

GRAPHING WORKSHEETS FOR KINDERGARTEN –  Winter graphing and counting pumpkins, leaves, or acorns, they are all there to be counted, Bakery I spy and graph – pretzels, pies, and cupcakes, all ready to be counted, a great Easter activity to practice counting, visual discrimination, and graphing, all in one, Free printable Halloween I spy game

TELLING TIME WORKSHEETS –  Telling time to the hour worksheets – learn to read and write time with analog and digital clocks, quarter past, quarter to and half past – more advanced telling time worksheets!

PATTERNS WORKSHEETS –  ABC pattern worksheets – fun worksheets for teaching patterns, draw and color pictures to make patterns, enjoy the sweet pictures while making patterns, Do-A-Dot Marker patterns – use the bingo daubers to copy and make patterns and colorful birthday patterns full of balloons, presents, and treats.

COUNTING WORKSHEETS –  Teach counting to 10 and 20, Counting backward worksheets – count from 100, 50, 20, and 10 all the way to number 1, Count and match worksheets 1-20 – count the pictures and match them with the correct number, Counting to 10 number worksheets – numbers 1 to 10 worksheets packed with learning, Skip counting snails worksheets – enjoy this spring printable while skip counting by numbers all the way up to 10, Counting beads: Skip counting worksheets for kindergarten – learn to skip count with cute beads and Counting backward from 100 to1

COUNTING WITH TEN FRAMES WORKSHEETS –  Snowflake ten frames counting – count the snowflakes, write the number, and color the ten frames, fall counting worksheets with five and ten frames – ten frame practices for the fall, counting stars: Ten frame worksheets for kindergarten – a fun ten frame practice activity, Blank ten frame templates – get these free templates for use with stickers or manipulatives

NUMBER CHARTS AND NUMBER LINES WORKSHEETS –  Kindergarteners will work on their numbers 1-10 and numbers 1-20 but also working all the way up to 100. Counting to 100: Free printable number charts, Number line to 20 worksheets, 100 Number Line. Find more Class 3 Maths Assignment PDF on AssignmentBag.com

CONNECT THE DOTS WORKSHEETS –  You will find activities such as dot-to-dots, spot and dot numbers, color by number, number order puzzles, missing numbers, and more! Number words 1-20 worksheets, Snowman dot to dot letters and numbers, Cat and dog dot to dot worksheets numbers 1-40, Dot to dot printables to 100 and connect the dots activity sheets (numbers 1-10).

WRITING NUMBERS WORKSHEETS –  Tracing the numbers 1-10, Hen and eggs number and tracing worksheets, Free printable number tracing worksheets 1-100, Numbers 1-20 tracing worksheets and tracing number words 1-10.

Some advantages of Class 3 Maths Assignment PDF – Free to Download

• Solving Class 3 Maths Assignment PDF helps to further enhance understanding of the topics given in your textbook which will help you to get better marks
• By solving one assignments given in your class by Mathematics teacher for class 3 will help you to keep in touch with the topic thus reducing dependence on last-minute studies
• You will be able to understand the type of questions that are expected in your Mathematics class test
• You will be able to revise all topics given in the ebook for Class 3 Mathematics as all questions have been provided in the question banks
• NCERT Class 3 Mathematics Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 3 Mathematics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 3 Mathematics Assignments PDF.

You can download free assignments for class 3 Mathematics from https://www.assignmentsbag.com

You can get free downloadable Class 3 Maths Assignment PDF from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 3, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Class 3 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

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OHSAA Announces 2024 Football Divisions and Regional Assignments

Theme picker.

Catholic school from Section III sues its league to be placed in division for smaller schools

• Updated: Apr. 29, 2024, 9:22 p.m. |
• Published: Apr. 29, 2024, 9:00 p.m.
• James McClendon | [email protected]

One of Section III’s smallest Catholic schools is suing its league to allow its sports teams to compete in a division reserved for smaller schools.

Watertown’s Immaculate Heart Central filed a lawsuit against the Frontier League in the New York State Supreme Court on April 22, according to court documents filed in Jefferson County.

IHC athletic director Kurt Robbins was not immediately available to comment on the lawsuit.

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Grading New York Giants' 2024 NFL Draft

How good of a haul did the New York Giants walk away with in the 2024 NFL Draft?

• Author: Brandon Olsen
• Publish date: Apr 28, 2024

In this story:

The New York Giants entered the 2024 NFL Draft with six picks and were one of the only teams to not make a trade throughout the draft. With those picks, they addressed premium positions of need and added depth to the back end of their roster.

Round 1, Pick 6: LSU WR Malik Nabers

At the beginning of the draft, three quarterbacks, one receiver, and one offensive lineman were drafted with the first five picks. 

That left the Giants with a decision to be the next team to reach for a quarterback or to take the best player available—they chose the latter.

Malik Nabers  was the fourth best player on our  Giants Country big board , as well as the second-ranked wide receiver in the draft behind the previously selected Marvin Harrison Jr. Nabers is immediately the most talented wide receiver on the Giants roster and should find himself as the top option for the duration of his rookie contract.

The Giants addressed a position of need while also grabbing the best player available: a massive win. Once again, Joe Schoen used his first draft pick on a premium position player. Grade: A+

Round 2, Pick 47: Minnesota S Tyler Nubin

The top safety in the draft is a New York Giant.  Tyler Nubin  has done it all at the college level and has the physical traits that should reasonably translate to the next level. This is one of the few times Schoen’s early pick was used on a non-premium position, but with the need on the roster and the importance in Shane Bowen’s defense, it was a necessity. Grade: A+

Round 3, Pick 70: Kentucky CB Andru Phillips

I wasn’t a big fan of the selection of  Andru Phillips  in the third round. I understand that he played a lot of Cover 3 and quarters at Kentucky, similar to what Giants defensive coordinator Shane Bowen called with the Tennessee Titans. What was missing from Kentucky was Cover 1, but just because someone hasn’t done something doesn’t mean they  can’t  do something.

My issue with the Phillips selection is that it feels redundant with Cor’Dale Flott on the roster and a more immediate need on the boundary. Unless the Giants feel that Flott or Phillips can play on the outside full-time, this is a depth pick in the third round. Grade: C-

Round 4, Pick 107: Penn State TE Theo Johnson

The  Giants Country  big board was very high on  Theo Johnson  despite his lack of production by college tight-end standards. The Penn State offense wasn’t favorable for any pass-catcher, especially for tight ends forced into pass protection. 

Given the question marks surrounding Darren Waller’s future with the organization, the Giants were bound to make a selection at tight end. They walked away with someone who should be able to contribute early as an athletic pass-catcher while he gets more accustomed to the NFL game, which is something to be happy about. Grade: B+

Round 5, Pick 166: Purdue RB Tyrone Tracy

My main hesitation with the selection of Tyron Tracy is that he’s already 24 years old and has just started playing running back after spending most of his career as a wide receiver. I think he has the skillset to contribute as a pass-catcher, but I wish the Giants brought in a more natural runner who is a proven contributor between the tackles here.

Tracy may become a great asset at this pick, but as it currently stands, I think the Giants need significant development in the running back room to have a good room. Grade: C+

Round 6, Pick 183: UCLA LB Darius Muasau

Darius Muasau is the kind of linebacker I envision as someone who won’t be a significant impact player on a down-to-down basis but could find his way onto the field rotationally and should play on special teams. Muasau played in a defensive system that was fairly similar at the linebacker spot to Bowen’s scheme, which immediately raises his floor.  Grade: C

Overall Grade

The Giants hit home runs with their first two picks and got great value with the Johnson pick in the fourth round, but they also made some uninspiring picks. Nailing the early picks matters more than a few average picks, so Giants fans should be happy with the draft's overall results. Grade: B+

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Latest Giants News

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Grading New York Giants’ Most Significant Off-Season Moves

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A Look Behind Some of the Giants New Jersey Number Assignments

Phil Lyman’s GOP lieutenant governor pick not eligible to run in Utah, elections office rules

Former lt. gov. greg bell ruled that lyman’s pick, layne bangerter, who lived in idaho until 2021, does not meet utah’s constitutional residency requirements..

(Trent Nelson | The Salt Lake Tribune) Phil Lyman and Layne Bangerter celebrate at the Utah Republican Nominating Convention in Salt Lake City on Saturday, April 27, 2024. Utah's top elections officer ruled Bangerter is inelligable to run for election in Utah.

Republican candidate for governor Phil Lyman, fresh off a victory at the party’s state convention Saturday , will have to find a new running mate after state elections officials ruled that his first pick, Layne Bangerter, does not meet Utah’s residency requirements .

Bangerter lived in Utah most of his life but was an Idaho resident until 2021. The Utah Constitution requires candidates for governor or lieutenant governor to be a “citizen of the state for five years next preceding the election.”

Lyman contended that meant that Bangerter only needed to live in the state for five years at some point in his life. “Layne Bangerter easily meets this requirement and is a fully qualified candidate for lieutenant governor,” the Lyman campaign said in a statement Monday.

But Republican Lt. Gov. Deidre Henderson — who oversees Utah’s elections and is up for reelection this year — asked former Lt. Gov. Greg Bell to rule on Bangerter’s eligibility, an attempt to avoid the obvious conflict of interest if Henderson decided Bangerter should be kicked off the ticket.

Bell determined that Bangerter was indeed not eligible.

“In consultation with legal counsel and the plain language of the constitutional provision, we interpret this qualification requirement to mean the applicant must have been a resident of the State of Utah for the consecutive five-year period immediately prior to the election,” Bell wrote in his analysis.

Bell wrote that, based on that interpretation, election officials are “expressly precluded from accepting his declaration of candidacy.”

The Salt Lake Tribune reported on Saturday that Bangerter Idaho resident before relocating to Utah in 2021, according to the website for his ranch in Gunlock. The Idaho Secretary of State’s office shows Bangerter made a donation to Republican Raul Labrador’s gubernatorial campaign using an Idaho address in 2022.

Bangerter also did not register to vote in Utah until 2022. He told The Tribune on Saturday that he had not moved back to Utah until 2021.

Lyman said Monday afternoon that he had seen Bell’s decision and his campaign had asked the Utah Supreme Court to issue a temporary restraining order preventing Bangerter from being disqualified until a judge can hear the case.

On Monday, Bangerter and Lyman filed a lawsuit in Third District Court against Henderson and her elections director, Ryan Cowley, demanding that Bangerter be allowed to be included on the ticket. According to the suit, Lyman’s campaign had “invested hundreds of thousands of dollars and countless hours in pursuing their campaign” and the refusal to allow Bangerter to file was hurting the campaign.

Lyman Lawsuit by Robert Gehrke on Scribd

It acknowledges that Bangerter was born in Brazil and lived in Utah from the time he was 18 months old until 1990, then did not live in the state again until 2021. The lawsuit argues that Bangerter has lived in the state for more than 30 years, but does not contend he has been in the state for the entirety of the past five years.

“It should be heard by the district court very soon,” Lyman said.

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Archived Content

Bold bloom filters, learning objectives.

• Implement the bloom filter using C++ built-in data structures
• Understand bitvectors and fundamental bitvector operations
• Measure the accuracy of a bloom filter over its multi-dimensional parameter space

Assignment Description

In this lab we will be implementing bloom filters and building up our understanding of probabilistic data structures as well as fundamental bit operations.

Lab Insight

Bloom filters are a great example of a probablistic data structure – a data structure whose accuracy is not guaranteed but is usually bounded in some meaningful way (or one-sided in error). Additionally data structures in this class generally have great performance with speeds or overall efficiency that are hard to beat. Among the data structures in this classification, the bloom filter is the most straightforward as it directly extends from what we now know about hashing.

In addition to the basics of implementation (which you are coding up here), in class we also discussed that the optimally accurate bloom filter can be determined if you know any two of the following three properties: (1) Size of bloom filter (2) Number of hashes (3) Expected number of items. You will explore that relationship by implementing an integer-hash bloom filter with variable hashes, sizes, and input items and observing how the filter compares to the underlying ground truth.

Checking Out the Code

All assignments will be distributed via our release repo on github this semester. You will need to have set up your git directory to have our release as a remote repo as described in our git set up .

You can merge the assignments as they are released into your personal repo with

The first git command will fetch and merge changes from the main branch on your remote repository named release into your personal. The --no-edit flag automatically generates a commit message for you, and the --no-rebase flag will merge the upstream branch into the current branch. Generally, these two flags shouldn’t be used, but are included for ease of merging assignments into your repo.

The second command will push to origin (your personal), which will allow it to track the new changes from release .

You will need to run these commands for every assignment that is released.

All the files for this lab are in the lab_bloom directory.

Part 1: The Bloom Filter Class

As every provided hash function takes an integer as input (and returns an integer as output), unlike most the assignments in this class our bloom filter is not templated! For the first part of this assignment, your task is to finish implementing this integer-hash bloom filter. The specific functions you should fill in are:

• BF::BF() (Both constructor and copy constructor)
• BF::contains()
• BF::bit_union()
• BF::intersect()

To help you debug the assignment, the BF class has an override to print the content of a bloom filter when passed to cout as well as five ‘hash’ functions of varying performance so you can explore the space of possible implementations. While you should read the doxygen to understand the specific details of each function, some tips to help you out are below.

Remember that functions can be stored as variables and passed as function arguments! In this assignment we actually go one step further and pass a vector of hashFunctions , which we have type defined for you in bloom.h to be any function that takes in an integer as input and returns an integer as output.

Don’t overthink add () or contains() ! If you understand how a bloom filter handles collisions and the probabilistic errors possible in a BF, they should be very straightforward.

The lab slides briefly review what a bit vector is and the fundamentals of bitwise union and intersection. Depending on your background you may find it easier to consider them as logical gates or the basic connectives of predicate logic. As a simple truth table:

Part 2: False Positive Rate Experiment

Once you have a functional BF class, its time to evaluate how the accuracy in a BF is a function of its size, the number of hashes, and the number of items inserted. As the bloom filter has one-sided error, the only mistakes it can make are when it identifies an item as being ‘present’ when it was not actually inserted into the bloom filter. Accordingly, the only measure of accuracy we need to track is the False Positive Rate . For a refresher on what that means conceptually, see the following table:

As seen in class (and re-iterated in the slides), \(FPR=\frac{FP}{(FP+TN)}\). From a coding point of view, we can estimate this by keeping track of the raw number of false positives and the raw number of true negatives. Then it is a simple matter of querying every number and tracking how many numbers not in our set were identified as being part of our set (FP) as well as the number of items we correctly identify as not present (TN). However in order to do this correctly, we need one additional piece of information – the size of the universe! Given this information, you can query the full range and get the correct estimate.

Warning: You should always assume the universe starts from 0 and ends at (but not including) the universe max. In other words, the universe parameter defines the size of the universe, not the final item in the universe.

Ex: A universe of 100 is the items 0 through 99.

The specific functions you should fill in are:

• measureFPR()

Part 3: Bit Mask Tutorial

When using vector<bool> , you can use standard array indexing [] to look up the value of any bit. But when using actual bit vectors, it is much harder to access a single bit. Here you are tasked with looking up specific bits in a vector<char> . For the purposes of the lab, you will first implement this for a single character and then extend that logic to work for an array of characters:

• getBitFromByte()
• getBitFromArray()

Figuring out how to actually accomplish this is the point of the lab exercise, but as a hint you should be familiar with the fundamental bit-wise operators discussed in class. A brief summary of them can be found in the lecture slides.

Part 4: (Optional) Data Exploration

Given the completed functions in parts 1 and 2, you have the ability to get the FPR for any combination of hashes, bit vector sizes, and input items (as well as the size of the universe). You are encouraged to play around with different parameter sets to see if the empirically derived accuracy has an optimal accuracy that matches the equation we saw in class with k hashes, m bits, and n items inserted:

If the accuracy you are seeing doesnt match, why do you think this is? What might you change to restore the optimality?

Submitting Your Work

The following files are used in grading:

All other files including any testing files you have added will not be used for grading.