Division estimation worksheets: Estimating quotients | 4th grade Math Worksheet

Опубликовано: October 10, 2023 в 5:26 pm


Категории: Miscellaneous

Estimating Quotients Worksheets

How to Estimate the Outcome of Division –
The division is usually thought of being the most difficult of the four basic mathematical operations. It is pretty easy to learn how to add, subtract, or even multiply. But the division is a bit more of technical operation. We need to identify first that in what number of sectors the dividend should be divided. The dividend is the number that is to be divided while the divisor is one that divides. Then comes the part of thinking whether the dividend will be evenly divided, and the answer will be a whole number or not.
But before doing all of this, the answer to a division sum can also be estimated. It is pretty easy to estimate the answer to a division sum, especially one involving a larger number of digits. All you have to do is write both the dividend and the divisor as a fraction and make the dividend the numerator and the divisor as the denominator. Then divide each digit of the dividend by its corresponding digit in the divisor section. This way, you can have a really quick estimated answer to your sum. This is a quicker method of solving a division sum and getting an approximately accurate answer.

  • Basic Lesson

    Demonstrates how to estimate quotients through the use of round estimation.
    Also includes practice problems. Calculate 126 ÷ 7.
    This can be estimated to 130/10. On dividing this, we get 13.
    Check this with the given problem. 13 x 7 = 91; choose a higher quotient.

    View worksheet

  • Intermediate Lesson

    Uses a larger more difficult numbers to round than the basic lesson.

    View worksheet

  • Independent Practice 1

    20 problems ask you to estimate quotients. The answers can be found

    View worksheet

  • Independent Practice 2

    20 practice problems that review estimating estimating quotients.
    The answers can be found below.

    View worksheet

  • Homework Worksheet

    12 problems to reinforce the lessons and practice pages. An example
    is provided.

    View worksheet

  • Skill Quiz

    10 problems that test quotient estimation skills.

    View worksheet

  • Homework and Quiz Answer Key

    Answers for the homework and quiz.

    View worksheet

  • Lesson and Practice Answer Key

    Answers for both lessons and both practice sheets.

    View worksheet

What’s In Tap Water?

There are 104 chemical elements found in the entire universe.
How many of those same chemical elements can you find in the tap water
in the state of New Jersey? Approximately 98! Makes you think twice before
turning on the tap now doesn’t it?

Free Printable Estimating Division worksheets [PDF]

by Manpreet Singh

Last Updated on October 31, 2022 by Editorial Team

Why do I need to learn estimating division? My answer is – to pick the most realistic and reasonable answer from the options provided. Often we come across multiple-choice questions where different options are provided. By those questions, the examiner just wants to evaluate your estimation skills. In real-life instances too, estimation proves to be a dependable skill for making correct choices among the options provided. That is why I suggest making the best use of the learning phase or school phase and do as many worksheets for estimating division as possible.

Types of division-based problems possible to solve with estimation

Division involving whole numbers is the easiest to estimate and is done the most often. Other types of problems one can solve by estimating are:

  • Estimation of the division of decimals: Rounding off the decimal numbers to the nearest whole numbers and then doing division mentally can give you the approximate quotient closest to the correct answer
  • Finding the most approximate remainder: When two whole numbers are divided, one can do the mental math to find the remainder if the number is not completely divisible
  • Confirming the correctness of quotient by multiplication method: It is also one of the methods where the divisor and quotient are multiplied to find if the process of division is done correctly. The product equals the dividend, which shows that division is done correctly.
  • Problems involving division of fractions: Quotients less than one can be estimated using division involving fractions. Mostly, fractions are telling about the relationship between the part and the whole. So, estimating fractions can help find the approximate value of a quantity, height, volume, etc.

How learning estimation of division helps in daily life?

Division means breaking any quantity into equal parts. Estimating promotes the computation of probabilistic prospects which adds to the skill of accurate measuring and helps ascertain its reasonability. Also, this math skill has got many real-life uses. Practically, it is not possible to carry a calculator all the time and find quotients; it is where the estimation steps in and provides support in the following ways:

  • Helps students cross-check the reasonability of the answer selected
  • Helps architects find the approximate height of the floors of a building
  • Helps in finding the approximate quantities to be distributed among a group
  • Helps in finding the approximate number of days and finding reasonable values like work done per hour, part of the project completed per day, etc. to decide the remuneration of workers.

Thus, estimating is a practical intelligence that anyone requires right from childhood to adult life. If you are looking for some more practice materials, refer to the worksheets for the estimating division enlisted below. These worksheets cover various aspects of attaining proficiency in finding estimated quotients, and remainders. You can download a free printable pdf version from the links given.

Why use division estimation worksheets?

Division is a basic skill to be learned after having mastered other operations like addition, subtraction, multiplication, etc. While division manipulatives teach the dividing activity the practical way, worksheets help strengthen conceptual learning. The worksheets for estimating division are helpful in learning:

  • Single, double, and triple-digit divisions closest to the round figure
  • Rounding to the nearest ten
  • Rounding any figure to the closest fraction
  • Rounding decimals to two places or three places to the nearest whole number quotients

How to make estimation division problem worksheets interesting?

Worksheets for division estimation are proven materials for practice, agreed! However, the very purpose of the worksheets will be defeated if students find them burdensome. So, it is better to adopt some teaching strategies to enhance the impact of worksheets[1]. A few must-try strategies are:

  • Choose worksheet challenge according to the grade: Teachers can select worksheets grade-wise. Worksheets for 2nd grade, 3rd grade, 4th grade, and others are the common classifications you can find for the purpose. This collection is designed to ensure that the challenges of the worksheet are at par with the proficiency attained. Too easy or too tough a challenge can drift the students from practicing on worksheets.
  • Give a demonstration to solve worksheets: Showing how to solve worksheets makes it easy for the students to learn the concept better. They develop a sense of comfort and become more confident in solving them.
  • Give the challenge of solving worksheets the fastest: A sense of competition introduces a fun element into the solving process, and engages learners deeply.


  1. İnan, Cemil & Erkuş, Serdar. (2017). The Effect of Mathematical Worksheets Based on Multiple Intelligences Theory on the Academic Achievement of the Students in the 4th Grade Primary School. Universal Journal of Educational Research. 5. 1372-1377. 10.13189/ujer.2017.050810.

Russian language lesson (correspondence excursion) on the topic “Isolated circumstances” within the framework of the municipal seminar “I know everything about my small homeland! I’m proud of her!” | Russian language and literature

Theme “Special circumstances” (grade 8)

Lesson objective:

to create conditions for students to discover new theoretical information about particular circumstances, to apply this information in language and speech practice.

Lesson type:

General methodological orientation

Planned educational outcomes:

Subject : know how isolated circumstances are expressed, be able to find adverbial phrases, determine its boundaries, correctly punctuate when separating circumstances expressed by single adverbial adverbs, adverbial adverbs. Show the difference between gerunds and adverbs derived from them.

Meta-subject : mastering the methods of selecting and systematizing material on a specific topic, the ability to independently search for information, the ability to transform, store and transmit information as a result of working with texts.

Personality : understand the decisive role of the native language in the development of one’s own personality, careful and attentive attitude to the Russian language, enrichment of students’ vocabulary.

Methods and forms of education:

Language observation, heuristic method, individual, group, pair.

Basic terms:

Separate circumstances, gerund, participle, adverb.

Lesson progress

Lesson step

Stage tasks

Teacher activities

Student activities

Performance results






  1. Organizational moment

Emotional, psychological and motivational preparation of students for the assimilation of the studied material.

Greeting students, checking readiness for the lesson, positive emotions.

– Good afternoon! Let me introduce myself. I, Lukina Svetlana Yuryevna, teacher of the Russian language and literature of school No. 91, Komarihinskiy settlement . (Slide 1)

Do you think something unites us with you?

– Yes, of course, we speak the same language, we live in the same country, in the same region, but wherever we live, the small homeland always remains in the heart, and the family remains the main thing for a person.

(Slide 2 (photo of the Bobrikov family).

I am proud that I belong to the Bobrikov family, very famous in the Chusovsky district. Our family has a good tradition: once every three years we all get together. At the last meeting on January 5, 2019, we gathered more than 70 people. And this is only ½ of the family. We are writing a book about history and family, collecting material bit by bit.

– For today’s lesson, I have prepared worksheets for you, in which you will work today at the lesson, in it I have collected the material necessary for the lesson.

Often with students we play the game “Find a soul mate”. And I suggest you play this game.


RESULT: You absolutely correctly found your relatives. You have united in groups (families). What brings all groups together?

Groups are united by the fact that all concepts are studied in the Russian language course of the 8th grade. The theme of the course is “Syntax and Punctuation”. Define Syntax, Punctuation.

Emotionally tune in to the lesson. Listen to teachers. Demonstrate readiness for the lesson.

Answer questions

Work in the draft workbook write down the last name, first name.

Get up from their desks, play a game

Give definitions


cognitive interest in the Russian language, responsibility for future activities


o organization of your workplace

2. Updating existing knowledge and how to apply it

Review theory about syntax and punctuation

– I came from a village with an interesting name Komarihinskiy. You probably think that the name is related to mosquitoes? … although, in one pre-revolutionary guidebook, the name of the village was explained as follows: “During the construction of the road, mosquitoes of unusually large sizes were found here, causing great trouble to the builders.” In fact, the station borrowed its name from the nearby village of Komarihinskaya (Komarikha), known since 1834. The village grew up at the railway station, which arose after the construction of the railway in 1878.

Slide 3 (Project “Brush and pen about the native village”)

– My sixth graders are creative people. They created a guide to interesting places in the village and called it “Brush and pen about the native village”, which I will use today in the lesson.

They believe that our village was glorified by a water tower built in 1882, which, like the Leaning Tower of Pisa, is tilted a few degrees from its base.

(Slide 4)

At different stages of the lesson, you will evaluate yourself, and enter the marks on the worksheets.

Listen to information. Answer.


have motivation for learning activities


perform educational and cognitive actions orally (build statements).

Subject : use knowledge of syntax and punctuation.

3. The collision of knowledge and ignorance.

Goal setting (based on clarification of the unknown) and planning of activity stages

Creation of conditions for setting the goal of cognitive activity, formulating the topic of the lesson and planning activities, colliding the knowledge of schoolchildren of gerunds and participles with the topic of the lesson.

The topic of our lesson “Isolated circumstances”, expressed by adverbial phrases and single adverbs”

Tell me, if you take each word in the topic of the lesson separately, do you understand them?

-What does the word SEPARATED mean?

– Detached, i.e. living alone, apart. In grammar, they say this about a semantic segment within a sentence.

You know, if we talk about the first meaning of the word SEPARATE, then the heroes of the stories of I. S. Turgenev “Biryuk” the forester Foma and Gerasim the hero of the story “Mu-mu”, who lived apart from people, as if shunning them.

You also know the circumstance as a member of the sentence. What will we learn in class then? What do we not know?

Today we will talk about the integral meaning of two 2 words in the topic of the lesson.


Give the definition of the word SEPARATE in the sense that they put into it.

Report on the completion of the task and their difficulties.


have a desire to be aware of their difficulties and strive to overcome them

Meta-subject establish causal relationships, desire conclusions, realize the insufficiency of their knowledge

Subject: use knowledge of gerunds and participles

4. Discovery of knowledge and identification of a way to apply new knowledge

Create conditions for the study of isolated circumstances. Highlighting the sequence of actions when applying new knowledge

The teacher offers material for research

– There are key concepts in any topic. I suggest that you correlate the concepts and their definitions that you need today in lesson . (Slide 6)

We work in notebooks. We correlate the concept and its definition, draw arrows.

I suggest you work in pairs.


His definition


A minor member of a sentence that denotes an attribute of an action or another attribute. Usually depends on the predicate.

Adverbial turnover

An independent part of speech that denotes an additional action with the main action expressed by the verb


A gerund with a dependent word.

An adverb answers questions…

How? When? Where? For what? For what purpose? Why? How many? Since when?

The gerund answers questions

Doing what? Having done what?

– Rate yourself

(Slides 7,8. Evaluation criteria)

We continue our tour of the village. The history of our village is part of the history of the whole country. During the Civil War, our village was on the front line.

– In memory of the events of those years, there are monuments in the garden near the railway station and near the school, which are looked after by students. Here is how Marshal of the Soviet Union Filipp Ivanovich Golikov writes about the events of those years in his book “Red Eagles”:

(a teacher or one of the students reads an excerpt ) (Slide 9. Marshal Golikov) ( Slide 10. 11. Monuments to the heroes of the Civil War)

“December 16, 1918 Art. Komarihinskaya.

The second battalion is now at station. Komarihinskaya…” (see Appendix)


1. In the second paragraph, find the adverbial phrase.

2. In the last paragraph, a single gerund.

Teacher’s question aimed at clarifying the boundaries of the unknown (after students report on the results of the assignment)

– Were there any difficulties with punctuation marks? What did they express? Make a conclusion: how is the topic of the lesson related to gerunds and participles?

(Slides 12, 13. Monument dedicated to the heroes who died during the Great Patriotic War)

Our village was not bypassed by the Great Patriotic War. 350 Komarihin went to the front, more than half of them did not return.

I ask you to read the text on your own in the Worksheet “On May 9 (on the 40th anniversary of the Victory) in the village of Komarihinskiy, a monument was opened to fellow villagers who did not return from the battlefields . ..) (see Appendix)

Task: Find the second sentence in the third paragraph. Try to figure out why the word slowly is not apart.

If the students had no difficulty, they are offered one more task. (Slide 14)

– Use the slide as a cheat sheet and do the following task using reasoning. (See Appendix)

He slipped and fell.

He walked slowly

Getting up, she knocked over the chair.

A blizzard rages outside the window without ceasing.

He worked tirelessly.

– And now check the work done by exchanging notebooks with a neighbor.

(Slide 15. work check. Evaluation criteria).

– Put yourself a grade in your notebook.

Students work in pairs. Carry out the task.

The presented work will be in the form of verbal conclusions.

Performing task

Answering the teacher’s questions. Talk about their difficulties, if any.

Give answers, draw conclusions.

Participles and participles are separated by commas in writing, i.e. stand apart.

I assume or answer that this word is an adverb, since it denotes a sign of action and refers to the predicate worked.

Evaluating the work done by my desk mate


Forming responsibility for future activities


extract the necessary information from the exercises, plan the ability to analyze, compare, resolve problem situations, give the necessary actions, actions, build small monologues, carry out joint activities

Subject: the ability to identify isolated circumstances.

Consolidation of new knowledge and working out how to apply it

To consolidate knowledge about isolated circumstances expressed by gerunds or participles, to consolidate the ability to apply this knowledge in various situations in practice.

– Small settlements on the map of Russia. Many of them have disappeared. How long do you think the village has been alive? As long as there is a school in it. School is what unites people, what gives confidence in the future. Our school celebrated its anniversary last year. 85 is a respectable term, but our school is always young in soul.

… blizzards are replaced by rains as before,

Graduates are leaving the door,

And the best years are yet to come.

Because an angel guards your walls

and everything they store.

– These are lines from a poem by our graduate Yudina Anastasia.

-What is a school? These are lessons, tasks, control. Our lesson is coming to an end. It’s time to sum up. I suggest you complete the task that you will be asked for the exam in grade 9.

“Among sentences 1-3, find an offer …” (see Appendix)

– Rate yourself.

I answer, they express their assumptions.

Performing task


development of educational motives M meta-subject

acquire the ability to use knowledge and skills in practical activities.


way of identifying isolated circumstances.

8. Reflection. Summing up lesson

Create conditions for the analysis of one’s own activities and the development of self-assessment skills

– To find out the grade for the lesson. Add up your scores and divide by three to get your score.

-To confirm that you really coped with all the difficulties, I suggest that you complete the following task.

-At the beginning of the lesson, you were looking for relatives and found them, and now I suggest that you take cell phones in your hands and write an SMS message to them (relatives) about how the lesson went. But one condition: in the text of the SMS there must be a separate circumstance or an answer to the question: “Why do we need separate circumstances in a speech?” Or maybe one of you will just write your impression of the lesson.

Children evaluate themselves.

Students answer the teacher’s questions, analyzing the stages of the lesson, pronouncing their successes and failures. Detect problems.


self-assessment based on success


the ability to correlate the goals and results of their activities, determine the degree of assimilation of the material, evaluate the success of their work in the lesson

9. Homework

Ensure that students understand the purpose, content, and methods of doing homework.

Apply new knowledge in a creative situation

I introduced you to a place that is especially dear to me. And I offer you: (Sly 16)

  1. make a tour of the top 3 places on the map of your city that are especially dear to you. I would be interested to know about them. You might end up with a great project.


  1. conduct a mini-study “What special circumstances do members of my family use.”

And complete the Maze. You, as the brave hero Theseus, will go through the labyrinth, finding the right path, and the knowledge that you received in the lesson will help you in this.

Analyze homework materials, ask teacher questions for clarification


Development of educational motives


planning their actions, selection of examples.


knowledge of the features of isolated circumstances, use of new knowledge in one’s own speech .

Appendix 1

Worksheet for the lesson “Special Circumstances” grade 8

Student’s FI _________________________________________________________________________________

Lesson grade _______________________________

Task 1 . Set matches. Draw arrows from the definition to the concept, question.


Concept, question


How? When? Where? For what? For what purpose? In what degree? How? Why? How many? Since when? How long?


Participle with dependent word

The adverbial turnover is …

A minor member of a sentence that denotes an attribute of an action or another attribute. Usually depends on the predicate.

An adverb answers questions…

Doing what? Having done what?

The gerund answers questions

An independent part of speech that denotes an additional action with the main action expressed by the verb.

Rate yourself

“5” – no errors

Task 2. Read. Task: 1. In the second paragraph, find the adverbial phrase. 2. In the last paragraph, a single gerund.

The second battalion at the Komarihinskaya station. Yesterday our units left the village without a fight. We left when the station and station buildings were on fire. What can you do? This is what the war demands.

There are no red regiments nearby. Most of them went to Perm. Again our regiment is standing, covering the withdrawal of the main forces 29th division.

The path from Chusovaya to Komarihinskaya is abundantly watered with blood. There was a fierce struggle between labor and capital.

Komarihinskaya station stands in a dense forest. When the shooting subsides, you might think that there is not a soul around. Forest thicket for hundreds of miles. A small steam locomotive, puffing, drags a car onto a siding. (F.I. Golikov “Red Eagles”. M: Military Publishing House – 1959)

Task 3. Read the text. Find the second sentence in the third paragraph. Try to figure it out: why the word is not in a hurry to apart.

On May 9, 1985, in the village of Komarihinskiy, a monument was unveiled to fellow villagers who did not return from the battlefields.

“The initiative to create the monument belonged to veterans of the Great Patriotic War. Gennady Andreevich Klepikov, chairman of the Komarikha Council, provided great assistance.

They erected a monument that is called the whole world. The money was transferred from the salary of teachers and school staff, workers and the administration of the timber industry. Forestry, railway, employees of the council, post office, pensioners, students. Complicated work on the execution of the design of the monument was carried out by the teacher of technical labor of the school Mikhail Pavlovich Gulyaev.

Timber industry workers improved the area around the monument. They worked without haste. Realizing that what they do will remain for many years.

The place on Lenin Street near the monument is sacred for all residents of the village. Every year on May 9, people come to the monument to honor with a minute of silence those who did not live to see the bright moment of the Great Victory.

Task 4. Complete the task, put punctuation where necessary.

He slipped and fell.

He walked slowly.

Getting up, she knocked over her chair.

Kostin went home without hesitation.

He worked tirelessly.

Rate yourself

“5” – no errors;

Task 5. Among sentences 1-3, find a sentence with a separate circumstance expressed as an adverbial phrase. Write down his number.

(1) Love for one’s native land, for one’s native culture, for one’s native village or city, for one’s own language begins small things – with love for one’s family, one’s home, one’s school. (2) This love, gradually expanding, turns into love for one’s country – for its history, its past and present, and then for all of humanity, for human CULTURE. (3) True patriotism is the first step towards effective internationalism.

Add up all the grades you got in the lesson and divide them by 3 to get the grade for the lesson.

A teacher who often uses group work in class is faced with the problem of dividing students into groups: there are often children in classes who no one wants to take into their group. The teacher should not leave the situation to chance, but play it exclusively in a positive way. To make the division procedure transparent, I use the game “Soulmates”.

The essence of the game: each student takes one of the cards laid out on the table and looks for a “soul mate”.

Cards with names: agreement, control, adjunction, nominal, definite-personal, indefinite-personal, impersonal, subject, predicate, definition, addition, circumstance, separate definition, separate circumstance, separate application, separate addition, homogeneous members, homogeneous members with a generalizing word, introductory words, interjections, appeals.

Task: students should unite into groups, by keyword or phrase: (grade 8 Russian)

PS You can not give a hint, then the process of grouping will also become a kind of repetition or generalization of knowledge.

Task: students should unite into groups, by keyword or phrase: (grade 5 Russian language)

Task: students should unite into groups, by keyword or phrase: (grade 6 literature)

I think every teacher will always have a few of his own ideas that he will be able to bring to life.

UDO TUSUR invites to full-time and distance professional development programs for teachers, teachers and methodologists of educational institutions of all levels

February 13, 2019

The Department of Additional Education of TUSUR has launched 25 new programs for teachers, teachers and heads of educational organizations.

Scientific and pedagogical workers of universities preparing for state accreditation:

  • corporate services and resources of the electronic information and educational environment of the university,
  • Pedagogy and psychology of higher education, taking into account the training of persons with disabilities and people with disabilities.

Teachers, teachers and methodologists:

  • development of educational audio and video materials,
  • development of pedagogical scenarios and creation of interactive educational materials (infographics, diagrams and diagrams, mental maps, time diagrams, interactive images, thematic maps, virtual tours, simulators, simulators, virtual labs, interactive worksheets, exercises, didactic games, interactive video, etc. ). ),
  • mastering the methods of organizing group and collaboration using LMS Moodle and web services,
  • implementation of interactive and gaming teaching methods in an electronic course,
  • preparation of educational materials for study using augmented reality technology,
  • development of tasks involving the use of mobile applications,
  • mastering pedagogical design and methods of designing an electronic course,
  • development of an electronic course in the Moodle system on the taught discipline,
  • mastering the methods and technologies of organization and quality control of the educational process using ICT.

Teachers and teachers of computer science:

  • IT Essentials: hardware and software of computer equipment (with the issuance of an international certificate),
  • the use of online compilers and integrators in the educational process,
  • Fundamentals of the Internet of Things (developing digital devices, creating a robotic platform, programming in Python, developing a user interface, documenting solutions related to the Internet of Things, managing RaspberryPi platforms, Arduino with RaspberryPi and using the Cisco Spark API),
  • object-oriented programming in a high-level programming language.

Annotated list of courses

In 2018, more than two and a half thousand students from Russia and other countries underwent advanced training, professional retraining, received diplomas, certificates and certificates.

Registration for courses and additional information:

  • website: do.tusur.ru.
  • by phone: (3822) 70-17-36,
  • by e-mail: [email protected],
  • in the office: Tomsk, st. 19th Guards Division, 9a.

department of additional education

Other news

TUSUR students have a unique opportunity to study for free with additional qualifications in a number of programs

June 28, 2023


TUSUR together with Basalt SPO launched training on working with the Alt operating system

June 28, 2023

20 students from the Krasnoyarsk and Krasnodar regions, Saratov, Tver and Tomsk regions started training under the program “Effective work in the Alt OS”.