# Word problem division: Division Word Problems for 3rd Grade

Posted on## Understanding Multiplication and Division in Word Problems |

Posted in division, elementary, multiplication

by Mrs. Kirk

So, the fun and games of learning how to make arrays, skip counting on number lines and using models to solve multiplication problems has lead to the equally exciting task of solving division problems. Everyone seems to be making great progress and making meaning of multiplication and division in real world problems, UNTIL … wait for it … wait for it … We mix the two together!

And here the real “fun” begins … A few students usually have an intuition about the structure of the problems and just “get it” with out much help, but the majority of students need direct, systematic instruction paired with hands on or pictorial examples to really, truly, deeply, understand the difference between multiplication and division in word problems. But where can we start?

#### Start with The Same Story!

I like to take the same story and write 3 word problems that use the same story, but ask 3 different questions. This really helps my students to see how multiplication and division can be the same and different in a word problem and help them to see to importance of analyzing the question. How many times have you had a student choose multiplication to solve a division problem because they “saw the word each”? Solving similar problems and then discussing the problems in relation to each other can really get students thinking deeper about problem solving.

For example, my 3 word problems might be:

- Jeff had 4 plates of cookies to take to his neighbors. He put 6 cookies on each plate. How many cookies was Jeff giving his neighbors?
- Jeff had 4 plates of cookies to take to his neighbors. He had 24 cookies and put an equal number of cookies on each plate. How many cookies did he put on each plate?
- Jeff had 24 cookies to take to his neighbors. He put the cookies on plates. Each plate had 6 cookies. How many plates did he use?

The three problems have the same story, but different clues are given and different questions are asked for each problem. (Get this FREEBIE here)

As we work through the problems, I ask my students these questions:

- What is the question asking me to find?
- Does the story tell me the total?
- Does the story tell me the number in each group?
- Does the story tell me the number of groups?

#### Draw pictures or make diagrams!

We write down the question and clues. Then draw a picture …

After discussing how we made our picture we make our number sentence.

#### Write a number sentence and label the answers.

#### Compare and Reflect!

#### Continue to have meaningful discussion as you practice!

As you continue working guided problems with students ask them to explain why they are choosing to multiplication or division. Encourage students to question each other when working in small groups or with partners. Have them write their own examples of word problems using the same story, but different questions.

#### And, of course, practice, practice, practice! Download this FREE page to practice!

#### Like this:

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division, math, math problems, multiplication, problem solving, problem solving skills, word problems

3 Comments

## Simple multiplication and division problems

Everything is very

superficial. No depth, no fullness

answer, showing on a specific task. Where

techniques used on each specified

stage? In what order are they entered?

Problems solved by multiplication and division?

It is necessary to show the peculiarity of work on

tasks not only in the traditional, but

and in UMK «Harmony».

** Application
theoretical knowledge
on practice. **

** System
assignments, tasks
topic. **

Practical

assignments is a form of learning

material related to practical

teaching methods. These methods form

practical knowledge and skills. Task

them is to keep for a long time

time gained knowledge.

In the classroom

mathematics system of practical knowledge

can be used at the stages of fixing

or repetition of learned material.

- Olya bought

3 pencils, 4 rubles each. How many

was this purchase worth it? - Afternoon

There are 4 plates left on the table. None

none of them had sausages. How many

all the sausages on those plates? - Each

bottle of 2 liters. lemonade. How many liters

lemonade in three bottles? at five? - To each rabbit

gave 3 carrots. How many carrots did you give

6 rabbits? - 10 oranges

Divided equally among 2 plates. How many

oranges on every plate? - For lighting

three classes it took 15 lamps, equally

for each class. How many lamps in each

class? - Make tasks

according to their decision: 1) 10 • 3 = 30 (l) answer: 30l;

2) 2• 6=12(kg) answer: 12 kg; 3) 3 •4=12(cm) answer:

12cm - Make tasks

according to the drawings so that they are solved

multiplication. Write solutions: - Notebook price

3r. How much does 5 of these notebooks cost? -
Includes a large barrel

buckets of water, and in a small one — 3 times less.

How many buckets of water are included in a small

barrel? - Girl

I bought 2 packs of cookies, 200 gr. each. Put

question and solve the problem. - compose

drawing for a problem that would be solved

so: 2•3, 3•3, 5•3.

Thus, when learning

children of any topic after

theoretical material

practical reinforcement. We know that

theory without practice is impossible.

When studying simple

multiplication and division problems

the teacher should pay great attention

attention to tasks related to these

actions. They contribute to the best

assimilation and memorization of the table

multiplication, the ability to apply the received

knowledge for practice in everyday life.

** Methods
used in
introduction of concepts
fastening, **

** at
repetition. **

Method (from ancient Greek.

«metodos» — a path to something) is a way to achieve

goals, ordered in a certain way

activity. (Pedagogy. S.P. Baranov)

Teaching methods

— these are ways of joint activity

teachers and students sent

to achieve the goals of education, upbringing,

development of schoolchildren.

** Method- **

is the assimilation of material in certain

forms of cognitive theoretical

or practice.

**
Method-** is a system of rules and techniques

approach to the study of phenomena and regularities

nature, society, thinking.

**
Method- ** is the way, the way to achieve

certain results of knowledge and

practices.

Pedagogy deals with

various methods that are used

in primary school when teaching any

school subject. Thus, bearing in mind the joint

activities of teacher and student

such methods: explanations of the material by the teacher,

conversation, independent work of students.

Depending on the purchase method

knowledge by children distinguish between methods: dogmatic,

heuristic, research. If

consider methods in terms of path,

then they talk about inductive, deductive

methods and analogies. All these methods are used

and when teaching mathematics, taking into account the peculiarities

the subject itself, spoke in

relationship, unity.

Selection of methods

learning is determined by many factors:

general learning objectives, content

the material being studied, the level of preparedness

children to master the relevant material.

Consider which

methods best used:

When studying

(introduction) concepts most commonly used **
verbal method ** . More difficult material

the teacher explains, i.e. uses the story.

* Story * is

narrative method

material studied by the teacher and activation

cognitive activity of students.

For example, at the very beginning, when studying

topics «Simple problems for multiplication and division»

give children a little history

about the quantities.

Children receive

ready-made knowledge. But more efficient

use conversation when introducing concepts.

* Conversation * . Teacher

through skillfully asked questions encourages

students to reason and analyze

in a certain logical sequence

studied facts and phenomena and independently

approach the relevant theoretical

conclusions and summaries.

During a conversation

children themselves are looking for answers to some questions,

trying to figure it out on their own

what they develop an active mental

activity.

Good to use

visual method for children to imagine

the current situation, especially

they have better developed visual

memory.

Visual aids

available:

— demo

1. Type-setting sheet,

designed to work with subject

pictures, movable numbers.

2. Colorful

typesetting canvases (plot

with slots).

3. Item sets

pictures.

4. Sets of subject

tasks to create tasks.

— individual

1. Cards with

math tasks.

2. Type-setting sheet.

Also used

practical methods.

Children take possession

material based on exercises, independent

assignments.

Used

also ** explanatory — illustrative** . The structure of these methods can be

method

divided into 2 parts: 1) theoretical

2) illustrative. Children are given information

in accordance with the curriculum.

Illustrative

material allows you to link explanation

with the student’s personal experience, makes an explanation

accessible. For example, when introducing the concept

«task» the teacher says the task

and illustrates it in the course of the text. Gives

simultaneously the concept of a condition and a question.

Usually all this is illustrated on typesetting

canvas. When fixing the material, also

verbal method is used, most often

conversation. During the conversation, it becomes clear how

children learned the material. Also used

visual method, i.e., various

visual aids for the child to imagine

the situation and showed (when solving problems,

for example, dividing into equal parts)

answer to the question.

Used

and method of practical exercises.

Solving problems with explanation

students. Can be used on these

lessons non-standard types of exercises,

staging a task by roles: one

student — says «condition», the second — «question»,

the third — «explains the decision», the fourth

— “decides”, the fifth — “reads the answer”.

When repeating

visual aid is used. For example,

task cards, cards with

drawings, according to which children make up

task.

At this stage

the method of practical

exercises. Children composing themselves

problem can be solved, so at the same time

used and independent work

students.

Can be used

introspection and self-control, where is the child

analyzes his work, actions,

which he performs, also a child

must control their mistakes, be able to

find and fix them.

Self-contained

work makes children think it

fosters working capacity, independence,

attention. Most often independent

work is carried out for self-control.

** SALES
PRINCIPLES OF LEARNING. **

Principle (from lat. Principium — beginning, basis):

1) the main starting position of which —

or theories, teachings, sciences, worldviews,

political organization; 2) internal

a person’s belief that defines him

attitude to reality, norms of behavior

and activities; 3) device base or

action of any device, machine

etc. (Sov. Encyclop. Dictionary).

Principle (from Lat.

basis, origin) — leading

idea, basic rule, basic requirement

to activities and behavior arising from

from the laws established by science.

(Pedagogy S. P. Baranov, L. R. Bolotina

etc.)

Learning principle

— these are the initial provisions that determine

the activities of the teacher and the nature of cognitive

students’ activities.

Didactic

principles are the most important, the main patterns

and laws that form the basis of didactic

process. They reflect the joint action

many regularities of the educational process,

regulate the activities of teachers and students,

retain their general significance in the study

all subjects and at all stages

learning. Therefore, didactic

principles are the basic principles that govern

content, organizational forms and methods

educational process in accordance with its

common goals and patterns.

topics «Simple multiplication problems

and division” implements the basic principles

didactics in the traditional system of education.

** Principle
scientific nature of teaching. **

Even in the elementary course of mathematics at

familiarization with the topic «Simple tasks

on multiplication and division ”students get acquainted

with different concepts: “multiplication, division,

task, solution”, etc. Realize the real

quantitative relationships between different

objects. Install dependency

between the data and the desired, the condition and the question,

draw conclusions, model, obtain

results. Tasks are solved

different ways, use different

visual aids. Distinguish between «form»

problem solution record” and “method of solving

tasks». Gradually work is going from simple

to more difficult.

** Principle
systematic training. ** Material

given in a particular system. Children first

get acquainted with arithmetic operations,

with the concept of «task», condition and question,

and then with different kinds of tasks.

** Principle
visibility. ** Children using

visual aids get acquainted with the new

material. Since at this age

the child’s visual memory is better developed,

than auditory. The child thinks concretely

images, then reliance on sensory knowledge

is a necessary condition for learning.

It is proposed to use images,

real items as pictures

in the picture, drawing, diagram. Especially

in the early stages of introducing children to various

types of tasks, use visualization.

For example: Problems for dividing by equals

parts and content. For a deeper

comprehension it is better to use some

items.

** Principle
consciousness and
activity. ** Students consciously learn

to this subject. When faced with a task,

by its decision, the child must learn the material,

because You can’t do without a task in life.

Often in the classroom we see and notice that

when learning new material (for example:

acquaintance with the task, increasing the number

several times), children who actively

work in the classroom, understand the material

and already at the next steps can decide

such tasks independently and without difficulty.

** Principle
strength. ** The teacher must achieve

solid acquisition of knowledge by children. For

to carry out consolidation, repetition,

explanation, generalization, practical exercises,

use visual aids. For completeness

knowledge, you need to highlight the main idea.

Knowledge, skills, skills will be stronger,

if children apply them in practice

activities in their daily lives.

** Principle
accessibility. ** Knowledge that students

receive when studying this topic, they

accessible, i.e. understandable, especially since

children, getting acquainted with this topic, relying on

for visual aids. Definitions studied

in this topic should be given by the teacher

language accessible to children. Let’s say

that the teacher only leads the children to the definition

conditions and question, and then gives the opportunity

children to formulate this definition.

Based on this, the teacher in an accessible language

gives an explicit definition of this concept.

So

a set of principles allows

characterize the entire educational process,

all aspects of the teacher’s activity

and cognitive activity of students.

Each principle has its rationale.

Guiding Principles for Teaching Mathematics

in elementary grades are:

## Word problems — online presentation

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Preparation for the exam in mathematics. Basic level Complex tasks

### 1. Text tasks

The concept of text

task

### 2. A text task is a description of some situation in natural language with the requirement to give a quantitative characteristic

of some component of this situation, to establish the presence or absence

of some relationship between the components

or to determine the type of this relationship

.

Problem structure

Condition

Requirement

(question)

– The dog chased the fox, which was 30 m away from it. AT

while the fox makes three jumps, the dog makes

only two. How many jumps must the dog make,

, to catch up with the fox? How far will

dog run?

### 3.

Compare tasks. 1. Masha found 3 mushrooms, Petya found 2 mushrooms. How many mushrooms did the children find in total? 2. How many mushrooms did the children bring home,

if

Masha found 3 mushrooms, and Petya found 2 mushrooms?

3. Masha found 3 mushrooms, and Petya found 2 mushrooms. They

put them in one basket. Find the number of mushrooms

in the basket.

The requirement is presented as a question.

Condition and requirement is given in one sentence

.

The requirement is formulated in

imperative form.

### 4. A requirement is an indication of what needs to be found. It can be expressed in an imperative or interrogative form.

Reformulate

tasks.

Masha found 3 chanterelles and 2 white mushrooms, and Petya-4

chanterelles. How many mushrooms did the children find in total?

Two girls simultaneously ran towards each other

along a sports track, the length of which is

420 m. When they met, the first ran

60 m more than the second. At what speed did each girl run

if they met

after 30 seconds?

### 5. Classification of problems

Number of actions

Number of conditions

Ways of solving

simple

Certain problems

For the triple rule

composite

Problems with

alternative condition

For finding the unknown 90 059 Undefined

tasks (missing

data)

Proportional

division

Redefined problems

(redundant

data)

Elimination of one of the

unknowns

Average

arithmetic

Percentages and parts

Solved from the end

(reverse)

Practical

Arithmetic

Technical

Algebraic Geometric

Geometric

Logical

reasoning

3+2=5 3+x=5

l—l—l

Practical method is a method in which

the answer is in the process of action with

items or their substitutes.

### 7. Solve the problem.

Petya

is taller than Kolya, Seryozha is lower than Kolya.

Who is taller?

A logical method is a method in which

the answer is found as a result of

logical reasoning.

Sometimes several methods are used in the course of

solving, in which case

it is considered that the problem has been solved

by the combined method.

### 8. Modeling in the process of solving problems

Modeling is one of the mathematical methods

knowledge of the surrounding reality, in which

models are built and studied.

The text problem is a verbal model

To solve the problem, it is necessary to build its

mathematical model. to

auxiliary, and then to

mathematical

2nd stage — intramodel solution

.

The values of

numerical expressions are found,

equations are solved.

Stage 3 — translation of the obtained solution

into natural language

Using the obtained solution,

the answer to the question is formulated drawing

— scheme

Verbal Mathematical

— drawing

— short entry

3+2

— table

Auxiliary

Decisive

Drawing

Olya

Kolya

?

Reference drawing

?

Scheme

3

2

?

Drawing

(requires introduction of scale

and ability to use tools)

◙—●—●—◙—●—◙

————— ———

?