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This image demonstrates the multiplication table through 10x10. I love this graphic because it is a clear way to show the patterns and numbers in multiplication. It shows the products of each two numbers multiplied. This can be used in the classroom to give students a way to study their multiplication tables and see patterns in multiplication they might not have recognized before. This relates to the ALCOS standard #7 for 3rd grade math: fluently multiply within 100. Because this table demonstrates multiplication up to 10x10, it demonstrates how to multiply within 100 with numbers 1-10. This lines up with my criteria because it is easy to understand the table, is all visual, and allows students to see and understand multiplication facts.

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This video uses popular children's movies/stories to represent themes and how to discover them. It allows the students to interact by quizzing the students on their knowledge of themes after learning what a theme is. It could be used in the classroom as a starter on a new lesson to give students a head start on the topic. It lines up with the ALCOS standard #2 4th grade English: discover the theme of a story. This video helps describe how to discover the theme of a story, so it is a great way to help teach this standard. It is perfect with my criteria because it is appropriate, accurately related to themes, and helps the learning of themes for students.

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3rd and 4th Grade Reading (What Is the Theme of a Story)

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When first seeing this website, I only thought it would provide games. As I looked into it, I realized it provided a helpful way to see how to multiply equal groups. It has great visuals and allows students to interact with the information presented. This could be used in the classroom as a guide when first beginning to multiply by showing how groups of items are multiplied together. It also allows students to test their knowledge before revealing the full answer. This also represents the ALCOS standard #1 for 3rd grade math: interpreting products of whole numbers. Because it describes multiplication through grouping, it is a great way to show how to find products of whole numbers when first learning how to multiply. The criteria lined up well with this website because it is kid-friendly, provides visuals for the students, and allows them to be interactive through the reading process.

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Math Help for Multiplication: Easy-to-understand lessons for kids, parents and teachers. Practice what you learn with games and quizzes.

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This image provides a simple and concise way to look at themes. It provides the basis and main things to know about a theme. It would be great to use in the classroom to pull up while students are reading or trying to come up with themes to help remind them quickly of what they're looking for. This also relates to ALCOS standard #2 4th grade English: discover the theme of the story. It quickly outlines exactly how to identify the theme, so it lines up very well. I think this fits my criteria because it fits the age group, perfectly represents theme, and helps students when first learning how to find themes.

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This video represents multiplication by showing groups of items. For example, 3 groups of 5 apple cores were multiplied together to show 3x5=15. This video is entertaining and allows students to see how multiplication can be seen in real life. This video can be used in the classroom to demonstrate how to multiply groups of items, or just multiply simple numbers in general. I love this video because it effectively describes the multiplication process in a fun way. This represents the ALCOS standard #1 for 3rd grade math: interpreting products of whole numbers. This video is a wonderful example of this standard because it shows how whole numbers from groups of items can create a product through multiplication. I love how this lines up with my criteria. It is easy to watch and stay focused on the video, it is very visual, and it allows places for students to think and understand how multiplying works.

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What is multiplication? | Multiplication for kids

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I LOVE this image because it gives a step-by-step process for finding a theme. It shows how you can find a theme through looking at characters' actions and their affects. It can be used in the classroom as an example template when students are working on discovering themes of stories. It also fits with the ALCOS standard #2 4th grade English: discover the theme of the story. It helps students understand how to find and interpret a theme from a story. This is age appropriate for 4th graders, is accurate to the subject, and helps teach students how to find themes on their own.

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This website does a great job of representing multiplication in a couple ways. For example, it shows visuals, describes multiplication terminology, how to use a number line to help represent multiplication, and properties of multiplication. It would be great to use in the classroom for visual learners, but what I really love about this website is that it shows information on multiple topics. While I chose the specific page on the basics of multiplication, there are numerous information pages on multiplication that can be used to help solidify multiplication ideas. This best relates to the ALCOS standard #1 3rd grade math: interpreting products of whole numbers. Because its main purpose is showing how to multiply whole numbers to form products, it fits this standard the best. This website lines up with my selection criteria because it was easy to use and provided many visuals for learning. There are also many ways to practice on this website as well, making it greatly interactive.

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$8 + 8 + 8 + 8 = ?$

$8 + 8 + 8 + 8 + 8 + 8 + 8 = ?$

Don't you think it's too tedious to add 8 so many times.

There is an easy and better way to do this.

Multiplication Definition in Math

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.

To understand better, let us take a multiplication example of the ice creams.

Each group has ice creams, and there are two such groups.

Total ice creams are $3 + 3 = 6$.

However, you have added two groups of 3 ice creams. Therefore, you have multiplied three ice creams by two. You may also write it as $2 × 3 = 6$.

As we can see, $3 + 3$ is the same as $2 × 3$.When we multiply two numbers, the answer is called product. The number of objects in each group is called multiplicand, and the number of such equal groups is called the multiplier. In our case, $3$ is the multiplicand, $2$ is the multiplier and 6 is the product.

There are many ways to read an equation that involves multiplication.

For example, $2 × 3 = 6$. It can be read as follows:

Two multiplied by three is six.

Two times three is six.

Two threes are six.

Symbol of Multiplication

Multiplication is represented by the signs cross (×), asterisk (*), or dot (·). While writing in your notebooks, you are most likely to use the cross. The asterisk and dot are used in computer languages and algebra (higher mathematics).

For example: $6 × 5 = 30$

$7 * 8 = 56$

$5 · 4 = 20$

Multiplying Integers

In order to multiply the integers, we need to see the sign of the integers.

Multiply two positive integers

The product of the two positive integers is always a positive integer.

For example: $5 × 6 = 30$

Multiply one positive and one negative integer

The product of a positive and negative integer is always a negative number.

For example: $(-5) × 6 = (-30)$

Multiply two negative integers

The product of two negative integers is always a positive integer.

For example: $(-5) × ( -6) = 30$

Multiplying Fractions

In order to multiply the fractions, the numerators and denominators are multiplied together such that:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

For example: Multiply $\frac{1}{2}$ and $\frac{3}{4}$.

$\frac{1}{2} \times {3}{4} = \frac{1 \times 3}{2 \times 4} = 38$

Multiplying Decimals

Multiplying the decimals is the same as multiplying the integers.

For example: Multiply $13.2$ and $3.5$.

Let us multiply $13.2$ and $3.5$ by removing the decimals here and consider them whole numbers. Hence,

$132 × 35 = 4620$

We put the decimal point back, then the product of the two decimal numbers will have decimal up to two positions from right to left, such that

$13.2 × 3.5 = 46.20$

Multiplying Numbers with Powers

In math, powers define a base raised to the exponent. For example: $3^2, {(-5)}^4$.

When the base is the same but power is different

Let the two expressions be $x^m$ and $x^n$. Here, the base is " x ".

When the terms with the same base are multiplied, the powers gets added, i.e., $x^m$ $x^n = x^{(m + n)}$

For example: $3^2$ $3^5=3^{2+5} = 3^7$

When the base is different but the exponent is the same

Let the two expressions be $x^m$ and $y^m$. Here, the power is " m ".

When the terms with the same exponents are multiplied, the bases are multiplied first and then we apply the exponent, i.e., $x^my^m = (xy)^m

For example: $3^24^2=(3 x 4)^2=12^2 = 144$

When the bases and powers are different

Let the two expressions be xn and ym. Here, the bases are x and y. The powers are n and m. When we multiply these expressions, each expression is evaluated separately and then multiplied. It can be written mathematically as

$x^ny^m = (x)^n(y)^m$

For example: $3^2 x 4^3=9 x 64 = 576$

Properties of Multiplication

Just like addition, multiplication also follows specific properties, which are as follows:

Commutative Property: This property states that when we multiply two numbers, the order will not cause any change in the product.

Let us consider $2 × 3 = 6$, for example. If we reverse the order, i.e., compute $3 × 2$, the answer will still be $6$.

Associative Property: This property states that if we multiply three numbers or more, one after the other, the order does not matter. For example: if we have to $2, 3$ and $4$:

If you jumble the order and multiply, the result will still not change.

Distributive Property: This property states that if you multiply a number by the sum of two numbers, the result will be equal to the sum of products you obtain by multiplying that number by those two numbers individually. For example, $3 × 8$.

You can write $8$ as $6 + 2$. Therefore $3 × 8 = 3 × (6 + 2) = 24$

Now, $3 × 6 = 18$. Also, $3 × 2 = 6$.

$18 + 6 = 24 = 3 × 8$. Therefore, distributive property holds true.

Tips to Master Multiplication

Here are some tips that will come in handy while multiplying:

Memorizing tables: Multiplication is all a game of tables. So, if you have tables at your fingertips, you will find little easy to multiply.

Making good use of the properties: If you are thorough with the properties of multiplication, you will be able to deconstruct complex problems into simpler ones. For example:

$3 × 13 = 3 × (10 + 3) = (3 × 10) + (3 × 3) (Distributive property)$

This also helps in deriving new facts from the known facts.
For example :

If you know $2 × 9 $ is $18$, using the commutative property of multiplication, you also know that $9 × 2$ is also $18$.

If you know $2 × 10$ is $20$ and $2 × 4 $ is $ 8$, using the distributive property of multiplication, you also know that $2 × 14$ is $ 28$.

Fun Facts

If you multiply any number by $1$, the answer will be the number itself. One is called the identity element under multiplication.

If you multiply any number by zero, the result is always zero.

Conclusion

Multiplication is not just an arithmetic tool. It is a life skill that students must master at a very early age to solve real life problems. We hope this helped you deepen your understanding of the subject.To read more such informative articles on other concepts, do visit our website. We, at Splashlearn, are on a mission to make learning fun and interactive for all students.

Solved Examples

Multiply $4 × 2$ using a number line.

$4 × 2$ means $4$ jumps of $2$ or $2$ jumps of $4$ which is $8$ in both cases.

$2 × 16 = 2 × (10 + 6) = (2 × 10) + (2 × 6) = 20 + 12 = 32$.

The property given above is the commutative property of multiplication i.e. $a × b = b × a$.

IV. What should we multiply to $(-24)$ to get the product as $48$?

Let the number be x.

$(-24) × x = 48$

$x = - 2$

V. Multiply $\frac{2}{5}$ and $\frac{15}{8}$.

$\frac{2}{5} x \frac{15}{8} = \frac{3}{4}$

Practice Problems

Frequently Asked Questions

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What is Multiplication? Definition, Symbol, Properties, Examples

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8 + 8 + 8 + 8 = ?$ $8 + 8 + 8 + 8 + 8 + 8 + 8 = ?$ Don't you think it's too tedious to add 8 so many times. There is an easy and better way to do this.

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This website is great because it introduces word problems by including steps followed by an in-depth tutorial. It would be great to use in the classroom to practice following the steps of a word problem as well as trying visual examples. It follows the ALCOS standard #3 3rd grade math: solve multiplication word problems within 100. This website provides examples of word problems within 100 and includes visuals as well. It follows my selection criteria as it is easy to understand and learn, it has great visuals to envision the word problems, and is an interactive website.

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Multiplication Word Problems - Maths with Mum

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Multiplication Word Problems Example Video Questions Lesson Share to Google Classroom Example Video Questions Lesson Share to Google Classroom There are 3 tables and there are 6 children on each table.The children are in equal groups of 6.There a 3 groups.We have 3 lots of 6, which we can write as a multiplication.3 ×6 = ...

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This is a website with a large list of themes. This can be helpful for students just learning about themes so that they can have an idea of common themes in stories. This might help them identify themes easier in the beginning of the process. It can be used in the classroom while students are recalling themes in stories or creating their own stories with a central theme. I think this best relates to the ALCOS standard #35 4th grade English: tell a story that supports a theme. This list provides common themes that can be used to build or mold a story. It follow my selection criteria well because it is a good list for 4th graders, relates well to the learning of themes, and can be greatly beneficial to the understanding and use of common themes in stories.

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Literature

Themes in literature are often varied and hidden. Sometimes you can get through an entire book and not realize what the author meant. However, this is a good basic list that you can build from. Remember that some books have multiple themes.

Beauty of simplicity

Capitalism - effect on the individual

Change of power - necessity

Change versus tradition

Chaos and order

Character - destruction, building up

Circle of life

Coming of age

Communication - verbal and nonverbal

Companionship as salvation

Convention and rebellion

Dangers of ignorance

Darkness and light

Death - inevitable or tragedy

Desire to escape

Destruction of beauty

Disillusionment and dreams

Displacement

Empowerment

Emptiness of attaining false dream

Everlasting love

Evils of racism

Facing darkness

Facing reality

Fading beauty

Faith versus doubt

Family - blessing or curse

Fate and free will

Fear of failure

Female roles

Fulfillment

Good versus bad

Greed as downfall

Growing up - pain or pleasure

Hazards of passing judgment

Heartbreak of betrayal

Heroism - real and perceived

Hierarchy in nature

Identity crisis

Illusion of power

Immortality

Individual versus society

Inner versus outer strength

Injustice

Isolation

Isolationism - hazards

Knowledge versus ignorance

Loneliness as destructive force

Losing hope

Loss of innocence

Lost honor

Lost love

Love and sacrifice

Man against nature

Manipulation

Materialism as downfall

Motherhood

Names - power and significance

Nationalism - complications

Nature as beauty

Necessity of work

Oppression of women

Optimism - power or folly

Overcoming - fear, weakness, vice

Patriotism - positive side or complications

Power and corruption

Power of tradition

Power of wealth

Power of words

Pride and downfall

Progress - real or illusion

Quest for discovery

Quest for power

Rebirth

Reunion

Role of men

Role of Religion - virtue or hypocrisy

Role of women

Self - inner and outer

Self-awareness

Self-preservation

Self-reliance

Social mobility

Technology in society - good or bad

Temporary nature of physical beauty

Temptation and destruction

Totalitarianism

Vanity as downfall

Vulnerability of the meek

Vulnerability of the strong

War - glory, necessity, pain, tragedy

Will to survive

Wisdom of experience

Working class struggles

Youth and beauty

Movies

Movies generally have one or two themes, but not many more. The themes in movies are often said outright instead of hinted at. Some of the popular themes from movies today include:

Poetry

Themes in poetry are often quite apparent, but that isn't always the case. Sometimes the theme doesn't make itself apparent and is instead up to the reader. Reading a poem aloud often helps with understanding the theme. Here are some examples:

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A Huge List of Common Themes - Literary Devices

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Literature Themes in literature are often varied and hidden. Sometimes you can get through an entire book and not realize what the author meant. However, this is a good basic list that you can build from. Remember that some books... Read more →

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This website is great to help find themes in stories or your own writing. For the classroom, I believe it is most beneficial to use while reading stories because it gives a great 3 step analysis on how to identify the theme. It makes you dig into the story to pull out the true meaning. It aligns with the ALCOS standard #2 4th grade English: discover the theme of the story. The 3-step process is great in providing a clear outline for finding themes in any story. I like how this website is advanced but age appropriate, related to my subject, and a great learning tool.

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This post is all about theme. We will explore the definition of a theme, give you examples of themes, and we will go through three steps that will help you find your theme in your story.

When we teach writers how to write a or a we emphasise how crucial theme is in the process. The best novels and the most life-changing memoirs you will ever read are the ones that help you discover a truth about the human condition.

A theme in a book should never be stated, but should be developed through character changes and plot escalation. A theme can be strengthened by the use of motifs.

In The Art Of Dramatic Writing, Lajos Egri says well-defined characters drive plots. He emphasises the consistency of change in life. Characters have to adapt, evolve, and 'synthesise' new philosophies. They do this after facing many overwhelming obstacles.

What is a theme?

1. Theme is the central idea of the story.

2. It is better if it is a full statement, with a subject and a verb.

3. It sums up what the story shows us about the human condition. It is not a moral. It is simply a statement.

1. Honesty is the best policy.

2. Who dares wins.

3. Fools rush in where angels fear to tread.

4. Home is where the heart is.

5. The past is a foreign country - they do things differently there.

6. You never really know anybody.

7. People are predictable.

8. People with nothing to lose are dangerous.

9. Love conquers all.

10. Blood is thicker than water.

11. You can choose your friends but you can't choose your family.

12. What does not kill you makes you stranger.

It's About The Meaning

If you understand your plot, the parts your characters, especially the protagonist and the antagonist, play in the story, and the effects this plot will have on your characters' lives, you will find the meaning of your story.

Once you understand the meaning, you will find the theme.

3 Steps To Help You Find Your Story's Theme

Ask these three questions to find your theme.

1. What is the story about? This is the plot of the story. Example: My story is about a man who hunts down the men who were acquitted after they killed his family.

2. What is the meaning behind the story? This is usually an abstract result of his actions. Example: My story says that when the system fails a person who has lost everything, he will find out how far he is prepared to go.

3. What is the lesson? This is a statement about the human condition. Example: People with nothing to lose are dangerous.

The Lajos Egri Theme Cheat Sheet:

Lajos Egri gives this simple formula to develop a theme:

1. Your wife committing adultery leads to you finding out you never really know anyone.

2. Embezzling money from your company and getting caught leads to you understanding honesty is the best policy.

3. A woman who meddles in other people's marriages leads to her realising that fools rush in where angels fear to tread.

How A Theme Helps

Once you have a theme for your book, use it to check if every scene fits in your novel.

Ask yourself: Does this scene build your story's theme?

Sources: The Basics of Fiction, Writers Write and Lajos Egri

© Amanda Patterson

If you enjoyed this, read these posts:

1. 5 Really Good Reasons To Outline Your Novel

2. Why Revenge is Such a Brilliant Plot for Beginner Writers

3. Cheat Sheets For Writing Body Language

4. Basic Plot Structure - The Five Plotting Moments That Matter

5. 9 Literary Terms You Need To Know

6. 106 Ways To Describe Sounds - A Resource For Writers

TOP TIP: If you want to learn how to write a book, sign up for our online course.

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3 Steps To Help You Find Your Story's Theme

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This post is all about theme. We will explore the definition of a theme, give you examples of themes, and we will go through three steps that will help you find your theme in your story. When we teach writers how to write a or a we emphasise how crucial theme is in the process.

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BrainPOP has been one of my favorite resources since I was in elementary school. They provide a helpful and educational lesson in an entertaining way. I love how this one can quickly describe themes for students. It can be used in the classroom for a quick refresher during a long lesson or a recap of something learned the day before. I think it also fits the ALCOS standard #2 4th grade English: discover the theme of the story. This video efficiently explains how to find a theme in a story. It fits my criteria because it is great for 4th graders, it is accurate for my subject, and really helps students grasp what a theme is and how to apply it.

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I love this website on long multiplication. It provides a description and walk-through tutorial on the process, while including videos throughout the tutorial showing how to work the problems. This could easily be used for students in the classroom to practice learning on their own. Since there are helpful videos and it is in depth, I think this would be a great way to introduce the idea of individual learning. It lines up with the ALCOS standard #8 5th grade math: fluently multiply multi-digit whole numbers. This matches because it shows how to multiply larger whole numbers together using long multiplication. I like how this fits with my selection criteria as it is easy to read, includes videos for visuals, and allows students to follow along with the videos and interactively learn.

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Long Multiplication is a special method for multiplying larger numbers.

It is a way to multiply numbers larger than 10 that only needs your knowledge of the ten times Multiplication Table.

Let us say we want to multiply

612 × 24

First we multiply 612 × 4 (=2,448),

then we multiply 612 × 20 (=12,240),

and last we add them together (2,448 + 12,240 = 14,688).

But we can do better!

When we multiply 612 × 20 we only need to multiply and place the result one column over (so it is the same as multiplying by 20).

We just have to be careful about lining up the columns. Here is how to do it (press the play button):

We could also put a zero where the space is, like this:

More Than Two Digits

The same idea works when multiplying by more than two digit numbers. We just have to move over more spaces:

Have a try yourself with these Long Multiplication Worksheets

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.