What is a Whole Number in Math?

What is a Whole Number in Math?

What is a whole number in math, is 0 a whole number, and how can you tell if a number is a whole number or not?

What is a whole number in math?

Do you remember when you first started learning how to count? At this early stage, you likely used your fingers as a simple counting tool. One, two, three, four, and so on. While the days of counting on your fingers are likely long behind you, the journey that you began then has led you to this point, where you are ready to learn about whole numbers, what they are, and how they fit into the number system.

Before we dive into learning about whole numbers, lets quickly review the definition of a natural number so that you can understand the difference between a natural number and a whole number later on.

What is a Natural Number?

In math, natural numbers are the numbers that we use for counting and ordering values or amounts. The set of natural numbers starts at 1 and is as follows: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …}

Natural numbers are sometimes referred to as counting numbers. Notice that the set of natural numbers does not include 0, fractions/decimals, or negative numbers.

We can visualize the natural numbers on a number line as shown in Figure 01 below:

Figure 01: What is a Natural Number?

What is a Whole Number?

Now that you know what a natural number is, you can extend that understanding to whole numbers.

In math, whole numbers are a set of numbers that includes all of the natural numbers as well as 0.

The set of whole numbers starts at 0 and is as follows: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …}

Notice that, just like the set of natural numbers, the set of whole numbers does not include fractions/decimals or negative numbers.

We can visualize the whole numbers compared to the natural numbers on a number line as shown in Figure 02 below:

Figure 02: What is a whole number?

Simply put, the set of whole numbers is just the entire set of natural numbers with zero included.

With this in mind, we can say that the set of natural numbers is a subset of the set of whole numbers, which is why the diagram in Figure 03 below is often used to demonstrate this relationship.

Figure 03: Natural numbers are a subset of whole numbers. All whole numbers (except zero) are natural numbers too.

The Role of Zero: Is 0 a Whole Number?

Next, let's explore commonly asked question regarding whole numbers: Is zero a whole number? The answer to this quest is yes!

Zero is a whole number.

When it comes to the universe of numbers (and its subsets), the value zero is important because it represents a quantity of “nothing” or an empty set. In the case of whole numbers, zero is the dividing point that separates the positive numbers from the negative numbers (since zero is neither positive or negative).

As you continue to study the universe of numbers, you will continue to consider negative numbers and the set of integers, which includes all zero, all of the natural numbers, and their negative counterpart.

The set of integers in comparison to whole numbers and natural numbers, as well as the role of zero, is shown in Figure 04 below.

The set of integers does not include any values with fractional or decimal part. It does not have a starting point and is as follows {…,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…}

Figure 04: Is zero a whole number? Zero is a whole number and an integer as well.

Figure 05: Whole numbers and natural numbers are subsets of integers.

Examples of Whole Numbers

Now you are ready to extend your understanding of whole numbers to a few examples with real-world context:

• Example #1: The number of members in the chess club. You can’t have a fraction of a person or a negative person as a member of a club, so the number used to describe the number of members will always be a whole number such as 7 or 12. And, of course, if nobody joins the chess club, you could say that there are zero members.

• Example #2: The amount of marbles in a bag. You can’t have a fraction of a marble or a negative marble, so the number used to describe the amount of marbles in a bag will always be a whole number such as 22 or 60. And, if the bag is empty, you could say that the amount of marbles is zero.

• Example #3: The number of cars for sale at a dealership. Again, it is not possible to have a fraction of a car or a negative car, so the number of cars for sale will be a whole number such as 5 or 116. If all of the cars are sold and there is nothing for sale at the dealership at any point in time, then the amount of cars for sale can be zero.

Figure 07: Whole Numbers in the Real-World: The number of cars available for sale at a dealership will always be a whole number such as 25 since it’s impossible to have a fraction of a car or a negative car and the amount of cars available can be zero if the lot is empty.

Conclusion: What is a Whole Number in Math?

In math, the universe of numbers can be broken into several subsets.

The most basic of these subsets are the Natural Numbers (also known as counting numbers), which related to elementary finger counting as follows: {1, 2, 3, 4, 5, …}.

Whole numbers are a set of numbers that includes all of the natural numbers as well as 0.

Unlike the set of natural numbers, which starts at 1, the set of whole numbers starts at 0 and is as follows: { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …}. Whole numbers can not be fractions or negative.

The set of whole numbers is just the entire set of natural numbers with zero included and we can say that the natural numbers are a subset of whole numbers.

While not a natural number, zero is a whole number and it plays an important role in the universe of numbers as a divider/boundary between the positive numbers and the negative numbers.

This understanding of whole numbers will help you as you continue on with your study of real numbers and their subsets, especially your next likely destination: integers.

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What is Finite Mathematics?

What is Finite Mathematics?

This Fascinating Field of Study Focuses on Math Concepts in the Finite Universe and Has Tremendous Real-World Applications.

What is Finite Mathematics?

Math can be a challenging subject, especially at the college level, but it can also be incredibly rewarding as the subject has practical applications that are useful in essentially every career path imaginable. This post will explore Finite Mathematics, what it entails, how difficult it is, and how it differs from calculus.

What is Finite Mathematics?

Finite Mathematics is an extremely interesting branch of math that primarily deals with concepts applicable to the finite (as opposed to infinite) universe. Despite its technical name, finite mathematics is primarily concerned with applying mathematics problem-solving and reasoning to real-world phenomena, making it a critical area of knowledge for students pursuing careers in business, social sciences, computer science, and other practical career disciplines.

What is Finite Mathematics?

Typical Finite Mathematics courses will cover any or all of the following math topics:

• Linear algebra: This topic focuses on vectors, vector spaces, linear transformations, and systems of linear equations. Linear algebra is integral to various fields of study ranging from business economics to applied physics.

• Set theory: This topic focuses on the study of sets, or collections of distinct numbers/objects. Set theory serves as a key foundation to several branches of mathematics.

• Combinatorics: This topic is the study of counting, arrangement, and combination of numbers/objects including permutations, combinations, and counting principles.

• Probability: This topic focuses on the analysis of uncertainty and random occurrences. The study of probability is a cornerstone of statistics.

• Graph theory: This topic focuses on the exploration of graphs and is highly applicable in computer science, where data structures are often represented in graphical form.

• Logic: While more abstract, this topic focuses on formalizing mathematical statements and investigating their validity in a mathematical/systematic way.

• Matrix algebra: This topic focuses on the study of matrices and their algebraic properties. Matrix algebra is closely tied to linear algebra.

• Finite calculus or difference equations: This topic focuses on discrete change, such as sequences and series. Finite calculus is often a precursor to calculus, which deals with the infinite universe.

Before moving on, it is worth noting that not all Finite Mathematics courses or textbooks will cover all these topics.

Is Finite Mathematics Hard?

As with any math course, the difficulty level of Finite Mathematics varies from student to student. Since Finite Mathematics relies heavily on logical reasoning, critical thinking, and the application of math formulas and algorithms, the difficulty is often directly related to how well you understand these related topics. If these areas are your strengths, you will likely find Finite Mathematics appropriately challenging for you (i.e. not too hard and not too easy).

Still, Finite Mathematics can be tricky at times even if you are proficient in logical reasoning, critical thinking, and the application of math formulas and algorithms. Why? Because, as previously mentioned, Finite Mathematics courses often cover a diverse range of topics that require students to be proficient in a variety of math skills and concepts.

However, with the right attitude and approach, most students can be successful in Finite Mathematics and you are likely to struggle much less than you would in a typical Calculus course. In any case, it is always important to remember that, when it comes to mathematics, once you understand the basic principles, more complex ideas become easier for you to grasp.

Is finite mathematics hard? Like any math course, the difficulty level will vary from student to student

Finite Mathematics vs. Calculus

So, what is the difference between Finite Mathematics and calculus?

The main difference between Finite Mathematics and calculus is the subject of infinity. Finite Mathematics restricts itself to finite sets, meaning that it does not explore the concept of infinity or infinite sets. On the other hand, calculus delves into the concept of infinity to describe continuous change.

In essence, Calculus takes the study of Finite Mathematics to the next level, which is why it is typically considered to be a more complex and challenging field of mathematics.

Because calculus is more complex than Finite Mathematics, it is often divided two sections: differential calculus and integral calculus. The topics covered in calculus are fundamental to physics, engineering, and economics, among other fields.

In contrast, Finite Mathematics focuses on discrete phenomena related to the finite universe of numbers. Unlike calculus, which focuses on exploring and describing smooth and continuous change, Finite Mathematics excels at analyzing distinct elements and systems that are countable and often rooted in real-world scenarios and data. As such, the topics covered in finite mathematics are often applicable to computer science, statistics, and operations research.

Despite these differences, Finite Mathematics and calculus share a very strong common foundation rooted in the exploration and application of logic and mathematical reasoning.

The skills taught in finite mathematics are often applicable to the field of computer science and research.

Conclusion: Finite Mathematics

In conclusion, whether or not Finite Mathematics is the right math course for you depends on your math skill level, personal interests, career aspirations, and comfort with mathematical logic and reasoning. While not as complex as calculus, Finite Mathematics is an engaging course with many real-world and career-relevant applications. Mastering this field of math will allow you to continue to pursue careers in a variety of desirable fields and industries. With the right mindset and approach, and a willingness to challenge yourself, you are likely to find the journey that is Finite Mathematics to be both valuable and rewarding.

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Bigfoot Sightings Map —Decoding Bigfoot's Trail Using Data

Decoding Bigfoot's Trail: How a Bigfoot Sightings Map Can Predict Bigfoots Whereabouts

Where is Bigfoot? By analyzing a comprehensive Bigfoot Sighting Map, you can see where sightings and concentrated and better predict Bigfoot’s movements and up-to-date location.

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Bigfoot Sighting Map Courtesy of the Bigfoot Mapping Project (click to enlarge)

Today’s post will focus on tracking the elusive Bigfoot, a creature that has managed to keep humanity on our toes for hundreds of years. And our tool for tracking the movements and potential locations of Bigfoot will be a detailed and comprehensive map of bigfoot sightings that will allow you to visualize and potentially predict Bigfoot's next move.

The legendary creature known as Bigfoot has been sighted in many parts of North America, leading to numerous theories about his movement patterns and general whereabouts. Bigfoot’s location has been an ongoing mystery that continues to baffle scientists and enthusiasts alike as it remains unclear whether or not Bigfoot is continuously on the move or if there are multiple Bigfoot-like creatures scattered around North America.

Given the mystery surrounding Bigfoot and his whereabouts, looking at a comprehensive bigfoot sighting map is great way to make educated and scientific predictions and conclusions about Bigfoot, his movements, and his location at any given time.

Bigfoot Sightings Map: Is Bigfoot a migratory creature? Does he stay in one place or is he nomadic? Is there more than one Bigfoot?

A Bigfoot sightings map is a two-dimensional grid that depicts all of the landmass of North America and has points plotted at all of the geographical locations where a Bigfoot sighting has been reported. Every plotted point represents one reported Bigfoot sighting. And, by compiling all of these sightings on a map, you can use the data to see where sightings are concentrated and also track/predict Bigfoot’s movement patterns.

Why is the Bigfoot sightngs map such a useful tool? From a scientific and mathematical standpoint, patterns often hint at reliability and predictability, and this is where any serious analysis of determining Bigfoot’s whereabouts should begin.

Analyzing a map of Bigfoot sightings can give you important and incredibly useful insights into Bigfoot's preferred geological living environment, potential movement patterns, and, most importantly, his current location.

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Bigfoot Sighting Map: Concentrated sightngs in the Pacific Northwest

Additionally, the sightings map can help you to determine if there are certain geological features favored by Bigfoot. For example, does he prefer dense forests over open plains? Does he prefer to be near major water sources, cave systems, weather conditions, etc.? Does Bigfoot tend to appear during specific seasons or times of day?

By better understanding these questions and there potential answers, you have a much better chance of determining Bigfoot’s current location at any given point in time.

Many Bigfoot sightings have been reported in the dense, remote forests of the Pacific Northwest regions of the United States and Canada. This pattern could suggest that Bigfoot prefers forested areas far from human habitation, perhaps for shelter or food resources. The more we understand these patterns, the better we can predict where he might show up next.

Of course, analyzing a Bigfoot sighting map isn't just about connecting dots or plotting points on a grid. The map itself is only a tool and it requires an understanding of the geographical, climatic, and ecological factors at play. Are there abundant food sources in the areas of reported sightings? What's the population density like? Answers to such questions deepen our understanding of Bigfoot's behavior and raise new questions as well.

In the case of being a Bigfoot detective and using science and data to track the elusive being, we are not merely passive observers, but active participants attempting to unravel the mysteries of Bigfoot's existence. And, in doing so, we contribute to the larger discourse on Bigfoot and his alleged movements.

Bigfoot Sighting Map: Is Bigfoot a migratory creature? Are there multiple Bigfoots?

As organizations continue to collect and analyze sightings data, a Bigfoot sighting map becomes an ever-evolving tool, gaining in accuracy and detail. It's a testament to the collective efforts and scientific curiosity of the Bigfoot community.

However, it is also important to note that, while it's easy to get caught up in the thrill of the chase, it's important to approach each reported sighting with a healthy dose of skepticism. Always consider the source and the circumstances of the sighting. Not every footprint in the mud belongs to Bigfoot.

If you are looking for an interactive and comprehensive Bigfoot map that is constantly updated, we recommend the Bigfoot Mapping Project’s website, where you can see up-to-date Bigfoot sightings, analyze geographical features such as elevation, and report a sighting of your own!

Source: The Bigfoot Mapping Project

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7 Trendy Middle School Sumer School Math Ideas

Your summer vacation has arrived, but a break from school doesn't mean that your kids have to stop developing their math skills.

Whether you’re teaching summer school courses, running a summer math camp, or looking to keep your kids practicing their math skills at home over break, the following ideas will help you make this summer an awesome mathematical learning experience!

1.) Watch and Learn

Summer break is a perfect time for your kids to improve their weaker areas and further develop their understanding of math topics.

Rather than relying on a one-size-fits-all summer curriculum, try taking advantage of the plethora of free math videos on YouTube and let students explore lessons that meet their individual needs. 

Here are 5 YouTube channels that share fun and engaging math video lessons that your kids will actually want to watch:

1. For the Basics: Math Antics

2. For More Complex Topics: Numberphile

3. For Auditory Learners: Numberock

4. For Visual Learners: Mashup Math

5. For Math in Story-Form: Math with Matthew

See Also: 10 Best YouTube Channels for STEAM Learning

2.) Project-Based Learning

Free from the demands of pacing guides and standardized curriculums, summer vacation is the perfect time for your kids to explore math concepts in the context of hands-on projects that are both engaging and enjoyable.

If you're looking for summer math project ideas that can be modified to appropriately challenge and engage math students at the elementary and middle school levels, check out this list of 10 Awesome End of Year Math Project Ideas.

See Also: Teaching Math Through Major League Baseball Summer Project

3.) Back to Basics

While summer vacation is a great time to further explore previously-learned math concepts and ideas, it's also an opportunity to take a step back and ensure that your kids' fundamental skills are where they need to be.

Whether it's working with fractions, breaking down word problems, or solving equations, your kids likely need extra time and opportunities to develop and improve important prerequisite skills.

If you're looking for free and helpful practice resources that are broken down by topic, I recommend the following websites:

• KutaSoftware.com

• K5Learning.com

• HomeSchoolMath.net

• PurpleMath.com

• EngageNY.org

• AdaptedMind.com

See Also: Are you using these 5 awesome websites for free math worksheets?

4.) Gamify

Teachers often struggle to get their kids interested in practicing and learning math during summer vacation.

If you're looking to provide your kids with learning opportunities that break away from the familiarity of routine classroom lessons and activities, try gamifying your approach.

Gamification is the process of taking something that already exists – a website, an enterprise application, an online community – and integrating game mechanics into it to motivate participation, engagement, and loyalty, according to www.brunchball.com.

You can gamify your math curriculum by having kids take on math-related games and puzzles in a physical and/or digital setting.

Looking for gamified math ideas? The following resources will get you started:

• Printable Math Challenges and Puzzles

• Digital Math Games

• Gamified Skill Practice

See Also: Can your middle schoolers solve these math puzzles?

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Are YOUR kids ready for these fun daily math challenges this summer?

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5.) Get Visual

Stanford professor and progressive math education guru Jo Boaler describes mathematics as "a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualization, and flexibility, the mathematics comes alive."

When your students aren't thinking about math in a visual context, they are missing out on developing a deep understanding of the material.

If you're looking to give your kids more opportunities to explore mathematics in a visual context, check out these Awesome, Research-Based Visual Math Activities suggested by Jo Boaler.

6.) Get Writing

Did you know that writing about math encourages creativity, exploration, and communicating one's thoughts and feelings?

When kids write about math, they learn to organize their thinking, use key vocabulary terms and phrases, and communicate mathematically—which leads to deep and meaningful understanding.

If you're looking for ways to get your kids writing about math this summer, check out this list of 5 Ideas for Writing in the Math Classroom.

See Also: 101 Think-Notice-Wonder Writing Prompts for Engaging Your Kids

7.) Get Reading

So you want your kids thinking about math over the summer, without formally practicing it?

Reading math-related fiction books is a great way to get your kids thinking creatively and mathematically during vacation. 

Looking for some fun and creative summer reading STEM books for the elementary, middle, and high school levels? Check out this list of 13 STEM Fiction Books Your Kids will Actually Enjoy Reading This Summer.

See Also: 10 Best Math Movies for Middle School Math Students

How do you plan on keeping your kids thinking mathematically over summer vacation? Share your thoughts in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

7 Handy Ideas for Packing Up Your Classroom

Another school year is almost in the books and you're ready to shift your attention away from testing, grading, and partying and towards packing up your classroom and starting your summer vacation.

Experienced teachers will tell you that spending a little extra time and effort on packing up your classroom the right way will make your life much easier in the long run. And it's easier than you think!

So, if you're willing to resist the temptation to randomly throw your stuff into boxes, the following tips will help you pack up the right way, without exhausting yourself. And, as a bonus, you'll ensure yourself a stress-free start when school picks up again in a few months.

1.) Take Pictures First

Save yourself the time of planning and arranging your ideal classroom setup next year by taking a few pictures of what your classroom looks like now. You'll be able to reference these photos when setting up your classroom again in the fall.

Take pictures of what your classroom setup looks like before you start packing up.

2.) Start Early

Waiting until the last second to pack up your classroom almost guarantees a stressful and disorganized experience. By starting the process three or four weeks prior to the last day of school, you can break the task down into smaller and more manageable pieces.

Don't wait until the last days of school to start packing up your classroom.

3.) Organization is Key

While organizing all of your supplies and paperwork will be the most time-consuming task of packing up, the payoff will be huge when you return to school in the fall. It's much easier to get your things in order now when your mind is used to being in the classroom every day.

Taking the time to organize your stuff before you pack will pay off in the long run.

4.) Get Students Involved!

Don't take on the burden of packing up your classroom alone. Your kids will be glad to help you and many of them will willingly stay after school or come in during lunch to help you pack, organize, and clean. 

Your students are like your own personal moving team.

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Looking for fun ways to get your kids WRITING about math and science?

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5.) Label Everything

You may know exactly what's in those storage bins right now, but you'll have no idea come the fall. By clearly labeling everything you pack, you can easily prioritize when unpacking again at the start of next school year. If you don't have a label maker, a strip of painter's tape and a sharpie work great!

Labeling helps keep you organized and makes unpacking much easier.

6.) Use Packing Tubes for Posters

Classroom posters, banners, and signs seem to always get crumpled and bent during the packing process. You can keep yours in excellent condition and reuse them year after year by keeping them safe in cardboard packing tubes. You can get them at any office supply store for around $5.

Packing tubes will keep your posters, banners, and signs from getting crumpled and bent.

7.) Throw Stuff Away

The end of the school year is a perfect time to assess which materials and resources are no longer useful. It's ok to throw away items that you never use, especially old textbooks and workbooks that are a pain to pack and unpack. If an item is not adding value to you and your students, get rid of it!

The end of the school year is the perfect time to purge yourself of useless items.

Do you have any additional advice for teachers packing up their classrooms? Share your thoughts in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.