Negative Exponent Rule Explained in 3 Easy Steps

Understanding the Negative Exponent Rule

Before you learn to understand and apply the Negative Exponent Rule, let’s recap what you already know about positive exponents.

For example, 5^2, or 5 squared, is equal to 5x5, or 25.

But what would change if the exponent (2 in this case) was negative instead of positive?

In math, when you think of the word negative or negate, the implication is that you must perform the opposite or inverse operation.

With positive exponents, you perform multiplication.

So, with negative exponents, you perform the opposite or inverse of multiplication, which is…

Division (because division is the inverse operation of multiplication).

Now you are ready to use the Negative Exponent Rule

Negative Exponent Rule in 3 Easy Steps

Now let’s look at the previous example again, except this time the exponent is -2 (negative two).

Step One: Rewrite the Value with Negative Exponent as a Fraction

Since we are performing division (the inverse of multiplication), we will rewrite the value as a fraction with a numerator of one.

Step Two: Trash the Negative Sign and Move the Value to the Denominator

To complete the fraction, get rid of the negative sign in front of the exponent and move the remaining value (5 squared) to the denominator of the fraction.

Notice that 5 to the negative second power is equal to one over 5 to the positive second power.

via GIPHY

Step Three: Trash the Negative Sign and Move the Value to the Denominator

The final step is to simplify rewriting 5 squared as 25 and concluding that 5^-2 is equal to 1/25 or 0.04.

Expressed as a fraction.

Expressed as a decimal.

Looking for a visual representation of how the negative exponent rule works?

Check out the free video lesson below to learn more about how the negative exponent rule.

---

Free Negative Exponents Worksheet

This lesson includes a free Negative Exponent Rule worksheet that accompanies the video lesson. Click the link below to get yours!

Download your free Negative Exponents Worksheet Lesson Guide PDF

Share your ideas, questions, and comments 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 . 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.

Celebrate National Chocolate Cupcake Day with These Free Math Puzzles

Celebrate National Chocolate Cupcake Day in Your Math Classroom with These Free Math Puzzles

Did you know that October 18th is National Chocolate Cupcake Day in the United States?

You can celebrate at home by baking up a batch of yummy chocolate cupcakes to share with family, friends, and co-workers!

And you can celebrate in your classroom with two fun math cupcake-themed math puzzles for students in grades 3-8!

The first Cupcake Day Challenge is a Multiplication Table Puzzle.

The second Cupcake Day Challenge is an Area Model Puzzle.

These activities are perfect for warm-up and cool-down activities as well as for supplementing your lesson plans, extra credit assignments, and homework.

1.) Chocolate Cupcake Day Multiplication Puzzle

This puzzle challenges students to use their math and reasoning skills to find the value of 6 different symbols contained within a multiplication table (it works like a bingo-table where the icon in each box represents the product of its corresponding column and row.)

*Keep reading to get the answer key.

2.) Chocolate Cupcake Day Area Model Puzzle

This puzzle challenges students to apply their understanding of multiplication to find the missing values in an area model that represents the products of two different numbers.

*Keep reading to get the answer key.

These puzzles are samples from my best-selling workbook 101 Math Challenges for Engaging Your Students in Grades 3-8.

The book is available as a PDF download and you can also get a hard copy on Amazon (Free Amazon Prime Shipping Included; pages are in black-and-white).

And here are the solutions to today's puzzles:
Multiplication Table Answer Key:

Area Model Answer Key:

Plain Cupcake=20, Sprinkle Cupcake=80, Chocolate Bar=5, Milk=4, Baker=100

You Might Also Like…

---

I am interested in…

Math Video Games Puzzles for Grades 1-6: Are Your Kids Ready?

Are Your Students Ready for Some Super Fun Video Games-Themed Math Puzzles?

Kids love playing video games. 

Whether it's on X-Box, Nintendo Switch, or a Smart Phone, your students are likely enjoying playing some sort of video game in their free time.

Sharing your enthusiasm for video games is a great way to build relationships with your kids—plus you can channel that enthusiasm towards math learning activities!

So go ahead and share today's video game-themed math puzzles with your kiddos! It makes for a great warm-up or cool-down activity to get your kids to practice applying logic, reasoning, and order of operations.

Why? Because kids love fun (and 100% free) math puzzles!

The following video game-themed math puzzles for elementary and middle school students are samples from my best-selling PDF math workbook: The Big Book of Super Fun Math Puzzles for Grades 1-6.

The puzzles are tiered by difficulty using the following color system used in the book.

Pink Level (Grades 1-2) | Blue Level (Grades 3-4) | Green Level (Grades 5-6+)

Free Video Games Math Puzzles for Grades 1-6+

(answer keys to follow)

Pink Level Puzzle ( for Grades 1-2)

Free Math Resources: Astronomy Day Math Puzzles for Grades 1-6

Blue Level Puzzle (for Grades 3-4)

Free Math Resources: Pet-Themed Math Puzzles for Grades 1-6

Green Level Puzzle (for Grades 5-6+)

Wait! Do You Want More Fun Math Puzzles to Share with Your Kids??

If you and your students like these pet-themed puzzles, then you should definitely get yourself a copy of the new book, which shares over 300 kid-friendly, differentiated, and printable math puzzles and activities!

It covers differentiated topics including:
-addition and subtraction
-multiplication and division
-order of operations
-inverse operations
-adding and subtracting fractions
-multiplication tables
-area models
-math writing activities

And the book includes a really cool Make Your Own Math Puzzle hands-on activity requiring only scissors and glue to complete. 

It also includes a complete answer key and several useful templates.

Take a Look Inside

You can access the entire Table of Contents by clicking here.

And you can click the links below to access some sample pages:

Pink Level Samples (for Grades 1 and 2): Sample A | Sample B

Blue Level Samples (for Grades 3 and 4): Sample A | Sample B | Sample C

Green Level Samples (for Grades 5 and 6+): Sample A | Sample B | Sample C

There are three puzzles per page and they include the familiar name/date/directions sections that are included in typical math worksheets, which makes them easier to print and share aswarm-up and exit-ticket activities, in lesson plans, and as extra credit and homework assignments.

Click here to get your copy of The Big Book of Super Fun Math Puzzles for Grades 1-6.

And check out the solutions to the pet-themed puzzles below:

Pink Level (Grades 1-2): Nintendo Switch=3, Pacman=10, Gameboy=5, ?=8

Blue Level (Grades 3-4): Nintendo Switch=11, Pacman=11, Gameboy=9, X-Box Controller=16, ?=176

Green Level (Grades 5-6+): Nintendo Switch=6, Pacman=6, Gameboy=17, X-Box Controller=76, ?=224

---

Sharing video game math challenges and puzzles with your students is just one effective strategy for boosting engagement in your classroom. Subscribe to our mailing list here to get more free daily resources, lesson plans, ideas, and insights for K-12 math teachers in your inbox every week.

Read More Posts About Math Education:

---

By Anthony Persico

Anthony is the lead educator and founder of Mashup Math. He lives in Denver, Colorado and is also a YouTube for Education partner. Follow him on Twitter at @mashupmath.

Teacher Burnout Is Real. Here Are 3 Effective Prevention Strategies

These Effective Strategies Will Help You to Maintain a Healthier Work-Life Balance and Prevent Teacher Burnout

A Post By: Anthony Persico

The demands of being a classroom teacher can be extremely stressful and often lead to burnout. These strategies and helpful reminders can help you achieve work-life balance and learn to manage teaching-related stress in healthy ways.

Edutopia describes teacher burnout as a state of continuous stress that leads to detachment and cynicism, exhaustion (both physical and emotional), and feeling ineffective and unaccomplished. It can also be described as depression caused by the workload involved with being a teacher.

When teachers fail to prioritize a healthy work-life balance, they put themselves at risk of burning out and losing their passion for being an educator. In fact, teacher burnout may be a leading factor in why 44% of new teachers quit the profession within their first five years.

However, there are many effective strategies that teachers can use to establish healthy boundaries between work and personal life, prevent themselves from being overextended and overstressed, and get through an entire school year without burning out.

3 Effective Strategies for Preventing Teacher Burnout

1.) Learn to Say No

Teachers often make more commitments than they can reasonably handle. While your heart is probably in the right place, you place yourself on the fast track to burnout when you say ‘yes’ too often.

In fact, once you establish yourself as someone who never says ‘no’, students, parents and administrators will only ask more of you, as they are skilled at squeezing every drop of energy a teacher has to offer.

But you have the right to say 'no' to unreasonable requests —without feeling guilty. In the long run, your students and your school will be better off having teachers who live healthy and balanced lives (rather than ones who are exhausted and burnt out).

Read More: Why Every Teacher Should Learn to Say 'No'

2.) Make Time for Yourself

Many teachers make the mistake of spending too much of their personal time working on school-related tasks. This imbalance can easily lead to feeling burnt out way before the school year has ended.

Establishing clear and firm boundaries between your work and personal life is a key element to establishing balance. Some ideas for setting boundaries include:

• No checking emails after the school day has ended.

• No grading or lesson planning on Fridays and Saturdays.

• Staying after school for extra help only two days per week.

• No committing to extracurricular activities.

In addition to setting boundaries, be sure to include non-negotiable personal time in your schedule for things like exercise, reading, and spending time with friends and loved ones.

Read More: A Message to New Teachers: Failure, Feedback, and Focus

3.) Practice Mindfulness

The everyday demands of teaching can be stressful and overwhelming. By practicing mindfulness through meditation, you can effectively learn to slow yourself down, maintain perspective, and deal with stress in a healthy way.

Mindfulness—a set of skills that allows one to be calm and focused on the present moment—can be a real game-changer for teachers looking to manage stress and avoid teacher burn out. Even a few minutes of practice each day can make a big difference.

The following infographic from Harvard Graduate School of Education shares more information on how teachers can use mindfulness to increase well-being, and overcome challenges.

Read More: 21 Time-Saving Strategies, Activities, and Ideas All Math Teachers Should Know

Building Mindfulness For Teachers Guide Learn more about early childhood education from Professional Education at the Harvard Graduate School of Education

Did you find this post on preventing teacher burnout helpful?

Subscribe to our mailing list here to get more free daily resources, lessons, and tips in your inbox every week.

Read More Posts About Math Education:

Anthony is the lead educator and founder of Mashup Math. He lives in Denver, Colorado and is also a YouTube for Education partner. Follow him on Twitter at @mashupmath.

I am interested in…

---

---

Box and Whisker Plots Explained in 5 Easy Steps

Box and Whisker Plot Definition

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

Box and whisker plots help you to see the variance of data and can be a very helpful tool.

This guide to creating and understanding box and whisker plots will provide a step-by-step tutorial along with a free box and whisker plot worksheet.

Let’s get started by looking at some basketball data!

How to Make a Box and Whisker Plot

Observe the following data set below that shares a basketball players points scored per game over a seven-game span:

Step One: The first step to creating a box and whisker plot is to arrange the values in the data set from least to greatest.

In this example, arrange the points scored per game from least to greatest.

Step Two: Identify the upper and lower extremes (the highest and lowest values in the data set).

The lower extreme is the smallest value, which is 5 in this example.

The upper extreme is the highest value, which is 32 in this example.

Step Three: Identify the median, or middle, of the data set.

In this example, the median is 17.

See Also: Check Out This Awesome Mean, Median, and Mode Activity

Step Four: Identify the upper and lower quartiles.

To find the lower quartile and the upper quartile, start by splitting the data set at the median into lower and upper regions.

The upper quartile is the median of the upper region, and the lower quartile is the median of the lower region.

In this example, the upper quartile is 20 and the lower quartile is 10.

Now we have all of the information that we will need to construct our box and whisker plot!

Step Five: Construct the Box and Whisker Plot

To construct a box and whisker plot, start by drawing a number line that fits the data set.

Start by plotting points over the number line at the lower and upper extremes, the median, and the lower and upper quartiles.

Next, construct two vertical lines through the upper and lower quartiles, and then constructing a rectangular box that encloses the median value point.

Then construct a vertical line through the median point that extends to the top and bottom of the rectangle.

This is the box in the box and whisker plot.

Finally, draw horizontal lines that connect the lower quartile to the lower extreme and the upper quartile to the upper extreme to complete the box and whisker plot.

The box and whisker plot is complete!

Box and Whisker Plot Worksheet

Are you looking to get some more practice with making and analyzing box and whisker plots?

Check out the following free box and whisker plot worksheet, which is available as a PDF download!

Click here to download your free Box and Whisker Plot worksheet.

Answer key included.

Box and Whisker Plot Video Lesson

Check out our free Box and Whisker Plots Explained video lesson on YouTube for a more in-depth look:

Tags:  box and whisker plot explained, box and whisker plot definition, box and whisker plot problems, box and whisker plot outliers, box and whisker plot worksheet, box and whisker plot range

---

Have thoughts? 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. 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.

Related Posts: