Easy Guide: Writing Numbers in Expanded Form with Decimals

Writing Numbers in Expanded Form (with Decimals)

When you write a number in expanded form (also known as expanded notation), you are expressing the number separated into its composite individual place values (and decimal values if necessary) in the form of an expression.

An easy way of thinking about writing numbers in expanded form is taking apart a number into its specific place values. The place value chart below is a good review of the value of each number slot.

Conversely, writing a number in standard form (or numeric form) is the opposite or reverse of writing a number in expanded form.

Click here to download this chart as an easy-to-print PDF file.

Writing a Number in Expanded Form Example

Example: Write 8,743 in expanded form

8,743 = 8,000 + 700 + 40 + 3

Note how the use of a place value chart can help you write numbers in expanded form.

Writing a Number in Expanded Form with Decimals Example

Example: Write 317.29 in expanded form.

317.29 = 300 + 10 + 7 + 0.2 + 0.09

This strategy applies to all problems that require you to read or write numbers in expanded form.

Check out the free video lesson below to learn more about how to write numbers in standard form with decimals and without.

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Share your ideas, questions, and comments below!

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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.

Free Guide: How to Use Minecraft Education Edition

Are you ready to learn how to use Minecraft: Education Edition with your kids at home or in your classroom?

This guide will help you get started using Minecraft Education Edition and will explain how to create an account, start a free trial, purchase the app in the app store (for Mac and PC computers and the iPad), and how to use Minecraft Edition to create meaningful learning experiences in all subject areas.

Why Teachers Are Using Minecraft: Education Edition

Minecraft is changing the way that our students are learning.

The world-building adventure game empowers students to make learning connections in a play environment that supports collaboration, ownership, autonomy, and agency. This game-based approach to teaching and learning embraces the way that today’s students learn new things and brings it into the classroom.

Because there are Minecraft–based learning experiences for every subject (more on that later), the applications are incredible and the sky is the limit when it comes to using Minecraft to improve learning outcomes, which is why it’s a powerful tool for teaching your students to love learning.

How Does Minecraft Help Students to Learn?

Today’s students need to develop skills that will allow them to succeed in a rapidly changing world. And it is widely believed that the jobs that today’s students will hold in the future do not even exist yet. Gamified learning tools, like Minecraft, equip students with:

 21st Century Skills

98% of teachers who use Minecraft in their classroom cited problem solving as the top skill their students learn from Minecraft. Teachers also reported improvements in creative thinking, reading and writing skills, and computational thinking. These skills are critical when it comes to helping our students to develop the necessary skills to succeed in technology-dependent society.

 Job Preparedness and STEM

 71% of teachers using digital games for learning reported improvement in computational thinking and numeracy skills, according to a study by the Joan Ganz Cooney Center. These skills are required for STEM careers including computer science and programming.

 Social-Emotional Development

Soft skills refer to the skills that a student develops through both social and emotional learning. Developing these skills is important because today’s students will need more than just technical skills to be successful in the future. According to the Minecraft 2030 report, teachers reported that Minecraft helped their students to improve problem solving, critical thinking, collaboration and communication skills.

You can visit Minecraft’s Classroom Impact page to learn more about this research and access dozens of case studies of how educators from around the world are using Minecraft to engage students in all subjects.

How to Log Into Minecraft Education Edition

 You will need a Microsoft Office 365 Education account to login. Your school account may already be verified with Office 365. You can verify by submitting your email address here. If you don’t already have an account, you will be redirected to the sign-up page.

How to Download a Minecraft Education Edition Free Trial

Once you have an Office 365 account, you can download a free trial.

Click here to download your free trial for Windows and Mac OS.

Click here to download your free trial for iPad from the app store.

How to Purchase a Subscription to Minecraft Education Edition

 A free trial allows for a limited number of logins before you will be asked to purchase a yearly subscription.

 You can purchase a subscription by visiting the Microsoft Store for Education.

Tips for Getting Started

 Here are 3 tips for getting started with Minecraft Education Edition:

1.) Educator Resources

 You can ease your way into using Minecraft in your classroom by utilizing the free online educator resources shared on the Minecraft Education website. This online resource library includes tutorials on how to play, community features that connect you with other Minecraft educators, and training modules for beginners.

Image Source: education.minecraft.net

 2.) Minecraft Education Subject Kits

The easiest way to get started using Minecraft in your classroom is by using the subject kits for each subject. This library shares hundreds of lessons created by other educators for all subjects, including math, art and design, and history. Click here to access the full subject kit library for free.

Image Source: education.minecraft.net

 3.)  Learn From Your Students

You do not have to be a Minecraft expert or know more about it than your students do to successfully use it in your classroom. The more likely case is that your students will be doing most of the teaching (which is why Minecraft is such a great tool for developing collaboration and soft skills) and this is not a bad thing. By taking advantage of your students’ knowledge and passion for the game, you will learn the finer points very quickly.

Given the tremendous potential for using Minecraft in your classroom, it is certainly worth the effort of giving it a shot. If you feel intimidated, try downloading a free trial and experimenting with the game itself. You can also hop onto the Minecraft Education Community page to connect with other educators, ask questions, and learn more about how other educators in your subject field got started.

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How are YOU using Minecraft to teach your students? 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.

10 Super Fun Math Riddles for Kids! (with Answers)

10 Super Fun Math Riddles and Puzzles for Kids Ages 10+ (Answers Included!)

A Post By: Anthony Persico

Some have been around for centuries, while are others are brand spanking new—but all have been selected as the most fun and engaging math riddles for those who love to challenge their problem-solving skills and have fun solving math puzzles. Enjoy!

The Educational Value of Math Riddles:

Fun and engaging math riddles and logic puzzles are an amazing way to get students to think critically, develop problem-solving skills, and think about mathematics in a creative way!

In fact, several recent studies have shown that students who work on math puzzles—with and without teacher supervision—improve their math problem-solving skills, learning abilities, and willingness to stick with challenging problems, according to Edutopia.

And if you are looking for a collection of super fun, challenging, and sometimes silly math riddles and brain teasers for kids, then it’s time to put your brain to the test!

Note that the following math riddles are best suited for kids ages and older and they are also fun for high school students and adults!

Are YOU ready?

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10 Super Fun Math Riddles for Kids:

Each of the following math riddles includes an image graphic and there is an answer key at the end!

But if you want more detailed explanations of how to answer every riddle, check out the Math Riddles Explained! video link below and be sure to give it a thumbs up!

Watch the Math Riddles Video:

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Free Worksheet Included!

There is also a link to download a Free Printable PDF Math Riddles Worksheet and Answer Key that shares all of these riddles at the end of this post!

All of the math riddles, puzzles, and brain teasers below are from the best-selling 101 Math Riddles, Puzzles, and Kids Ages 10+! PDF workbook, which is now available!

10 Awesome Maths Riddles and Brain Teasers for Kids:

Math Riddle #1: Truth or Square?

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Truth or Square?

Would you like FREE math resources in your inbox every day? Click here to sign up for my free math education email newsletter (and get a free math eBook too!)

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Math Riddle #2: How Old Is Lucy?

Keep reading the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve How Old is Lucy?

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Math Riddle #3: Triple Threat

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Triple Threat!

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Are you looking for more super fun Math Riddles, Puzzles, and Brain Teasers to share with your kids?

The best-selling workbook 101 Math Riddles, Puzzles, and Brain Teasers for Kids Ages 10+! is now available as a PDF download. You can get yours today by clicking here.

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Math Riddle #4: Matchstick Mayhem

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Matchstick Mayhem!

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Math Riddle #5: The In-Between

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve The In-Between!

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Math Riddle #6: Which Weighs More?

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Which Weighs More?

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Math Riddle #7: Big Spender!

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Big Spender!

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Math Riddle #8: Mystery Parking!

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Mystery Parking!

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Math Riddle #9: Cuppla’ Coins

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Cuppla’ Coins!

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Math Riddle #10: Pascal’s Triangle

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Pascal’s Triangle!

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Math Riddle #11: Bonus!

Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve the Bonus Riddle!

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ANSWER KEY:

1. 14 Total Squares (detailed explanation)

2. Lucy is 37 (detailed explanation)

3. 1, 2, and 3 (detailed explanation)

4. 0+4=4 or 5+4=9 (detailed explanation)

5. A Decimal Point (detailed explanation)

6. Neither. They both weigh the same! (detailed explanation)

7. The hoodie costs $125, the shoes cost $25 (detailed explanation)

8. 87 (flip the image upside down) - (detailed explanation)

9. One is a quarter and one is a nickel (detailed explanation)

10. 6 (detailed explanation)

11. 1, 5, 10, 10, 5, 1 (detailed explanation)

Free PDF Worksheet:

Click here to get your Free Math Riddles PDF Worksheet and Answer Key!

And click here to sign up for our math education mailing list to start getting free K-12 math activities, puzzles, and lesson plans in your inbox every week!

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Are you looking for more super fun Math Riddles, Puzzles, and Brain Teasers to share with your kids?

My best-selling workbook 101 Math Riddles, Puzzles, and Brain Teasers for Kids Ages 10+! is now available as a PDF download. You can get yours today by clicking here.

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Did I miss your favorite math riddle for kids? Share your thoughts, questions, and suggestions 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.

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Free Math Coloring Worksheets for 5th and 6th Grade

Are you looking for free math coloring worksheets to share with your 5th grade and 6th grade students?

(Were you looking for math coloring pages for grades 3 and 4?)

The following free math coloring worksheets for grade 5 and grade 6 are available as printable PDF files. They incorporate mathematical thinking and problem solving as well as understanding of addition, subtraction, multiplication, division, and order of operations.

Each coloring worksheet can be used to supplement your lessons and they also make perfect warm up and cool down activities, homework assignments, and extra credit.

Keep reading to access the full PDF file that shares all five math coloring worksheets for 5th graders and 6th graders. To download each worksheet individually, right-click an image and save it to your computer.

Check This Out: Free PDF Math Puzzles for All Grade Levels

Math Coloring Worksheets for 5th and 6th Grade

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Math Coloring Worksheet #1/5: Monkey Math!

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Math Coloring Worksheet #2/5: Summer Fruit!

Are Your Kids Ready for These Candy-Themed Math Puzzles for Grades 1-6?

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Check This Out: Free Growth Mindset Math Poster for Your Classroom!

Math Coloring Worksheet #3/5: Toys and Games!

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Are YOU looking for some super fun daily math puzzles for your students in grades 3-8? Our best-selling 101 Daily Math Challenges workbook is now available as a PDF download!

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Math Coloring Worksheet #4/5: Pirate Adventure!

Check This Out: 10 Super Fun Math Riddles for Kids (with Answers)

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Math Coloring Worksheet #5/5: Snack Time!

Click here to download all 5 free Math Coloring Worksheets for 5th Grade and 6th Grade Students as a PDF file AND access the answer key to each puzzle.

And click here to access free math coloring worksheets for grades 3 and 4!

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You Might Also Like…

Have any questions or ideas? 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.

Reflection Over The X and Y Axis: The Complete Guide

What is a Reflection in Math?

Learning how to perform a reflection of a point, a line, or a figure across the x axis or across the y axis is an important skill that every geometry math student must learn.

In real life, we think of a reflection as a mirror image, like when we look at own reflection in the mirror.

This idea of reflection correlating with a mirror image is similar in math.

This complete guide to reflecting over the x axis and reflecting over the y axis will provide a step-by-step tutorial on how to perform these translations.

 First, let’s start with a reflection geometry definition:

Math Definition: Reflection Over the X Axis

A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.

Math Definition: Reflection Over the Y Axis

A reflection of a point, a line, or a figure in the Y axis involved reflecting the image over the Y axis to create a mirror image. In this case, the Y axis would be called the axis of reflection.

What is the rule for a reflection across the X axis?

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4). Notice that the x-coordinate for both points did not change, but the value of the y-coordinate changed from 4 to -4.

What is the rule for a reflection across the Y axis?

The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same.

For example, when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P’, the coordinates of P’ are (-5,4). Notice that the y-coordinate for both points did not change, but the value of the x-coordinate changed from 5 to -5.

You can think of reflections as a flip over a designated line of reflection. You can often visualize what a reflection over the x axis or a reflection over the y axis may look like before you ever apply any rules of plot any points. This aspect of reflections is helpful because you can often tell if your transformation is correct based on how it looks. If the new image resembles a mirror image of the original, you’re in good shape! If it does not, you probably did something wrong.

Examples of Reflection Over the X Axis and Y Axis:

Notice how the reflection rules for reflecting across the x axis and across the y axis are applied in each example.

Check out the video lesson below to learn more about reflections in geometry and for more free practice problems:

You can download the free lesson guide that accompanies this video lesson by clicking here.

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Looking for More Geometry Transformation Help?

Free Guide to Geometry Dilations and Scale Factor

Free Guide to Rotations (90, 180, 270, 360)

Free Guide to Translations on the Coordinate Plane

Tags:  Reflection over the x-axis (x axis), Reflection across the x-axis (x axis), Reflection over the y-axis (y axis), Reflection across the y axis (y axis), Reflection in the x-axis (x axis), Reflection in the y axis, Reflection geometry definition, Reflection math definition

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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.