Box and Whisker Plots Explained in 5 Easy Steps

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Box and Whisker Plots Explained in 5 Easy Steps

Box and Whisker Plot Definition

Source: Mashup Math MJ

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

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

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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.

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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.

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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

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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.

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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.

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

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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.

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

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

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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.

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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!

The box and whisker plot is complete!

Box and Whisker Plot Worksheet

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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!

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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.

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Are Your Kids Ready for These Halloween Math Activities?

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Are Your Kids Ready for These Halloween Math Activities?

Are You Ready to Celebrate Halloween with Your Math Students This Year?

Are your students excited to celebrate Halloween this year?

If so, then you can channel their enthusiasm for this spooky time of year towards learning math with some brand new Halloween-themed two truths and one lie math activities for grades 3-8.

Go ahead and share these activities at any point during your math lessons this month to boost student engagement and bring some holiday festiveness into your classroom. You may also like our 13 Days of Spooky Math Puzzles and these fun hands-on Halloween math activities for all ages. Enjoy!

 

Image Source: Mashup Math FP

 

The following Halloween Math Activities for elementary and middle school students are samples from my best-selling PDF math workbooks: 101 Two Truths and One Lie! Math Activities for Grades 3-5 and 101 Two Truths and One Lie! Math Activities for Grades 6-8.

Two Truths and One Lie (2T1L) math activities revolve around your students being presented with three facts, images, or statements (only two of which are true). The objective is for students to identify which statement is false and justify why (verbally, in writing, or both).

2T1L activities are an excellent strategy for boosting student engagement, sparking mathematical thinking, and opening small-group or full-class discussions. They are great for warm-up and cool-down activities during the first or final minutes of class.

Click here to learn more about how you can use two truths and one lie math activities to engage your students.

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Free Halloween Math Activities for Grades 3, 4, and 5

(keep reading to get puzzles for grades 6, 7, and 8)

3rd Grade

4th Grade

5th Grade

Answer Key: 3rd Grade: 3 | 4th Grade: 2 | 5th Grade: 2

You can learn more about 2T1L activities and access more free samples here.


Wait! Get 100+ More Two Truth and One Lie Math Activities for Your Students!


Free Halloween Math Activities for Grades 6, 7, and 8

6th Grade

7th Grade

8th Grade

Answer Key: 6th Grade: 2 | 7th Grade: 2 | 8th Grade: 1

You can learn more about 2T1L activities and access more free samples here.

Looking for more Two Truths and One Lie Math Activities?

You can now share 101 Daily Two Truths & One Lie! Math Activities for Grades 3, 4, & 5 OR Grades 6, 7, & 8 with your kids with our brand new PDF workbooks!

Here are a few more free samples that you can download and share with your kids (right-click to download each graphic and save it to your computer):

Looking for more for grades 3, 4, & 5? Download your 101 ‘Two Truths and One Lie!’ Math Activities for Grades 3, 4, & 5 eBook!


Of course, sharing math 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:


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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.

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A Look Inside: The Big Book of Super Fun Math Puzzles for Grades 1-6

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A Look Inside: The Big Book of Super Fun Math Puzzles for Grades 1-6

Are You Looking for The Ultimate Collection of Fun Math Puzzles and Activities to Share with Your Elementary Math Students?

After publishing our best-selling 101 Daily Math Challenges for Students in Grades 3-8 workbook, we received tons of requests from elementary math teachers for more fun and engaging math puzzles and activities for the lower levels. And we are super excited to share our brand new workbook with teachers of students in grades 1-6!

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The Big Book of Math Puzzles for Grades 1-6

Our brand new PDF eBook is made specifically for students in grades 1-6.

The puzzles in the book are tiered by difficulty using the following system. There are over 100 puzzles for each level:

Pink Level Puzzles (Grades 1 and 2)

Blue Level Puzzles (Grades 3 and 4)

Green Level Puzzles (Grades 5 and 6+)

The workbook covers topics including:

-addition and subtraction
-multiplication and division
-order of operations
-multiplication tables
-area models
-math writing activities
-tons of math puzzles based on grade level
-make your own puzzles hands-on activity
-and much more!

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

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

Looking for Some Sample Puzzles?

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Pink Level Sample Pages (for Grades 1 and 2)

Click the links below to access sample pages from the Pink Level section, which is geared towards math learning standards typically covered in grades 1 and 2.

This section contains over 100 different puzzles. Click here to view the full table of contents.

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

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Blue Level Sample Pages (for Grades 3 and 4)

Click the links below to access sample pages from the Blue Level section, which is geared towards math learning standards typically covered in grades 3 and 4.

This section contains over 100 different puzzles. Click here to view the full table of contents.

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

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Green Level Sample Pages (for Grades 5 and 6+)

Click the links below to access sample pages from the Green Level section, which is geared towards math learning standards typically covered in grades 5-6 and up.

This section contains over 100 different puzzles. Click here to view the full table of contents.

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

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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.

Limited Offer! Use the promo code MATHISFUN at checkout to get 10% off your order!

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


Of course, sharing math 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:


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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.

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What Math Teaching Strategies Work Best? 16 Math Education Experts Share Their Suggestions.

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What Math Teaching Strategies Work Best? 16 Math Education Experts Share Their Suggestions.

What Math Teaching Strategies Work Best? 16 Math Education Experts Share Their Suggestions.

Math Education Experts Share What Tools and Strategies They Use to Support Students.

A Post By: Anthony Persico

What works in math education is constantly evolving. Math teaching strategies and techniques that were once commonplace in the classroom several years ago are now being replaced with more effective, research-backed methods aimed at making mathematics a more approachable, meaningful and equitable subject.

I recently reached out to 16 math education experts, including Stanford University Math Education Professor Jo Boaler, and asked the following question: What new belief, behavior, teaching habit, or tool has most improved your teaching over the past 12-18 months and why?

The diverse collection of responses below will help you to identify some new strategies to add to your teaching toolbox and ultimately assist you in becoming a more effective math educator who is better equipped to meet the needs of your students. Enjoy!

What math teaching strategies are the experts using?

What math teaching strategies are the experts using?


Eddie Woo

Eddie is an Education Ambassador for the University of Sydney, the founder of YouTube’s MisterWooTube channel, and the author of Woo’s Wonderful World of Mathematics and It’s a Numberful World. You can follow him on Twitter @misterwootube.

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Eddie Says…

I have been exploring the power of open-endedness in mathematics classroom over the last couple of years, and love the way that it has helped me tease out mathematical thinking in my students. It’s so easy for students to fixate on getting the “right answer” when facing a question in mathematics, and I love the way that open problems emphasize the aspects of reasoning and communication. It’s also fantastic to see how easily a task can be reshaped so that it has a low floor and a high ceiling, to ensure that struggling learners can access the activity and highly competent mathematicians can also find rich avenues for exploration and investigation.


Chris Woods

Chris is a High School Math Teacher, STEM Presenter, and host of the STEM Everyday Podcast. You can follow him on Twitter @dailystem.

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Chris Says:

In the past few years, I’ve made the change to get kids holding shapes and equations in their hands more often. It usually starts by handing out some combination of paper, scissors, rulers, colored pencils, tape, and glue sticks to my students, nothing fancy. What happens next is I try to help them “see” how a surface area formula works by building a triangular prism or help them “visualize” how a parabola is formed by drawing a series of lines on a grid. And when math is more than just numbers and letters on a worksheet or an answer on a calculator, it is suddenly something beautiful, creative, and worthy of exploration and discovery.


Kristen Acosta

Kristen is a K-6 Math Coach, Teacher, and Presenter. You can access her math resources at www.kristenacosta.com and follow her on Twitter @kristenmacosta.

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Kristen Says:

It’s amusing that number lines have been around forever, but are so underutilized in helping students with making connections to a bigger picture. When I stumbled upon Clothesline Math (used as an open number line), my students’ number sense improved greatly. Clothesline Math has helped my students see the interconnectedness of how math works.

You can learn more about clotheslines math on Kristen’s website.


Kyle Pearce

Kyle is a K-12 Mathematics Consultant who delivers presentations and workshops, blog contributor at Tap Into Teen Minds, and co-host of the Make Math Moments podcast. You can follow him on Twitter @MathletePearce.

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Kyle Says:

Over the past 12-18 months, one of the biggest epiphanies I’ve had is how important it is to actually understand the math. I’m not talking about how to “do it”, but developing the conceptual understanding of the how and why it works, the connections from one idea to another, and how it develops in young children all the way to high school mathematics. Currently, I’ve been building my own understanding of Proportional Reasoning and I’ve built out a full course for members of the Make Math Moments Academy. You can learn more about it here: makemathmoments.com/academy.


Makeda Brome

Makeda is a math educator and 2020 Teacher of the Year Recipient in Port St. Lucie, Florida. You can follow her on Twitter @thebromenator.

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Makeda Says:

Over the last year-and-a-half, I have become more and more aware of social justice education on teaching and how I play an integral role in that. While our classrooms may be more diverse, much of our teaching practices have not changed to support the diversity in our classrooms. Twitter chats and movements like #ClearTheAir, #HipHopEd, and #EduColor have helped me become a better math educator for all of my students and I now support other teachers in doing the same. All of our students deserve equal learning opportunities, I hope the math community commits to engaging in this work!


Brian Aspinall

Brian is a K-12 math educator, TEDx presenter, and author of Code Breaker: Increase Creativity, Remix Assessment, and Develop a Class of Coder Ninjas!. You can follow him on Twitter @mraspinall.

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Brian Says:

For me, two tools have greatly impacted my teaching pedagogy. Both Scratch and Minecraft offer a sandbox environment for students to create content, try something new, immerse themselves in mathematics and be creative. Not only do they support a constructivist approach to learning, students receive immediate feedback from the tools, freeing up teacher time to consolidate with other students.

Brian shares lesson plan examples on his blog at brianaspinall.com and in his books, Code Breaker and Block Breaker.

Learn more: How to use Minecraft: Education Edition in Your Classroom


Alice Keeler

Alice is a YouCubed Consultant, Speaker, Google Certified Teacher, and author of several books including Teaching Math with Google Apps: 50 G Suite Activities. You can follow her on Twitter @alicekeeler.

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Alice Says:

Students who think they struggle in math are all thinkers. I have yet to meet a kid who isn't a thinker. Instead of giving them DOK 1 problems I use OpenMiddle and other interesting problems where step one is... hmmm, I'm not sure, let me think about it. Turns out they are math people.

The other thing I do is tell a story using Google Slides to explain the math problem. Show your feelings, step .1 take a selfie, show how you collaborated, you're required to google something... and explain it.


Jennifer Chang Wathall

Jennifer is an advocate for Concept-Based Curriculum and author of Concept- Based Mathematics: Teaching for Deep Understanding in Secondary Schools. You can connect with her on Twitter @JenniferWathall and visit her website www.jenniferchangwathall.com for more information.

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Jennifer Says:

I enjoyed a glorious 27-year teaching career and something that completely transformed my practice was embedding an inductive teaching approach. The inductive teaching approach creates an environment for students to uncover the beauty and creativity of mathematics for themselves through inquiry based learning.

The inductive teaching approach encourages students to inquire through experimentation, enables connections between different topics to be made, and supports deep conceptual mathematical understanding which gives students the ability to apply and transfer to different contents.

Learn More: What Does Inquiry-Based Learning Look Like in the Math Classroom?


Berkeley Everett

Berkeley is a K-5 Math Coach, facilitator to UCLA’s Math Project, designer for Math Visuals. You can follow him on Twitter @BerkeleyEverett.

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Berkeley Says:

Is it possible for tasks to differentiate themselves while communicating the idea that math is about relationships (not answers)? This year I took my questions to another level with Open Questions from Marian Small. Instead of "12 is 2/3 of ___" she would pose "___ is 2/3 of ___." Suddenly the task is more accessible and more challenging. Plus, it encourages students to focus on ideas and relationships instead of answers. For more, check out Marian Small's great books, including Good Questions (look for the 3rd Edition).



Lauren Baucom

Lauren is a High School Math Teacher, doctoral student at the University of North Carolina at Greensboro, and national presenter. You can follow her on Twitter @LBmathemagician.

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Lauren Says…

Collective learning is a new term that I am fascinated by, and love finding evidence of it in educational spaces. As educators, we often focus on the learning that we hope is occurring in the students who enter our classrooms. As math coaches, we hope to see the confirmation of learning as educators make adjustments to their practice. Both of these are examples of individual learning. There is a powerful type of learning that is harder to visualize, collective learning, or the learning that is happening between a group of people. For example, in a classroom that promotes student discourse, two students may learn different things from a lesson. The conversation that is facilitated between them will multiply the learning that occurs in that room, as each student brings their individual learning and jointly shares with the others. As a teacher, I often forget about asking myself, “What did we learn collectively today?”, not as an offshoot of “I taught it, so they learned it.”, but from the richness that was created from being together.


Peter Liljedahl

Peter is an Education Professor at Simon Fraser University in British Columbia, Canada and Math Education Consultant. You can follow him on Twitter @pgliljedahl.

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Peter Says:

My favorite practice for the last few years is the use of visibly random groups. Although it is something I have been researching and publishing on for many years, it is a practice that still keeps giving me new surprises every year. It emerged as a reaction to my research that was showing that both self-selected and strategically formed groups create a space where the students know what their role will be that day—and for many, that role was not to think. Random groups do not create this. In addition, random groups bypass all our biases of what students are capable of, reduces social barriers, and drives more autonomous learning behavior. More recently, it has also shown that students take random groups as a sign of confidence in them as learners and thinkers.


Margie Pearse

Margie is a math coach and curriculum head, a contributor to Edutopia, and the author of Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking. You can follow her on Twitter @pearse_margie.

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Margie Says:

I was greatly influenced by The Formative 5. I taught in a district that was committed to infusing literacy strategies across content areas, so assessing BDA style in math was something I was very familiar with, but The Formative 5 took the idea of checking for understanding throughout a lesson one step further. I knew there were certain points in each lesson where understanding was critical to moving forward, but I couldn’t put my finger on it until the idea of a Hinge Point was introduced in the book and that was revolutionary to me.


Sunil Singh

Sunil is a math learning specialist and author of Math Recess: Playful Learning in an Age of Disruption and Pi of Life. You can follow him on Twitter @Mathgarden.

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Sunil Says…

As a math educator, we tend to be caught up in the micro details of problem solving and strategies more often than not. While this makes sense, given the analytical nature of mathematics, I have found that some of the more valued human qualities are equally important in students trusting the journey of learning mathematics. For me, the idea of kindness as a virtue, has become a pillar in teaching mathematics. Through kindness we build trust and friendship, which facilitates a learning environment that allows risk, failure, and the acquisition of resilience.


Denis Sheeran

Dennis is a math education specialist, administrator, and the author of Hacking Mathematics: 10 Problems That Need Solving and Instant Relevance: Using Today's Experiences to Teach Tomorrow's Lessons. You can follow him on Twitter @MathDenisNJ and visit his website www.denissheeran.com for more information.

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Denis Says…

I've been an administrator for the past seven years, supervising math teachers and departments in NJ. In fact, it was in the early part of that experience that I was inspired to write Instant Relevance, Using Today's Experiences to Teach Tomorrow's Lessons. One of the biggest shifts that needs to happen in the classroom is less teacher talking and more student discourse. The saying goes, "whoever is doing the talking is doing the learning" and that needs to be a focus in math classrooms. So, I came across a tool that measures the amount of time teachers and students are talking in the classroom by identifying your voice, multiple voices, and volume and then graphs the data for you on demand. It's called TeachFX. They call themselves a Fitbit for teachers that measures student engagement. As a full time math consultant now, I use the tool during professional development sessions and during teacher observations to give objective feedback to teachers after observing their classrooms. You'd be shocked to find out how much talking most teachers really do, when they do it, and how that contrasts what they thought they'd be doing.


Mark Chubb

Mark is a math teacher, instructional coach, and blog contributor to Building Mathematicians. You can follow him on Twitter @MarkChubb3.

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Mark Says…

For years, I have believed the most important thing we can do as educators is to plan for rich learning experiences, so our students could learn through problem solving. After years of being a math coach, I now see that providing rich experiences isn't enough. If we are aiming to make sure we are maximizing learning in our classrooms it takes us as the teachers to be learning about our students as developing mathematical thinkers, and to be continually curious about their understanding. That is, we need to be noticing and wondering about our students regularly. This is the essence of what assessment means. Here are strategies and practical advice to help us notice and wonder about our students: Noticing and Wondering - A Powerful Tool for Assessment.

Learn More: Using Notice-Wonder Activities to Support Math Learning


Jo Boaler

Jo is a Professor of Math Mathematics Education at Stanford University, founder of YouCubed, and author of Mathematical Mindsets and Limitless Mind: Learn, Lead, and Live Without Barriers. You can follow her on Twitter @joboaler.

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Jo Says:

My teaching has been most helped by the knowledge that connected brains are the most powerful and that when we engage students in mathematics through multiple forms of activity - drawing, writing, moving, modeling, building, calculating, and more—they learn most effectively. Mindset messages are very important, but they need to be accompanied by the opening of mathematics teaching, so that students see the potential for growth. When we combine growth messages with open, growth teaching, mathematics becomes a beautiful subject for students. We share many ways to do this on www.youcubed.org and in my book Mathematical Mindsets.

Learn More: 5 Growth Mindset Books Every Math Teacher Should Read


Of course, the above strategies, suggestions, and ideas for teaching math just scratch the surface of all there is to learn about the art of teaching mathematics effectively. Subscribe to our mailing list here to get more free daily resources, lesson plans, and insights for K-12 math teachers in your inbox every week.

Read More Posts About Math Education:

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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.

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Fraction to Decimal: An Easy Way to Convert

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Fraction to Decimal: An Easy Way to Convert

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Image Source: Google Calculator

An Easy Way to Convert Fraction to Decimal

Are you ready to learn how to convert a fraction to a decimal?

(Click here to learn how to do the opposite and convert a decimal to a fraction)

Before you learn an easy way to convert a fraction to a decimal (with and without a calculator), you need to understand what decimals and fractions are:

  •  A decimal number is used to represent a non-whole number where a decimal point is used followed by digits that represent a value that is smaller than one.

 
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  • A fraction represents a part of a whole number. A fraction is a ratio between the upper number (the numerator) and the lower number (the denominator). The numbers are stacked vertically and separated with a bar.

 
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The key takeaway from these definitions is that decimals and fractions are different ways of representing the same thinga number that is not whole.

How to Convert Fraction to Decimal

You can easily convert a fraction to a decimal by using a few simple strategies:

1.) By Using a Calculator

The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator. The resulting answer will be the value of the fraction expressed as a decimal number.

For example, to convert the fraction 7/8 to a decimal using a calculator, simply perform 7 divided by 8 and press enter. The resulting decimal would be 0.875.

Therefore, you can say that 7/8 expressed as a decimal is 0.875

Image Source: Google Calculator

Image Source: Google Calculator

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2.) Without a Calculator

How can you convert a fraction to a decimal without a calculator?

The solution is using long division.

For example, if you wanted to convert the fraction 7/8 to a decimal without using a calculator, you would have to use long division where the dividend is 7 and the divisor is 8.

Just like in the last example, by using the long division strategy, you can conclude that 7/8 expressed as a decimal is 0.875


How to Change Fraction to Decimal on Calculator

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Screenshot from www.calculatorsoup.com

If you need a fast and easy way to convert a fraction to a decimal, then you can take advantage of the many free online fraction to decimal conversion calculators that are available.

This free decimal to fraction calculator from www.calculatorsoup.com not only performs the conversion, but also shows the calculations (how the long division was performed to get the result), which is a handy tool since it will not only help you find a correct answer, but also understand the process as well.

To use the fraction to decimal calculator, simply input the decimal value and press calculate. This calculator can convert both a fraction and a mixed number to decimal.

Are you looking to learn more about working with decimals and understanding place value? Click here for more free resources


Fraction to Decimal Chart

A fraction to decimal chart is a handy tool for making quick conversions.

While there are many free fraction to decimal chart resources available online, I prefer this free fraction to decimal chart from www.sciencemadesimple.net for its readability and simplicity.

Pro tip: Keep a printed copy of your fraction to decimal chart with you while you study and practice math. This strategy will help you to memorize the common conversions (ex. 1/2=0.5 or 1/8=0.125).

Fraction to Decimal Worksheet (with Answers)

Do you need more practice with learning how to convert a fraction to a decimal? The following decimal to fraction worksheet and answer key will give you plenty of opportunities to apply the three step process to converting a decimal to a fraction.

Click here to download your free Fraction to Decimal Worksheet with Answers.

And if you are looking for a more in-depth lesson on how to convert fraction to a decimal, check out this free fraction to decimal video lesson:

 
 

Share your ideas, questions, and comments below!

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

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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.

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