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Students can gain a little background info on moths (or the teacher can too) to connect with the subject matter and bringing math to life!

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Peppered Moth and natural selection - Moths Count

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In the mid-twentieth century controls were introduced to reduce air pollution and as the air quality improved tree trunks became cleaner and lichen growth increased. Once again the normal pale Peppered Moths were camouflaged and the black forms were more noticeable.

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Counting using percentages
Counting per 100 moths
50% = one half
Since we have 2 groups that equal 100%, the % of one + % of another must always equal 100

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Play the simulation game one time in the light forest and one time in the dark forest. (helps students understand about counting using percentages). Record data in the shared google sheet: https://docs.google.com/spreadsheets/d/1MAPUi5-kKHrHgirJPVagwDxG_hHBZWywCeFOounA8nw/edit?usp=sharing

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Counts are out of 100 (percentages)

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Free Online Chart and Graph Maker

Chartle.com is a free online tool where you can create and make your own charts and graphs. We support line charts, bar graphs, bubble charts, pie and donut charts as well as scatter, radar and polar graphs and charts. Select a chart type and enter data for your chart and the chart will be created instantly. You can set all kinds of properties like colors, labels, grid, legend and title. You can also annotate your chart with text and shapes. The result can be saved for later editing or can be saved as image or shared online.

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Chartle.com is a free online tool where you can create and make your own charts and graphs. We support line charts, bar graphs, bubble charts, pie and donut charts as well as scatter, radar and polar graphs and charts. Select a chart type and enter data for your chart and the chart will be created instantly.

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By converting our sims to HTML5, we make them seamlessly available across platforms and devices. Whether you have laptops, iPads, chromebooks, or BYOD, your favorite PhET sims are always right at your fingertips.Become part of our mission today, and transform the learning experiences of students eve…

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When the goal is to analyze the data, go with an easy to do graphing app.
Take a few minutes to explore the tool.
Quick Hints: Change nothing on the first page.  Second page of settings, add x axis as years and y axis is population. For our data on the second page, choose 12 items and 2 groups.  Group 1 a light color and group 2 a dark color.

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Free Online Chart and Graph Maker

Chartle.com is a free online tool where you can create and make your own charts and graphs. We support line charts, bar graphs, bubble charts, pie and donut charts as well as scatter, radar and polar graphs and charts. Select a chart type and enter data for your chart and the chart will be created instantly. You can set all kinds of properties like colors, labels, grid, legend and title. You can also annotate your chart with text and shapes. The result can be saved for later editing or can be saved as image or shared online.

# data[].attributes.attachment_link.description
Chartle.com is a free online tool where you can create and make your own charts and graphs. We support line charts, bar graphs, bubble charts, pie and donut charts as well as scatter, radar and polar graphs and charts. Select a chart type and enter data for your chart and the chart will be created instantly.

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Now that we have a graph that was made quickly, class time can be used to discuss.  If the current trend continues when will the populations for each color be at 50%?  What is the rate of change (slope of a line) for each population between various years? Turn the line graph into a bar graph to compare how the data looks using different styles of graphs. Can go back to the shared data from the simulation and use the online graphing tool to graph the class data. Students can decide which graph to use.

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Math in Daily Life: How much will you have saved when you retire? Is it better to lease or buy a car? Learn the answers to these and other mathematical questions that affect our daily decisions.

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Birth & Death Rates | Ecology Global Network

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World Birth and Death Rates Estimated 2011 Birth Rate Death Rate * 19 births/1,000 population * 8 deaths/1,000 population * 131.4 million births per year * 55.3 million people die each year * 360,000 births per day * 151,600 people ... Continue reading →

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If you've ever worked on a personal data science project, you've probably spent a lot of time browsing the internet looking for interesting datasets to analyze. It can be fun to sift through dozens of datasets to find the perfect one, but it can also be frustrating to download and import several CSV files, only to realize that the data isn't that interesting after all. Luckily, there are online repositories that curate datasets and (mostly) remove the uninteresting ones.

In this post, we'll walk through several types of data science projects, including data visualization projects, data cleaning projects, and machine learning projects, and identify good places to find datasets for each. Whether you want to strengthen your data science portfolio by showing that you can visualize data well, or you have a spare few hours and want to practice your machine learning skills, we've got you covered.

But first, let's answer a couple quick, foundational questions:

What is a dataset?

A dataset, or data set, is simply a collection of data.

The simplest and most common format for datasets you'll find online is a spreadsheet or CSV format - a single file organized as a table of rows and columns. But some datasets will be stored in other formats, and they don't have to be just one file. Sometimes a dataset may be a zip file or folder containing multiple data tables with related data.

How are datasets created?

Different datasets are created in different ways. In this post, you'll find links to sources with all kinds of datasets. Some of them will be machine-generated data. Some will be data that's been collected via surveys. Some may be data that's recorded from human observations. Some may be data that's been scraped from websites or pulled via APIs.

Whenever you're working with a dataset, it's important to consider: how was this dataset created? Where does the data come from? Don't jump right into the analysis; take the time to first understand the data you are working with.

Public Data Sets for Data Visualization Projects

A typical data visualization project might be something along the lines of "I want to make an infographic about how income varies across the different states in the US". There are a few considerations to keep in mind when looking for a good data set for a data visualization project:

It shouldn't be messy, because you don't want to spend a lot of time cleaning data.

It should be nuanced and interesting enough to make charts about.

Ideally, each column should be well-explained, so the visualization is accurate.

The data set shouldn't have too many rows or columns, so it's easy to work with.

A good place to find good data sets for data visualization projects are news sites that release their data publicly. They typically clean the data for you, and also already have charts they've made that you can replicate or improve.

1. FiveThirtyEight

FiveThirtyEight is an incredibly popular interactive news and sports site started by Nate Silver. They write interesting data-driven articles, like "Don't blame a skills gap for lack of hiring in manufacturing" and "2016 NFL Predictions".

FiveThirtyEight makes the data sets used in its articles available online on Github.
View the FiveThirtyEight Data sets
Here are some examples:

2. BuzzFeed

BuzzFeed started as a purveyor of low-quality articles, but has since evolved and now writes some investigative pieces, like "The court that rules the world" and "The short life of Deonte Hoard".

BuzzFeed makes the data sets used in its articles available on Github.
View the BuzzFeed Data sets
Here are some examples:

3. NASA

NASA is a publicly-funded government organization, and thus all of its data is public. It maintains websites where anyone can download its datasets related to earth science and datasets related to space. You can even sort by format on the earth science site to find all of the available CSV datasets, for example.

Public Data Sets for Data Processing Projects

Sometimes you just want to work with a large data set. The end result doesn't matter as much as the process of reading in and analyzing the data. You might use tools like Spark or Hadoop to distribute the processing across multiple nodes. Things to keep in mind when looking for a good data processing data set:

The cleaner the data, the better - cleaning a large data set can be very time consuming.

The data set should be interesting.

There should be an interesting question that can be answered with the data.

A good place to find large public data sets are cloud hosting providers like Amazon and Google. They have an incentive to host the data sets, because they make you analyze them using their infrastructure (and pay them).

4. AWS Public Data sets

Amazon makes large data sets available on its Amazon Web Services platform. You can download the data and work with it on your own computer, or analyze the data in the cloud using EC2 and Hadoop via EMR. You can read more about how the program works here.

Amazon has a page that lists all of the data sets for you to browse. You'll need an AWS account, although Amazon gives you a free access tier for new accounts that will enable you to explore the data without being charged.
View AWS Public Data sets
Here are some examples:

5. Google Public Data sets

Much like Amazon, Google also has a cloud hosting service, called Google Cloud Platform. With GCP, you can use a tool called BigQuery to explore large data sets.

Google lists all of the data sets on a page. You'll need to sign up for a GCP account, but the first 1TB of queries you make are free.
View Google Public Data sets
Here are some examples:

6. Wikipedia

Wikipedia is a free, online, community-edited encyclopedia. Wikipedia contains an astonishing breadth of knowledge, containing pages on everything from the Ottoman-Habsburg Wars to Leonard Nimoy. As part of Wikipedia's commitment to advancing knowledge, they offer all of their content for free, and regularly generate dumps of all the articles on the site. Additionally, Wikipedia offers edit history and activity, so you can track how a page on a topic evolves over time, and who contributes to it.

You can find the various ways to download the data on the Wikipedia site. You'll also find scripts to reformat the data in various ways.
View Wikipedia Data sets
Here are some examples:

Public Data Sets for Machine Learning Projects

When you're working on a machine learning project, you want to be able to predict a column from the other columns in a data set. In order to be able to do this, we need to make sure that:

The data set isn't too messy - if it is, we'll spend all of our time cleaning the data.

There's an interesting target column to make predictions for.

The other variables have some explanatory power for the target column.

There are a few online repositories of data sets that are specifically for machine learning. These data sets are typically cleaned up beforehand, and allow for testing of algorithms very quickly.

7. Kaggle

Kaggle is a data science community that hosts machine learning competitions. There are a variety of externally-contributed interesting data sets on the site. Kaggle has both live and historical competitions. You can download data for either, but you have to sign up for Kaggle and accept the terms of service for the competition.

You can download data from Kaggle by entering a competition. Each competition has its own associated data set. There are also user-contributed data sets found in the new Kaggle Data sets offering.
View Kaggle Data sets View Kaggle Competitions
Here are some examples:

8. UCI Machine Learning Repository

The UCI Machine Learning Repository is one of the oldest sources of data sets on the web. Although the data sets are user-contributed, and thus have varying levels of documentation and cleanliness, the vast majority are clean and ready for machine learning to be applied. UCI is a great first stop when looking for interesting data sets.
View UCI Machine Learning Repository
You can download data directly from the UCI Machine Learning repository, without registration. These data sets tend to be fairly small, and don't have a lot of nuance, but are good for machine learning.

Here are some examples:

9. Quandl

Quandl is a repository of economic and financial data. Some of this information is free, but many data sets require purchase. Quandl is useful for building models to predict economic indicators or stock prices. Due to the large amount of available data sets, it's possible to build a complex model that uses many data sets to predict values in another.

View Quandl Data sets.

Here are some examples:

Public Data Sets for Data Cleaning Projects

Sometimes, it can be very satisfying to take a data set spread across multiple files, clean them up, condense them into one, and then do some analysis. In data cleaning projects, sometimes it takes hours of research to figure out what each column in the data set means. It may sometimes turn out that the data set you're analyzing isn't really suitable for what you're trying to do, and you'll need to start over.

When looking for a good data set for a data cleaning project, you want it to:

Be spread over multiple files.

Have a lot of nuance, and many possible angles to take.

Require a good amount of research to understand.

Be as "real-world" as possible.

These types of data sets are typically found on aggregators of data sets. These aggregators tend to have data sets from multiple sources, without much curation. Too much curation gives us overly neat data sets that are hard to do extensive cleaning on.

10. data.world

data.world describes itself at 'the social network for data people', but could be more correctly describe as 'GitHub for data'. It's a place where you can search for, copy, analyze, and download data sets. In addition, you can upload your data to data.world and use it to collaborate with others.

In a relatively short time it has become one of the 'go to' places to acquire data, with lots of user contributed data sets as well as fantastic data sets through data.world's partnerships with various organizations includeing a large amount of data from the US Federal Government.
View data.world Data sets
One key differentiator of data.world is the tools they have built to make working with data easier - you can write SQL queries within their interface to explore data and join multiple data sets. They also have SDK's for R an python to make it easier to acquire and work with data in your tool of choice (You might be interested in reading our tutorial on the data.world Python SDK.)

11. Data.gov

Data.gov is a relatively new site that's part of a US effort towards open government. Data.gov makes it possible to download data from multiple US government agencies. Data can range from government budgets to school performance scores. Much of the data requires additional research, and it can sometimes be hard to figure out which data set is the "correct" version. Anyone can download the data, although some data sets require additional hoops to be jumped through, like agreeing to licensing agreements.
View Data.gov Data sets
You can browse the data sets on Data.gov directly, without registering. You can browse by topic area, or search for a specific data set.

Here are some examples:

12. The World Bank

The World Bank is a global development organization that offers loans and advice to developing countries. The World Bank regularly funds programs in developing countries, then gathers data to monitor the success of these programs.
View World Bank Data sets
You can browse World Bank data sets directly, without registering. The data sets have many missing values, and sometimes take several clicks to actually get to data.

Here are some examples:

13. /r/datasets

Reddit, a popular community discussion site, has a section devoted to sharing interesting data sets. It's called the datasets subreddit, or /r/datasets. The scope of these data sets varies a lot, since they're all user-submitted, but they tend to be very interesting and nuanced.
View Top /r/datasets Posts
You can browse the subreddit here. You can also see the most highly upvoted data sets here.

Here are some examples:

14. Academic Torrents

Academic Torrents is a new site that is geared around sharing the data sets from scientific papers. It's a newer site, so it's hard to tell what the most common types of data sets will look like. For now, it has tons of interesting data sets that lack context.
View Academic Torrents Data sets
You can browse the data sets directly on the site. Since it's a torrent site, all of the data sets can be immediately downloaded, but you'll need a Bittorrent client. Deluge is a good free option.

Here are some examples:

Bonus: Streaming data

It's very common when you're building a data science project to download a data set and then process it. However, as online services generate more and more data, an increasing amount is generated in real-time, and not available in data set form. Some examples of this include data on tweets from Twitter, and stock price data. There aren't many good sources to acquire this kind of data, but we'll list a few in case you want to try your hand at a streaming data project.

15. Twitter
Get started with the Twitter API
Twitter has a good streaming API, and makes it relatively straightforward to filter and stream tweets. You can get started here. There are tons of options here - you could figure out what states are the happiest, or which countries use the most complex language. We also recently wrote an article to get you started with the Twitter API here.

16. Github
Get started with the Github API
Github has an API that allows you to access repository activity and code. You can get started with the API here. The options are endless - you could build a system to automatically score code quality, or figure out how code evolves over time in large projects.

17. Quantopian

Quantopian is a site where you can develop, test, and operationalize stock trading algorithms. In order to help you do that, they give you access to free minute by minute stock price data. You could build a stock price prediction algorithm.

Get started with Quantopian

18. Wunderground
Get started with the Wunderground API
Wunderground has an API for weather forecasts that free up to 500 API calls per day. You could use these calls to build up a set of historical weather data, and make predictions about the weather tomorrow.

Bonus: Personal Data

The internet is full of cool data sets you can work with. But for something truly unique, what about analyzing your own personal data? Here are some popular sites that make it possible to download and work with data you've generated.

19. Amazon

Amazon allows you to download your personal spending data, order history, and more. To access it, click this link (you'll need to be logged in for it to work) or navigate to the Accounts and Lists button in the top right. On the next page, look for the Ordering and Shopping Preferences section, and click on the link under that heading that says "Download order reports".

Here is a simple data project tutorial that you could do using your own Amazon data to analyze your spending habits.

20. Facebook

Facebook also allows you to download your personal activity data. To access it, click this link (you'll need to be logged in for it to work) and select the types of data you'd like to download.

Here is an example of a simple data project you could build using your own personal Facebook data.

21. Netflix

Netflix allows you to request your own data for download, although it will make you jump through a few hoops, and warns the process of collating your data may take 30 days. As of the last time we checked, the data they allow you to download is fairly limited, but it could still be suitable for some types of projects and analysis.

Next steps

In this post, we covered good places to find data sets for any type of data science project. We hope that you find something interesting that you want to sink your teeth into!

If you do end up building a project, we'd love to hear about it. Please let us know!

At Dataquest, our interactive guided projects are designed to help you start building a data science portfolio to demonstrate your skills to employers and get a job in data. If you're interested, you can signup and do our first module for free.
If you liked this, you might like to read the other posts in our 'Build a Data Science Portfolio' series:
At Dataquest, our interactive guided projects are designed to help you start building a data science portfolio to demonstrate your skills to employers and get a job in data. If you're interested, you can signup and do our first module for free.

About the author

Vik Paruchuri

Vik is the CEO and Founder of Dataquest.

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21 Places to Find Free Datasets for Data Science Projects

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If you've ever worked on a personal data science project, you've probably spent a lot of time browsing the internet looking for interesting datasets to analyze. It can be fun to sift through dozens of datasets to find the perfect one, but it can also be frustrating to download and import several CSV files, only to realize that the data isn't that interesting after all.

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View the U.S. Drought Monitor data in tabular format for a selected area.

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Our Core Purpose: We answer questions, so our users can grow their appreciation, understanding, and love of the game.

Our Values: We strive to work with respect, reliability with oomph, and craftsmanship, and also to promote the democratization of sports data.
Read about our history and our team
Work at Sports Reference: We are a profitable, bootstrapped, remote-first company that offers competitive salaries and outstanding benefits. (More)

Our Corporate Sponsorships include:

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Sports Reference | Sports Stats, fast, easy, and up-to-date | Sports-Reference.com

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Our Core Purpose: We answer questions, so our users can grow their appreciation, understanding, and love of the game. Our Values: We strive to work with respect, reliability with oomph, and craftsmanship, and also to promote the democratization of sports data.

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7 Real-World Issues That Can Allow Students To Tackle Big Challenges

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By Michael Niehoff - How can we creatively collaborate, critically think and communicate in ways that will make our world a better place to live? Letting our students practice working on these seven big issues can present hundreds of relevant challenges can be a big step toward that future.

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WHO's annual World Health Statistics reports present the most recent health statistics for the WHO Member States.

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Completing your first project is a major milestone on the road to becoming a data scientist and helps to both reinforce your skills and provide something you can discuss during the interview process. It's also an intimidating process. The first step is to find an appropriate, interesting data set. You should decide how large and how messy a data set you want to work with; while cleaning data is an integral part of data science, you may want to start with a clean data set for your first project so that you can focus on the analysis rather than on cleaning the data.

Based on the learnings from our Introduction to Data Science Course and the Data Science Career Track, we've selected data sets of varying types and complexity that we think work well for first projects (some of them work for research projects as well!). These data sets cover a variety of sources: demographic data, economic data, text data, and corporate data.

Need more? Check out our list of free data mining tools.
Free Data Sets for Students

1. United States Census Data: The U.S. Census Bureau publishes reams of demographic data at the state, city, and even zip code level. It is a fantastic data set for students interested in creating geographic data visualizations and can be accessed on the Census Bureau website . Alternatively, the data can be accessed via an API. One convenient way to use that API is through the choroplethr . In general, this data is very clean and very comprehensive.

2. FBI Crime Data: The FBI crime data is fascinating and one of the most interesting data sets on this list. If you're interested in analyzing time series data, you can use it to chart changes in crime rates at the national level over a 20-year period . Alternatively, you can look at the data geographically .

3. For access to global financial statistics and other data, check out the IMF Economic Data: International Monetary Fund's website.

4. Dow Jones Weekly Returns: Predicting stock prices is a major application of data analysis and machine learning. One relevant data set to explore is the weekly returns of the Dow Jones Index from the Center for Machine Learning and Intelligent Systems at the University of California, Irvine.

5. Data.gov.uk: The British government's official data portal offers access to tens of thousands of data sets on topics such as crime, education, transportation, and health.

6. After the collapse of Enron, a free data set of roughly is now famous and provides an excellent testing ground for Enron Emails: 500,000 emails with message text and metadata were released. The data set text-related analysis. You also can explore other research uses of this data set through the page.

7. UNICEF: If data about the lives of children around the world is of interest, UNICEF is the most credible source. The organization's public data sets touch upon nutrition, immunization, and education, among others.

8. Reddit released a really interesting data set of Reddit Comments: every comment that has ever been made on the site. It's over a terabyte of data uncompressed, so if you want a smaller data set to work with Kaggle has hosted the comments from May 2015 on their site.

9. Wikipedia: Wikipedia provides instructions for downloading the text of English-language articles , in addition to other projects from the Wikimedia Foundation.

10. Lending Club: Lending Club provides data about loan applications it has rejected as well as the performance of loans that it issued. The free data set lends itself both to categorization techniques (will a given loan default) as well as regressions (how much will be paid back on a given loan).

11. Walmart has released historical Walmart: sales data for 45 stores located in different regions across the United States.

12. Yelp: Yelp maintains a free dataset for use in personal, educational, and academic purposes. It includes 6 million reviews spanning 189,000 businesses in 10 metropolitan areas. Students are welcome to participate in Yelp's dataset challenge.

(This post was originally published October 13, 2015. It was last updated August 21, 2018.) Now it's time to get cracking! If you want to jumpstart your data science career, check out Springboard's Introduction to Data Science course, or, for those with more experience, our Career Track data science bootcamp.

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19 Free Public Data Sets for Your First Data Science Project - Springboard Blog

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Completing your first project is a major milestone on the road to becoming a data scientist and helps to both reinforce your skills and provide something you can discuss during the interview process. It's also an intimidating process. The first step is to find an appropriate, interesting data set.

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No Expectations/Standards Selected

Ontario Alignment By Grade

Ontario Alignment By Overall Expectation

CCSS Alignment By Standard

Proportional Reasoning With Green Energy

This is a 3 Act Math Task that focuses on "Green Energy" proportional reasoning questions related to solar panels in order to address proportions both visually using area models and proportions written as equivalent fractions. Special thanks goes to Dave Raney from CPE Inc. for allowing us to use his video and photos as well as Kathleen Quenneville, Energy & Environmental Officer at GECDSB for her feedback to create problems around solar energy.

Act 1: Introduce the Task

Show students the act 1 video.

Then ask students to do a rapid write of what they notice and what they wonder.

Students will then share out their noticings and wonderings while I jot their ideas down on the whiteboard.

While we may explore some other wonderings, the first question I intend to address is:

How many solar panels are there?

I'll flash this image on the screen and then ask students to make a prediction.

I'll give students some time to think independently, then chat with a neighbour to discuss their predictions while encouraging them to share their thinking. Then, we share out to the whole group and jot down predictions.

When students have shared out their predictions, we will show students the blue prints for the solar panel system with the total number of modules (582).

Now that students have invested some thinking into this context, we are going to extend our thinking to this question which may or may not have come up in the notice/wonder rapid write:

How much greenhouse gas emissions can the solar panels offset?

Act 2: Reveal Some Information

Show students this image showing the carbon dioxide from 4,848 km of driving a passenger car that is offset for every 5 solar panels that are in service on the roof of the school.

Act 3: Reveal the Solution

Show students the act 3 animated solution video showing three different representations for solving this problem.

Double Number Line

Double Area Model

Proportion of Two Equivalent Fractions

Extension

Consider asking students the following extension question:

How many homes can all 582 solar panel modules power?

Show students this image that states 4 solar panels provide 1,576 kWh of power per year and the average home consumes 9,000 kWh of power each year.

Download The Task and Resources

Grab all the videos, images and resources by clicking download below:

Download

New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

Share With Your Learning Community:

I'm Kyle Pearce and I am a former high school math teacher. I'm now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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MFM2P [ Measurement and Trigonometry - MT1, Measurement and Trigonometry - MT2, Measurement and Trigonometry - MT3, Modelling Linear Relations - LR1, Modelling Linear Relations - LR2, Modelling Linear Relations - LR3, Quadratic Relations in y = ax^2 + bx + c Form - QR1, Quadratic Relations in y = ax^2 + bx + c Form - QR2, Quadratic Relations in y = ax^2 + bx + c Form - QR3]

MHF4U [ Characteristics of Functions - CF3, Exponential and Logarithmic Functions - EL2, Exponential and Logarithmic Functions - EL3]

MPM1D [ AG3, Analytic Geometry - AG1, Analytic Geometry - AG2, LR1, LR2, LR3, MG1, MG2, MG3, NA1, Number Sense and Algebra - NA2]

MPM2D [ AG1, AG2, AG3, QR2, Quadratic Relations - QR3, Quadratic Relations - QR4, T2, T3]

Algebra [ A-CED.1, A-CED.2, A-REI.6]

Functions [ F-BF.1, F-BF.3, F-IF.4, F-LE.1, F-LE.2, F-LE.3, F-TF.5]

Geometry [ G-C.5, G-C.8, G-C.9, G-GMD.3, G-GMD.4, G-GPE.4, G-GPE.5, G-GPE.7, G-MG.1, G-MG.2, G-SRT.11]

Grade 1 [ 1.NBT.4, 1.OA.1]

Grade 2 [ 2.NBT.5, 2.OA.2]

Grade 3 [ 3.NBT.2, 3.NF.1, 3.NF.3, 3.OA.1, 3.OA.5, 3.OA.9]

Grade 4 [ 4-MD.3, 4.MD.2, 4.NBT.6, 4.NF.3, 4.OA.1]

Grade 5 [ 5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.NBT.6, 5.NF.1, 5.OA.1, 5.OA.2, 5.OA.3]

Grade 6 [ 6.EE.1, 6.EE.2, 6.G.1, 6.G.2, 6.NS.1, 6.RP.2, 6.RP.3]

Grade 7 [ 7.EE.4, 7.G.3, 7.G.4, 7.G.6, 7.RP.1, 7.RP.3, 7.SP.2, 7.SP.6]

Grade 8 [ 8.EE.1, 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8, 8.F.2, 8.F.3, 8.F.4, 8.F.5, 8.G.5, 8.G.7, 8.G.9, 8.SP.1]

Practice [ MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]

Statistics & Probability [ S-ID.6, S-MD.4]

Download The Tip Sheet!

Using 3 Act Math Tasks in your classroom is an amazing way to transform your math class into a SENSE MAKING MACHINE.This guide will get you off on the right foot to maximize learning with each and every task.

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Solar Panels 3 Act Math Activity | Panel Problem Proportions

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No Expectations/Standards Selected Ontario Alignment By Grade Ontario Alignment By Overall Expectation CCSS Alignment By Standard This is a 3 Act Math Task that focuses on "Green Energy" proportional reasoning questions related to solar panels in order to address proportions both visually using area models and proportions written as equivalent fractions.

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This applet allows you to create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line.

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Calculator Use

Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8.

To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator.

Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

if you are adding fractions

if you are subtracting fractions

How to Add or Subtract Fractions

1. Find the least common denominator

2. You can use the LCD Calculator to find the least common denominator for a set of fractions

3. For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator

4. Multiply the numerator and denominator of your first fraction by that number

5. Repeat Steps 3 and 4 for each fraction

6. For addition equations, add the fraction numerators

7. For subtraction equations, subtract the fraction numerators

8. Convert improper fractions to mixed numbers

9. Reduce the fraction to lowest terms

How to Multiply Fractions

1. Multiply all numerators together

2. Multiply all denominators together

3. Reduce the result to lowest terms

How to Divide Fractions

1. Rewrite the equation as in "Keep, Change, Flip"

2. Keep the first fraction

3. Change the division sign to multiplication

4. Flip the second fraction by switching the top and bottom numbers

5. Multiply all numerators together

6. Multiply all denominators together

7. Reduce the result to lowest terms

Fraction Formulas

There is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

Adding Fractions

The formula for adding fractions is:

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd} \)

Example steps:

\( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)

\( = \dfrac{14}{24} = \dfrac {7}{12} \)

Subtracting Fractions

The formula for subtracting fractions is:

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd} \)

Example steps:

\( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Multiplying Fractions

The formula for multiplying fractions is:

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} \)

Example steps:

\( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Dividing Fractions

The formula for dividing fractions is:

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} \)

Example steps:

\( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \)

\( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \)

Related Calculators

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Notes

Last updated: March 18, 2019

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Use this fraction calculator to add, subtract, multiply and divide fractions. Shows the work and the steps to do math with fractions. Reduces fractions to lowest terms.

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Several real-world data sets for a variety of graphs, especially scatter plots.

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Use this matrix to locate data sets. The number in a cell where a row and column intersect indicates how many data sets exist for those topics. If the number is 1, clicking on that cell will take you directly to that data set.