ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Try the partial quotient strategy to divide instead of confusion with long division

Updated on January 21, 2017

Division Anchor chart with multiple strategies

Students can sole with partial quotient and bar models to model an understanding of the word problem.
Students can sole with partial quotient and bar models to model an understanding of the word problem.

What is the partial quotient method?

In today's classroom, the NCTM and other mathematics associations are promoting researched based strategies to help students understand how to do math without feeling that they will just never understand math. Educators are teaching skills to facilitate a growth mindset when it comes to learning and applying math in everyday situations.

The partial quotient is a division strategy that allows students to multiply to divide using facts they know. They divide a part at a time until they get to zero or a remainder. Teachers are being encouraged to use this strategy because not only does it differentiate and allows kids to use what they know at their own level, but it makes it constantly reinforces the meaning of division.

Students are on a continuum of number sense growth and the more they practice the more they begin to see patterns. Remember that essentially you are multiplying to divide.The goal is to break the whole up until the whole number is gone or there is a small remainder.Students should think about how many digits are in the whole number. If I am dividing 245 by 5, I know that 245 has 3 digits so I first try to multiply 5x100, too big! So let's try 5x10=50 or 5x20=100 or we can do 5x40=200. I choose 5x 40=200, then subtract that from 245 and get 45. Now I can do 5x9=45. So 245 divided by 5= 40+9= 49 is the solution. Watch the following videos to see an example worked out step by step.

Watch as I guide through both the long division method and the partial quotient method.


Division is repeated subtraction

From grade to grade students need to be able to use their prerequisites to build new understandings.Division is essentially repeated subtraction.When students get this fundamental fact, they can feel more comfortable understanding how division relates to multiplication. Since multiplication is repeated addition and division is its inverse, students need to be able to see how a whole can be broken up, separated, shared, partitioned into groups, or subtracted repeatedly.

Students can see division as repeated subtraction by using models through hands-on experiences.

Example: Take 20 buttons and divide it by 4. 20-4=16, 16-4=12, 12-4=8, 8-4=4, 4-4=0. Because 4 was taken away 5 times, 20 divide 4=5. When a student has this fundamental understanding they can divide larger numbers because the connection to subtraction gives them a starting point to grow from.

Solving Division Problems using bar models

Now in grade school kids are required not only to be able to compute solutions but to also be able to problem solve multiple to steps before using their computation skills. Using a bar model to visualize what is known and what is not known helps students to process the steps without getting confused. When students reading levels cause them to struggle through the text, slowing down to figure out what is known and what is unknown using a model, helps students stay on track throughout the problem solving process.

Remediate when students struggle with division concepts

If your child or students are not able to connect with division strategies take them back to the basics of multiplication. Students have to understand multiplicative thinking. To do so they have to see that groups can be repeated to represent a whole. when this understanding is solid then they can move on to breaking up the whole by subtracting from it repeatedly. This process along with hands-on activities, for students to see concrete models and make groups, will aid in building understanding or repair misunderstandings.

I would also suggest having students watch multiplication videos that incorporate music, my students learned a lot of their facts watching the Schoolhouse rock multiplication videos. Students should also do skip counting on a numberline, to see the jumps between intervals.

many free games and drills are available online to aid student practice to build their fluency. Furthermore, having kids chart their progress with division and creating growth goals will help them see their number sense increase and help to foster their ownership of their own learning.

How well did your teacher introduce Division?

How was your experience learning division in elementary?

See results


    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)