ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Primary School Maths

Updated on July 29, 2020

How Numeracy Is Taught at My Son's School

I'd always been intrigued and puzzled by how maths and numeracy is taught at schools. Fortunately my son's primary school has an enlightened policy of explaining to parents the various techniques that they use. I had the opportunity to be shown the methods and the school also issued a small booklet that explained the approach step by step.

I found this information fascinating, useful and a bit of an eye-opener. I thought I would share it and see how my son's school's methods compare to other UK schools and to schools across the world.

Primary School National Maths Strategy/Curriculum

The way maths and numeracy is taught at school seems to continually discussed and revised. Just this month (June 2012), Michael Gove (Secretary of State for Education) unveiled proposals to overhaul the maths/numeracy curriculum. It is proposed that there will be more emphasis on learning specific key tasks. For example 11 year olds will be expected to learn up to their 12 times table (currently the target is up to the 10 times table).

Secretaries of State will come and go, but children will always have to learn how to add, subtract, multiply and divide. This article will focus on how this basic numeracy is taught at my son's school. There is much debate about whether children should learn by rote (for example by chanting their times tables) or by developing a deeper understanding of how numbers work. I'm pleased to say that my son's school use a wide spectrum of strategies to enable all children to achieve success.

My Son's Primary School's Numeracy Strategy

This is an overview taken from a handout:-

"Addition and subtraction, and multiplication and division, are taught alongside each other so that the children can see the relationship between them, recognising that multiplication can be repeated addition and division can be repeated subtraction. Children are also encouraged to understand the importance of estimation and other checking including using inverse operations.

A variety of recording and calculation methods are taught as a progression. However, teachers are flexible in their approach and will realise that some children are ready to progress to the next step and some children will need consolidation on the previous step. This is addressed through appropriately differentiated teaching. It is also important to understand that not all children will reach the final stage in each progression but they will be able to perform a calculation successfully."

So that's the official line. It might be good mathematical practice but it's not plain English! To be fair to the school they also provided examples of how addition, subtraction, multiplication and division is actually taught. I'll set out the approach in detail.

How Addition is Taught at Primary School

This is the progression (starting with the easiest methods) that my son's school follows for addition:

Counting On - Just counting- 11 + 5 = 11, 12, 13, 14, 15, 16. I guess using fingers, or for larger numbers, number lines or squares.

Using a Known Fact - Just learning simple additions. E.g. 3 + 2 = 5.

Number Bonds - Learn which pairs of numbers add up to 10 and 20.

Using a Derived Fact - This builds on a known fact or number bond. For example 15 + 5 = 20, therefore 16 + 5 = 21.

Hundred Squares - A lot easier to understand this with actual examples- check this link, add using a hundred square

Adding Several Numbers - Look for pairs of numbers that add up to 10 and add these first. Children are also taught to start with the largest number. Also children look for pairs that make 9 or 11 and add these by adding 10 and then adjusting by 1.

Partitioning and Recombing Best explained with an example:

85 + 16 = 85 + 15 + 1 = 100 + 1 = 101

Partioning in Tens and Units - Adding the tens up first, followed by the units. For example:-

82 + 25 = (80 + 20) + (2 + 5) = 100 + 7 = 107

I can see how all the previous steps build to this point which in turn leads to the final traditional "Standard Written Method with Exchanging"- see the last step below. There are couple of points that strike me. Firstly it must be painful for bright children to go through all these steps- especially if they have been taught the fundamentals at home. I hope that schools have strategies to avoid such frustration. Secondly it's impossible, when you know how to add up, to fully appreciate the benefit of this step by step approach. Your natural inclination is to be impatient and say why not just teach the final method. I now understand how these steps should allow children of all abilities to build their numeracy skills in a relatively consistent and reliable manner.

Counting on in Multiples of 100, 10 or 1 Here's and example:

86 + 57 = 86 + 50 + 7

86 + 50 = 136 + 4 = 140 + 3 = 143

Adding Significant Digits First An extension of partitioning. Add hundreds, then tens and then units. Children are expected to do these sums in their heads, perhaps with jotted notes to help them


625+ 48 =




= 673

Adding Near Multiples of 10

Example 527 + 298 = (527 + 300) - 2 = 827 - 2 = 825

Compensation Small extension of previous step

527 + 83 = (527 + 100) -17 = 627 - 17 = 610

Standard Written Methods with Exchanging

This is the method I remember from school. Adding the units first and carrying below the line, as per this example:-

Primary School Mathematics Tuition

Is Primary School Mathematics Tuition Better Now Than It Has Ever Been?

See results


    0 of 8192 characters used
    Post Comment
    • tirelesstraveler profile image

      Judy Specht 

      8 years ago from California

      Excellent hub. My tutor when I was little taught me some of these techniques. Interestingly enough when the new math came into vogue during the 70's they were thrown out the window. The real key is helping kids to enjoy playing with numbers instead of being afraid of math.

      Nursery rhymes are a good start. One two buckle my shoe....

    • SuffolkJason profile imageAUTHOR


      9 years ago from Ipswich, Suffolk, England, United Kingdom

      Thanks for taking the time to give me some feedback. Regarding multiplication and division, I don't have any more information than this bald statement. In my opinion (I'm not an teacher or trained mathematician- other O level Maths years ago) showing children that, for example, they count add three, four times to make twelve would be a logical way to introduce multiplication. I'm sure that's how I first grasp the concept of multiplication (again that was a very long time ago).

      On the second point. In my opinion great teachers have the ability to put themselves in the shoes of their pupils and understand how to break complicated concepts into understandable steps. I also think that all pupils much prefer to understand the logic of why things work rather than just learn techniques by rote. Personally, I never feel confident about a topic unless I understand not only what the rules are but also why the rules work.

    • profile image


      9 years ago

      There are a couple of points I find very interesting from your post. I have recently graduated as a Maths teacher in Northern Ireland, which follows a different curriculum to the rest of the UK.

      1) "recognising that multiplication can be repeated addition and division can be repeated subtraction."

      This is something which we were always told to avoid teaching as it was viewed to be the incorrect way of teaching the concepts of multiplication and subtraction. Is there any more information on this?

      2) "Your natural inclination is to be impatient and say why not just teach the final method. I now understand how these steps should allow children of all abilities to build their numeracy skills in a relatively consistent and reliable manner."

      A great point. Obviously your son's school policy of showing the parents in such detail how the topics are taught has been very successful in your case. Perhaps something more schools should follow. In our training college there was a debate about whether children should be taught the core concepts (how to add) and derive the rules (the methods you described) from these, or whether they should be taught the rules and use these to build to the core concepts. I would usually fall upon the side of the former argument, but your post has provided an excellent insight into reasoning behind the latter.


    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)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)