Monthly Archives: February 2019

Maths by Month – March (updated 2019)

Category : Uncategorized

Welcome to the March installment in this series of posts designed to explore the Operation Maths topics on a month-by-month basis, giving teachers greater insights into the concepts at hand, when they are most relevant.

While each monthly overview will specifically zone in on the Operation Maths topics for that particular month, the information and suggestions will be relevant to ALL primary teachers, whether they are Operation Maths users or not.

HINT: To ensure you don’t miss out on any future Maths by Month blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Pssst! The Edco Primary Publications launches for 2019 will be taking place around the country during March and April. As well as launching the new SESE programme Explore with Me, the new English Core Skills Let’s Talk Literacy and Bua na Cainte 4, they will also be showcasing Operation Maths, Number Facts and other Edco publications. Click on the link above for more information and to register.

Operation Maths for Junior Infants to Sixth Class:

Teachers of Infants to Second Class: if you have not yet recorded the results of the Operation Maths End of Februaury Assessments please check out the Excel Record Spreadsheets to accompany the rest of the assessments in the Assessment Booklets; if you have any suggestions for how to improve these, please leave them here.

Operation Maths users can also access a class specific, month-by-month list of relevant links and online resources via the Weblinks document, accessible on www.edcolearning.ie. 

  1. Log into your edcolearning account
  2. Click on the At School Book/Pupil’s Book for your class level.
  3. Click on the Edco Resources icon (on book cover image on left-hand side)
  4. Select Weblinks from list of categories and then click to download the document.
  • Also accessible on  www.edcolearning.ie.  are the custom-made digital resources to support these topics. These will all be viewable when you click on the Edco Resources icon as directed above.

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources
Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for March:

  • Engineer’s Week runs from Saturday 2nd to Friday 8th March. There are obvious connections between Maths and Engineering, a fact which is being celebrated by the STEM (Science, Technology, Engineering and Maths) movement globally. Click on the link above to download a primary school challenge pack which contains lots of ideas to help you organise fun challenges that create a positive awareness and spark enthusiasm about the engineering profession in young people.
  • Pancake (Shrove) Tuesday is Tuesday 5th March. Recipes naturally provide great opportunities for real world maths, for example identifying the measures and amounts required, adding the correct measures to the mix, adapting the recipes to suit more or less people, etc. For more maths-related activities check out these pancake problems.
  • World Book Day is on Thursday 7th March, and while the primary resources accessible on the site are mainly literacy linked, there are numeracy ideas also, including “Not Another Maths Book” activity sheet. Other numeracy and literacy linked suggestions for this global celebration include:
    • Carry out a survey to find out the favourite books / authors of the children in your class. Or choose a page from a book. Work out the average number of words per sentence. Both of these are included among many other suggestions from Teaching Ideas for World Book Day.
  • With both Ireland’s ultimate and penultimate game in the 2019 Six Nations still to be played, there is still time to delve into some of the mathematical possibilities:
    • With older children, use the opportunity to explore the rugby union scoring system, and to identify what scores (up to 30, for example) are possible (how?) or impossible.
    • Calculate the number of games to be played; what if the competition had less or more teams, how many games would need to be played then?
    • Use the language of chance to discuss the possible outcomes for each nation in the competition and recognise that while it is impossible to predict the actual outcomes, we can use of knowledge of the teams performances to make informed predictions.
    • Calculate the dimensions of the pitch
    • Run a Fantasy Rugby League in your class
    • Make score predictions for each match and plot how these scores would be recorded on the Six Nations Table

We’re here to help!
If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter 


Digging Deeper into … 2-D Shapes and 3-D Objects (infants to second class)

Category : Uncategorized

3-D shapes or 3-D objects?

In the PDST Shape and Space manual, it is suggested that “using the word ‘shape’ to describe both 2-D shapes and 3-D shapes can cause confusion for pupils”. For example, asking pupils to ‘describe the shape of this shape’ highlights one problem. Another problem is that pupils must be able to think of all cuboids as being ‘the same shape’, while mathematically speaking all cuboids are not the same shape.

The manual goes on to suggest that it would be more helpful to refer to 3-D things as ‘objects’. Using ‘objects’ also reinforces the notion that if it can be physically handled/picked up, it must be a 3-D object, as opposed to a 2-D shape which should always only have length and width, not depth/height.

So, throughout the Operation Maths books, this topic is titled 3-D objects to avoid confusion and to provide clarity for the pupils. However, wherever there is reference to “strand unit”, the term 3-D shapes is used, as this is the term used in the 1999 Primary Maths curriculum.

So what first? 2-D or 3-D?

2-D and 3-D objects are very inter-related, to the point that there is often much debate about which of the topic should be taught first; 2-D shapes, 3-D objects or teach them both concurrently.

Since 2-D shapes are lacking the third dimension of depth or height that their 3-D relations possess, this makes them quite abstract as only flat, drawn/printed shapes are truly 2-D. Whereas, 3-D objects can be picked up, manipulated, used for constructions etc., making them much more suited to the concrete learning experiences that are essential in the early years. They are the objects that we find in the real-world. Thus, since 2-D shapes are only flat representations of the faces of 3-D objects, it could be argued that it would be more logical, and more in line with the concrete-pictorial-abstract (CPA) approach, to teach about 3-D objects before 2-D shapes.

On the other-hand, it could be argued that 2-D shapes should be taught first as it is likely than young children would be more familiar with them. For example, the vocabulary of 2-D shapes features more regularly in common speak than the vocabulary of 3-D objects. Many children will likely have encountered many 2-D shapes from picture books and patterns around their homes, etc. And so, it remains inconclusive as to which order of progression is most beneficial!

In the Operation Maths books, the children meet the specific topic of 2-D shapes prior to that of 3-D objects each school year. However, it is envisaged that by the time the children in the junior classes are formally engaging with 2-D shapes, they have already encountered and informally explored both 2-D shapes and 3-D objects via the monthly themes (laid out in the long-term and short-term plans of each TRB) and in the suggested Aistear play activities (detailed also in the TRB) of which, the Aistear theme of construction is particularly relevant.

Infant classes

Whether considering 2-D shapes or 3-D objects, the suggested progression within each topic is very similar:

  • Undirected play
  • Sorting and ordering activities
  • Building and making (including making patterns)
  • Identifying

Undirected play may include sand and water play, use of formal construction toys, constructing using “junk” or found materials; any activities that allow the children to handle and manipulate shapes and objects.
In the Operation Maths TRBs for junior and senior infants there are ample suggestions for suitable activities, under the headings of various themes. “Undirected play” does not imply that the teacher is superfluous to the process; rather while the children are the instigators, the teacher can play a vital role, observing the way in which the children interact with the materials, and asking the children to explain what they did, how they did it and why they did it that way. This can be a great way to assess the prior knowledge and language that the children may already have.

Sorting and ordering activities include the Early Mathematical Activities (EMA) used early on in the infant classes; thus it is likely that shapes and/or objects have already been used as part of these activities, for example sorting and matching according to colour, size etc; ordering according to length/height etc.

At this point, the children should also be prompted to sort the shapes and objects according to their respective properties as relevant and appropriate:

  • Sort 2-D shapes according to the number of corners and the number and type of sides (straight, curved or both; sides that are different or the same).
  • Sort 3-D objects according to those that roll/do not roll, slide/do not slide, build/do not build, are hollow/solid; as a development, according to the number of corners and the number and type of faces and edges (please see end of post for more information on faces and edges).
  • The teacher can also isolate shapes/objects to create sets and then ask the children to identify the rule of the set: “What’s my rule?” (see image above). The children can also be encouraged to play the “What’s my rule?” game in groups.
  • Isolate a particular shape/object in the room and ask the children to locate others that are the same/similar and make a set of like objects/shapes.
  • The children may also be naming the shapes as part of these explorations; however this is not necessary as it is more important that they appreciate the similarities and difference between shapes, rather than identifying them.

Building and making with shapes/objects may have already been explored informally as part of the undirected play phase. The purpose now is to develop this into more formal teacher-directed tasks and activities:

  • Build the tallest building/castle that you can. What objects did you use/not use and why?
  • Dip a face of a 3-D object in paint and use it to print. Make a pattern using the prints. What do you notice?
  • Try printing with different faces of the same 3-D object. Are the resulting prints the same or different?
  • Push 3-D objects into sand/plasticine to make imprints. Or (if able) trace around the 3-D objects on paper to make designs.
  • Use cut-out shapes, gummed shapes, tangrams and/or pattern blocks to make pictures and patterns.
  • Use the shapes to cover surface of your book/mini-white board; which shapes did you use/not use and why?
  • Combine two shapes/objects to make a new shape/object.

As part of the building and making activities the children may begin to realise how certain shapes/objects can be combined to become other shapes/objects. Similarly, through the reverse of these activities, and other shape cutting activities, the children should begin to realise that shapes can also be separated (partitioned) to reveal new shapes. This can include deconstructing 3-D objects to reveal their net. These activities can be revisited once the children can also name the shapes/objects, so as to arrive at certain understandings and become more accurate with mathematical language eg that two squares can make a rectangle; that, when using tangrams, two of the same size triangles can be rearranged to make a square, a larger triangle etc.

Identifying the specific shapes/objects evolves from the previous activities as the children begin to realise that it is the specific properties and attributes of a shape/object that defines it, eg all shapes with three corners (and three sides) are triangles, irrespective of their size or colour and irrespective of the measure of sides and corners (later to be referred to as angles). Activities which will serve to reinforce this include “Guess the shape/object” using descriptions (see below), guessing unseen shapes/objects from touch (eg in a feely bag), locating a specific shape from a collection using touch alone.
Through the experiences of printing and imprinting with the 3-D objects, it is also hoped that the children realise that the flat faces of 3-D objects are in fact 2-D shapes.

First and Second classes

The children in these classes will continue to sort, describe, compare and name shapes as done in infants, but to now also include new shapes and objects i.e. semi-circle (1st), oval and cone (2nd). They will continue to construct and make shapes, extending this to creating and drawing the shapes themselves.

They will further explore the combining and partitioning of 2-D shapes, and this understanding will extend to include the fractions of halves (1st) and quarters (2nd). The properties of 2-D shapes will be further explored
in second class via the stand units of symmetry, angles and area (i.e. tessellating 2-D shapes)

Q: How many faces on a cylinder? Three or two?
Traditionally, in Ireland, and in Irish textbooks, a cylinder was recorded as having three faces. However, this is not mathematically correct, as strictly speaking a face is flat, and a 2D shape (figure), so therefore a cylinder has in fact only two faces, (both circles), and one curved surface. And while it may be argued that a cylinder has a third face i.e. the rectangular shape you see when you disassemble the net of the 3-D object, in this disassembled state it is no longer a cylinder, since it can no longer roll, a specific property of all cylinders.
Another way to think about the faces of 3-D objects is to consider the number and shape of the resulting outlines of tracing around, or printing, each surface of the 3-D object. It is only possible to trace around the opposite ends/bases of the cylinder, since only these are flat, thus it has only two faces, both of which are circular in shape. Similarly, it is only possible to trace around one surface on a cone, which therefore means it has only one face (a circle) and one curved surface.
And how many edges on a cylinder? Officially none, as an edge is where two flat faces meet and the faces on a cylinder are on opposite sides and do not touch/meet. However, that leaves the problem of how to describe the place where each face meets the curved surface.  So in Operation Maths, as occurs typically in other primary texts in other countries, there is a distinction made between straight edges (which are in fact true edges) and curved edges (which strictly speaking are not edges).

Further Reading & Resources:


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