# Operation Maths Digital – a completely integrated print and digital package!

## Operation Maths Digital – a completely integrated print and digital package!

Operation Maths provides an extensive range of digital resources with endless possibilities. In this post, I will discuss the various types of digital resources that are available and how they can be used in the classroom.

### Overview

The Operation Maths digital resources include:

• e-Manipulatives which can be used  as Ready to go activities and Create activities
• Maths Around us videos
• Write-hide-show videos
• Scratch activities

### e-Manipulatives

The fully flexible, easy-to-use, online e-Manipulatives are designed for teacher-led learning and to encourage whole-class participation. This impressive range of e-Manipulatives is optimised for use on an Interactive Whiteboard or a whiteboard with a projector so that teachers get the best results every time. They also facilitate a CPA approach to maths instruction.

The full range covers key maths areas:

• Sorting & Shop e-Manipulative
• Place Value e-Manipulative
• 100 Square e-Manipulative
• Bar Modelling e-Manipulative
• Counting Stick e-Manipulative
• Fractions e-Manipulative
• Clock e-Manipulative

Lets look at each of these in more detail:

The Sorting & Shop e-Manipulative allows the teacher to easily drag and drop shapes, animals, fruit, classroom objects, shop items, upper and lowercase letters, and numbers onto a workspace. It can be used blank or with various backgrounds, including frames, sets,  2×2, 5×5 grids etc . Of all the backgrounds, the shop background is particularly useful as it allows the teacher to create a shop scene with price tags, coins and sale tags, which can be used to explore a wide range of mathematical scenarios such as using small amounts of money in infants right up to scenarios involving percentage increase and decrease in the senior classes.

The Place Value e-Manipulative provides a wide range of place value tables which the teacher can use to demonstrate re-grouping. Each place value table contains either base-ten blocks, counters to represent the place value discs that accompany the 3rd-5th books, straws or money, and decimal values are included in a selection of the tables. Two tables may be shown on screen at the same time to facilitate comparisons between numbers. There is also the facility to display up to 5-digit whole numbers, which, in my experience, had not been possible previously as all other interactive manipulatives only extend to 4-digit numbers at most.

The 100 Square e-Manipulative is another extremely versatile tool. It can be used in numbers only, counters only or counters and numbers. You can very easily hide and reveal individual cells, whole sections of the grid or the entire grid.  I have gotten a huge amount of use of out it recently, with first and second classes, using it in numbers only mode, hiding all the numbers and just revealing one number. I then ask the children what number comes after/before this, what numbers is missing above/below etc. This is particularly good to assess the children’s ability to identify numbers around the decuples/decades (ie 30, 40, 50 etc) which are widely recognised as hurdles for many children.

This tool can also be used to model the 100 dots grid (on the inside back cover of Operation Maths 3 and 4) as a means to explore the commutative and distributive properties and the connections between various groups of facts.

The Bar Modelling e-Manipulative allows the teacher to create the bar models used in the text books quickly and easily. Bars can be dragged, dropped and resized and the teacher can change their colour. The teacher can also type and draw freehand on the workspace, making this a very useful resource for demonstrating the strategy of bar modelling

The Counting Stick e-Manipulative replicates the physical counting stick that a teacher might use in the classroom. The teacher can set the starting value and the steps value, and reveal or hide numbers along the counting stick. Decimal and negative numbers may also be shown on the Counting Stick e-Manipulative and two counting sticks can be shown at the same time, in order to compare various numbers.

The teacher can use the Fractions e-Manipulative to present fraction bars (linear models), fraction circles and pizzas (both area models). The teacher can change the fraction that is shown on screen, randomise fractions and hide or show the fraction
value, decimal value and percentage value. Two fractions may be shown on screen at the same time.

Analogue and digital clocks are provided with the Clock e-Manipulative. The teacher can choose to show one analogue clock, one digital clock, two analogue clocks, two digital clocks or an analogue and a digital clock at the same time.

All of the e-Manipulatives can be used as Ready to go or Create activities

Ready to go activities are already set up within each e-Manipulative with pre-programmed questions that appear on screen, meaning that the teacher doesn’t have to waste time looking in a book for the accompanying questions. The questions can also be answered on the children on their MWBs, thereby encouraging whole-class participation.

Create activities are so called because the teacher can open the e-Manipulatives and choose how to use it to best suit them, their class and the concept at hand. There are suggestions for Create activities printed in the TRB which show how the tools can be re-used in infinite ways to achieve a countless number of specific learning outcomes. And the Ready to go activities themselves will also provide the teachers with examples of how each e-Manipulative may be used.

### Operation Maths videos

There are two types of videos; Maths Around Us videos and Write – Hide – Show videos. These videos have the advantage that they were custom-built to align with content in the children books and the commentator’s voice is noticeably Irish, which make them stand out from those video series that have been imported from other countries.

Another advantage of these is that they have been designed so the teacher only needs to press play and the questions and wait times are all built in, allowing the children to look, listen and responses on their MWBs. This means that they not only encourage active participation but they allow the teacher the opportunity to informally assess the pupils via their responses.

### Maths Around Us videos

The series of Maths Around Us videos is full of real-world examples of maths in the environment and provides numerous opportunities for discussion and engagement. Take a look at this sample video below:

### Write – Hide – Show videos

These are videos of the e-Manipulatives in use that focuses on the teaching method of ‘Write – Hide – Show’. These videos provide quick, easy-to-use scenarios and set-ups that engage children and pose meaningful maths questions. They also showcase the flexibility of the e-Manipulatives and provide inspiration for teachers’ own expansions. Take a look at this sample video below:

### Scratch programming activities (3rd to 6th class)

Not only have these activities been written especially for Operation Maths but Operations Maths is only the only maths scheme available currently in Ireland with integrated programming (coding) activities. Each activity is integrated with the Pupils’ Books, comes with step-by-step instructions for teachers and pupils and highlights the connection between maths and coding in an easy-to-follow, visual manner.

Encourage your pupils to practice maths ideas at home with the useful Follow-on weblinks based on recommended games. Each Follow-on weblink is author-approved and is linked to a specific topic, for a specific class level, in the Pupils’ Book. The weblinks can be printed for children to take home and have fun practicing maths with their parents or guardians. Teachers can also use the weblinks in class as a lesson starter, for consolidation and assessment or, indeed, at any time.

### And finally….

• All the digital resources are all completely integrated with the print and eBooks; when viewing the eBook, the teacher need only click on the specific digital icon on the page to open the resource up in a new window/tab (ensure that pop-ups for the Edco Learning site are enabled)
• Nearly all of the digital resources can be used in conjunction with the free mini white-boards, ensuring the maximum participation of the children.
• As there are numerous ways to use each of the e-Manipulatives, they offer unlimited opportunities for assessment for learning and whole-class participation
• They have been specially designed to help children to focus on the maths
• They are user-friendly and approachable with bright, clear colours and layout

Teachers can access all the Operation Maths digital resources through Edco’s dynamic online digital hub, www.edcolearning.ie.

## Enabling Computational Fluency

‘Fluency requires the children to be accurate, efficient and flexible.’ (Russell, 2000)

One of the main aims of Operation Maths, from junior infants to sixth class,  is to enable the children to be computationally fluent. And, the main way to achieve this, is to enable them to become flexible thinkers.

In the presentation below from the IPPN Education Expo 2017, the concept of computational fluency is explored, while also outlining how Operation Maths supports this approach in its programme.

## Operation Maths: also the most child-friendly primary maths programme!

Not only is Operation Maths the most teacher-friendly programme currently available, but it is also the most child-friendly. Read on to find out why.

### Enabling children to understand maths, not just do maths

In case you haven’t picked up on it already, Operation Maths is all about understanding, understanding, understanding!

As mentioned before, Operation Maths is based on a concrete, pictorial, abstract (or CPA) approach.

Concrete activities and experiences are emphasised and outlined throughout the pupil books. The Teachers Resource Book (TRB) also provides further suggestion for the ways in which a teacher can use concrete activities with their class.
These experiences are then further developed via the pictorial activities; this may be through interaction with the digital resources and/or via the write-in activities in the books. Of the CPA approach, exploring pictorial representations of materials, numbers, shapes etc., is a vital (but sometimes neglected, particularly at the senior end) step on a child’s journey towards understanding.
All of this should greatly enhance the children’s ability to visualise and understand maths and be more prepared when they meet the more traditional, abstract activities.

### Active participation

The high number of concrete based activities within Operation Maths ensures that the children have regular, if not daily, opportunities to be engaged in active learning. The inclusion of free mini-whiteboards  (MWBs) as part of the programme also encourages the active involvement of all the class in any activities as all children must visibly participate. Moreover, the custom-made suite of write-hide-show videos and Maths around us videos (see below for samples) further increase the opportunities to use the MWBs. I challenge you to show the estimation video to your class and not have them all excited and active!

### Mastery curriculum

Research suggests that changing chapters/topics every week, especially in senior end and especially the case of number topics, is not conducive to developing a strong understanding for the various topics and that preferable to this is a mastery curriculum approach, where the children are afforded a longer time to engage with, and ultimately master, the concepts. Therefore, in Operation Maths, these topics have a dedicated two weeks block, allowing the children to fully engage with the concepts before moving to a different topic, thereby increasing the likelihood for the children to master the content. So, if you look at the contents page of the Operation Maths books, you will notice that there are fewer chapters than usual but that many of these are “double” chapters, designed to be taught over ten school days, as opposed to five.

### A better understanding of the operations

Similarly, research suggests that teaching opposite or inverse operations together, allows the children to better grasp the connections between the two, therefore promoting deeper conceptual understanding. So, in the senior end, addition and subtraction are taught together as part of the same chapter(s), as are multiplication and division. A similar approach is taken to the operations in first and second class once the children have been formally introduced to subtraction.

### A seamless transition…

I was primarily involved in authoring all of the number and algebra chapters in the 3rd to 6th class books, while my co-authors Michael Browne and Siobhán Kelleher authored the chapters for measures, data, shape and space for the same classes. This means that, for the children, their experience of the content is very cohesive as it flows seamlessly from one class to the next.
Similarly the 5th and 6th class books were written in light of the NCCA Bridging documents and Project Maths at junior cycle in second level. In particular, extra attention was paid to the correct and accurate use of mathematical terminology which also helps ensure that the child’s transition from primary maths to second level maths is also as seamless as possible.

### Other ways in which Operation Maths promotes the development of deeper connections and understanding include:

• Linkage: the topics are all taught in a very connected way, with cross references being made where appropriate. In particular, measures are not just confined to their own chapters: they are taught in an integrated way across all suitable chapters and particularly across number
• Integration: The use of maths across other subjects is also emphasised regularly and particularly as part of the suggested activities in the TRBs. In the senior end there are also themed revision pages in the Pupil’s Book, where maths is explored through History, Geography, Sports etc.
• The books have a clean, uncluttered design making them easier for children to focus on the concepts and not be distracted by unnecessary images
• In the senior end, the Pupil’s Book also has clear and detailed teaching panels (easily identifiable by their yellow background) right throughout each chapter, to aid both the teachers and the children, and can be particularly useful if the children are working independently or in small groups.
• To help make connections with the environment there are dedicated Maths Around Us videos in the digital resources, Maths Around Us activities in the Pupil’s Book and Maths Trails in the TRB photocopiables and in selected Discovery Books

## Operation Maths: the most teacher-friendly primary maths programme

Designed by a team of practically minded teachers, our aim was to make it as simple as possible for any teacher to use Operation Maths, while also reducing their planning and preparation work. This is why the content of the Operation Maths Teacher Resource Books (TRBs) is the most comprehensive currently available.

### For the senior end:

Each topic dedicated section in the Teacher’s Resource Book (or TRB which is free to adopting schools) includes:

• An overview of the topic that doubles as a short term plan and includes learning outcomes, vocabulary, resources, differentiation, assessment, linkage, integration etc., etc. Simply photocopy this and use it both as a plan and as a way to record progress through each topic. All of these plans are also available to download as MS Word documents from www.edcolearning.ie
• A brief synopsis of potential difficulties that a class or individuals may have with the topic.
• A day-by-day breakdown (see opposite) of suggestions to teach the topic that is so comprehensive, the like of which has not been seen before. This includes daily suggestions for oral and mental starters, concrete activities, questions, games as well as guidance for the suitable pages to use from the books.
• Suggestions for further activities that will further enhance the children’s ability to understand the topic
• Detailed instructions for how to use the digital resources specific to that topic.

Also included in the senior end TRBs:

• Long term planning is in the introductory section of each TRB and not only is there a plan/grid with month-by-month suggestions of when to teach each topic for every class but, specifically for those teaching in multi-classes, there are versions of the plans that would suit a 3rd & 4th class combination and another for a 5th & 6th class combination.
• A starters bank containing a whole suite of oral and mental maths activities.
• A games bank with suggestions for simple, fun games, most of which are based on readily available resources such as dice, playing cards etc.
• Reinforcement photocopiables (a minimum of one per chapter) for the lower attainers (LAs) which provide opportunities for extra practice for those requiring it.
• Early finishers photocopiables (one per chapter) for the higher attainers (HAs) providing them with rich tasks to challenge them to think deeper and broader about the concept.
• Dear Family Letters: these slips, which can be sent home in a homework journal or copy, explain to the family about the topic and suggest how they might support the child at home.
• Target boards: designed for display on the class IWB, these are accompanied by questions specific to each class level and chapter.
• A range of other photocopiables and cut-outs which can be used to further enhance the children’s understanding of the topic at hand.

### For the junior end:

For the junior end , the TRB each section covers a specific month and each month has an overarching theme eg Capacity,  which then connects the other activities even if then are from another strand unit. Each month section is then subdivided into fortnights to aid planning and then subdivided further into weeks eg January week 3.

Each of the monthly sections includes:

• Two fortnightly overviews of the topic(s) that doubles as a short term plan and includes learning outcomes, skills, vocabulary, resources, concrete materials,  differentiation, assessment, linkage, integration and home-school links. Simply photocopy this and use it both as a plan and as a way to record progress through each topic. All of these plans are also available to download as MS Word documents from www.edcolearning.ie
• A weekly breakdown (see below) of suggestions to teach the topic that includes suggestions for warm-ups (starters), activities, questions, games as well as guidance for the suitable pages to use from the books.
• Suggestions for stations in the 1st & 2nd class books that will further enhance the children’s ability to understand the topic
• Suggestions for Aistear links in the infants books (see doc above).
• Detailed instructions for how to use the digital resources specific to that topic.

Also included in the junior end TRBs:

• Long term planning is covered with the yearly scheme in the introductory section of each TRB and outlines the strand units within each month and cross references this to the relevant pages within the pupils books.
• A reproduction of the curriculum objectives for the specific class level and details when each is covered during the year
• Early finishers photocopiables for the higher attainers (HAs) providing them with rich tasks to challenge them to think deeper and broader about the concept.
• A range of other photocopiables, games and cut-outs which can be used to further enhance the children’s understanding of the topic at hand.

## Understanding maths, not just doing maths…the Operation Maths way!

Operation Maths is a pioneering new maths programme for junior infants to sixth class.

Written by a team of six experienced teachers, Operation Maths is built on a concrete, pictorial, abstract approach, or CPA approach, (based on Jerome Bruner’s conception of the enactive, iconic and symbolic modes of representation) which research has consistently shown to be the most effective instructional approach to enable students to acquire a thorough understanding of the concepts required.

This blog post, and future posts, will explain some of the various features of the Operation Maths programme as well as outlining further ways in which this programme can be used to its full potential  to enable your students to truly understand maths, not just do it!

### Background & Research

As authors, we researched, and were inspired by, the maths books and schemes used in those countries which are the highest-ranking internationally in relation to attainment in primary maths, for example Singapore, Hong Kong, Japan and Finland.

We also looked at best practice in New Zealand, Australia, Great Britain and the United States, as well as the recommendations of our own home-grown publications including the PDST handbooks, NCCA publications (e.g. Bridging Guidelines, Assessment Guidelines etc.) and programmes such as Aistear and Mata sa Rang.

Finally, this was blended with the requirements of our primary school curriculum, in order to create a scheme that is truly innovative in its approaches and strategies and the most forward-thinking maths programme currently available for the Irish market.

### Programme Components

For pupils in infants to second class:

• At School Book
• At Home Book
• FREE Pupil Assessment Booklet
• FREE Mini-white board
• FREE Frames (five, ten or twenty frame)

For pupils in third class to sixth class:

• Pupils book
• Discovery book
• FREE Pupil Assessment Booklet
• FREE Mini-white board
• FREE place value manipulative

• FREE Teacher copies of all the relevant pupil resources
• FREE Teachers Resource Book (TRB) which contains all necessary plans, teaching strategies, photocopiables, games, starters etc.
• FREE access to all of the Operation Maths digital resources on edcolearning.ie, including ebooks, editable plans, and a whole suite of custom made videos  and eManipulatives which greatly enhance the teaching and learning experience for both teachers and pupils.

Furthermore, Operation Maths is the most teacher-friendly  and child-friendly programme currently available.