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.
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.
Dear Family, below is a brief guide to understanding the topic of symmetry, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about symmetry. The digital resources are organised according to approximate class level:
You can also find class specific tips at the back of your child’s Operation Maths At Home book, for infants to second class, and in the Operation Maths Dear Family letters for third to sixth class.
Understanding Symmetry
Symmetry is introduced in second class and is a stand-alone maths topic in only second to fourth classes. That said, it also features as part of the topic of 2-D shapes in fifth and sixth classes where the children in those classes are asked to “classify 2-D shapes according to their lines of symmetry”.
While there are different types of symmetry (which children will explore deeper in second level maths), the primary curriculum specifies line symmetry, also known as mirror symmetry, reflective or reflection symmetry.
In school, the children will often have the chance to use special child-safe mirrors to explore this concept, and to look at the mirror image of arrangements of various items. It would be really valuable for the children to be able to do something similar at home, with any suitable small mirrors that might be available (Tip: mirrors with straight outside edges rather than curved edges are better for this, eg a small mirror from the lid of a make-up pallet). Draw your child attention to the way in which the pattern appears to be reversed e.g. in the image above the order of the real cubes is orange, yellow, green, but in the reflection we see green, yellow, orange.
Practical Suggestions for Supporting Children
Symmetry at home: explore the symmetry that is all around you:
Look for examples of symmetry in clothes, furniture, windows, dishes, ornaments, doors, etc.
If going for a walk, look out for examples of symmetry in nature eg flowers, leaves.
Is there symmetry in any of the numbers we write? What about letters of the alphabet; lower-case and/or upper case (capital letters)? What about the letters in your name?
Take some time to use mirrors to explore symmetry (as mentioned above, small square, or rectangular, cosmetic mirrors are ideal for this). Using the mirrors the children can create and check symmetrical patterns using cubes, counters, objects etc. They can look for symmetry in numbers and capital letters (eg the letters on the cover of their Operation Maths book, other books, newspapers, boxes, food containers etc). Can your child answer the following questions?
What letters or numbers look the same in the mirror? What shapes or images look the same in the mirror?
Can you put the mirror along the middle of any letters and numbers so that they look complete? Does this work with any other shapes or images?
For some shapes/numbers/letters, is there more than one than one way, that the mirror can be placed?
Using the mirrors the children can create and check symmetrical patterns using pieces of lego, blocks or other suitable objects etc.
Place a mirror to the right or left of the arrangement. Describe what can be seen in the reflection.
Change the position of the mirror, perhaps above or below the arrangement. Does the reflection in the mirror look the same? Is it different? How? Why?
Repeat using different items and/or arrangements. Ask your child to predict what the mirror image will look like before they actually look into the mirror.
If your child has his/her Operation Maths twenty frame at home (free with Operation Maths 1 and 2) it can be used to create a symmetry challenge (see below). One person uses counters, lego pieces, buttons etc, to make an arrangement and the other person makes its mirror image. You could also do something similar with a chessboard/draughtboard and the playing pieces.
In second class, the children are being introduced to simple symmetry. If your child knows very little about symmetry already, a good starting point is to watch some of the videos below.
Intro to Symmetry: A YouTube video that introduces and explores reflectional (mirror) symmetry.
Symmetry Land: Learn about lines of symmetry through this song from Numberock
Symmetry Painter: This simple activity allows you to paint on one side and watch as the symmetrical image magically appears on the other side!
Symmetry Matching: 3 different games where you choose the matching symmetrical half.
Symmetry Sorting: 3 different games where you decide if the image shown is symmetrical or not symmetrical.
Pattern Blocks: Use these interactive pattern blocks to make numerous designs, pictures etc on one side of the screen. And then challenge yourself, or another, to complete the symmetrical image on the other side.
Symmetry: A selection of simple games from ixl.com. You can do a number of free quizzes each day without having a subscription.
Math Games: a simple symmetry game ideal for beginners.
Digital Resources for Third and Fourth Classes
NB: Children in these classes may also enjoy the links for second class above
Symmetry Shapes: You will be shown a shape and you must create the reflection or mirror image of the shape as reflected in the line of symmetry. Click on the grid squares to colour them in, and then click check to see if you are correct.
Symmetry Counters: Similar to the game above, an arrangement of counters will be shown and you move the other counters to create the reflection or mirror image of the arrangement, as reflected in the line of symmetry.
Symmetry Invaders: Can you complete the symmetrical images to win this space invaders-type game?
Wishing you all a healthy and happy New Year and here’s hoping that there are better times ahead for us all.
But, for the meantime, we are all back in the reality of providing distance learning for our classes. As we journey forward together, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, including:
Dear Family, our ever-expanding series of posts, aimed at parents and families, supporting children’s mathematical development at home
Digging Deeper, our series of posts, aimed at teachers, providing deeper insights into the underlying theory, approaches and pedagogies behind the various maths topics
About Operation Maths posts, for teachers who want to find out more about the Operation Maths program itself.
HINT: To ensure you don’t miss out on any future 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
Operation Maths for Junior Infants to Sixth Class:
Second Class: Money, Symmetry, Operations (addition and subtraction without renaming, including subtraction as deduction) and Fractions.
HINT: Teachers of Infants to Second Class – if not yet done, don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of December Assessments
To access lists of relevant links and online resources, navigate towards the end of the relevant Dear Family posts, for a whole suite of suggestions, organised into approximate class levels.
Don’t forget that integrated with your digital Operation Maths pupil books, are numerous custom-made digital resources to support each maths topic. Just click any of the hyperlinks while viewing the digital book to bring you direct to the relevant resource.
TIP! If there are any digital resources for a particular page, they will also be briefly given and described in the footer of that page (both print and digital books).
Backward Day! The 31st of January marks this little-known celebration which encourages us to reverse or invert the typical societal rules. Without encouraging anarchy, there are obvious opportunities here to explore symmetry, mirror writing etc.
Challenge your class to write out the capital letters of the alphabet backwards; not only starting with z but writing each letter as flipped image of itself.
Ask them to consider in advance which letters might appear the same when flipped backwards and what letters will appear different.
The children’s letters can be checked using small plastic mirrors to see if the image in the mirror is correct.
The children can also be asked to do the same thing with the digits 0-9 or even bigger numbers.
Most parts have had some snow already, and there could be more! The Routty Math Teacher has a whole library of Solve it Friday puzzles many of which align themselves with feasts and seasons. Sign up here to get access to the library and then check out weeks 16-19 for snow-themed puzzles.
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
Welcome to the December installment of this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.
As we journey together through on this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.
Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.
HINT: To ensure you don’t miss out on any future 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
Operation Maths for Junior Infants to Sixth Class:
Junior Infants: Analysis of Number (Numeration) looking at the number four
HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of December Assessments
To access lists of relevant links and online resources, navigate towards the end of the relevant Dear Family posts, for a whole suite of suggestions, organised into approximate class levels.
Don’t forget that integrated with your digital Operation Maths pupil books, are numerous custom-made digital resources to support each maths topic. Just click any of the hyperlinks while viewing the digital book to bring you direct to the relevant resource.
TIP! If there are any digital resources for a particular page, they will also be briefly given and described in the footer of that page (both print and digital books).
This year, Computer Science Education Week runs from 7-13 December, during which time, they are also encouraging everybody, young and old, to engage with their annual Hour of Code event. Coding is the future! Computers are changing every industry on the planet. Every 21st-century student should have the opportunity to build technology. Click on the links above to access Hour of Code and other computer science activities for learners of all ages. Operation Maths users can also access the tailor-made Operation Maths Scratch lessons on https://edcolearning.ie
Mash-up Maths have a Christmas-themed 12 Days of Holiday Math Challenges, suitable for 1st class up. It can be better to hide all the puzzle initially, and then, reveal just one line at a time and ask the children to record and justify all the possible solutions based on what they know at that point. As they move through each line, they can then explain why they should now discard certain options. This is a better way to engage all of the children in thinking mathematically, rather than it just becoming a race to the solution (which can often turn-off those less mathematically-inclined). For more of this type of problem sign up to the Mash-up Maths weekly newsletter, to receive lots of other themed maths puzzles and challenges like this Grinch-themed challenge.
Interested in more Christmas-themed maths problems? From Dec 1-24 the German Maths Society posts a daily problem (in English) on its online Advent Calendar. There are 3 levels of difficulty, 4th class to adults.
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
Dear Family, given below is a brief guide to understanding the topic of fractions, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about fractions. The digital resources are organised according to approximate class level:
You can also find class specific tips at the back of your child’s Operation Maths At Home book, for infants to second class, and in the Operation Maths Dear Family letters for third to sixth class.
Understanding fractions
Fraction comes from a Latin word meaning “to break (something) in pieces”; it’s related to the word fracture, meaning to break into pieces, usually used to describe a broken bone. In maths, fractions are the result of dividing something (a shape, object or amount), into a number of equal pieces or parts.
Equal is very important; if we divide something into two parts, but they are not equal, then they are not halves. Therefore it is very important to emphasise to children from the very beginning that the parts made must be equal; in school we often talk about it being a fair share.
And while fractions might seem straight-forward enough, i.e. dividing something into equal parts, even the basic fractions can be interpreted in many ways:
3/4 (say “three quarters”) can be describing 3 parts of something that is is divided into 4 equal parts, eg 3/4 of the square is red (above) or 3/4 of the blocks are red (below).
3/4 can also be interpreted as three out of four i.e. that 3 out of 4 cubes are red or that 3 out of every group of 4 cubes are red (below).
3/4 can also be interpreted as three divided by four or 3 ÷ 4 which gives a value of 0.75, the decimal equivalent for 3/4 (below).
Initially much of children’s exploration of fractions in school, will focus on creating and identifying various fractions (starting with familiar fractions such halves, quarters, eighths, tenths etc).
They will also learn to recognise fraction forms that are the same value (i.e. equivalent fractions eg 1/2, 2/4, 4/8, 5/10 etc), and comparing and ordering fractions. In the senior classes, children will work with less familiar, more complex fractions as well as calculating with, adding, subtracting, multiplying and dividing fractions.
Practical Suggestions for Supporting Children
Use fractions and the language of fractions at home, e.g. when dividing up food (cutting up pizzas, cake, bars of chocolate), when baking (e.g. half a teaspoon, a quarter of a cup, half a dozen eggs).
Look for fractions when out shopping, e.g. half price. Ask your child to calculate the current price, or what the price was before the reduction.
Be careful about using fractional language accurately, e.g. there’s no such thing as a big half or a small half! To make fractions, we must create equal parts. Encourage your child to be accurate and to recognise that if something is divided into two parts that are not equal, they are not halves.
Fractions names can be confusing for children: it makes sense that each part of something divided into ten equal parts is a tenth… similarly for fifth, sixth, eighth, ninth etc. But each part of something divided into two equal parts is a half (plural is halves) and each part of something divided into four equal parts is a quarter. Furthermore, when speaking one eighth (1/8) it can be difficult to distinguish from eight (8). Try to say and explain fraction names clearly, and encourage your child to say them clearly also, so that they appreciate the difference between these similar-sounding words.
If your child is experiencing difficulties with converting fractions, adding, subtracting or multiplying fractions, encourage him/her to use concrete materials (eg paper plates, paper straws and or pieces of paper) and/or draw pictorial representations, e.g. pie pieces or number lines, to help them visualise what is happening and develop his/her “fraction sense”.
Khan Academy Fractions: Watch the videos and then answer the practice questions on halves and fourths (another name for quarters). Afterwards, try the activities in Second Grade. You can also register for a free Khan Academy account to record your progress and explore other areas of First Grade Maths.
Hit the Button: Use the Halves game to practice calculating half of a number
Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Khan Academy Fractions (Third Grade): Watch the videos and then answer the practice questions. Afterwards, try Equivalent Fractions, and for more challenging, look at the Fourth Grade Activities. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
I Know it! – Fractions (Third Grade): Scroll down to the Fractions & Decimals section to do any of the activities. You could also try the Fractions sections in Fourth Grade.
Hit the Button: Use the Halves game to practice calculating half of a number
Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the fractions game.
Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Digital Resources for Fifth and Sixth Classes
Happy Numbers Fourth Grade: Pupils should start with the activities in Module 3. And then progress to Fifth Grade to do the activities in Module 3 and 4
I Know it! – Fractions (Fourth Grade): Scroll down to the Fractions & Decimals section to do any of the activities. You could also try the Fractions sections in Fifth Grade.
Hit the Button: Use the Halves game to practice calculating half of a number
Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the fractions game.
Splash Learn – Fractions: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for fifth class pupil’s start with fourth grade games and for sixth class pupils start with fifth grade games.
Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Welcome to the third installment in this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.
As we journey together through on this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.
Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.
HINT: To ensure you don’t miss out on any future 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
Operation Maths for Junior Infants to Sixth Class:
Junior Infants: Analysis of Number (Numeration) looking at numbers one to three
HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of October Assessments
To access lists of relevant links and online resources, navigate towards the end of the relevant Dear Family posts, for a whole suite of suggestions, organised into approximate class levels.
Don’t forget that integrated with your digital Operation Maths pupil books, are numerous custom-made digital resources to support each maths topic. Just click any of the hyperlinks while viewing the digital book to bring you direct to the relevant resource.
TIP! If there are any digital resources for a particular page, they will also be briefly given and described in the footer of that page (both print and digital books).
The Bebras® Computing Challenge 2020 runs from 2nd to 13th November; it introduces computational thinking (i.e. the thinking skills behind coding and programming tasks) to students, by allowing them to solve interactive tasks online. The tasks can be answered without prior knowledge about computational thinking or information and communication technology. The aim of Bebras is to get students all over the world excited about computing. The challenges are divided into five different age categories from 8-18 years old. On the link above, both teacher and student can explore previous challenges and, even if your class or school doesn’t register to take-part (which is free), the past challenges are very engaging and worthwhile to explore as a whole class or groups.
The 11 November marks the anniversary of the ending of the Great War, “the war to end all wars”, which is now typically referred to as World War 1. For 5th and 6th class teachers, who are planning to explore this topic in history, check out these Maths Activities from the Trench Brothers Education Zone.
Codes and code breaking were a very important part of warfare tactics during both World War 1 and 2. To find out more about the maths of code breaking click on the link.
Science Week 2020 runs from 8th-15th November. There are obvious links between Maths and Science, a fact which is being celebrated by the STEM (Science, Technology, Engineering and Maths) movement globally. Of the STEM areas, coding is one of the most exciting, not least of all to kids! And Operation Maths is the only Irish maths programme that has integrated coding activities via the Scratch Lessons for Operation Maths 3-6. Check out the scratch lessons that are included in the Operation Maths digital resources via your TRB or edcolearning.ie For infants, the Aistear Themes are an ideal way to explore STEM using a thematic focus (and lay the foundations for the development of computational thinking skills); consult the Junior and Senior Infants TRB for the monthly Aistear suggestions.
For some more primary-focused STEM activities, check out the links below:
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
Dear Family, given below is a brief guide to understanding the topic of multiplication and division, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about place value. The digital resources are organised according to approximate class level:
You can also find class specific tips in the Operation Maths Dear Family letters for third to sixth class.
Understanding Multiplication and Division
Like addition and subtraction, multiplication and division is not just about multiplying and dividing to get a correct answer (although accuracy is always to be valued in maths); the focus is very much on understanding and visualising what is happening to the amounts/numbers, how they are changing, why they are changing and how the same calculation can be done in many different ways. This is often referred to as developing a child’s number sense.
In Operation Maths, the children are always encouraged to use materials and pictures, and to explore different strategies (ways) to get their answers. They are also encouraged to compare their strategies with the strategies of others, and to explain or justify why one way might be more efficient (faster and/or simpler) than another way.
From Operation Maths 3, possible thinking strategies for 2x, 5x, 10x.
In particular, the children are encouraged to refer to some key, benchmark facts, that, in turn, can be used to work out other facts. These include doubling and halving (which can be used to multiply and divide by 2, 4 and 8) and multiplying and dividing by 10, which in turn can be used to multiply by 5 (half 10 times the number) and multiplying by 9 (one group/set less than 10 times).
These benchmark facts (or friendly facts), combined with other strategies, ensures that the child develops both understanding of, and fluency with, the basic multiplication and division facts, which in turn cam be applied to more complex situations later, such as bigger numbers or fractions and decimals. Pictured below are examples of some useful thinking strategies for the basic multiplication and division facts.
While multiplication and division are separate operations, they are also very closely related, being the inverse (or opposite) of each other e.g. 3 x 10 = 30, 30 ÷ 10 = 3, 30 ÷ 3 = 10. This is another strategy that the children can use i.e. think multiplication to do division, or vice versa. Beginning in third and fourth classes, the children will explore multiplication and division as being the inverse of each other, which will progress towards using the inverse (opposite) operation to check their calculations.
Therefore, nowadays, there is less emphasis on just learning off “tables”, (i.e. memorising answers) and more emphasis on thinking strategies to use what they know, to solve what they do not know.
Practical Suggestions for Supporting Children
Invite your child to help out with any opportunity to do multiplication and/or division at home, or when out and about, e.g. how much for 5 packets of the same sweets? If buying a multipack of anything, how much roughly for each item? etc.
Encourage your child to use strategies when multiplying and dividing and/or to explain their strategies. Ask your child to explain how they know, or worked out the answer.
“I don’t believe you…prove it!” When your child arrives at an answer, ask him/her to show you how they got an answer, to prove that that is the answer, and encourage them to think of other ways to arrive at the same answer. Are there ways that might be more efficient (better) than others?
Encourage your child to estimate. Estimation is a very important skill; this involves quickly getting a rough or ‘ballpark’ idea of the answer, e.g. 3 boxes of sweets at €4.79 each is just under €15 because €4.79 is almost €5. Encourage your child to quickly estimate answers e.g. How much, roughly, is that going to cost? Do we have enough money?
Digital Resources for Third and Fourth Classes
Happy Numbers Second Grade: Third class pupils could start, and work through Module 6, Foundations of Multiplication and Division, and then progress to Third Grade, Modules 1 and 3. Fourth class pupils could start with Third Grade or go straight to Fourth Grade and work through the activities in Module 2.
The Array: An introduction to rectangular arrays (rows and columns) and how they can be used to understand multiplication.
Arithmetic Arrays: Solve multiplication and division questions using the help of rectangular arrays. Three levels in each game.
Partial Product Finder: This is not a game, but it is a tool, that can be used to show an array for multiplication calculations involving 1 or 2 digits
Hit the Button: a great site for practicing quick-fire Times Tables and Division Facts. For a slower-paced version of this try the Mental Maths Train, a multiple choice game.
That Quiz – Arithmetic: Use this quiz to practice different types of multiplication and division calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.
Multiplication.com: A site dedicated to multiplication games, but also includes division games and games for addition and subtraction.
I Know it! – Multiplication and Division (Grade three): Scroll down to the multiplication and/or division sections to do any of the activities. If too simple, go to the multiplication and/or division sections in Grade Four
Multiplication practice games and Division practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Digital Resources for Fifth and Sixth Classes
Happy Numbers Fourth Grade: Pupils could start, and work through Module 2, and then progress to Fifth Grade, Module 1 and 2, which includes multiplication and division with decimal numbers
Khan Academy Fourth Grade: Fifth class pupils could try any of the quizzes on multiplication or division to check what they know already, and either re-do some of the units or move on to Fifth Grade. Similarly, sixth class pupils could try the quizzes in Fifth Grade and then re-do or move on to other/new topics as appropriate. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Arithmetic Arrays: Solve multiplication and division questions using the help of rectangular arrays. Three levels in each game.
Partial Product Finder: This is not a game, but it is a tool, that can be used to show an array for multiplication calculations involving 1 or 2 digits
Hit the Button: a great site for practicing quick-fire Times Tables and Division Facts.
That Quiz – Arithmetic: Use this quiz to practice different types of multiplication and division calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.
Multiplication.com: A site dedicated to multiplication games, but also includes division games and games for addition and subtraction.
I Know it! – Multiplication and Division (Fifth Grade): Scroll down to the multiplication and/or division sections to do any of the activities. If these are too difficult, go to the multiplication and/or division sections in Grade Four
Multiplication practice games and Division practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Welcome to the second installment in this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.
As we journey together through on this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.
Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.
HINT: To ensure you don’t miss out on any future 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
Operation Maths for Junior Infants to Sixth Class:
HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of October Assessments
To access lists of relevant links and online resources, navigate towards the end of the relevant Dear Family posts, for a whole suite of suggestions, organised into approximate class levels.
Don’t forget that integrated with your digital Operation Maths pupil books, are numerous custom-made digital resources to support each maths topic. Just click any of the hyperlinks while viewing the digital book to bring you direct to the relevant resource.
TIP! If there are any digital resources for a particular page, they will also be briefly given and described in the footer of that page (both print and digital books).
The October plan for third to sixth classes has deliberately allowed for a free week, to enable teachers to engage with Maths Week, held every year at this time. This year, Maths Week will run from 10-18 October, and while it will be a very different celebration this year, with no public gatherings, it will still be possible to participate virtually. So why not start to consider now, how your school might get involved in this national celebration of maths, and don’t forget to register your school at the link above. You can also follow the links in the site to find out more about Maths Art (which, coincidentally, links very well with October Operation Maths for 3rd and 4th classes i.e. tessellations in 2D shapes), Maths and history and code breaking. Check out their resource packs by class level also.
You could also make Maths Week become a game-themed week in your class. Teachers of third to sixth classes could use the Games Bank in the Operation Maths TRB. Teachers of infants to second classes can use any of the games listed in the short-term plans in their TRBs.
Another option for Maths Week, if you didn’t already do it in September, is Jo Boaler’s Week of Inspirational Maths. Click on the link for an overview of the activities in Week of Inspirational Math, and scroll down to the bottom of the page to access all the resources; Kindergarten roughly aligns with Infants, Grade 1 and 2 with 1st & 2nd classes, and Grades 3-5 roughly align with 3rd-6th classes.
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
Dear Family, given below is a brief guide to understanding the topic of addition and subtraction, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about place value. The digital resources are organised according to approximate class level:
You can also find class specific tips at the back of your child’s Operation Maths At Home book, for infants to second class, and in the Operation Maths Dear Family letters for third to sixth class.
Understanding Addition and Subtraction
Of all the topics in primary maths, this is probably THE one with which the grown-ups feel most familiar…sure isn’t all just about either adding or subtracting (take away), plus (+) or minus (-), total or difference?
In some ways, it is, and in other ways, it’s not.
As the song goes, ‘it’s not what you do, it’s the way that you do it’ and the same is true for addition and subtraction at primary level; it’s not so much about getting a correct answer (although accuracy is always to be valued in maths) as understanding and visualising what is happening to the amounts/numbers, how they are changing, why they are changing and how the same calculation can be done in many different ways. This is often referred to as developing a child’s number sense.
In Operation Maths, the children are always encouraged to use materials and pictures, and to explore different strategies (ways) to get their answers. They are also encouraged to compare their strategies with the strategies of others, and to explain or justify why one way might be more efficient (faster and/or simpler) than another way.
In particular, the children are encouraged to refer to some key, benchmark facts, that, in turn, can be used to work out other facts. These include doubles (e.g. 4 + 4, 9 + 9 etc), near doubles (e.g. 4 + 5, 9 + 10 etc) and number bonds for 10 (e.g. 4 + 6, 9 + 1 etc). These benchmark facts (or friendly facts), combined with other strategies, such as count on (for adding smaller numbers eg 0, 1, 2, and 3), adding 10 and make a ten, ensures that the child develops both understanding of, and fluency with, the basic addition and subtraction facts, which in turn cam be applied to more complex situations later, such as bigger numbers or fractions and decimals. Pictured below are examples of some useful thinking strategies for the basic addition and subtraction facts.
While addition and subtraction are separate operations, they are also closely very closely related, being the inverse (or opposite) of each other e.g. 10 + 20 = 30, 30 – 20 = 10, 30 – 10 = 20. This is another strategy that the children can use i.e. think addition to do subtraction, or vice versa. Beginning in first and second classes, the children will explore addition and subtraction as being the inverse of each other, which will progress towards using the inverse (opposite) operation to check their calculations.
Therefore, nowadays, there is less emphasis on just learning off “tables”, (i.e. memorising answers) and more emphasis on thinking strategies to use what they know, to solve what they do not know.
Practical Suggestions for Supporting Children
Involve your child in any adding and subtracting that happens at home, or when out and about, e.g. buying tickets for the cinema, buying items of clothes, etc.
Encourage your child to use strategies when adding and subtracting and/or to explain their strategies. Ask your child to explain how they know, or worked out the answer.
“I don’t believe you…prove it!” When your child arrives at an answer, ask him/her to show you how they got an answer, to prove that that is the answer, and encourage them to think of other ways to arrive at the same answer. Are there ways that might be more efficient (better) than others?
Encourage your child to estimate. Estimation is a very important skill; this involves quickly getting a rough or ‘ballpark’ idea of the answer, e.g. €31 and €52 is roughly €80. Encourage your child to quickly estimate totals and differences, e.g. How much, roughly, is that going to cost? Do we have enough money? About how much will we have left?
Splash Learn – Addition and Subtraction Games: An assortment of games organised according to US grade levels; junior and senior infants should choose among the games for kindergarten level.
Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Digital Resources for First and Second Classes
Happy Numbers First Grade: First class pupils could work through the activities from Modules 1, 2, 4 and 5. Second class could go to the activities for Second Grade and work through the activities from Modules 1 and 4.
That Quiz – Arithmetic: Use this quiz to practice different types of addition and subtraction calculations.
I Know it! – Addition & Subtraction: Scroll to the addition and subtraction sections to do any of the activities. If too simple, go to Grade Two, to try the activities involving addition and subtraction of 2-digit numbers only.
Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Digital Resources for Third to Sixth Classes
Happy Numbers Third Grade: Third class pupils could work through the activities from Module 2, Topics C and D. Fourth class pupils, and above, could go to the activities for Fourth Grade and work through the activities in Module 1.
That Quiz – Arithmetic: Use this quiz to practice different types of addition and subtraction calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.
Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)
Dear Family, given below is a brief guide to understanding the topic of comparing and ordering as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about comparing and ordering. The digital resources are organised according to approximate class level:
You can also find class specific tips at the back of your child’s Operation Maths At Home book, for infants to second class.
Understanding Comparing and Ordering
Comparing and ordering is probably something that happens a lot in any home already!
“She’s got more than me! That’s not fair!”
“I want to be first!”
“I want to have the biggest piece!”
In maths, comparing is when two items, amounts or portions are examined to see if they are the same (equal), and if not, which is the larger/has more and which is the smaller/has less. Statements can be made to show how the two relate to each other; for example they are equal (=), there are more bananas than apples (opposite); there are less pears than strawberries.
Initially, the children will be identifying which group has more/less, and which number is less than or greater than another number. Then, they will begin to describe the relationship in more detail e.g. there is one more banana than apples; there is one less pear than strawberries.
In second class, the children will begin to use mathematical symbols (inequalities) to show the relationship eg 5 > 4 (five is greater than four); 2 < 3 (two is less than three).
Once the children are comfortable comparing two items, amounts or portions, they will then be able to progress to ordering three or more, for example ordering four numbers, smallest to largest, or vice versa. Number word order is also an important aspect of this i.e. identifying the number that comes before or after another number.
Ordering also involves being able to use the ordinal numbers 1st, 2nd, 3rd, 4th, 5th…. and ordinal words such as first, second, third ….. and last.
Practical Suggestions for Supporting Children
The next time your child complains that somebody has got more than them, ask them to prove it! If it is sweets, can the child count the amounts to explain or justify that they do indeed have less than another? Or even when sharing out items like this, deliberately give more to somebody and ask your child(ren) to check if the amounts are all the same and, if not, to explain how the amounts are different. And what could be done to make it fairer.
When organising, tidying, sorting at home, ask your child to compare the groups of items they encounter. Ask questions such as:
“Which has more/less?”
“Which is larger/smaller?”
“Do you want more tomatoes or more grapes in your lunch?”
Try to incorporate ordinal number words such as first, second, third…last into your daily routine.
Who was first up out of bed? Who was second? Who was third? Who was last?
Who was first, second etc to be dressed, ready to go to school, finished homework etc.
When giving instructions: “First put on your socks, second put on your shoes, third put on your coat.”
When playing games discuss who will go first, second, third etc.
When standing in a queue talk about your position i.e. where you are standing.
Monitor your child closely when they start writing the ordinal numbers, and don’t take them for granted, as the abbreviation system is not always obvious:
Talk about the dates on the calendar. Say the ordinal number word clearly so that the child appreciates the difference in the sound of these numbers and the counting numbers eg seventh not seven.
“Your birthday is on the 3rd (third) of October.”
“We will be going back to school on the 6th (sixth) of January”
Play hand grab: Get your child to put their hand into some lego, marbles, or other similar items and to put the handful ‘grabbed’ out onto a table. You child can then repeat this, or somebody else can get a handful. Look at the two amounts on the table. Estimate which has more. Then check which has more by either counting or laying both sets of items out in two lines, side-by side, so that you can clearly see which line has more. You could also ask your child to count to find out how many more are in the longer line.
Play an ordering numbers game. Write down all/some of the numbers that your child knows, (eg 0-5 for junior infants, 0-10 for senior infants 0-20 for first class and any set of random numbers within 100 for second class), with each number on a separate piece of paper/post-it. Mix up the numbers and place them face down. Get your child to:
Pick up a number and say it.
Place all the numbers in order smallest to largest (variation: largest to smallest).
Say what number is missing, after you remove one.
Pick out 3 or three numbers and put them in order smallest to largest or vice versa
Play guess my number. Get your child to write down a number within their familiar numbers range (see above). Work out the number by asking questions to narrow the possibilities. For example, is it greater than 5? Is is less than 5? etc. Next round, you write down a number and your child asks you the questions.
You can also play any of the online interactive games below.
Digital Resources for Infants
Happy Numbers Kindergarten: Work through the activities from Module 1, Topic D and Module 3, Topic E, F and G.
Todo Math: Learn ordinal numbers as you watch the toys line up for ice-cream
Ordinal numbers: Watch the ostrich race and use ordinal numbers to identify the finishers
Caterpillar Ordering: Choose between ordering (where you put the given numbers in order) or sequencing (where you complete the sequence with the correct numbers from those given). Has various levels including 1-5, 1-10, 1-20.
Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10 or up to 20.
Comparing: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. There is also a suitable ordering game: order numbers up to 10
Caterpillar Ordering: Choose between ordering (where you put the given numbers in order) or sequencing (where you complete the sequence with the correct numbers from those given). Has various levels including 1-100.
Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10, up to 20, up to 100 (in tens) or up to 100 (any number).
Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct number on the number line, but then the game progresses in difficulty as the player must work out where a given number would be placed on the blank number line. Choose the whole number game.
As we embark on this new school year, and with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.
Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.
HINT: To ensure you don’t miss out on any future 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
Operation Maths for Junior Infants to Sixth Class:
To access lists of relevant links and online resources, navigate towards the end of the relevant Dear Family posts, for a whole suite of suggestions, organised into approximate class levels.
Don’t forget that integrated with your digital pupil books, are numerous custom-made digital resources to support each maths topic. Just click any of the hyper links while viewing the digital book (see example of purple icon below) to bring you direct to the relevant resource.
TIP! If there are any digital resources for a particular page, they will also be briefly given and described in the footer of that page (both print and digital books).
Check out the “Maths and me” attitudes questionnaire, situated after the last assessment in the Operation Maths Pupil Assessment booklet for 3rd to 6th classes. Suggest to the children that they fill this using a particular colour on one of the first days of the school year to be then revisited later in the year. At this point, the children can again record their attitudes in a different colour and reflect upon any changes they made, if any.
Maths about me: another great activity for the start of a new school year. The children write facts about themselves that are appropriate to their ability eg height, age, shoe size, telephone number, distance from school (use google maps), time that they get up or go to bed etc. This can be recorded on the inside front cover of the discovery book, filled in on a pre-made template from the internet, used to make a large class display or even become a more complex problem solving activity in the more senior classes.
The Math in Learning Names: Another one for kick-starting the year; make learning names easier (for both you as the teacher, and for the other students) with these quick and fast sorting ideas, which incorporate maths and language features, such as vowels, syllables etc.
Inspire your class for the year ahead: Most people have this belief that there is such a thing as a maths brain, a belief which Jo Boaler, among others, strongly challenges. Since 2015, in conjunction with her youcubed team at Stanford University, they have put together resources, videos etc for a Week of Inspirational Maths. They now have lessons and activities aimed at infants to 6th, as well as second level. Click on the link for an overview of the activities in Week of Inspirational Math, and scroll down to the bottom of the page to access all the resources; Kindergarten roughly aligns with Infants, Grade 1 and 2 with 1st & 2nd classes, and Grades 3-5 roughly align with 3rd-6th classes.
New year, new initiative! Number Talks is an excellent maths methodology that is gaining traction globally, and more recently, nationally thanks to the promotion of the PDST. Better still, the rationale behind it aligns itself very closely with the underlying principle of Operation Maths, that is teaching children to understand maths, not just do maths. To find out more about number talks and to access a whole suite of ready-made resources for all class levels just click on the link above.
Maths Week (10-18 October) will all too quickly be upon us! And while it will be a very different celebration this year, with no public gatherings, it will still be possible to participate virtually. So why not start to consider now, how your school might get involved in this national celebration of maths, and don’t forget to register your school.
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
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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.
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FREE Teacher copies of all the relevant pupil resources
Intro to Symmetry:
Symmetry Painter:
Symmetry Matching:
Symmetry Sorting:
Vertical and Horizontal Lines of Symmetry:
Symmetry Shapes:
Symmetry Invaders:
I know it – Symmetry: 
Fractions Intro:
Battleship Numberline:
Arithmetic Arrays:
Partial Product Finder:
That Quiz – Arithmetic
Multiplication.com:
Arithmetic Arrays:
Todo Math:
Ordinal numbers:
Caterpillar Ordering:
Coconut Ordering:
Ordinal Numbers:
Ordinal Numbers:
White Rose Comparing:
Caterpillar Ordering:
That Quiz – Inequalities:
Check out the “Maths and me” attitudes questionnaire, situated after the last assessment in the Operation Maths Pupil Assessment booklet for 3rd to 6th classes. Suggest to the children that they fill this using a particular colour on one of the first days of the school year to be then revisited later in the year. At this point, the children can again record their attitudes in a different colour and reflect upon any changes they made, if any.