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
The Operation Maths blog is a collection of articles offering support, guidance and tips for teachers, parents and families, whether they are Operation Maths users, or not. Many of the posts also contain links to other resources.
The posts fall into one of the following categories:
About Operation Maths: A series of posts, aimed at teachers unfamiliar with Operation Maths, that explore the programme in more detail, highlighting its rationale, purpose and features.
Maths by Month: Posts which outline, on a month by month basis, the upcoming topics for that month, at each class level
Digging Deeper into… A series of posts, aimed at teachers, which delve deeper into the underlying mathematical concepts and pedagogy for each strand unit in the Primary Mathematics Curriculum (1999)
Dear Family: aimed at parents and families, supporting children’s mathematical development at home, these posts provide brief guides to understanding each of the topics, practical suggestions, and links to digital resources, organised according to approximate class level.
About Operation Maths
A series of posts, aimed at teachers unfamiliar with Operation Maths, that explore the programme in more detail, highlighting its rationale, purpose and features.
A series of posts, aimed at teachers, which delve deeper into the underlying mathematical concepts and pedagogy for each strand unit in the Primary Mathematics Curriculum (1999)
Aimed at parents and families, supporting children’s mathematical development at home, these posts provide brief guides to understanding each of the topics, practical suggestions, and links to digital resources, organised according to approximate class level. New Dear Family posts coming soon!
Dear Family, given below is a brief guide to understanding the topic of data 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 data. 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 Data
Data, as the name suggests, is all about information, and in maths it is about organising information in such a way that it is easy to read and interpret. Most of us are quite familiar with information from surveys, voting etc., presented in graphs, charts and tables in various print and digital media. But graphing is only one part of the data presentation and analysis process, and this process is essentially the same, whether at the junior or senior end of primary school, or even at a more advanced level of statistics:
It starts when someone ask a question, that doesn’t have an obvious and/or immediate answer. This could be a question like who do most people intend to vote for in the next election or what is the favourite colour of a group of people or which sweet occurs most often in a box.
Information is then collected relevant to the question. This may be collected via a digital or face-to-face survey. It may be collected from a large or small representative sample of people.
This collected information or data is represented in a structured way that makes it easier to read. This might be a type of graph, pie chart or table.
This represented data is then examined and compared (analysed and interpreted) in such a way as to be able to make statements about what it reveals and, in turn, to possibly answer the initial question; if the question remains unanswered, it may be necessary to re-start the process again, perhaps using different methods.
In the senior end of primary school the children will encounter more complex data and charts/graphs, while also analysing data in more complex ways, such as calculating the average (also know as mean), in 5th & 6th class, and identifying the most frequently occurring value in a data set (also known as mode) in 6th class.
Practical Suggestions for Supporting Children
Let’s get organised! As mentioned earlier, data is all about organising information in an easy-to-interpret way. So any activities which involve sorting or organising can become a data analysis activity, for example:
What lollipop flavour/colour occurs most often in the bag (see image)? Ask your child to organise the lollipops in such a way that we can see the answer, without the need to count. This could be done with a box of wrapped sweets also, for example, Quality Street, Heroes, Celebrations etc. For more challenging questions, ask your child to tell you how many more/fewer of one type than another type.
What toy type do you have most of? When tidying up the toys, lay them out in rows alongside each other (parallel rows, similar to above), with the same type in each row. Of what toy type is there the most? The least?
Hat sort: Organise your hats into rows of winter hats and summer hats or hats with rims and hats without rims or even just according to colour. You can do something similar with other clothes types also.
You can also organise buttons or Lego pieces or building blocks in a similar way …. or any suitable material you may have at home.
Real-world examples: Anytime you come across any examples of the data process, share these experiences with your children. It could be completing a review (survey) for an online purchase or a holiday stay. It could be survey or election results you come across on the internet, radio or TV. If a graph is used, ask your child to tell you the type of graph it is and to tell you what they notice, or can tell, from the information shown.
League tables (soccer, GAA, rugby), are an ideal example of data presented in a table. Look at a table of results together, ask your child to interpret the information given, what it tells us, and what the various headings mean. Discuss an upcoming game: if your preferred team wins, how will that affect the table?
Planning a party and not sure what to do or where to go? Why not ask your child to survey his/her playmates with 3 or 4 possible options and then use the collated results to determine the destination?
Do a survey: You could do a traffic survey outside your house or a bird watch survey in your back garden. Or just encourage your child to come up with their own questions that they would like to answer. Survey your friends and family and then graph/present the collected information. Digital technologies (for example Microsoft Excel and Google Docs/Sheets) make it very easy to create a variety of very effective graph types.
Digital Resources for Infants
Fruit Fall: A simple game where the fruit that is caught is laid out in rows on a grid.
Graphs: a selection of 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
Khan Academy – Picture Graphs: Watch the videos and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics.
That Quiz – Graphs: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. From the options on the left hand side select pictogram, how many, difference, minimum, maximum, easier content. Do the set 10 questions, if you get 10 or 9 correct go up a level, and/or choose normal content.
IXL.com – Graphs: a selection of interactive quizzes. 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.)
Math Games – Graphing: games to practice graphing skills; go to the activities for your class level.
Khan Academy – Data: A unit of work including video tutorials and practice questions. You can also register for a free Khan Academy account to record your progress and explore other areas and/or try more difficult material.
That Quiz – Graphs: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. Ensure that the level is set to 1. Each time do the set 10 questions, if you get 10 or 9 correct go up a level, if not stay at that level. There are lots of different types of activities: it automatically starts on bar charts, and you can choose pictogram, line (trend graph), circle (pie chart), multi-bar also. There are many question options also: plot, how many, difference, minimum, maximum, mean (average, 5th up) and mode (6th class).
IXL.com – Graphs: a selection of interactive quizzes. 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.)
Math Games – Graphing: games to practice graphing skills; go to the activities for your class level.
Line and angles is a strand unit in the Primary Maths Curriculum for 2nd class up. For most people, when they think about angles, they also think about degrees, for example a 90° (ninety degree) angle. Yet in primary school, we don’t introduce degrees, as a way to describe, measure and construct angles, until 5th class. So what are they doing before that?
Initially, children are exploring angles as ‘turns’ i.e. recognising angles in terms of rotation: quarter-turns, half-turns and full turns. The children explore this themselves by turning to show the different turns, in both clockwise (turning right) and anticlockwise (turning left) directions.
In school, the children will also be shown other real-world examples of angles, including angles made by the hands of a clock, by the blades of an open scissors, by a door opening and closing, etc. We also look at angles (or corners/vertices) in 2-D shapes, for example in rectangles and triangles… even the names of these shapes pay homage to the angles that made them what they are today! (triangle = tri (or 3) angle; rectangle = rect (right/proper) angle)
In third class, the children will begin to use the term right angle, as a more mathematically correct way to describe the quarter turn (when movement is involved) or square corner (when there is no movement i.e. the angle is static) that they met in second class. The children will also learn to identify and name a variety of angles: angles less than a right angle (acute angles), angles more than a right angle (obtuse or reflex, more than 2 right angles/a straight angle) and angles equal to 2 right angles (straight angle). Then, in 5th and 6th class, they will begin to use degrees to identify, measure and construct various types of angles. This requires the use of a protractor, from a maths set, and it is not the most obvious or straightforward tool to use, so plenty of practice is required (see video links below in the Digital resources section for 5th and 6th class).
You can’t have an angle without having at least two connecting lines, therefore lines are an integral part of this area of maths. Like angles, not all lines are the same and the children learn to recognise and describe lines as horizontal, vertical, oblique, parallel or perpendicular.
Practical Suggestions for Supporting Children
Ask your child to teach you about the angles and lines in your home. What different types of lines can be seen? What different types of angles can be seen? Can they name them?
Line Hunt: ask your child to show you some lines that they can see at home. Ask them to run their finger along the lines so they get a sense of the line’s direction and position.
Make a right angle finder: From a scrap piece of paper, tear out a large circular shape. Fold the shape in two, and then fold it in two again. The two straight edges/lines meet at a corner to make a right angle. Ask your child:
‘Have you heard any other name for this type of angle?’ (square corner, quarter turn)
‘Can you find any angles this size in this room? What are they called?’ (right angles)
‘Can you find any angles greater than/smaller than right angles in this room?’
What’s in name? Write out your name in all capital letters. Name the different line types and angle types you can see. Are there any lines of symmetry in the letters? How many lines of symmetry and where? Click here to see some possible answers.
You gotta hand it to ’em! Look closely at your hand… can you see angles in the lines made by your fingers? Estimate the degrees and then click here to see possible answers.
Programming If your child does programming, or is interested in trying it out, they could use a free programme such as Scratch to draw various line and angle types.
Khan Academy – Right Angles: Read through and then answer the practice questions. Afterwards, for something more challenging, look at the Fourth Grade Activities, which explore different types of lines and angles. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Turns on a compass: Compare the start and end positions of the dial and decide how it turned.
Turn the man: Explore how many times you need to turn the man to match the images.
Pattern Blocks: Explore the lines and angles that can be made with these interactive pattern blocks. Also includes a protractor feature for measuring the angles.
Geoboard: Make lots of different angles and lines using this interactive geoboard, free from the Math Learning Centre.
Math Games: Identify the parallel, perpendicular and intersecting lines
Geometry: a selection of games from ixl.com, including types of angles, obtuse, acute or straight, types of lines. 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.)
Angle Alien Attack: Defend the Earth from an alien invasion using your knowledge of angles. Choose to read the angles from the protractor or estimate them without a protractor.
Alien Angles: Create a specified angle to destroy the aliens. Challenging, but great for developing the ability to estimate angles. A similar game is Rocket Angles; this time you must estimate and input the measure of the given angle in degrees.
Estimating Angles: In this game you must stop the angle size as near as possible to the target measure in degrees.
Pattern Blocks: Explore the lines and angles that can be made with these interactive pattern blocks. Also includes a protractor feature for measuring the angles.
Geoboard: Make lots of different angles and lines using this interactive geoboard, free from the Math Learning Centre.
That Quiz – Angles: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. Ensure that the level is set to 1. Each time do the set 10 questions, if you get 10 or 9 correct go up a level, if not stay at that level. Start with only the “Measure” option on the left-hand side ticked, and when you bring the mouse across the screen, it changes into a transparent protractor. Other options included calculating the value of a missing angle in a triangle, (Triangle), and calculating the value of a missing angle in intersecting lines (Line) or parallel lines (Parallel).
Geometry: a selection of games from ixl.com, including classifying triangles and quadrilaterals. 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.)
Math Games: selection of interactive geometry quizzes, that includes lines and angles.
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 Counting and Numeration
Counting and numeration is about the counting words we use to tell the amount in a group, and the numbers we write for those counting words. And counting is not just about chanting a series of numbers …’one, two, three, four, five…’. It is about using these numbers with meaning, for example, understanding that the word ‘five’ can be written as 5, that it comes after four and comes before six, and that it can be used to describe the amount in a group of five items (and not just the label for the last item in the count). So, even though your child may know how to count to 10 or 20 or more, by the time they come to primary school, this does not necessarily mean that they understand the meaning of each number, or its place in the counting sequence. This is often described as the difference between rote counting (chanting a sequence of numbers) and rational counting (counting with understanding); for more on this, please check out the one minute video below.
Counting and numeration is a strand unit in Primary Maths for children in junior infants to second class only. Children in the senior classes will still do a lot of counting and numeration activities, but mainly as part of the strand unit place value. In the younger classes, the type of learning activities are very similar at every class level; the main difference is that each class level will have different number limits. In school, we expect that most children should be able to read, write and use numbers:
0-5 by the end of junior infants, and be able to count to 10
0-10 by the end of senior infants, and be able to count to 20
Up to 99 by the end of first class
Up to 199 by the end of second class
That is not to say that you should limit your child to only counting up to the number limit for his/her class level. In reality, children will encounter much larger numbers in the real world, than they will encounter in their maths books, so feel free to include larger numbers when you meet them. But, bear in mind that, even if a child can read or say a large number, it doesn’t necessarily mean that they understand it.
Practical Suggestions for Supporting Children
Count, count and count some more! Count out the plates at the table, count out sweets or treats, count steps as you go up and down stairs, count down the days left to a birthday; use every opportunity for your child to hear you count, and when ready involve them in the counting.
Watch Numberblocks and Numberjacks. Many of the episodes from these two award-wining series from the BBC are available on-line and may also be available on your TV if you have BBC.
Develop counting skills though play:
Play tea-time with the toys, where each toy gets one cup, one plate, one bun etc. No toy should have more than one, and no toy should have none. These activities help to reinforce the one-to-one correspondence required in counting correctly.
Play counting games at home (for example throw items into a basket/box and count them as you throw) and ordering games, for example where you layout playing cards in order. Or guessing games, where you estimate (guess carefully) the number of items in a container, bag etc., and then count to check.
Play board games where the child has to throw a dice, recognise the number of dots shown, and then move on a counter that number of places.
Play games where each number in a sequence (e.g. 1 to 10; 45 to 55; 103 to 113) is written on piece of paper/card and placed face-down. The child must turn over every piece in turn and read aloud the number. Then, he/she should put the numbers in a line in order. Finally, you could play hide and seek: remove a number from the line and your child has to tell you the missing number.
Play counting games on car journeys, e.g. each child in the car picks a colour and counts every car of that colour that they see or meet on the road. The winner is the person who hits the highest number before the driver’s patience wears out!
When your child starts to write numbers, you will need to monitor their number formation very carefully; it it very important that they don’t get into the habit of writing a number incorrectly.
Draw your child’s attention to numbers around your home and in the wider environment, e.g. numbers on signposts, car registrations, phone numbers, the number of pieces in a jigsaw, page numbers on catalogues, the numbers on houses or hotel rooms. When you spot a number, ask them to read it out.
With older children, when you are talking about numbers be careful to use the correct language e.g. for 125 say ‘one hundred and twenty five’ not ‘one-two-five’
It’s an unfortunate convention, but the way we talk about numbers every day, can often be mathematically incorrect and/or confusing. For example, when calling out a mobile number, that starts with 08….. we will likely say ‘oh eight‘…… Yet 0 is a digit called zero, whereas O (said as ‘oh’) is a letter of the alphabet and not a number at all! So, when verbalising numbers with zero, try to get into the habit of saying ‘zero’ instead of ‘oh’.
Numbers that end in ‘-teen’ or ‘-ty’ can be difficult for some children. In particular, some children can have difficulty hearing the difference between numbers ending in ‘-teen’ and ‘-ty’ when they are spoken out loud, e.g. ‘fifty’ (50) sounds very like ‘fifteen’ (15) when spoken, yet their values are very different. Try to say these type of numbers clearly, and encourage your child to say them clearly also, so that they appreciate the difference between these similar-sounding numbers.
Count the Yeti 1-10: Count the number of yetis and shoot the correct number at the top.
Helicopter Rescue: Find on the number path the direct number that the computer asks, or find the number in between two given numbers. Has different levels: numbers up to 10, up to 20, up to 30, up to 50 and up to 100.
Caterpillar Count: Count and collect the numbers in order up to 15, to watch the caterpillar change into a butterfly.
Treasure Hunt: Help the pirate find his lost treasure by clicking on the island that shows the correct number. Select ‘Find the biggest number’ option and then adjust to set the maximum number.
Chopper Squad: Find a number 1 more/less or 10 more/less than a given number. Has different levels: numbers up to 20, up to 30, up to 50 and up to 100.
Blast Off: In the Find a Number game (red labels) you are asked to find, from 3 options, the direct number that the computer asks, or find the number in between two given numbers. Has different levels: numbers 10-20, 10-30, 30-60, and 60 to 99.
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 and 1-20.
Count and match: Count the items and drag over the matching numeral (up to 10)
Happy Numbers Pre-Kindergarten: Work through the activities from Module 1, counting to 5 and/or Module 3, counting to 10. Alternatively, go to Kindergarten, Module 1, numbers to 10
I Know it! – Counting: Scroll to numbers + counting + place value to do any of the activities.
Splash Learn – Counting Games: An assortment of games organised according to US grade levels; junior and senior infants should choose among the games for kindergarten level.
Counting: a selection of 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)
Helicopter Rescue: Find on the number path the direct number that the computer asks, or find the number in between two given numbers. Has different levels: numbers up to 10, up to 20, up to 30, up to 50 and up to 100.
Chopper Squad: Find a number 1 more/less or 10 more/less than a given number. Has different levels: numbers up to 20, up to 30, up to 50 and up to 100.
Blast Off: In the Find a Number game (red labels) you are asked to find, from 3 options, the direct number that the computer asks, or find the number in between two given numbers. Has different levels: numbers 10-20, 10-30, 30-60, and 60 to 99.
Treasure Hunt: Help the pirate find his lost treasure by clicking on the island that shows the correct number. Select ‘Find the biggest number’ option and then adjust to set the maximum number.
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.
Happy Numbers Kindergarten: First class could explore the activities from Module 5, Numbers 10 – 20 and Counting to 100.
I Know it! – Counting: Scroll to counting and number patterns to do any of the activities.
Splash Learn – Counting Games: An assortment of place value games organised according to US grade levels; first class should choose from among the games for first grade, and second class should choose from the games for first and second grade.
Counting: a selection of 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 Early Mathematical Activities (EMA) 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 Early Mathematical Activities.
You can also find class specific tips at the back of your child’s Operation Maths At Home book
Understanding Early Mathematical Activities
Early Mathematical Activities is a strand in Primary Maths for children in junior infants only, although the activities can also suit children at the beginning of senior infants, as revision, as well as being suitable for many children in their final preschool year. The focus is on doing activities, that develop the child’s mathematical thinking, but that do not involve number or counting. The children will be:
identifying things that are the same, and things that are different
matching pairs of items that are identical and/or items that belong together
classifying (sorting) items into into groups that are identical and/or belong together
comparing items and sets of objects to determine which is larger or has more, and ordering objects according to to a certain criteria e.g. their length, size, weight etc.
All of these type of activities help prepare the children for later, similar activities, involving numbers and counting.
As mentioned, an essential skill is for the children to recognise objects and images that are the same and that are different. The objects may be completely identical in all features, or have the same colour but a different shape or size. The children will learn to match identical items (e.g. socks) and to match items that are different but belong together (e.g. fork and spoon). Later, the children will learn to sort items into different groups, depending on the purpose.
Practical Suggestions for Supporting Children
Most of the Early Mathematical Activities can be incorporated into the various tidying and sorting/organising activities that occur regularly around the home:
Putting away or sorting clothes. Ask your child:
‘What items are identical (or exactly the same)and belong together in matching pairs?’ For example socks.
‘What items are identical or exactly the same and but don’t belong together in matching pairs?’ For example any t-shirts, or jeans, or pieces of underwear that are identical.
‘What items are not exactly the same, but do belong together?’ For example, a pyjama top and bottom set, a shorts and t-shirt set etc.
‘What items are the same colour?’
‘What items are different from everything else?’
Sorting, for example, the drawer of kitchen utensils and/or cutlery:
Organise the contents into groups of items that are identical or exactly the same.
What items don’t belong in any group e.g. a large soup ladle or wooden spoon? These items are different.
Can you find any items that are similar, and do the same thing but do not look exactly the same? e.g. different types of spoons
Can you find items that are not the same but usually go/belong together? E.g. fork and knife
Tidying up the toy box or play room. Ask your child to suggest ways to sort the items into groups e.g.
Sort according to type: all the similar items together, e.g. books, cars, dolls etc
Sort according to colour: all the red items together, all the yellow items together
Sort according to size: all of the large items together, all of the small items together
Sort according to owner: all of each child’s toys together
Organise the Lego pieces; you might sort them according to colour, shape, size or purpose e.g. all the wheels together, all the doors and windows together, all the mini-figures together etc.
Identifying colours:
Pick up something and ask your child to find another one that is the same colour or a different colour.
Organise items into groups of the same colour. Ask your child to name the colour.
Ask your child to show you an example of items that are the same colour, but not exactly the same (i.e. different shades of the same colour), and to use the words dark and light to describe these colours e.g. light blue and dark (or navy) blue.
Play ‘I spy with my little eye something the colour of …..red’. Repeat with other colours.
Go on a walk outside. Ask your child if they can you find any items from nature that are identical or exactly the same? Can he/she find any items that are different?
Digital Resources for Early Mathematical Activities
Dear Family, given below is a brief guide to understanding the topic of place value 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 Place Value
Place value is about exploring the base-ten number system we use: how our numbers are made up of digits, each of which represent different values, depending on their position or place in the number. In the senior classes the children will explore place value in numbers with a decimal point, as well as numbers without a decimal point (whole numbers).
No matter how large a number is, you really only need to know how to read a three-digit number, to be able to read any size number. This is because the digits are always organised in groups of three, as you can see in the image below. However, we do also need to know the significance of the commas. For example, three (3) million, six hundred and twenty-three (623) thousand, nine hundred and fifteen (915) = 3,623,915: the comma closest to the units is read as thousand, the next comma is read as million, etc.
At its most basic level, central to understanding our place value system, is to recognise that 10 single items or units or ones, can be grouped together to make a ten; that 10 tens can be grouped together to make a hundred; that 10 hundreds can be grouped together to make a thousand etc. In school, the children have lots of different materials that they can group together, or exchange, such as cubes, bundles of sticks, counters on ten frames and place value discs. At home, the children could bundle cotton buds or cocktail sticks or trading cards into groups of tens and fasten them with an elastic, or group identical pieces of lego into sticks of ten, or count out beads or buttons or pieces of pasta into small containers or bags as groups of tens.
Example of materials that might be used in school: place value discs, bundling sticks and base ten blocks
In school, the type of place value learning experiences that the children have, are very similar at every class level; the main difference is that each class level will have different number limits. In school, we expect that by the end of first class, most children will understand place value in numbers up to 99, in second class up to 199, in third class up to 999, in fourth class up to 9,999, in fifth class up to 99,999 and in sixth class there is no limit … millions, billions, trillions even!
That is not to say that you should limit your child to the number limit for his/her class level. In reality, children will encounter much larger numbers in the real world, than they will encounter in their maths book, so feel free to throw bigger numbers at them. But, bear in mind that, even if a child can read or say a complicated number, it doesn’t necessarily mean that they understand its place value.
Practical Suggestions for Supporting Children
Ask your child to read out loud any numbers they meet around your home and in the wider environment, e.g. numbers on signposts, car registrations, the number of pieces in a jigsaw, page numbers on catalogues, the numbers on houses or hotel rooms, larger numbers on fact books e.g. Guinness Book of World Records, recorded times for races, etc.
Correct language: When you are talking about numbers be careful to use the correct language e.g. for 91,856 say ‘ninety one thousand, eight hundred and fifty six’ not ‘nine-one-eight-five-six’ and for 23.95 say ‘twenty three point nine five’.
Zero does not equal ‘oh’! It’s an unfortunate convention, but the way we talk about numbers every day can often be mathematically incorrect and/or misleading. For example, when calling out a mobile number, that starts with 08….. we will likely say ‘oh eight‘…… Yet 0 is a digit called zero, whereas O or ‘oh’ is a letter of the alphabet and not a number at all! So, when verbalising numbers with zero, try to get into the habit of saying ‘zero’ instead of ‘oh’.
Numbers that end in ‘-teen’ or ‘-ty’ can be difficult for some children. In particular, some children can have difficulty hearing the difference between numbers ending in ‘-teen’ and ‘-ty’ when they are spoken out loud, e.g. ‘fifty’ (50) sounds very like ‘fifteen’ (15) when spoken, yet their values are very different. Try to say these type of numbers clearly, and encourage your child to say them clearly also, so that they appreciate the difference between these similar-sounding numbers.
Rounding large or awkward numbers is something we do to make them easier to say or report. For example, if there was 91,856 people at a concert or a match, the media might report that there was just over ninety thousand or there was almost ninety two thousand people in attendance. When you encounter numbers in the media, encourage your child to round them; ask him/her what the number would be roughly/approximately. If you come across a number that has already been rounded, together you could guess/speculate as to what the exact number might have been.
Make place value fun!
Play counting games on car journeys, e.g. each child in the car picks a colour and counts every car of that colour that they see or meet on the road. The winner is the person who hits the highest number before the driver’s patience wears out!
Race to the page! Challenge your child to try to find certain page numbers, in books with plenty of pages, as quickly as they can. Use a dictionary or other reference book, or even an Argos catalogue and call out a page number, for example ‘three hundred and ninety’ and see how quickly that page can be found. If you have more than one copy of a suitable big book or catalogue, two players can race against each other.
Khan Academy – Intro to Place Value: this video and the videos that follow, explore place value in 2-digit numbers and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other areas of Grade 1 maths.
White Rose Place Value: a series of lessons on place value within 20. These lessons could be followed up with other place value lessons in year 1 or year 2.
Place Value Grouping Video: Watch a video of how ones (units) can be grouped into tens, to make various numbers.
Candy Machine: Help make up the orders of candy sticks by using bundles of tens and ones
Dienes Penalty Shoot Out: Identify the number of counters and create numbers using Dienes blocks (aka Base Ten Blocks). Choose game mode to earn penalty chances, and then numbers up to 20, 50 or 100.
Place Value Basketball: Select the correct number to match the image. Work your way up through the various options/levels.
Lifeguards: Click and drag into the place value grid, the correct number of place value discs to make up the given number. Choose between 0-50 or 0-100 options. You can also play a similar game called Shark Numbers
Maths Goalie – Reading numbers: Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then number to 20 or 100.
Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then T O (Tens and Ones) in either column.
Rocket Rounding: A multiple choice game involving rounding numbers: start with rounding numbers up to 99 and with the easier option of having a number line and then try to play the other more difficult option, no number line.
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.
Splash Learn – Place Value: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for first class pupil’s start with Kindergarten games and for second class pupils start with first grade games.
Place Value: a selection of 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 and Fourth Classes
Khan Academy – Place Value: in this video and the videos that follow, explore place value in 3-digit numbers and then answer the practice questions (says Grade 2, but is suitable for 3rd class). Fourth class student can access similar activities for 4-digit numbers and larger here. You can also register for a free Khan Academy account to record your progress and explore other topics.
White Rose Place Value: a series of lessons on place value suitable for 3rd class. These lessons could be followed up with other place value lessons in year 3 or year 4.
Place Value House: video lesson that explores hundreds, tens and ones (units), suitable for 3rd class.
Expanded Form: A video that introduces expanded form and explains how we can expand numbers to see the parts that make it, suitable for 3rd class.
Dienes Penalty Shoot Out: Identify the number of counters and create numbers using Dienes blocks (aka Base Ten Blocks). Choose game mode to earn penalty chances, and then numbers up to 1,000 or 5,000.
Place Value Basketball: Select the correct number to match the image. Work your way up through the various options/levels.
Lifeguards: Click and drag into the place value grid, the correct number of place value discs to make up the given number. Choose between 0-500 or 0-1,000 options. You can also play a similar game called Shark Numbers
Maths Goalie – Reading numbers: Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then number to 1,000 or 10,000.
Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either H T O (for third class) or Th H T O (for fourth class) in either column.
Rocket Rounding: A multiple choice game involving rounding numbers to the nearest 10 or 100, up to 999 or 9,999. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.
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.
I Know It! – Place Value: Scroll down to place value to do any of the activities with suitable number limits. There are some more advanced activities in the third grade section.
Splash Learn – Place Value: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for third class pupil’s start with second grade games and for fourth class pupils start with third grade games.
Place Value Games: An assortment of place value games using numbers of various sizes. Third class pupils should start with games up to 999 (three-digit numbers) and fourth class should start with games up to 9,999 (four-digit numbers)
That Quiz – Place Value: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. In place value, the lowest level is 3. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. There are lots of different types of activities: For Identification (it automatically starts on this) you must identify the value of certain digits; other options are conversions, rounding and sums.
Place Value: a selection of 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
Khan Academy – Place Value: in this video and the videos that follow, learn about place value in larger numbers and then answer the practice questions. You can also access similar activities for decimal numbers here. If you register for a free Khan Academy account, you can record your progress and explore other topics.
Happy Numbers – Place Value: A series of interactive lessons and activities on numbers up to one million. Do Module 1 Topic A, B and C
White Rose Place Value: a series of lessons on place value suitable for 5th class. These lessons could be followed up with other place value lessons in year 5 or year 6.
How big is a billion? It is very difficult to visualise the size of a million, or a billion, of anything. This video demonstrates the length of a thousand, a million, and a billion coins if they were placed top to bottom.
Maths Goalie – Reading numbers: Read the numbers in word form and then input the same number but in standard form. Choose reading numbers, and then numbers to 1,000,000 or 10,000,000.
Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either whole numbers or decimal numbers, in either column.
Rocket Rounding: A multiple choice game involving rounding numbers, using whole numbers or decimal numbers. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.
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 or decimals game.
I Know It! – Place Value: Scroll down to place value to do any of the activities with suitable number limits. There are some more advanced activities in the fourth grade section.
Splash Learn – Place Value: 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.
That Quiz – Place Value: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. In place value, the lowest level is 3. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. There are lots of different types of activities: For Identification (it automatically starts on this) you must identify the value of certain digits; other options are conversions, rounding and sums. Sixth class pupils looking for a challenge could try scientific notation.
Place Value: a selection of 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)
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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.
The Operation Maths blog is a collection of articles offering support, guidance and tips for teachers, parents and families, whether they are Operation Maths users, or not. Many of the posts also contain links to other resources.
Fruit Fall:
Curious George – Hat Grab:
Fishing Game:
Khan Academy – Picture Graphs: 
Pictograph Game 
I Know It – Graphing:
How to make a graph using MS Excel:
How to make a graph using Google Docs/sheets:
Interactive programme to create line (trend) graphs
Interactive programme to create bar/pie charts
Create a Graph: 
Splash Learn – Data Games: These games cover 
Mashup Math – Video Lessons
Averages and Bar Models:
Turns, Angles and Lines: A series of video lessons from White Rose Maths, including for Year 2, 
Lines & Angles
Khan Academy – Right Angles:
Turns on a compass:
Turn the man:
Right or Left:
I Know It! Classifying Angles
Measuring Angles with a Protractor:
Khan Academy – Measuring Angles:
Angle Alien Attack:
Estimating Angles:
The Gingerbread Man Game:
Ladybird Spots
Curious George Hide and Seek
Curious George Apple Picking:
Count the Yeti 1-10
Helicopter Rescue:
Caterpillar Count:
Treasure Hunt: 
Caterpillar Ordering:
Count and match:
Maths Visuals – Counting by one:
Maths Visuals – Place Value Concepts:
Coconut Ordering:
Splash Learn – Sort objects by colour
ixl.com – Which are exactly the same?
Place Value Grouping Video:
Candy Machine:
Place Value Basketball:
Lifeguards:
Maths Goalie – Reading numbers:
Expanded Form:
Place Value Basketball:
Place Value Games:
Happy Numbers – Place Value:
White Rose Place Value:
How big is a billion?