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.
The final month of the school year is almost upon us, and as usual, this heralds the last installment in this year’s series of posts designed to explore the Operation Maths topics on a month-by-month basis.
As we move towards the end of this challenging school year, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, via:
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:
Junior Infants: will be reinforcing their understanding of the numbers 0-5 via the topic of money.
Third to sixth classes: Operation Maths 3-6 is specifically structured so that the programme can be completed by the end of May, thus covering all of the topics in advance of the standardised testing. Depending on your own specific school circumstances, you may find yourself looking for inspiration to fill the maths lessons from now until the end of month. Whether you’re an Operation Maths user or not, there are a whole suite of suitable ideas for June maths on this blog post.
To access lists of relevant links and online resources (eg lessons, videos, games etc), 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).
We have a separate post entitled Maths for June where there is a whole suite of ideas, that are ideal as end-of-year maths, whether you’re an Opeation Maths user of not.
Maths outside: not only is this typically the time of the year when teachers are bringing their classes outdoors for learning, but this yer we are being encouraged to be outside as much as possible.
Outdoor Classroom Day was May 20 2021. This global event promotes the use of the outdoors to teach, explore and learn. If you missed this day, you might like to do an Outdoor Classroom Day in June instead. There are lots of resources with suggestions for all subject areas, including maths, https://outdoorclassroomday.com/.
For more ideas for outdoor maths you could also check out:
the Maths Around Us activity ideas in your Operation Maths book
the Maths Around Us videos accessible at https://www.edcolearning.ie/
Spatial awareness is being able to describe the position of something/someone in relation to another, using words and/or gestures, and being able to represent spaces and locations using models and/or drawings. For example, it includes being able to tell another where to find shoes, books etc., and it would also include being able to draw a simple map for someone with directions for how to get somewhere.
This maths topic has a lot in common with language, communication and geography skills. The concepts of spatial awareness also lay the foundations for all aspects of geometry, be it at upper primary, secondary or an even higher level.
Essentially your children need to develop an understanding that:
The spatial relationships between objects and places can be described and represented, for example using positional words (such as over, under, up, down, on, beside, in, above, below, near, far, right, left), and directional words (go straight, go through, stop, turn left, turn right, clockwise, anticlockwise).
These relationships may be viewed, described and represented differently depending on the perspective of the viewer (in particular, consider left and right; if we’re facing each other and I hold up my right hand, it is opposite your left hand).
Developing the ability to mentally visualise the representations will enhance a person’s ability to picture how a shape will look when rotated when turned, flipped etc. Therefore, we should encourage our children to imagine or picture places and locations e.g. “Think: when we go to Granny’s house, do we turn right or left at the end of our road/street/driveway?”
Practical Suggestions for Supporting Children
When doing things together at home, or when out and about, try to use the language of spatial awareness as much as possible with your child, for example using positional words (such as over, under, up, down, on, beside, in, above, below, near, far, right, left), and directional words (go straight, go through, stop, turn left, turn right, clockwise, anticlockwise).
Always remember that most spatial language depends on the perspective and direction/location of the person using it; an object could be very close to me but far away from you. Of all the spatial words, left and right are possibly the most confusing: an object to my right, will be to your left if you are facing me. Therefore, be especially mindful of using these words correctly with your child. Click here to read more on the difficulties with left and right.
Play, play, play! Games and puzzles such as jigsaws, tangram puzzles, using mazes, grids and board games all promote the development of spatial skills. Twister is a particularly good example of a suitable game.
Children often find looking at maps really interesting! When out and about or travelling somewhere, use maps to track where you are going. If you visit a tourist attraction (e.g. zoo, forest park etc.), let your child have a copy of the accompanying map/guide so that he/she can be responsible for directing the family around. Other ideal outdoors activities include treasure hunts and outdoor mazes.
Look at Google Maps. Find your local area in satellite mode; can your child(ren) pick out any familiar features? Can they trace their regular journeys to the school, shops, friend’s houses etc?
Coding is a STEM area that develops spatial awareness and the ability to mentally visualise various representations. Your child could explore basic coding via simple coding programs and apps, such as Lightbot and Scratch Jr.
Math Games – Geometry: Select any of the positions games from Junior Infants or Senior Infants
Geometry: a selection of games from ixl.com. Select any of the games from Junior Infants, Section F and Senior Infants, Section I. 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 – Geometry: Select any of the positions games from First Class or Second Class
Geometry: a selection of games from ixl.com. Select any of the games from First Class, Section O. 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 May installment of Maths by Month. Summer is officially here, made even more real by some of the recent spells of fine weather. Hopefully we get to enjoy more good weather this coming month!
As we move towards testing season, and the end of this challenging school year, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, via:
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:
To access lists of relevant links and online resources (eg lessons, videos, games etc), 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).
Another teacher has created a selection of attractive and free posters Star Wars that also promote a growth mindset to maths at the same time. To download yours, go to his blog here.
Outdoor Classroom Day is May 20 2021. This global event encourages us to use the outdoors to teach, explore and learn. There are lots of resources with suggestions for all subject areas, including maths, https://outdoorclassroomday.com/.
For more ideas for outdoor maths you could also check out:
the Maths Around Us activity ideas in your Operation Maths book
the Maths Around Us videos accessible at https://www.edcolearning.ie/
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 April installment of Maths by Month. Spring is well and truly in the air, and summer is just around the corner!
Hopefully, face-to-face teaching will continue to be the norm for this month. But, even if distance learning at home returns, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, on both fronts, via:
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:
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).
April Fool! While April 1 fell during the Easter break this year, it’s never too late to celebrate a bit of silliness! For example, there are 125 sheep and 5 dogs in a flock. How old is the shepherd? Would your students spot straight away that this is unsolvable or will they try to calculate an answer? Take a look at how some of Robert Kaplinsky’s students tried to attack this.
Anthony from Mashup Math also has a selection of April Fool’s Day puzzles available from his blog, which could be shared with students at home.
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 patterns and sequences, 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 patterns and sequences. 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 Patterns and Sequences
A pattern is a set of numbers, shapes, objects etc., arranged in a particular order, according to a particular rule. There are two main types of patterns:
Repeating patterns: (see image above) symbols, shapes, numbers etc., that repeat in a specific way eg ABC ABC ABC ABC… is a repeating pattern, the core of which is ABC because this is the smallest piece that repeats each time.
Increasing (growing) and decreasing (shrinking) patterns: An ordered set of shapes or numbers that are arranged according to a rule, eg 10, 9, 8, 7, 6, 5, …. is a decreasing (shrinking) pattern, where the numbers are going down by 1 each time (i.e. its rule is -1), whereas 5, 10, 15, 20, 25… is an increasing (growing pattern), where the numbers are going up by 5 each time (i..e its rule is +5). Often the word sequence is also used to describe an increasing or decreasing pattern, particularly if it is a pattern of numbers (see image below).
Patterns are all around us in life and in our homes, for example on clothes, curtains, fabrics, walls, tiles, furniture, animals, car tyres, photo frames, packaging, etc.
Two of the images above are of repeating patterns and one is a growing pattern…. but which is which?
In the early years of school, children are enabled to identify patterns that are around them, and to copy and/or extend them. They are also encouraged to create their own patterns using objects and shapes that are available.
As they get older, the children are enabled to examine patterns in more detail, for example to identify the core of repeating patterns and/or to identify the rule of growing/shrinking patterns (sequences).
With Operation Maths 5 and 6, children are enabled to explore more complex patterns and to use more advanced strategies to extend the patterns (see image below) as well as predicting trends etc., in real-life examples and data.
Practical Suggestions for Supporting Children
Draw your child’s attention to patterns around your home and in the wider environment:
Patterns on clothes, curtains, fabrics, tiles, animals, car tyres, photo frames, packaging, etc.
Patterns made with toys, building blocks, threading beads, lego, etc.
Number patterns in the environment, e.g. how the speedometer goes up in tens; that on many streets, the odd numbers are on the houses on one side of the street and the even numbers are on the other side; etc.
items that come in twos (hands, feet, shoes, gloves, socks etc), tens (eg fingers and toes; biscuits and bars in some packets) and fives (5 seats in a standard car).
When you spot a pattern, ask your child to tell you about it, what they notice etc. Can they tell you more about the type of pattern it is (e.g. repeating or growing/shrinking)
Do you know how to knit and/or crochet? Explore the structure of patterns together with your child.
Many puzzles and riddles are based on patterns and these are often widely available in newspapers, magazines, on the Internet, or you can often buy inexpensive puzzle books in discount stores. You could encourage your child to try to solve these and/or you could share and solve puzzles and riddles as a family.
Create pattern puzzles at home using materials around the house, and challenge your child to complete them; e.g. put out a fork, knife, spoon, knife, fork……, and ask your child to say what comes next.
Counting is a an essential skill required to understand, and explore number sequences. Any and all activities, that encourage your child to count in 1s, 2s, 10s, 5s etc., are very valuable. For more counting suggestions and ideas, please refer to the Dear Family Guide to Counting and Numeration.
Children in 5th and 6th classes will also looking at the order in which number sentences should be calculated. Referred to as the order of operations, in Operation Maths we use the mnemonic ‘Bless My Dear Aunt Sally!’ to remind the children how to calculate number sentences correctly i.e. we calculate each part in this order:
Brackets
Multiplication or Division (whichever occurs first, reading left to right)
Addition or Subtraction (whichever occurs first, reading left to right)
Digital Resources for Junior and Senior Infants
White Rose Maths – Pattern: lessons for infant classes covering Pattern; scroll down to session 4 and 5 for videos and activities.
Planet Pal: What colour dog comes next in the pattern? Simple game suitable for infants.
Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty.
Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.
Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out your own choice of tiles make patterns.
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.
Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10 or up to 20.
Happy Numbers: pupils in Senior Infants could work through the pattern activities (patterns in adding 0 and 1) from Module 4, Topic H.
Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum).
Khan Academy: A series of videos and practice questions exploring Even and Odd Numbers (Grade 2). You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty.
Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.
Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out your own choice of tiles make patterns.
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).
Happy Numbers: First class pupils could work through the pattern activities (patterns in adding 0 and 1) from Module 4, Topic H. Second class pupils could do the activities on the Meaning of Even and Odd Numbers, Module 6, Topic D
Maths Frame – Errors on a Venn Diagram: Identify the numbers which have been placed in the wrong position on the Venn diagram and drag them to their correct place. Choose the criteria of odd or even numbers.
Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum).
Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty.
Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.
Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out your own choice of tiles make patterns.
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.
Maths Frame – Sequences: Find the correct number in a sequence. Lots of choice over level, count forwards or back, count in whole numbers, multiples of 10, multiples of 100, decimals and fractions.
Happy Numbers Third Grade: Third and fourth class pupils could work through the activities from Module 3, Topic E.
Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum).
Khan Academy: A series of videos and practice questions exploring Number Patterns (Grade 5) and Order of Operations (Grade 6). You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Maths Frame – Sequences: Find the correct number in a sequence. Lots of choice over level, count forwards or back, count in whole numbers, multiples of 10, multiples of 100, decimals and fractions.
Maths Frame – Order of Operations: Use a calculator to carry out calculations with more than one step using brackets and the memory.
Function Builder: Use this virtual function machine to explore how to change an input to a different output. You can also choose the mystery option, (where you have to work out the rule i.e. how the input is being changed each time) and/or a patterns option.
Happy Numbers Fifth Grade: Fifth class pupils, and above, could go to the activities for Fifth Grade and work through the activities in Module 1, Topics A and B.
Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum).
You can also find class specific tips in the Operation Maths Dear Family letters for fifth and sixth class.
Understanding Number Theory
Number Theory in primary school, is about exploring the shapes of numbers, and how numbers can be visually arranged and represented. It is largely concerned with subcategories of whole numbers:
odd and even numbers, and what is the resulting number when you add or multiply odd and/or even numbers
factors and multiples, and how to identify all the possible factor pairs e.g. if you lay out 12 playing cards on a table what are the different ways to arrange them to make a rectangular shape? 1 row of 12, 2 rows of 6, 3 rows of 4 etc
prime and composite numbers; prime numbers have only one factor pair, the prime number x 1 eg 13 playing cards can only be arranged as 1 row of 13 or 13 rows of 1, which is the same factor pair (1, 13)
square numbers, triangular numbers and rectangular numbers; some numbers can take the shape of a square (eg 4, 9, 16, 25 etc) and some can take the shape of a triangle (1, 3, 6, 10, 15, 21 etc)
While Operation Maths 5, for fifth class, is the first book to have a chapter devoted to this topic, the children will have explored elements of this topic in previous classes:
odd and even numbers were explored formally in Operation Maths 1, 2 and 3
the language of factors and multiples is used in Operation Maths 3, 4, 5 and 6 as part of the multiplication and division chapters.
The emphasis in Operation Maths is on the child being able to build, manipulate and represent numbers in ways and contexts that are relatable. This will help the child to be better able to visualise numbers, manipulate numbers and understand the connections between them.
Practical Suggestions for all Children
Draw your child’s attention to these number types wherever they or you encounter examples of them.
Use materials around your home to help make these concepts more real to your child(ren):
Use pairs of socks, shoes, gloves etc to model addition, subtraction, multiplication and division with odd and even numbers.
Lay out playing cards, coins, poker chips, plastic cups/plates, lego pieces, toy building blocks etc to represent certain numbers and to explore the shapes that can be made .
Examine square tiles and/or paving slabs that maybe around your home, how many of these squares together are needed to make a bigger square shape? Are there any patterns? Can you show/build/calculate the first 10 square or triangular numbers?
Mathigon Polypad: Use this excellent tool to explore and identify factors of any number, and therefore identify if the number is prime or composite. Can also be used to explore square numbers. Select Tiles > Numbers > Number Tiles and drag out tiles to represent a number. Watch here for a video guide (pupils in 5th and 6th class should start with numbers less than 20 first, and then explore bigger numbers when ready)
Maths Frame – Errors on a Venn Diagram: Identify the numbers which have been placed in the wrong position on the Venn diagram and drag them to their correct place. Choose one or two criteria: to arrange numbers by whether they are odd or even, or multiples of a given number, or prime or square numbers.
Multiples and Factors: multiple choice game, finding the Lowest Common Multiple (LCM) or the Highest Common Factor (HCF). Questions increase in difficulty depending on accuracy.
Maths Frame – Maths Invaders: Shoot the spaceship with the correct answer and dodge the incoming fire. Select play game and then scroll down to select Recognising Multiples, Factors, Prime, Square and Cube Numbers.
PhET – Factors: Choose the Factors option to identify the factors of given numbers
Sieve of Eratosthene: Use this interactive sieve to remove multiples, and therefore, identify all the prime numbers from 1-400
That Quiz: Use the factors quiz to practice identifying prime and composite numbers, prime factors, HCF and LCM. Use the exponents quiz to practice roots and exponents.
Number Theory and Exponents: two sections of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the games just below, or at, your class level.
Dear Family, given below is a brief guide to understanding the topic of decimals and percentages, 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 decimals and percentages. The digital resources are organised according to approximate class level:
Decimals, or decimal fractions, to give them their full title, are fractions of a whole amount, where the whole has been divided into ten parts (tenths), a hundred parts (hundredths), a thousand parts (thousandths) etc. They are typically written using a decimal point. This means that an amount that is the same value may be describes as a fraction, as a decimal fraction and as both, e.g.:
Percentages are very closely related to both fractions and decimals: per cent means out of 100, therefore an amount of percent is the same as that amount of hundredths, e.g.:
In Operation Maths, the children are first formally introduced to decimals (tenths only) in third class and then to hundredths in fourth class and thousandths in fifth class. The children are also introduced to percentages in fifths class. However, it is worth noting that the children would have informally explored decimals since being introduced to euro and cent in first class.
Since decimals are inherently linked with both fractions and the place value system, (also introduced in first class), the children’s understanding of decimals and percentages in the senior classes will build on this prior knowledge.
Practical Suggestions for Supporting Children
Draw your child’s attention to decimals and percentages around your home and in the wider environment, e.g:
Decimals on products 1.5 litre bottle of water, 2.5 kg bag of dog food, petrol or diesel sold per litre as cents to tenths (e.g. 125.9c/litre)
Percentage discount: 20% off, 10% off, 50% extra free etc.
The percentage left for a device to fully charge or for a program/movie to fully download.
The percentage power left in the battery
Recorded times (as decimal fractions of a second) for races, etc.
When you are talking about decimal numbers be careful to use the correct language e.g. for 23.05 say ‘twenty three point zero five’. (Remember: 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’).
Matholia – Decimals: A series of video lessons. Third class should focus on decimals to tenths, and fourth class on decimals to hundredths.
Khan Academy – Decimals: in this video and the videos that follow, explore decimal fractions and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics.
Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself.
Caterpillar Ordering: Choose ordering to order numbers with tenths (1 decimal place)
Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10, 1 decimal place or 2 decimal places or both.
Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).
Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either T O . t (1 decimal place, for third class) or T O . t h (2 decimal places, for fourth class) in either column.
Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. 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 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 decimals game.
I Know It! – Decimals: Scroll down to Decimals (Third Grade) to do any of the activities with tenths (third class) and/or hundredths (fourth class). There are some more advanced decimal activities in the fourth grade section, both in the section on Numbers & Place Value and in the section on Fractions & Decimals.
Splash Learn – Decimals: An assortment of decimal games organised according to US grade levels; third classes could do the games that include tenths only and fourth classes could look at all the Fourth Grade games.
That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals (choose decimal option on left hand side), Inequalities for comparing decimals and/or fractions and Reduce for converting decimals to an alternative form.
Decimals: 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)
Matholia – Decimals and Percentage: A series of video lessons. For decimals, fifth and sixth classes should focus on the lessons involving decimals to thousandths (3 decimal places).
Khan Academy – Ratios, Rates and Percentages: Scroll down to the sections on percentages to explore them in this series of lessons, and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics.
Happy Numbers – Decimal Fractions: A series of lessons and activities exploring decimals to thousandths and operations involving the same. Work through the activities in Modules 1, 2 and 4.
Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself.
Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).
Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. 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 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 decimals game.
I Know It! – Decimals & Percent: Scroll down to Fractions-Decimals-Percent (Fifth Grade) to do any of those activities. There are also more decimal activities spread throughout the Place Value, Addition, Subtraction, Multiplication and Division sections.
Decimal Games & Percentage Games: An assortment of games using numbers of various sizes. Fifth and Sixth class should do the games up to 3 decimal places.
That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals and/or percent (choose desired options on left hand side), Inequalities for comparing decimals, percentages and/or fractions and Reduce for converting decimals and percentages to an alternative form.
Decimals and Percents: 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, below is a brief guide to understanding the topic of directed numbers (fifth and sixth classes only), 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 directed numbers.
You can also find class specific tips in the Operation Maths Dear Family letters for fifth and sixth class.
Understanding Directed Numbers
Directed Numbers are numbers with both size and direction; one direction is positive, and the other is negative. For example, temperature is typically described in a number of degrees either above zero (positive values) or below zero (negative values). Positive and negative numbers are also referred to as integers.
In Operation Maths, the children are first introduced to directed numbers in fifth class, where the focus is on the children appreciating where directed numbers can be encountered in real life, for example:
Temperature
Bank statements/ money accounts: having money is shown as positive (+) and owing money or overdrafts are shown as negative (-)
Elevations above and below sea level
Floors below the ground floor in a large building are often labeled as -1, -2 etc
Golf scores are written as above and below par
Goal difference in soccer league tables
Depths in a swimming pool
In school, the children are encouraged to use the words positive and negative, rather than plus and minus; for example for the value -6 we should say negative six rather than minus six. This is particularly important for when the children start adding positive and negative numbers (in Operation Maths 6): for example (–3) + (+9) should be read as ‘negative three add/plus positive nine’ rather than ‘minus 3 plus plus 9’. It is also important that the children recognise that positive numbers can be written either with, or without, the positive sign, therefore we can assume that any number, without a sign, is positive.
Practical Suggestions for all Children
Draw your child’s attention to wherever they or you encounter directed numbers (see above for possible examples).
If your child is having difficulty visualising, comparing, ordering etc directed numbers, encourage them to think of a real example. One of the most-relatable of these is that of temperatures and the thermometer. Look at a real thermometer or use an online virtual example such as this one.
As explained above, encourage your child to use the words positive and negative, rather than plus and minus, when describing directed numbers.
Digital Resources for Fifth and Sixth Classes
Integers: Video lesson that introduces integers (positive and negative numbers) and where they occur in real life
Khan Academy Negative Numbers: A series of videos and practice questions exploring negative numbers. Afterwards, for more of a challenge, look at Integers and Whole Numbers. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Maths Frame – Empty Number Line: Practice placing positive and negative integers in the correct position; choose -5 to 5 initially and then move to the next levels to challenge yourself.
What is the Temperature? Identify the temperature shown on the thermometers. A way to practice directed numbers in a real-life context. Includes values above and below zero, and has options for various ranges.
Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers from -10 to 10 to order integers.
Number Lines in Disguise: A challenge and interactive game (scroll down) from NRICH; Can you work out the number marked by the dot? Includes positive and negative numbers.
That Quiz: Inequalities for comparing numbers, Arithmetic for addition calculations involving directed numbers and Number Line for identifying numbers by their position. In each of these activities there is the option to include negative numbers along with positive; just make sure the the “negative” option is selected on the left hand side.
Number Line App: This virtual tool can be used to explore the position of values on a number line,including positive and negative numbers; also to model addition and subtraction involving positive and negative numbers.
Directed Numbers Counters: These double sided counters can be used to model addition and subtraction involving positive and negative numbers (ensure that the “sign” option is ticked).
Integers (Directed Numbers): a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities.
Integers: Practice games from Math Games. Choose your class level.
Dear Family, below is a brief guide to understanding the topic of area, 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 area. 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 Area
Area is the size a surface takes up: the size of the space that the grass of your garden covers, the size of the space on the cover of an Operation Maths book, the size of space that your house covers on its site. As children often confuse area and perimeter encourage them to compare these concepts to real examples eg:
Garden: Area = the ground covered by lawn, decking and/or patio; perimeter = the length of fencing or walls.
Room: Area = the space covered by flooring (carpets, tiles etc.); perimeter = the length of the skirting boards or length of walls.
Playground or school yard: Area = the space covered by tarmac, grass etc; perimeter = the length of the fencing or walls.
Area is measured in square units. Like other measures, area has been traditionally measured using two separate systems: imperial units/US customary units (square foot, square yards, acres, square miles) and metric measures (square centimetres i.e. cm2 , square metres i.e. m2 , hectares and square kilometres i.e. km2). In Ireland, the changeover to all metric measures began in the early 1970s and was completed in 2005. Therefore, only metric measures are taught in Irish schools.
In school, the children are first introduced to area in second class, where, using non-standard measures, like books, copies, cards, envelopes (see above), they start to estimate and measure how many are required to cover various surfaces. They will be enabled to consider space on a surface and which has the greater area (covers more) or the lesser area (covers less) as shown below.
In third and fourth classes the children measure area by counting square units. In fifth and sixth classes the children estimate, measure and calculate area using the standard metric square units (square centimetres i.e. cm2 , square metres i.e. m2 , hectares and square kilometres i.e. km2) will also explore “short cuts” like using formulas for area ie Area of a Rectangle = Length x Width. However, it is hope that the children come to deduce this “short cut” for themselves, after lots of exploratory work, rather than just being given it.
Draw your child’s attention to area and perimeter in their lives at home and beyond, and make distinctions between the two maths terms:
Garden: Area = the ground covered by lawn, decking and/or patio; perimeter = the length of fencing or walls.
Room: Area = the space covered by flooring (carpets, tiles etc.); perimeter = the length of the skirting boards or length of walls.
Playground or school yard: Area = the space covered by tarmac, grass etc; perimeter = the length of the fencing or walls.
Encourage younger children to play with shapes like pattern blocks, tangrams etc. How many of one shape is required to cover another?
Encourage your child to identify their own personal benchmarks for these metric measures e.g. the top of a child’s little finger covers approximately 1 cm2 ; look around the house to find a window or mat of anything that is approximately 1 m2 . This will help the child relate to these units of area and to internalise them.
Involve your child in any area measuring activity that might be required around the home. Reseeding the lawn? How much grass seed is required for that area? Getting new carpet or flooring? Painting the walls? How do you calculate the area to make sure the correct amount is bought?
Khan Academy – Area (Third Grade): 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/grades.
Happy Numbers Third Grade: Pupils could start the activities in Module 4, Topic A, B and D. When completed they could move on to all the topics in Grade 4, Module 2, Topic A.
Area Builder: Choose GAME. You will be challenged to build a shape with an area of a specific number of square units. (You could also try the EXPLORE option allows you to build shapes of various areas).
Khan Academy – Area (Third Grade): Watch the videos and then answer the practice questions. Afterwards, for something more challenging, look at the Fourth Grade activities on Area and Perimeter. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Happy Numbers Third Grade: Pupils could start the activities in Module 4, Topic A, B and D. When completed they could move on to all the topics in Grade 4, Module 2, Topic A.
Area Builder: Choose GAME. You will be challenged to build a shape with an area of a specific number of square units. (You could also try the EXPLORE option allows you to build shapes of various areas).
That Quiz – Geometry: Options to calculate the area of rectangles, triangles, circles and trapezoids. You can also choose to calculate the length of the perimeter of the shapes.
Welcome to the March installment of Maths by Month.
Whether your children return to face-to-face teaching this month, or continue to engage in distance learning at home, 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: Operations (addition, without and with renaming, and subtraction without and with renaming, the latter of which is new content while the other material will be revision of first class work); Length (including the formal introduction of the centimetre as a standard unit of measure).
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).
Engineer’s Week runs from Saturday, 27 February – Friday, 5 March. There are obvious connections between Maths and Engineering, a fact which is being celebrated by the STEM (Science, Technology, Engineering and Maths) movement globally. Click on the link above to access lots of ideas to help you organise fun challenges that create a positive awareness and spark enthusiasm about the engineering profession in young people.
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; consult the Junior and Senior Infants TRB for the monthly Aistear suggestions.
For some more primary-focused STEM activities, check out the links below:
World Book Day is on the first Thursday of March, and while the primary resources accessible on the site are mainly literacy linked, there are lots of possibilities for numeracy and literacy linked activities for this global celebration including:
Book measurements: Find the longest, widest and thickest/deepest book from a collection of books. How can you prove you are correct? (Great way to link with length if you are doing it this month!)
Carry out a survey to find out the favourite books / authors of the children in your class.
Choose a page from a book. Work out the average number of words per sentence.
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
Happy Numbers Pre-Kindergarten – Above and Below:
Right or Left:
Turns on a compass:
Turn the man:
Caterpillar Ordering:
Khan Academy:
Odd & Even: A selection of games to identify the odd and even numbers: 
Function Builder:
Maths Frame – Errors on a Venn Diagram:
Cubes
Math Games: Practice games on 
White Rose Maths – Decimals: a series of lessons, including 
Khan Academy – Decimals:
Happy Numbers – Decimal Fractions:
I Know It! – Decimals:
White Rose Maths – Decimals & Percent: a series of lessons, including 
I Know It! – Decimals & Percent:
Integers
Maths Frame – Empty Number Line: 
Number Lines in Disguise:
Number Line App:
Happy Numbers Third Grade:
