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.
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 copncepts 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
Dear Family, below is a brief guide to understanding the topic of length, 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 length. 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 Length
Length is the distance between two points; the length of the pencil is the distance from one end to the other; the length of a person is the distance from their feet to the top of their head. Certain lengths will often be described using other words; lengths that are typically vertical will be described as height; if an something is 2-D or 3-D the side with the shorter(est) length will typically be described as the width or breadth or depth. There are many adjectives to describe length: long, tall, wide, broad, deep, short, narrow, shallow etc.
In school, the children are enabled to compare, estimate and measure length. In the infants classes, the children work with non-standard units (e.g. what is the length of the table in paper clips, markers or straws?) and then they are gradually introduced to the standard metric units of length i.e. metre (first class), centimetre (second class), kilometre (third class) and millimetre (fifth class). Children in the older classes will also be introduced to, and work with, more complex concepts related to length, such as perimeter and scale on maps etc.
Talk about length, width, distances etc with your children. Draw their attention to length in their lives at home and beyond:
Long items and short items; tall people and short people; narrow bridges and wide roads; deep end of the swimming pool and the shallow end.
Look at the labels on children’s clothes; do they notice how, in many shops, there is a number on the label (eg 128, 134, 140 etc) that indicates the height of the child in cm. What other clothing items mention cm?
If competing in, or spectating at, running races (eg Community Games, Athletics Ireland events) or swim meets, take note of how the distances are usually in m and km.
Look at road signs indicating distances in km; explore map apps and sat navs on devices (e.g. Google Maps) to identify the distance between your location and your destination.
If looking at maps, locate the scale reference to get a sense of how the distances represented on the map relate to the distances in reality.
Encourage your child to develop their own personal benchmarks for metric measures e.g. the width of a child’s little finger is approximately 1 cm; the width of a child’s outstretched arms (arm span) is often 1 m; the length of a child’s ‘giant’ step is often 1 m; the width/depth of a bank card or loyalty card is approximately 1 mm. This will help the child relate to these units of length and to internalise them.
At home, use a height chart to measure and record your child’s height. Or mark and measure heights on a piece of furniture, door jamb, etc. Return to this every six months or so, to allow your child to reflect on their own growth.
What objects do you have at home that can measure length? Measuring tapes, rulers etc., could be left somewhere, easily accessible, so that they can be used for play purposes. Allow the children to explore how they work and use them to measure the length/height of the items and people. Draw your child’s attention to the markings and their meaning, and to how many mm there are in a cm or a m, how many cm in a m etc.
Involve your child in any measuring activity that might be required around the home. Getting new furniture? How big is each piece? Will there be enough room for it? Getting new curtains or blinds? Measure together the width and drop that is required. Getting new carpet? What length of a roll is needed?
Enlist the help of older siblings if available. As they explain and support the younger members of the family, they will also be developing and consolidating their own knowledge and skills, especially communicating mathematically.
White Rose Length & Height: a series of lessons on comparing and measuring lengths and heights. These series of lessons could be followed up with other measurement lessons in year 1 and/or year 2
Khan Academy – Length (First Grade): Watch the videos and then answer the practice questions. Afterwards, for something more challenging, look at the Second Grade Activities. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Happy Numbers First Grade: Pupils could start the activities in Module 3, Topic B. When completed they could move on to all the topics in Grade 2, Module 2.
That Quiz – Measurement: Measure the length of the fish in cm. Select level 1 on the left hand side.
Measurement: a selection of games from ixl.com. Choose the games to do with long/tall and short, length and centimetres. You can do a number of free quizzes each day without having a subscription.
That Quiz – Measurement: Measure the length of the fish. Select level 1 on the left hand side, initially and then work up to level 2 and 3.
That Quiz – Geometry: Options to calculate the perimeter of rectangles, triangles, circles and trapezoids. You can also choose to calculate the area of the shapes.
I know it – Third Grade: Scroll down to Measurement (metric units of length) to select those activities. For perimeter activities scroll down to Geometry (perimeter). There are similar activities in Fourth Grade and Fifth Grade.
Measurement: a selection of games from ixl.com. Choose the games to do with length and metric units of length. You can do a number of free quizzes each day without having a subscription.
Welcome to the February installment of Maths by Month.
As we proceed with the current reality of distance learning, 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: Weight, Time (to quarter hours on an analogue clock and to half hours on a digital clock) and Estimation (how to estimate to total of addition calculations within 99). The development of keen estimation skills is very important throughout Operation Maths and work here will lay future foundations.
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).
Lá ‘Le Bríde, is Monday, February 1st. The story of St. Brigid’s Cloak could be used as springboard into a pattern activity, or a discussion on exponential growth with older students.
Ireland’s first game in the 2021 Six Nations (against Wales in the Principality Stadium) is on Sunday 7th February. Some mathematical possibilities:
With older children, use the opportunity to explore the rugby union scoring system, and to identify what scores (up to 30, for example) are possible (how?) or impossible.
Calculate the number of games to be played; what if the competition had less or more teams, how many games would need to be played then?
Use the language of chance to discuss the possible outcomes for each nation in the competition and recognise that while it is impossible to predict the actual outcomes, we can use of knowledge of the teams performances to make informed predictions.
Make score predictions for each match and plot how these scores would be recorded on the Six Nations Table
Storytelling Week runs from 30 January to 6 February. While this is primarily a UK based event, it does serve as a timely reminder of the rich role that mathematical stories can play in the early years. For teachers of infants to second class, be sure to check out the Literacy suggestions within the Integration section of each short term plan in the TRB.
Pancake (Shrove) Tuesday is Tuesday 16th February. Recipes naturally provide great opportunities for real world maths, for example identifying the measures and amounts required, adding the correct measures to the mix, adapting the recipes to suit more or less people, etc. For more maths-related activities check out these pancake problems.
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, below is a brief guide to understanding the topic of symmetry, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about symmetry. The digital resources are organised according to approximate class level:
You can also find class specific tips at the back of your child’s Operation Maths At Home book, for infants to second class, and in the Operation Maths Dear Family letters for third to sixth class.
Understanding Symmetry
Symmetry is introduced in second class and is a stand-alone maths topic in only second to fourth classes. That said, it also features as part of the topic of 2-D shapes in fifth and sixth classes where the children in those classes are asked to “classify 2-D shapes according to their lines of symmetry”.
While there are different types of symmetry (which children will explore deeper in second level maths), the primary curriculum specifies line symmetry, also known as mirror symmetry, reflective or reflection symmetry.
In school, the children will often have the chance to use special child-safe mirrors to explore this concept, and to look at the mirror image of arrangements of various items. It would be really valuable for the children to be able to do something similar at home, with any suitable small mirrors that might be available (Tip: mirrors with straight outside edges rather than curved edges are better for this, eg a small mirror from the lid of a make-up pallet). Draw your child attention to the way in which the pattern appears to be reversed e.g. in the image above the order of the real cubes is orange, yellow, green, but in the reflection we see green, yellow, orange.
Practical Suggestions for Supporting Children
Symmetry at home: explore the symmetry that is all around you:
Look for examples of symmetry in clothes, furniture, windows, dishes, ornaments, doors, etc.
If going for a walk, look out for examples of symmetry in nature eg flowers, leaves.
Is there symmetry in any of the numbers we write? What about letters of the alphabet; lower-case and/or upper case (capital letters)? What about the letters in your name?
Take some time to use mirrors to explore symmetry (as mentioned above, small square, or rectangular, cosmetic mirrors are ideal for this). Using the mirrors the children can create and check symmetrical patterns using cubes, counters, objects etc. They can look for symmetry in numbers and capital letters (eg the letters on the cover of their Operation Maths book, other books, newspapers, boxes, food containers etc). Can your child answer the following questions?
What letters or numbers look the same in the mirror? What shapes or images look the same in the mirror?
Can you put the mirror along the middle of any letters and numbers so that they look complete? Does this work with any other shapes or images?
For some shapes/numbers/letters, is there more than one than one way, that the mirror can be placed?
Using the mirrors the children can create and check symmetrical patterns using pieces of lego, blocks or other suitable objects etc.
Place a mirror to the right or left of the arrangement. Describe what can be seen in the reflection.
Change the position of the mirror, perhaps above or below the arrangement. Does the reflection in the mirror look the same? Is it different? How? Why?
Repeat using different items and/or arrangements. Ask your child to predict what the mirror image will look like before they actually look into the mirror.
If your child has his/her Operation Maths twenty frame at home (free with Operation Maths 1 and 2) it can be used to create a symmetry challenge (see below). One person uses counters, lego pieces, buttons etc, to make an arrangement and the other person makes its mirror image. You could also do something similar with a chessboard/draughtboard and the playing pieces.
In second class, the children are being introduced to simple symmetry. If your child knows very little about symmetry already, a good starting point is to watch some of the videos below.
Pattern Blocks: Use these interactive pattern blocks to make numerous designs, pictures etc on one side of the screen. And then challenge yourself, or another, to complete the symmetrical image on the other side.
Symmetry: A selection of simple games from ixl.com. You can do a number of free quizzes each day without having a subscription.
Math Games: a simple symmetry game ideal for beginners.
Digital Resources for Third and Fourth Classes
NB: Children in these classes may also enjoy the links for second class above
Khan Academy – Symmetry: 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.
Symmetry Shapes: You will be shown a shape and you must create the reflection or mirror image of the shape as reflected in the line of symmetry. Click on the grid squares to colour them in, and then click check to see if you are correct.
Symmetry Counters: Similar to the game above, an arrangement of counters will be shown and you move the other counters to create the reflection or mirror image of the arrangement, as reflected in the line of symmetry.
Symmetry Invaders: Can you complete the symmetrical images to win this space invaders-type game?
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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
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:
Comparing Lengths
Comparing Lengths:
Let’s Compare:
Comparing Lengths
White Rose Length & Height:
Khan Academy – Length
Happy Numbers First Grade:
Splash Learn – Measurement Games: 
Splash Learn – Measurement Games: 
Intro to Symmetry:
Symmetry Painter:
Khan Academy – Symmetry:
Vertical and Horizontal Lines of Symmetry:
Symmetry Shapes:
Symmetry Invaders:
I know it – Symmetry: 
Math Games: