Dear Family, your Operation Maths guide to Length

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:

• Junior & Senior Infants
• First and Second classes
• Third to Sixth classes

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.

Like weight and capacity, length has been traditionally measured using two separate systems: imperial units/US customary units (inches, feet, miles etc) and metric measures (metres, centimetres, millimetres, kilometres etc). 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 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.

Do you know how the metric system came into being? It has an interesting history! Watch this video and/or read this article. For more background info on length you can read these posts from Maths is Fun and SplashLearn.

Practical Suggestions for all Children

• 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.
• Draw the children’s attention to any other situation where length needs to be considered: height requirements for fairground or theme park rides; height requirements for children’s car seats, maximum size of baggage allowed with airlines, etc.

Digital Resources for Infants

Comparing Lengths: A video lesson from Matholia

Comparing Lengths: A story lesson from Matholia

Measuring Length (non standard units): A video lesson from Matholia

Long and Short with Kermit & Grover: The Sesame Street favourites explore long and short.

Number Jacks: Going Wrong, Going Long. Another episode for length is Measured Response

Happy Numbers Kindergarten: Work through the activities from Module 3, Topic A and B.

Let’s Compare: A comparing sizes game, including picking out the biggest, smallest, shortest etc

I know it – Longer/Taller or Shorter: Interactive quiz for Kindergarten. Also available: Measure length in non-standard units. 

Long, tall, short, wide, narrow: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription.

Digital Resources for First and Second Classes

Measuring Length (non standard units): A video lesson from Matholia

Units of Length – Metre: A video lesson from Matholia. Follow this with Measuring Length in Metres

Units of Length – Centimetre:  A video lesson from Matholia. Follow this with Measuring Length in Centimetres

Comparing Lengths: A video lesson from Matholia

Bar Models: A video lesson from Matholia, showing how to use bar models to solve length addition problems. Follow this with how to solve length subtraction problems.

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.

Splash Learn – Measurement Games: (First Grade) Estimate and measure length. Second class class could try the Second Grade games, choosing metric units. 

I know it – Length: Interactive quizzes on longer/taller and shorter, measuring length, estimating length in centimetres and measuring length in centimetres.

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.

Digital Resources for Third to Sixth Classes

Converting metres and centimetres: A video lesson from Matholia. Follow this with converting metres to centimetres

Converting metres and kilometres: A video lesson from Matholia.

Bar Models: A video lesson from Matholia, showing how to use bar models to solve length multiplication problems. Follow this with how to solve length division problems.

White Rose Length & Perimeter: a series of lessons, that could be followed up with other measurement lessons in year 3, year 4, year 5, and/or year 6.

Khan Academy – Perimeter (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, the Metric System and/or Converting Metric Units. Or even the Fifth Grade activities on Converting Metric Length Units. You can also register for a free Khan Academy account to record your progress and explore other topics/grades. 

Finding the Area & Perimeter of a Rectangle: A video lesson from Mashup Math.

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.

Splash Learn – Measurement Games: These games cover how to measure length, measure the perimeter of regular shapes, the perimeter of non-regular shapes,  calculate a side length when given perimeter, calculate the perimeter of simple shapes, perimeter of complex shapes, converting metric units, including metric units with decimals.

Coconut Ordering Game: Select Length to order amounts of cm and m.

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. 

Comparing and converting metric units: Practice games incorporating metric units of weight, capacity and length.

Maths by Month – February (updated 2021)

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:

• Junior Infants: Analysis of Number Comparing and Ordering and Combining and Partitioning amounts up to five.
• Senior Infants: Analysis of Number (Numeration) looking at the number nine; Comparing and Ordering and Combining and Partitioning amounts to up to nine.
• First Class: Representing and Interpreting Data, Place Value within 99, Counting and Numeration to 100 and exploring Pattern in repeated addition, and addition facts on the 100 square. The Operation Maths 100 square eManipulative will be invaluable for these latter activities.
• 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.
• Third class: Decimals, 3D Objects and Addition & Subtraction
• Fourth class: Length and Addition & Subtraction
• Fifth class: Fractions, Decimals & Percentages and Length
• Sixth class: Data and Length

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). 

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources. Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for February:

• 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.
  • Calculate the dimensions of the pitch
  • Run a Fantasy Rugby League in your class
  • 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.
• Valentine’s Day is Sunday 14th February. Try out these themed problems  and challenges (suitable from first class up) from Mashup Math and, from the Routty Math Teacher, this selection of five Valentine’s Day-inspired starters, that are sure to engage your students and get them thinking critically about maths.
• 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, your Operation Maths guide to Symmetry

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:

• Second classes
• Third and Fourth classes

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.

• Art and Maths are often very connected, and this is especially the case with symmetry. Why not try making a symmetrical butterfly, symmetry painting and/or your name as symmetrical art? For more art ideas search Google for symmetry art for kids. Older children could also explore mirror writing and how Leonardo da Vinci used it.

Digital Resources for Second Classes

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.

Symmetry: A series of video lessons from White Rose Maths, including for Year 2,  Lines of Symmetry, Draw the Whole.

Intro to Symmetry: A YouTube video that introduces  and explores reflectional (mirror) symmetry.  

Symmetry Land: Learn about lines of symmetry through this song from Numberock

Symmetry Painter: This simple activity allows you to paint on one side and watch as the symmetrical image magically appears on the other side!

Symmetry Matching: 3 different games where you choose the matching symmetrical half.

Symmetry Sorting: 3 different games where you decide if the image shown is symmetrical or not symmetrical.

I know it – Symmetry: Interactive quiz for Grade 1. After, you could try the Grade 2 quiz

Pattern Blocks: Use these interactive pattern blocks to make numerous designs, pictures etc on one side of the screen. And then challenge yourself, or another, to complete the symmetrical image on the other side. 

Symmetry: A selection of simple games from ixl.com. You can do a number of free quizzes each day without having a subscription. 

Math Games: a simple symmetry game ideal for beginners.

Digital Resources for Third and Fourth Classes

NB: Children in these classes may also enjoy the links for second class above

Symmetry: A series of video lessons from White Rose Maths, including for Year 4 Lines of Symmetry and Complete a Symmetric Figure.

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.

Vertical and Horizontal Lines of Symmetry: learn about different types of lines of symmetry from Mashup Math

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?

I know it – Symmetry: Interactive quiz for Grade 3. After, you could try the Grade 4 or Grade 5 quiz

IXL: A selection of symmetry games from ixl.com. You can do a number of free quizzes each day without having a subscription.

Maths is Fun: Background information on reflection (mirror) symmetry

Math Games: a whole suit of symmetry games, for a range of class levels; start with second class and work your way up.

Line Symmetry Quiz: Identify the number of lines of symmetry in each shape by dragging the answers into the correct places.

Maths by Month – January (updated 2021)

Wishing you all a healthy and happy New Year and here’s hoping that there are better times ahead for us all.

But, for the meantime, we are all back in the reality of providing distance learning for our classes. As we journey forward together, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, including:

• Dear Family, our ever-expanding series of posts, aimed at parents and families, supporting children’s mathematical development at home
• Digging Deeper, our series of posts, aimed at teachers, providing deeper insights into the underlying theory, approaches and pedagogies behind the various maths topics
• About Operation Maths posts, for teachers who want to find out more about the Operation Maths program itself.

HINT: To ensure you don’t miss out on any future blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Operation Maths for Junior Infants to Sixth Class:

• Junior Infants: Analysis of Number (Numeration) looking at the number five, Comparing and Ordering and Combining and Partitioning amounts up to five.
• Senior Infants: Analysis of Number (Numeration) looking at the number eight; Comparing and Ordering and Combining and Partitioning amounts to up to eight; Weight
• First Class: Counting and Numeration (within 99), Place Value within 60, Operations (including developing mental strategies for addition and subtraction within 20) and Comparing and Ordering (comparing sets and identifying the inequality)
• Second Class: Money, Symmetry, Operations (addition and subtraction without renaming, including subtraction as deduction) and Fractions.

HINT: Teachers of Infants to Second Class – if not yet done, don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of December Assessments

• Third class: Fractions and Length
• Fourth class: Multiplication & Division and Decimals
• Fifth class: More Division and Data
• Sixth class: Multiplication & Division and Fractions, Decimals & Percentages

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). 

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources. Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for January:

• Backward Day! The 31st of January marks this little-known celebration which encourages us to reverse or invert the typical societal rules. Without encouraging anarchy, there are obvious opportunities here to explore symmetry, mirror writing etc.
  • Challenge your class to write out the capital letters of the alphabet backwards; not only starting with z but writing each letter as flipped image of itself.
  • Ask them to consider in advance which letters might appear the same when flipped backwards and what letters will appear different.
  • The children’s letters can be checked using small plastic mirrors to see if the image in the mirror is correct.
  • The children can also be asked to do the same thing with the digits 0-9 or even bigger numbers.
• Most parts have had some snow already, and there could be more! The Routty Math Teacher has a whole library of Solve it Friday puzzles many of which align themselves with feasts and seasons. Sign up here to get access to the library and then check out weeks 16-19 for snow-themed puzzles.

We’re here to help! If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter 

Maths by Month – December (updated 2020)

Welcome to the December installment of this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.

As we journey together through on this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.

Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.

HINT: To ensure you don’t miss out on any future blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Operation Maths for Junior Infants to Sixth Class:

• Junior Infants: Analysis of Number (Numeration) looking at the number four
• Senior Infants: 3D Objects, Spatial Relations and Time (the days of the week).
• First Class: Money, Place Value within 20, Patterns and Capacity.
• Second Class: Time (the calendar) Place Value within 99 and Representing and Interpreting Data

HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of December Assessments

• Third Class: Multiplication and Division, Time and Money
• Fourth Class: Fractions and Patterns & Sequences
• Fifth Class: Fractions and 3D Objects
• Sixth Class: Fractions  and 3D Objects

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). 

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources. Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for December:

• This year, Computer Science Education Week runs from 7-13 December, during which time, they are also encouraging everybody, young and old, to engage with their annual Hour of Code event.  Coding is the future! Computers are changing every industry on the planet. Every 21st-century student should have the opportunity to build technology. Click on the links above to access Hour of Code and other computer science activities for learners of all ages. Operation Maths users can also access the tailor-made Operation Maths Scratch lessons on https://edcolearning.ie 
• Check out the NRICH Primary Advent Calendar. They have lots of other Christmas-themed activities that can be accessed here: https://nrich.maths.org/public/search.php?search=christmas. They also have an Advent-themed sudoku challenge that some of the more-able senior class pupils might like to tackle.
• Mash-up Maths have a Christmas-themed 12 Days of Holiday Math Challenges, suitable for 1st class up. It can be better to hide all the puzzle initially, and then, reveal just one line at a time and ask the children to record and justify all the possible solutions based on what they know at that point. As they move through each line, they can then explain why they should now discard certain options. This is a better way to engage all of the children in thinking mathematically, rather than it just becoming a race to the solution (which can often turn-off those less mathematically-inclined). For more of this type of problem sign up to the Mash-up Maths weekly newsletter, to receive lots of other themed maths puzzles and challenges like this Grinch-themed challenge.
• Interested in more Christmas-themed maths problems? From Dec 1-24 the German Maths Society posts a daily problem (in English) on its online Advent Calendar. There are 3 levels of difficulty, 4th class to adults.

We’re here to help! If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter 

Dear Family, your Operation Maths guide to Fractions

Dear Family, given below is a brief guide to understanding the topic of fractions, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about fractions. The digital resources are organised according to approximate class level:

• First and second classes
• Third and fourth classes
• Fifth and sixth classes

Understanding fractions

Fraction comes from a Latin word meaning “to break (something) in pieces”; it’s related to the word fracture, meaning to break into pieces, usually used to describe a broken bone. In maths, fractions are the result of dividing something (a shape, object or amount), into a number of equal pieces or parts.

Equal is very important; if we divide something into two parts, but they are not equal, then they are not halves. Therefore it is very important to emphasise to children from the very beginning that the parts made must be equal; in school we often talk about it being a fair share.

And while fractions might seem straight-forward enough, i.e. dividing something into equal parts, even the basic fractions can be interpreted in many ways:

3/4 (say “three quarters”) can be describing 3 parts of something that is is divided into 4 equal parts, eg 3/4 of the square is red (above) or 3/4 of the blocks are red (below).

3/4 can also be interpreted as three out of four i.e. that 3 out of 4 cubes are red or that 3 out of every group of 4 cubes are red (below).

3/4 can also be interpreted as three divided by four or 3 ÷ 4 which gives a value of 0.75, the decimal equivalent for 3/4 (below).

Initially much of children’s exploration of fractions in school, will focus on creating and identifying various fractions (starting with familiar fractions such halves, quarters, eighths, tenths etc).

They will also learn to recognise fraction forms that are the same value (i.e. equivalent fractions eg 1/2, 2/4, 4/8, 5/10 etc), and comparing and ordering fractions. In the senior classes, children will work with less familiar, more complex fractions as well as calculating with, adding, subtracting, multiplying and dividing fractions.

Practical Suggestions for Supporting Children

• Use fractions and the language of fractions at home, e.g. when dividing up food (cutting up pizzas, cake, bars of chocolate), when baking (e.g. half a teaspoon, a quarter of a cup, half a dozen eggs).
• Look for fractions when out shopping, e.g. half price. Ask your child to calculate the current price, or what the price was before the reduction.
• Be careful about using fractional language accurately, e.g. there’s no such thing as a big half or a small half! To make fractions, we must create equal parts. Encourage your child to be accurate and to recognise that if something is divided into two parts that are not equal, they are not halves.
• Fractions names can be confusing for children: it makes sense that each part of something divided into ten equal parts is a tenth… similarly for fifth, sixth, eighth, ninth etc. But each part of something divided into two equal parts is a half (plural is halves) and each part of something divided into four equal parts is a quarter. Furthermore, when speaking one eighth (1/8) it can be difficult to distinguish from eight (8). Try to say and explain fraction names clearly, and encourage your child to say them clearly also, so that they appreciate the difference between these similar-sounding words.
• If your child is experiencing difficulties with converting fractions, adding, subtracting or multiplying fractions, encourage him/her to use concrete materials (eg paper plates, paper straws and or pieces of paper) and/or draw pictorial representations, e.g. pie pieces or number lines, to help them visualise what is happening and develop his/her “fraction sense”.

Want to find out more about fractions? Check out this article How can I Teach my Child about Fractions?

Digital Resources for First and Second Classes

Khan Academy Fractions: Watch the videos and then answer the practice questions on halves and fourths (another name for quarters). Afterwards, try the activities in Second Grade. You can also register for a free Khan Academy account to record your progress and explore other areas of First Grade Maths. 

Hit the Button: Use the Halves game to practice calculating half of a number

Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Digital Resources for Third and Fourth Classes

Happy Numbers Third Grade: Third and fourth class pupils could work through the activities in Module 5. 

White Rose Fractions: a series of lessons on Fractions for year 3 and year 4.

Khan Academy Fractions (Third Grade): Watch the videos and then answer the practice questions. Afterwards, try Equivalent Fractions, and for more challenging,  look at the Fourth Grade Activities. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

Fractions Intro: An interactive fractions simulation which explores fractions, equivalent fractions and improper fractions. The accompanying fractions game has various levels of difficulty. Other related fractions simulations at this site include Build a Fraction, Fraction Matcher, Equivalent Fractions and Mixed Numbers.

That Quiz – Fractions: Use this quiz to practice Identifying Fractions and Comparing Fractions. You can choose different options from the menu on the left-hand side.

I Know it! – Fractions (Third Grade): Scroll down to the Fractions & Decimals section to do any of the activities. You could also try the Fractions sections in Fourth Grade.

Hit the Button: Use the Halves game to practice calculating half of a number

Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the fractions game.

Splash Learn – Fraction Games: An assortment of games organised according to US grade levels; start with the games for third grade level. If too simple, go to the Grade Four games.

Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Digital Resources for Fifth and Sixth Classes

Happy Numbers Fourth Grade: Pupils should start with the activities in Module 3. And then progress to Fifth Grade to do the activities in Module 3 and 4

White Rose Fractions: a series of lessons on fractions. These lessons could be followed up with other fraction lessons in year 5 and/or year 6.

Khan Academy Fractions: Learn how to Add and Subtract Fractions and Multiply Fractions. Afterwards, for more of a challenge,  look at more on Add & Subtract Fractions, Multiply Fractions and Divide Fractions. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

Fractions Intro: An interactive fractions simulation which explores fractions, equivalent fractions and improper fractions. The accompanying fractions game has various levels of difficulty. Other related fractions simulations at this site include Build a Fraction, Fraction Matcher, Equivalent Fractions and Mixed Numbers.

Thinking Blocks for Fractions: an ideal way to start using bar models, or further practice using bar models, to model fraction word problems and computation. Sixth class pupils could also try out the thinking blocks activities on ratio.

That Quiz – Fractions: Use this quiz to practice Identifying Fractions,  Comparing Fractions and Operations with Fractions. You can choose different options from the menu on the left-hand side.

I Know it! – Fractions (Fourth Grade): Scroll down to the Fractions & Decimals section to do any of the activities. You could also try the Fractions sections in Fifth Grade.

Hit the Button: Use the Halves game to practice calculating half of a number

Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the fractions game.

Splash Learn – Fractions: An assortment of place value games organised according to US grade levels; start with the grade below your current class level i.e. for fifth class pupil’s start with fourth grade games and for sixth class pupils start with fifth grade games.

Fractions practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Maths by Month – November (updated 2020)

Welcome to the third installment in this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.

As we journey together through on this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.

Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.

HINT: To ensure you don’t miss out on any future blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Operation Maths for Junior Infants to Sixth Class:

• Junior Infants: Analysis of Number (Numeration) looking at numbers one to three
• Senior Infants: Counting, Analysis of Number (Numeration, Combining, Partitioning) looking at numbers six and seven, Algebra (extending patterns), 2D Shapes and Data
• First Class: Counting and Numeration (numbers to 50), Operations and Time
• Second Class: Extending and Using Pattern, Time and Operations 

HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of October Assessments

• Third Class: Multiplication and Division, Time and Money
• Fourth Class: Multiplication and Division, 3D objects and Time
• Fifth Class: Multiplication and Division,  The Circle and Money
• Sixth Class: Number Theory, Multiplication and Division and The Circle

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). 

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources. Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for November:

• The Bebras^® Computing Challenge 2020 runs from 2nd to 13th November; it introduces computational thinking (i.e. the thinking skills behind coding and programming tasks) to students, by allowing them to solve interactive tasks online. The tasks can be answered without prior knowledge about computational thinking or information and communication technology. The aim of Bebras is to get students all over the world excited about computing. The challenges are divided into five different age categories from 8-18 years old. On the link above, both teacher and student can explore previous challenges and, even  if your class or school doesn’t register to take-part (which is free), the past challenges are very engaging and worthwhile to explore as a whole class or groups.
• The 11 November marks the anniversary of the ending of the Great War, “the war to end all wars”, which is now typically referred to as World War 1. For 5th and 6th class teachers, who are planning to explore this topic in history, check out these Maths Activities from the Trench Brothers Education Zone.
• Codes and code breaking were a very important part of warfare tactics during both World War 1 and 2. To find out more about the maths of code breaking click on the link.
• Science Week 2020 runs from 8th-15th November. There are obvious links between Maths and Science, a fact which is being celebrated by the STEM (Science, Technology, Engineering and Maths) movement globally. Of the STEM areas, coding is one of the most exciting, not least of all to kids! And Operation Maths is the only Irish maths programme that has integrated coding activities via the Scratch Lessons for Operation Maths 3-6. Check out the scratch lessons that are included in the Operation Maths digital resources via your TRB or edcolearning.ie For infants, the Aistear Themes are an ideal way to explore STEM using a thematic focus (and lay the foundations for the development of computational thinking skills); consult the Junior and Senior Infants TRB for the monthly Aistear suggestions.

For some more primary-focused STEM activities, check out the links below:

• https://thestemlaboratory.com/kindergarten-stem-activities/
• https://www.playdoughtoplato.com/stem-activities-for-kids/
• https://www.stem.org.uk/resources/elibrary/resource/31235/primary-school-activity-booklet
• https://www.steampoweredfamily.com/education/free-stem-activities-for-the-classroom/
• https://www.yearofengineering.gov.uk/school

We’re here to help! If you have any questions on Operation Maths, Number Facts or anything related to primary maths over the course of the school year, please PM or contact Edco Primary Maths via Facebook and/or Twitter 

Dear Family, your Operation Maths guide to Multiplication and Division

Dear Family, given below is a brief guide to understanding the topic of multiplication and division, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about place value. The digital resources are organised according to approximate class level:

• Third and fourth classes
• Fifth and sixth classes

Understanding Multiplication and Division

Like addition and subtraction, multiplication and division is not just about multiplying and dividing to get a correct answer (although accuracy is always to be valued in maths); the focus is very much on understanding and visualising what is happening to the amounts/numbers, how they are changing, why they are changing and how the same calculation can be done in many different ways. This is often referred to as developing a child’s number sense.

In Operation Maths, the children are always encouraged to use materials and pictures, and to explore different strategies (ways) to get their answers. They are also encouraged to compare their strategies with the strategies of others, and to explain or justify why one way might be more efficient (faster and/or simpler) than another way.

In particular, the children are encouraged to refer to some key, benchmark facts, that, in turn, can be used to work out other facts. These include doubling and halving (which can be used to multiply and divide by 2, 4 and 8) and multiplying and dividing by 10, which in turn can be used to multiply by 5 (half 10 times the number) and multiplying by 9 (one group/set less than 10 times).

These benchmark facts (or friendly facts), combined with other strategies, ensures that the child develops both understanding of, and fluency with, the basic multiplication and division facts, which in turn cam be applied to more complex situations later, such as bigger numbers or fractions and decimals. Pictured below are examples of some useful thinking strategies for the basic multiplication and division facts.

While multiplication and division are separate operations, they are also very closely related, being the inverse (or opposite) of each other e.g. 3 x 10 = 30, 30 ÷ 10 = 3, 30 ÷ 3 = 10. This is another strategy that the children can use i.e. think multiplication to do division, or vice versa. Beginning in third and fourth classes, the children will explore multiplication and division as being the inverse of each other, which will progress towards using the inverse (opposite) operation to check their calculations. 

Therefore, nowadays, there is less emphasis on just learning off “tables”, (i.e. memorising answers) and more emphasis on thinking strategies to use what they know, to solve what they do not know. 

Practical Suggestions for Supporting Children

• Invite your child to help out with any opportunity to do multiplication and/or division at home, or when out and about, e.g. how much for 5 packets of the same sweets? If buying a multipack of anything, how much roughly for each item? etc.
• Encourage your child to use strategies when multiplying and dividing and/or to explain their strategies. Ask your child to explain how they know, or worked out the answer.
• “I don’t believe you…prove it!” When your child arrives at an answer, ask him/her to show you how they got an answer, to prove that that is the answer, and encourage them to think of other ways to arrive at the same answer. Are there ways that might be more efficient (better) than others?
• Encourage your child to estimate. Estimation is a very important skill; this involves quickly getting a rough or ‘ballpark’ idea of the answer, e.g. 3 boxes of sweets at €4.79 each is just under €15 because €4.79 is almost €5. Encourage your child to quickly estimate answers e.g. How much, roughly, is that going to cost? Do we have enough money?

Digital Resources for Third and Fourth Classes

Happy Numbers Second Grade: Third class pupils could start, and work through Module 6, Foundations of Multiplication and Division, and then progress to Third Grade, Modules 1 and 3. Fourth class pupils could start with Third Grade or go straight to Fourth Grade and work through the activities in Module 2. 

White Rose Multiplication and Division: a series of lessons on multiplication and division. These lessons could be followed up with other multiplication and division lessons in year 3 and year 4.

Khan Academy Third Grade: Third class pupils should start with Intro to Multiplication and then progress through 1-digit Multiplication, Intro to Division and  More with Multiplication and Division.  Watch the videos and then answer the practice questions. Fourth class pupils could work through the Multiplication and Division activities in Fourth Grade. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

The Array: An introduction to rectangular arrays (rows and columns) and how they can be used to understand multiplication.

Arithmetic Arrays: Solve multiplication and division questions using the help of rectangular arrays. Three levels in each game.

Bunny Times: A game that gradually teaches and tests multiplication in a visual and conceptual way.

Partial Product Finder: This is not a game, but it is a tool, that can be used to show an array for multiplication calculations involving 1 or 2 digits

Thinking Blocks for Multiplication and Division: an ideal way to start using bar models, or further practice using bar models, to model word problems and computation.

Hit the Button: a great site for practicing quick-fire Times Tables and Division Facts. For a slower-paced version of this try the Mental Maths Train, a multiple choice game.

That Quiz – Arithmetic: Use this quiz to practice different types of multiplication and division calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.

Multiplication.com: A site dedicated to multiplication games, but also includes division games and games for addition and subtraction.

Estimating answers to multiplication and division calculations to win chances to take penalties in a shoot out.

I Know it! – Multiplication and Division (Grade three): Scroll down to the multiplication and/or division sections to do any of the activities. If too simple, go to the multiplication and/or division sections in Grade Four 

Splash Learn – Multiplication & Division Games: An assortment of games organised according to US grade levels; start with the games for third grade level. If too simple, go to the Grade Four games.

Multiplication practice games and Division practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Digital Resources for Fifth and Sixth Classes

Happy Numbers Fourth Grade: Pupils could start, and work through Module 2, and then progress to Fifth Grade, Module 1 and 2, which includes multiplication and division with decimal numbers

White Rose Multiplication and Division: a series of lessons on multiplication and division. These lessons could be followed up with other multiplication and division lessons in year 5 and/or year 6.

Khan Academy Fourth Grade: Fifth class pupils could try any of the quizzes on multiplication or division to check what they know already, and either re-do some of the units or move on to Fifth Grade. Similarly, sixth class pupils could try the quizzes in Fifth Grade and then re-do or move on to other/new topics as appropriate. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

Arithmetic Arrays: Solve multiplication and division questions using the help of rectangular arrays. Three levels in each game.

Partial Product Finder: This is not a game, but it is a tool, that can be used to show an array for multiplication calculations involving 1 or 2 digits

Thinking Blocks for Multiplication and Division: an ideal way to start using bar models, or further practice using bar models, to model word problems and computation.

Hit the Button: a great site for practicing quick-fire Times Tables and Division Facts. 

That Quiz – Arithmetic: Use this quiz to practice different types of multiplication and division calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.

Multiplication.com: A site dedicated to multiplication games, but also includes division games and games for addition and subtraction.

Estimating answers to multiplication and division calculations to win chances to take penalties in a shoot out.

I Know it! – Multiplication and Division (Fifth Grade): Scroll down to the multiplication and/or division sections to do any of the activities. If these are too difficult, go to the multiplication and/or division sections in Grade Four 

Splash Learn – Multiplication & Division Games: (Fifth Grade) An assortment of games organised according to US grade levels. If these are too difficult, go to the Grade Four games.

Multiplication practice games and Division practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Maths by Month – October (updated 2020)

Welcome to the second installment in this year’s Maths by Month posts, designed to explore the Operation Maths topics on a month-by-month basis.

As we journey together through this school year, with all the uncertainties and possibilities that it may bring, rest assured that Edco Primary Maths and the Operation Maths blog will continue to support teachers, schools and families, along the way.

Central to this will be our Digging Deeper series of posts aimed at teachers and the ever-expanding series of Dear Family posts, aimed at parents and families, supporting children’s mathematical development at home. In addition, for teachers who want to find out more about the Operation Maths program, check out the About Operation Maths posts.

HINT: To ensure you don’t miss out on any future blog-posts, please subscribe to the Operation Maths blog via email, on the top right hand of this page.
Another way to keep up to date an all new maths-related developments is to like/follow the Edco Primary Maths page on Facebook and/or Twitter 

Operation Maths for Junior Infants to Sixth Class:

• Junior Infants: Early Mathematical Activities (comparing and ordering), Algebra (extending patterns), Analysis of Number (Numeration looking at number one)
• Senior Infants: Data, Algebra (extending patterns), Time, Counting, Analysis of Number (Numeration, Combining, Partitioning)
• First Class: Counting and Numeration, Operations, Extending and Using Pattern
• Second Class: Comparing and Ordering, Operations, Counting and Numeration

HINT: Teachers of Infants to Second Class – don’t forget to use the Operation Maths Assessment Records on excel for recording and collating the End of October Assessments

• Third Class: Addition and Subtraction and 2-D Shapes
• Fourth Class: Addition and Subtraction and 2-D Shapes
• Fifth Class: Addition and Subtraction and Time
• Sixth Class: Addition and Subtraction and Time

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). 

HINT: If you are new to Operation Maths this year or have changed class level, be sure to check out the Quick Start Guide to the Operation Maths books and the companion Quick Start Guide to the Operation Maths Digital Resources. Don’t forget that Operation Maths also has you covered for planning whether you’re teaching a single class or multi-class. 

Other suggestions for October:

• The October plan for third to sixth classes has deliberately allowed for a free week, to enable teachers to engage with Maths Week, held every year at this time. This year, Maths Week will run from 10-18 October, and while it will be a very different celebration this year, with no public gatherings, it will still be possible to participate virtually. So why not start to consider now, how your school might get involved in this national celebration of maths, and don’t forget to register your school at the link above. You can also follow the links in the site to find out more about Maths Art (which, coincidentally, links very well with October Operation Maths for 3rd and 4th classes i.e. tessellations in 2D shapes), Maths and history and code breaking. Check out their resource packs by class level also.
• You could also make Maths Week become a game-themed week in your class. Teachers of third to sixth classes could use the Games Bank in the Operation Maths TRB. Teachers of infants to second classes can use any of the games listed in the short-term plans in their TRBs.
• Another option for Maths Week, if you didn’t already do it in September, is Jo Boaler’s Week of Inspirational Maths. Click on the link for an overview of the activities in Week of Inspirational Math, and scroll down to the bottom of the page to access all the resources; Kindergarten roughly aligns with Infants, Grade 1 and 2 with 1st & 2nd classes, and Grades 3-5 roughly align with 3rd-6th classes.
• Other STEM projects to consider during October:
  • Space Week 4-10 October
  • Codeweek.eu 10-25 October

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, your Operation Maths guide to Addition and Subtraction

Dear Family, given below is a brief guide to understanding the topic of addition and subtraction, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about addition and subtraction. The digital resources are organised according to approximate class level:

• Infant classes
• First and second classes
• Third to sixth classes

Understanding Addition and Subtraction

Of all the topics in primary maths, this is probably THE one with which the grown-ups feel most familiar…sure isn’t all just about either adding or subtracting (take away), plus (+) or minus (-), total or difference?

In some ways, it is, and in other ways, it’s not.

As the song goes, ‘it’s not what you do, it’s the way that you do it’ and the same is true for addition and subtraction at primary level; it’s not so much about getting a correct answer (although accuracy is always to be valued in maths) as understanding and visualising what is happening to the amounts/numbers, how they are changing, why they are changing and how the same calculation can be done in many different ways. This is often referred to as developing a child’s number sense.

In Operation Maths, the children are always encouraged to use materials and pictures, and to explore different strategies (ways) to get their answers. They are also encouraged to compare their strategies with the strategies of others, and to explain or justify why one way might be more efficient (faster and/or simpler) than another way.

In particular, the children are encouraged to refer to some key, benchmark facts, that, in turn, can be used to work out other facts. These include doubles (e.g. 4 + 4, 9 + 9 etc), near doubles (e.g. 4 + 5, 9 + 10 etc) and number bonds for 10 (e.g. 4 + 6, 9 + 1 etc). These benchmark facts (or friendly facts), combined with other strategies, such as count on (for adding smaller numbers eg 0, 1, 2, and 3), adding 10 and make a ten, ensures that the child develops both understanding of, and fluency with, the basic addition and subtraction facts, which in turn cam be applied to more complex situations later, such as bigger numbers or fractions and decimals. Pictured below are examples of some useful thinking strategies for the basic addition and subtraction facts.

While addition and subtraction are separate operations, they are also closely very closely related, being the inverse (or opposite) of each other e.g. 10 + 20 = 30, 30 – 20 = 10, 30 – 10 = 20. This is another strategy that the children can use i.e. think addition to do subtraction, or vice versa. Beginning in first and second classes, the children will explore addition and subtraction as being the inverse of each other, which will progress towards using the inverse (opposite) operation to check their calculations. 

Therefore, nowadays, there is less emphasis on just learning off “tables”, (i.e. memorising answers) and more emphasis on thinking strategies to use what they know, to solve what they do not know. 

Practical Suggestions for Supporting Children

• Involve your child in any adding and subtracting that happens at home, or when out and about, e.g. buying tickets for the cinema, buying items of clothes, etc.
• Encourage your child to use strategies when adding and subtracting and/or to explain their strategies. Ask your child to explain how they know, or worked out the answer.
• “I don’t believe you…prove it!” When your child arrives at an answer, ask him/her to show you how they got an answer, to prove that that is the answer, and encourage them to think of other ways to arrive at the same answer. Are there ways that might be more efficient (better) than others?
• Encourage your child to estimate. Estimation is a very important skill; this involves quickly getting a rough or ‘ballpark’ idea of the answer, e.g. €31 and €52 is roughly €80. Encourage your child to quickly estimate totals and differences, e.g. How much, roughly, is that going to cost? Do we have enough money? About how much will we have left?

Digital Resources for Junior and Senior Infants

Happy Numbers Pre-Kindergarten: Work through the activities from Module 5, addition and subtraction stories. Alternatively, go to Kindergarten, Module 4, Number Pairs, Addition and Subtraction to 10.

I Know it! – Addition & Subtraction: Scroll to the addition and subtraction sections to do any of the activities.

Splash Learn – Addition and Subtraction Games: An assortment of games organised according to US grade levels; junior and senior infants should choose among the games for kindergarten level.

Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Digital Resources for First and Second Classes

Happy Numbers First Grade: First class pupils could work through the activities from Modules 1, 2, 4 and 5. Second class could go to the activities for Second Grade 

and work through the activities from Modules 1 and 4.

White Rose Addition & Subtraction: a series of lessons on addition and subtraction. These lessons could be followed up with other addition and subtraction lessons in year 1 or year 2. 

Khan Academy Addition and Subtraction: 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 areas of First Grade Maths. Second classes could also look at Addition and Subtraction within 100 in Second Grade Maths

Math and Learning Videos 4 Kids: This YouTube channel has lots of videos on Addition within 100,  Addition of 2-digit numbers, Subtraction with regrouping, assorted addition worksheets and assorted subtraction worksheets.

Hit the Button: a great site for practicing quick-fire Number Bonds (up to 10, 20 or 100) and Doubles 

Thinking Blocks Junior: A simpler version of the original Thinking Blocks game for addition and subtraction, this is an ideal way for first or second classes to start using bar models to model word problems and computation.

That Quiz – Arithmetic: Use this quiz to practice different types of addition and subtraction calculations. 

I Know it! – Addition & Subtraction: Scroll to the addition and subtraction sections to do any of the activities. If too simple, go to Grade Two, to try the activities involving addition and subtraction of 2-digit numbers only.

Splash Learn – Addition and Subtraction Games: An assortment of games organised according to US grade levels; start with the games for first grade level. If too simple, go to the Grade Two games.

Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum) 

Digital Resources for Third to Sixth Classes

Happy Numbers Third Grade: Third class pupils could work through the activities from Module 2, Topics C and D. Fourth class pupils, and above,  could go to the activities for Fourth Grade and work through the activities in Module 1. 

White Rose Addition & Subtraction: a series of lessons on addition and subtraction. These lessons could be followed up with other addition and subtraction lessons in year 3, year 4, year 5 and/or year 6. 

Khan Academy Addition and Subtraction (Third Grade): Watch the videos and then answer the practice questions. For something more challenging,  look at Addition and Subtraction in Fourth Grade Maths. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

Hit the Button: a great site for practicing quick-fire Number Bonds (up to 100) and Doubles. 

Thinking Blocks for Addition and Subtraction: an ideal way to start using bar models, or further practice using bar models, to model word problems and computation.

That Quiz – Arithmetic: Use this quiz to practice different types of addition and subtraction calculations. You can use the options on the left hand side to make the types of calculations easier or more difficult.

Estimating sums and differences to win chances to take penalties in a shoot out.

I Know it! – Addition & Subtraction (Grade three): Scroll down to the addition and subtraction section to do any of the activities. If too simple, go to the addition and subtraction section in Grade Four or Grade Five.

Splash Learn – Addition and Subtraction Games: An assortment of games organised according to US grade levels; start with the games for third grade level. If too simple, go to the Grade Four games.

Addition practice games and Subtraction practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)