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) 

Dear Family, your Operation Maths guide to Comparing and Ordering

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

• Infant classes
• First and second classes

Understanding Comparing and Ordering

Comparing and ordering is probably something that happens a lot in any home already!

• “She’s got more than me! That’s not fair!”
• “I want to be first!”
• “I want to have the biggest piece!”

In maths, comparing is when two items, amounts or portions are examined to see if they are the same (equal), and if not, which is the larger/has more and which is the smaller/has less. Statements can be made to show how the two relate to each other; for example they are equal (=), there are more bananas than apples (opposite); there are less pears than strawberries.

Initially, the children will be identifying which group has more/less, and which number is less than or greater than another number. Then, they will begin to describe the relationship in more detail e.g. there is one more banana than apples; there is one less pear than strawberries.

In second class, the children will begin to use mathematical symbols (inequalities) to show the relationship eg 5 > 4 (five is greater than four); 2 < 3 (two is less than three).

Once the children are comfortable comparing two items, amounts or portions, they will then be able to progress to ordering three or more, for example ordering four numbers, smallest to largest, or vice versa. Number word order is also an important aspect of this i.e. identifying the number that comes before or after another number.

Ordering also involves being able to use the ordinal numbers 1st, 2nd, 3rd, 4th, 5th…. and ordinal words such as first, second, third ….. and last.

Practical Suggestions for Supporting Children

• The next time your child complains that somebody has got more than them, ask them to prove it! If it is sweets, can the child count the amounts to explain or justify that they do indeed have less than another? Or even when sharing out items like this, deliberately give more to somebody and ask your child(ren) to check if the amounts are all the same and, if not, to explain how the amounts are different. And what could be done to make it fairer.
• When organising, tidying, sorting at home, ask your child to compare the groups of items they encounter. Ask questions such as:
  • “Which has more/less?”
  • “Which is larger/smaller?”
  • “Do you want more tomatoes or more grapes in your lunch?”
• Try to incorporate ordinal number words such as first, second, third…last into your daily routine.
  • Who was first up out of bed? Who was second? Who was third? Who was last?
  • Who was first, second etc to be dressed, ready to go to school, finished homework etc.
  • When giving instructions: “First put on your socks, second put on your shoes, third put on your coat.”
  • When playing games discuss who will go first, second, third etc.
  • When standing in a queue talk about your position i.e. where you are standing.
• Monitor your child closely when they start writing the ordinal numbers, and don’t take them for granted, as the abbreviation system is not always obvious:
  • Straightforward enough: fourth = 4th; sixth = 6th; seventh = 7th; tenth = 10th.
  • Less obvious: fifth = 5th; eighth = 8th; ninth = 9th
  • Tricky! first = 1st; second = 2nd; third = 3rd
• Talk about the dates on the calendar. Say the ordinal number word clearly so that the child appreciates the difference in the sound of these numbers and the counting numbers eg seventh not seven.
  • “Your birthday is on the 3rd (third) of October.”
  • “We will be going back to school on the 6th (sixth) of January”
• Play hand grab: Get your child to put their hand into some lego, marbles, or other similar items and to put the handful ‘grabbed’ out onto a table. You child can then repeat this, or somebody else can get a handful. Look at the two amounts on the table. Estimate which has more. Then check which has more by either counting or laying both sets of items out in two lines, side-by side, so that you can clearly see which line has more. You could also ask your child to count to find out how many more are in the longer line.
• Play an ordering numbers game. Write down all/some of the numbers that your child knows, (eg 0-5 for junior infants, 0-10 for senior infants 0-20 for first class and any set of random numbers within 100 for second class), with each number on a separate piece of paper/post-it. Mix up the numbers and place them face down. Get your child to:
  • Pick up a number and say it.
  • Place all the numbers in order smallest to largest (variation: largest to smallest).
  • Say what number is missing, after you remove one.
  • Pick out 3 or three numbers and put them in order smallest to largest or vice versa
• Play guess my number. Get your child to write down a number within their familiar numbers range (see above). Work out the number by asking questions to narrow the possibilities. For example, is it greater than 5? Is is less than 5? etc. Next round, you write down a number and your child asks you the questions.
• You can also play any of the online interactive games below.

Digital Resources for Infants

Happy Numbers Kindergarten: Work through the activities from Module 1, Topic D and Module 3, Topic E, F and G.

Todo Math: Learn ordinal numbers as you watch the toys line up for ice-cream

Ordinal numbers: Watch the ostrich race and use ordinal numbers to identify the finishers

Make a cake song: Learn ordinal numbers using a recipe song

Caterpillar Ordering: Choose between ordering (where you put the given numbers in order) or sequencing (where you complete the sequence with the correct numbers from those given).  Has various levels including 1-5, 1-10, 1-20.

Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10 or up to 20. 

Ordinal Numbers: Video showing children lining up for a bus

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

Splash Learn: Compare Objects  and Compare Numbers

Comparing: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. There is also a suitable ordering game: order numbers up to 10

Digital Resources for First and Second Classes

Ordinal Numbers: Video showing ordinal numbers, 1st to 20th.

White Rose Comparing: a series of lessons on comparing objects and numbers; also introduces/uses the mathematical symbols <, > and =. These series of lessons could be followed up with the lessons on ordering and ordinal numbers 

White Rose Maths Ordering Numbers: A lesson on ordering number up to 100

Math and Learning Videos 4 Kids: This YouTube channel has lots of videos including Comparing Numbers and Greater Than, Less Than.

Caterpillar Ordering: Choose between ordering (where you put the given numbers in order) or sequencing (where you complete the sequence with the correct numbers from those given).  Has various levels including 1-100.

Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10, up to 20, up to 100 (in tens) or up to 100 (any number).

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

I Know It! Play some of these activities Ordinal Numbers (Up to 10); Ordinal Numbers (Up to 20); Ordering Numbers Up To 20; Ordering Numbers Up To 100; Comparing Numbers to 20; Comparing Numbers to 100.

That Quiz – Inequalities: Select the correct sign each time

Splash Learn – Counting and Comparison Games: Practice number word order, ordering numbers and comparing amounts. 

Comparing: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. There are also some ordering games: order numbers up to 10; order numbers up to 30; order numbers up to 100; ordinal numbers up to 10th; ordinal numbers up to 100th