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. 

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

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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) 

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Digital Resources for Third and Fourth Classes

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

 

 

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

 

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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.  

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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.

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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.

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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.

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

 

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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.

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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.

 

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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

 

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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.

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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.  

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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.

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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.

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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.

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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.

 

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

 

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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.

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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.

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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. 

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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.

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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.  

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

 

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

 

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

 

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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

 

 

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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.

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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.

 

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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.

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

 

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

 

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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 

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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.

 

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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

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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.

 

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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.  

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

 

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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

 

 

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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.

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

 

 

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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.

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

 

 

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

 

 

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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 

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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.

 

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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)