Dear Family, your Operation Maths guide to Patterns and Sequences

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

• Junior and Senior Infants
• First and Second Classes
• Third and Fourth Classes
• Fifth and Sixth Classes

Understanding Patterns and Sequences

A pattern is a set of numbers, shapes, objects etc., arranged in a particular order, according to a particular rule. There are two main types of patterns:

• Repeating patterns: (see image above) symbols, shapes, numbers etc., that repeat in a specific way eg ABC ABC ABC ABC… is a repeating pattern, the core of which is ABC because this is the smallest piece that repeats each time.
• Increasing (growing) and decreasing (shrinking) patterns: An ordered set of shapes or numbers that are arranged according to a rule, eg 10, 9, 8, 7, 6, 5, …. is a decreasing (shrinking) pattern, where the numbers are going down by 1 each time (i.e. its rule is -1), whereas 5, 10, 15, 20, 25… is an increasing (growing pattern), where the numbers are going up by 5 each time (i..e its rule is +5). Often the word sequence is also used to describe an increasing or decreasing pattern, particularly if it is a pattern of numbers (see image below).

Patterns are all around us in life and in our homes, for example on clothes, curtains, fabrics, walls, tiles, furniture, animals, car tyres, photo frames, packaging, etc.

In the early years of school, children are enabled to identify patterns that are around them, and to copy and/or extend them. They are also encouraged to create their own patterns using objects and shapes that are available.

As they get older, the children are enabled to examine patterns in more detail, for example to identify the core of repeating patterns and/or to identify the rule of growing/shrinking patterns (sequences).

With Operation Maths 5 and 6, children are enabled to explore more complex patterns and to use more advanced strategies to extend the patterns (see image below) as well as predicting trends etc., in real-life examples and data.

Practical Suggestions for Supporting Children

• Draw your child’s attention to patterns around your home and in the wider environment:
  • Patterns on clothes, curtains, fabrics, tiles, animals, car tyres, photo frames, packaging, etc.
  • Patterns made with toys, building blocks, threading beads, lego, etc.
  • Number patterns in the environment, e.g. how the speedometer goes up in tens; that on many streets, the odd numbers are on the houses on one side of the street and the even numbers are on the other side; etc.
  • items that come in twos (hands, feet, shoes, gloves, socks etc), tens (eg fingers and toes; biscuits and bars in some packets) and fives (5 seats in a standard car).
• When you spot a pattern, ask your child to tell you about it, what they notice etc. Can they tell you more about the type of pattern it is (e.g. repeating or growing/shrinking)
• Do you know how to knit and/or crochet? Explore the structure of patterns together with your child.
• Many puzzles and riddles are based on patterns and these are often widely available in newspapers, magazines, on the Internet, or you can often buy inexpensive puzzle books in discount stores. You could encourage your child to try to solve these and/or you could share and solve puzzles and riddles as a family.
• Create pattern puzzles at home using materials around the house, and challenge your child to complete them; e.g. put out a fork, knife, spoon, knife, fork……, and ask your child to say what comes next.
• Counting is a an essential skill required to understand, and explore number sequences. Any and all activities, that encourage your child to count in 1s, 2s, 10s, 5s etc., are very valuable. For more counting suggestions and ideas, please refer to the Dear Family Guide to Counting and Numeration.
• Children in 5th and 6th classes will also looking at the order in which number sentences should be calculated. Referred to as the order of operations, in Operation Maths we use the mnemonic ‘Bless My Dear Aunt Sally!’ to remind the children how to calculate number sentences correctly i.e. we calculate each part in this order:
  1. Brackets
  2. Multiplication or Division (whichever occurs first, reading left to right)
  3. Addition or Subtraction (whichever occurs first, reading left to right)

Digital Resources for Junior and Senior Infants

White Rose Maths – Pattern: lessons for infant classes covering Pattern; scroll down to session 4 and 5 for videos and activities.

 

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FCPS – Patterns: videos for Kindergarten on Patterns Everywhere and Creating Different Patterns

 

 

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Grover’s Winter Games: Choose the snowboarding game to complete shape patterns. 

 

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Peep’s Feet – Patterns: Help Peep and friends by completing the repeating patterns.

 

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Planet Pal: What colour dog comes next in the pattern? Simple game suitable for infants.

 

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Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty. 

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Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.

 

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Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out  your own choice of tiles make patterns.

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The Gingerbread Man Game: Play the ordering game for numbers up to 5, and up to 10.

 

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

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

 

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Happy Numbers: pupils in Senior Infants could work through the pattern activities (patterns in adding 0 and 1) from Module 4, Topic H. 

 

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I Know it – Patterns: A practice game

 

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Splash Learn – Patterns: Practice how to Extend Number Patterns (rule given), Extend Number Patterns (rule not given) and Generate Numerical Patterns.

 

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Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum). 

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Math Games – Patterns: Selection of practice games; choose your class level

 

Digital Resources for First and Second Classes

White Rose Maths: a series of lessons on Counting in 2s and 5s (Year 1), Pattern in Shapes (Year 1), Counting in 2s, 5s, 10s and 3s (Year 2), Pattern in 2-D Shapes (Year 2), Pattern in 3-D Shapes (Year 2). 

 

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FCPS – Patterns: videos on Repeating Patterns 1, Repeating Patterns 2, Growing Patterns 1, Growing Patterns 2. 

 

 

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Matholia: A playlist of video lessons on  Patterns in Numbers; videos 1-6 are suited to first and second classes. Also available is a video on Patterns with 2-D shape and Patterns with 3-D Solids

 

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Khan Academy: A series of videos and practice questions exploring Even and Odd Numbers (Grade 2). You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

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Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty. 

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Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.

 

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Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out  your own choice of tiles make patterns.

 

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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.

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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).

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Happy Numbers: First class pupils could work through the pattern activities (patterns in adding 0 and 1) from Module 4, Topic H. Second class pupils could do the activities on the Meaning of Even and Odd Numbers, Module 6, Topic D

 

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Odd & Even: A selection of games to identify the odd and even numbers: Coconut Odd or Even, Fruit Splat Odd or Even, Carroll Diagrams Odd and Even.

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Maths Frame – Errors on a Venn Diagram: Identify the numbers which have been placed in the wrong position on the Venn diagram and drag them to their correct place. Choose the criteria of odd or even numbers.

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I Know it: A selection of practice games including Patterns, Odd & Even Numbers (Grade 1), Patterns in Tables (Grade 1), Odd & Even Numbers (Grade 2), Patterns in Tables (Grade 2)

 

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Splash Learn – Patterns: Practice how to Extend Number Patterns (rule given), Extend Number Patterns (rule not given) and Generate Numerical Patterns.

 

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Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum). 

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Math Games – Patterns: Selection of practice games; choose your class level

 

Digital Resources for Third and Fourth Classes

White Rose Maths – Spot the Pattern: a lesson for Year 3

 

 

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Matholia: A playlist of video lessons on  Patterns in Numbers; videos 7-9 are suited to third and fourth classes. Also available is a video on Patterns with 2-D shape and Patterns with 3-D Solids

 

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Khan Academy: A series of videos and practice questions exploring Patterns in Arithmetic (Grade 3) and Factors Multiples and Patterns (Grade 4) You can also register for a free Khan Academy account to record your progress and explore other topics/grades.    

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Top Marks – Shape Patterns: sequencing game where you need to complete the pattern of different coloured 2D shapes. It is a multiple choice game with three levels of difficulty. 

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Pattern Blocks: Make numerous designs, pictures etc with these interactive pattern blocks. You can also choose a puzzle to complete.

 

 

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Mathigon Polypad: Use this excellent tool to create, copy and extend patterns. Select Tiles > Geometry and then drag out  your own choice of tiles make patterns.

 

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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.

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Maths Frame – Sequences: Find the correct number in a sequence. Lots of choice over level, count forwards or back, count in whole numbers, multiples of 10, multiples of 100, decimals and fractions. 

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Happy Numbers Third Grade: Third and fourth class pupils could work through the activities from Module 3, Topic E. 

 

 

 

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I Know it: A selection of practice games including Odd & Even Numbers (Grade 2), Patterns in Tables (Grade 2), Odd & Even Numbers (Grade 3)

 

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Splash Learn – Patterns: Practice how to Extend Number Patterns (rule given), Extend Number Patterns (rule not given) and Generate Numerical Patterns.

 

 

 

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Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum). 

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Math Games – Patterns: Selection of practice games; choose your class level

 

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Patterns & Sequences: information on both of these topics from Maths is Fun. 

 

 

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Digital Resources for Fifth and Sixth Classes

White Rose Maths: Number Sequences with Fractions (Year 5), Find a Rule (Year 6) and Order of Operations (Year 6).

 

 

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Khan Academy: A series of videos and practice questions exploring Number Patterns (Grade 5) and Order of Operations (Grade 6). You can also register for a free Khan Academy account to record your progress and explore other topics/grades.    

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Maths Frame – Sequences: Find the correct number in a sequence. Lots of choice over level, count forwards or back, count in whole numbers, multiples of 10, multiples of 100, decimals and fractions. 

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Maths Frame – Order of Operations: Use a calculator to carry out calculations with more than one step using brackets and the memory.

 

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Function Builder: Use this virtual function machine to explore how to change an input to a different output. You can also choose the mystery option, (where you have to work out the rule i.e. how the input is being changed each time) and/or a patterns option.

 

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Happy Numbers Fifth Grade: Fifth class pupils, and above, could go to the activities for Fifth Grade and work through the activities in Module 1, Topics A and B.  

 

 

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Splash Learn – Patterns: Practice how to Extend Number Patterns (rule given), Extend Number Patterns (rule not given) and Generate Numerical Patterns.

 

 

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Mashup Math – Multiples of 10 and Place Value Patterns: A video lesson that introduces this concept.

 

 

 

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Patterns: a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities (Please note that the class levels used here don’t exactly match the class level content in the Irish maths curriculum). 

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Math Games – Patterns: Selection of practice games; choose your class level. Also available are practice games on Input/Output tables

 

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Patterns & Sequences; Order of Operations: information on these topics from Maths is Fun. 

 

 

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Dear Family, your Operation Maths guide to Number Theory

Dear Family, below is a brief guide to understanding the topic of number theory (fifth and sixth classes only), as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about number theory.

Understanding Number Theory

Number Theory in primary school, is about exploring the shapes of numbers, and how numbers can be visually arranged and represented. It is largely concerned with subcategories of whole numbers:

• odd and even numbers, and what is the resulting number when you add or multiply odd and/or even numbers
• factors and multiples, and how to identify all the possible factor pairs e.g. if you lay out 12 playing cards on a table what are the different ways to arrange them to make a rectangular shape? 1 row of 12, 2 rows of 6, 3 rows of 4 etc
• prime and composite numbers; prime numbers have only one factor pair, the prime number x 1 eg 13 playing cards can only be arranged as 1 row of 13 or 13 rows of 1, which is the same factor pair (1, 13)
• square numbers, triangular numbers and rectangular numbers; some numbers can take the shape of a square (eg 4, 9, 16, 25 etc) and some can take the shape of a triangle (1, 3, 6, 10, 15, 21 etc)
• square roots and exponential numbers.

While Operation Maths 5, for fifth class, is the first book to have a chapter devoted to this topic, the children will have explored elements of this topic in previous classes:

• odd and even numbers were explored formally in Operation Maths 1, 2 and 3
• the language of factors and multiples is used in Operation Maths 3, 4, 5 and 6 as part of the multiplication and division chapters.

The emphasis in Operation Maths is on the child being able to build, manipulate and represent numbers in ways and contexts that are relatable. This will help the child to be better able to visualise numbers, manipulate numbers and understand the connections between them.

Practical Suggestions for all Children

• Draw your child’s attention to these number types wherever they or you encounter examples of them.
• Use materials around your home to help make these concepts more real to your child(ren):
  • Use pairs of socks, shoes, gloves etc to model addition, subtraction, multiplication and division with odd and even numbers.
  • Lay out playing cards, coins, poker chips, plastic cups/plates, lego pieces, toy building blocks etc to represent certain numbers and to explore the shapes that can be made .
  • Examine square tiles and/or paving slabs that maybe around your home, how many of these squares together are needed to make a bigger square shape? Are there any patterns? Can you show/build/calculate the first 10 square or triangular numbers?

Digital Resources for Fifth and Sixth Classes

White Rose Maths: a series of lessons for Year 5 covering Multiples, Factors and Primes, followed by Square and Cube Numbers. For Year 6 there are lessons that include Factors & Common Factors and Multiples, Primes, Square and Cube Numbers.

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Matholia: A number of video lessons that include An Introduction to Multiples and An Introduction to Factors 

 

 

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Mashup Math – Square Numbers and Square Roots: A video lesson that introduces this concept.

 

 

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Khan Academy: A series of videos and practice questions exploring Odd & Even Numbers (Grade 3), Factors, Multiples, Prime and Composite Numbers (Grade 4) and Intro to Exponents (Grade 6). You can also register for a free Khan Academy account to record your progress and explore other topics/grades.  

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Mathigon Polypad: Use this excellent tool to explore and identify factors of any number, and therefore identify if the number is prime or composite. Can also be used to explore square numbers. Select Tiles > Numbers > Number Tiles and drag out tiles to represent a number. Watch here for a video guide (pupils in 5th and 6th class should start with numbers less than 20 first, and then explore bigger numbers when ready)

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Odd & Even: A selection of games to identify the odd and even numbers; these might serve useful as revision: Coconut Odd or Even, Fruit Splat Odd or Even, Carroll Diagrams Odd and Even.

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Maths Frame – Errors on a Venn Diagram: Identify the numbers which have been placed in the wrong position on the Venn diagram and drag them to their correct place. Choose one or two criteria: to arrange numbers by whether they are odd or even, or multiples of a given number, or prime or square numbers.

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Multiples and Factors: multiple choice game, finding the Lowest Common Multiple (LCM) or the Highest Common Factor (HCF). Questions increase in difficulty depending on accuracy.  

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Maths Frame – Maths Invaders: Shoot the spaceship with the correct answer and dodge the incoming fire. Select play game and then scroll down to select Recognising Multiples, Factors, Prime, Square and Cube Numbers.

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PhET – Factors: Choose the Factors option to identify the factors of given numbers

 

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Sieve of Eratosthene: Use this interactive sieve to remove multiples, and therefore, identify all the prime numbers from 1-400

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Transum – Factor Trees: Complete the Factor Trees to identify the prime factors. Other related activities can be chosen from the Tabs at the top, including Sieve of Eratosthenes, Pick the Primes, HCF and LCM

 

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Hit the Button: Choose the Square Numbers option

 

 

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Cubes: use this virtual tool to create models of various cubed numbers; click on the settings cog to input your own dimensions

 

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Maths Fishing – Square and Cube Numbers: Practise your multiplication skills. Choose game 18, squared numbers, or 19, cubed numbers. A similar game to this is Archery Arithmetic; again, choose game 18 and/or 19 

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That Quiz: Use the factors quiz to practice identifying prime and composite numbers, prime factors, HCF and LCM. Use the exponents quiz to practice roots and exponents.

 

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Splash Learn – Algebra Games: These games include Factors, Multiples, Prime and Composite Numbers

 

 

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Number Theory and Exponents: two sections of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the games just below, or at, your class level. 

 

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Math Games: Practice games on Factors and Multiples, Prime and Composite Numbers, Square Roots. Choose your class level. 

 

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Math is Fun: Background information on even and odd numbers, factors and multiples, prime and composite numbers,  square numbers and square roots and exponents

 

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Dear Family, your Operation Maths guide to Decimals and Percentages

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

• Third and Fourth classes (Decimals only)
• Fifth and Sixth classes (Decimals and Percentages)

Understanding Decimals and Percentages

Decimals, or decimal fractions, to give them their full title, are fractions of a whole amount, where the whole has been divided into ten parts (tenths), a hundred parts (hundredths), a thousand parts (thousandths) etc. They are typically written using a decimal point. This means that an amount that is the same value may be describes as a fraction, as a decimal fraction and as both, e.g.:

1/2 (1 half) = 5/10 (5 tenths) = 0.5 = 50/100 (50 hundredths) = 0.50 etc

Percentages are very closely related to both fractions and decimals: per cent means out of 100, therefore an amount of percent is the same as that amount of hundredths, e.g.:

25% (twenty five percent) = 25 hundredths = 25/100 = 0.25

In Operation Maths, the children are first formally introduced to decimals (tenths only) in third class and then to hundredths in fourth class and thousandths in fifth class. The children are also introduced to percentages in fifths class. However, it is worth noting that the children would have informally explored decimals since being introduced to euro and cent in first class.

Since decimals are inherently linked with both fractions and the place value system, (also introduced in first class), the children’s understanding of decimals and percentages in the senior classes will build on this prior knowledge.

Practical Suggestions for Supporting Children

• Draw your child’s attention to decimals and percentages around your home and in the wider environment, e.g:
  • Decimals on products 1.5 litre bottle of water, 2.5 kg bag of dog food, petrol or diesel sold per litre as cents to tenths (e.g. 125.9c/litre)
  • Percentage discount: 20% off, 10% off, 50% extra free etc.
  • The percentage left for a device to fully charge or for a program/movie to fully download.
  • The percentage power left in the battery
  • Recorded times (as decimal fractions of a second) for races, etc.
• When you are talking about decimal numbers be careful to use the correct language e.g. for 23.05 say ‘twenty three point zero five’. (Remember: 0 is a digit called zero, whereas O or ‘oh’ is a letter of the alphabet and not a number at all! So, when verbalising numbers with zero, try to get into the habit of saying ‘zero’ instead of ‘oh’).

Digital Resources for Third and Fourth Classes

White Rose Maths – Decimals: a series of lessons, including Tenths as Decimals, Hundredths as Decimals, Writing Decimals, Comparing Decimals, Ordering Decimals and Rounding Decimals.

 

 

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Matholia – Decimals: A series of video lessons. Third class should focus on decimals to tenths, and fourth class on decimals to hundredths.

 

 

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Khan Academy – Decimals: in this video and the videos that follow, explore decimal fractions and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Happy Numbers – Decimal Fractions: A series of lessons and activities; scroll down to do Module 4 (Fourth Grade)

 

 

 

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Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself. 

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Caterpillar Ordering: Choose ordering to order numbers with tenths (1 decimal place)

 

 

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Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10, 1 decimal place or 2 decimal places or both.

 

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Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).

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Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either T O . t (1 decimal place, for third class) or T O . t h (2 decimal places, for fourth class) in either column.

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Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

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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 decimals game. 

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I Know It! – Decimals: Scroll down to Decimals (Third Grade) to do any of the activities with tenths (third class) and/or hundredths (fourth class). There are some more advanced decimal activities in the fourth grade section, both in the section on Numbers & Place Value and in the section on Fractions & Decimals. 

 

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Splash Learn – Decimals: An assortment of decimal games organised according to US grade levels; third classes could do the games that include tenths only and fourth classes could look at all the Fourth Grade games.

 

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That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals (choose decimal option on left hand side), Inequalities for comparing decimals and/or fractions and Reduce for converting decimals to an alternative form. 

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

Digital Resources for Fifth and Sixth Classes

White Rose Maths – Decimals & Percent: a series of lessons, including Decimals as Fractions, Thousandths, Rounding Decimals, Order & Compare Decimals, Percentages, Percentages as Fractions and Decimals, Adding Decimals 1, Adding Decimals 2, Subtracting Decimals 1, Subtracting Decimals 2, Multiplying Decimals,  and Dividing Decimals.

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Matholia – Decimals and Percentage:  A series of video lessons. For decimals, fifth and sixth classes should focus on the lessons involving decimals to thousandths (3 decimal places).

 

 

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Khan Academy – Decimal Place Value: explore decimal fractions in this series of lessons, and then answer the practice questions. If you wish, follow this up with Adding Decimals, Subtracting Decimals, Multiplying Decimals, Dividing Decimals or a series of lessons covering all Decimal Operations. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Khan Academy – Ratios, Rates and Percentages: Scroll down to the sections on percentages to explore them in this series of lessons, and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Mashup Math: A collection of video lessons including Writing Decimals in Expanded Form, Converting Decimals to Fractions, Adding & Subtracting Decimals, Multiplying & Dividing Decimals and Percent Increase Problem.

 

 

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NCETM – Linking Fractions, Decimals and Percentages: A series of video lessons aimed at years 5 and 6

 

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Happy Numbers – Decimal Fractions: A series of lessons and activities exploring decimals to thousandths and operations involving the same. Work through the activities in Modules 1, 2 and 4.

 

 

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Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself. 

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Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).

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Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

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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 decimals game. 

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I Know It! – Decimals & Percent: Scroll down to Fractions-Decimals-Percent (Fifth Grade) to do any of those activities. There are also more decimal activities spread throughout the Place Value, Addition, Subtraction, Multiplication and Division sections. 

 

 

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Splash Learn – Decimals: An assortment of decimal games aimed at Fifth Grade

 

 

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Decimal Games & Percentage Games: An assortment of games using numbers of various sizes. Fifth and Sixth class should do the games up to 3 decimal places.

 

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That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals and/or percent (choose desired options on left hand side), Inequalities for comparing decimals, percentages and/or fractions and Reduce for converting decimals and percentages to an alternative form. 

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

 

Dear Family, your Operation Maths guide to Directed Numbers

Dear Family, below is a brief guide to understanding the topic of directed numbers (fifth and sixth classes only), as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about directed numbers.

Understanding Directed Numbers

Directed Numbers are numbers with both size and direction; one direction is positive, and the other is negative. For example, temperature is typically described in a number of degrees either above zero (positive values) or below zero (negative values). Positive and negative numbers are also referred to as integers.

In Operation Maths, the children are first introduced to directed numbers in fifth class, where the focus is on the children appreciating where directed numbers can be encountered in real life, for example:

• Temperature
• Bank statements/ money accounts: having money is shown as positive (+) and owing money or overdrafts are shown as negative (-)
• Elevations above and below sea level
• Floors below the ground floor in a large building are often labeled as -1, -2 etc
• Golf scores are written as above and below par
• Goal difference in soccer league tables
• Depths in a swimming pool

In school, the children are encouraged to use the words positive and negative, rather than plus and minus; for example for the value -6 we should say negative six rather than minus six. This is particularly important for when the children start adding positive and negative numbers (in Operation Maths 6): for example (–3) + (+9) should be read as ‘negative three add/plus positive nine’ rather than ‘minus 3 plus plus 9’. It is also important that the children recognise that positive numbers can be written either with, or without, the positive sign, therefore we can assume that any number, without a sign, is positive.

Practical Suggestions for all Children

• Draw your child’s attention to wherever they or you encounter directed numbers (see above for possible examples).
• If your child is having difficulty visualising, comparing, ordering etc directed numbers, encourage them to think of a real example. One of the most-relatable of these is that of temperatures and the thermometer. Look at a real thermometer or use an online virtual example such as this one.
• As explained above, encourage your child to use the words positive and negative, rather than plus and minus, when describing directed numbers.

Digital Resources for Fifth and Sixth Classes

Integers: Video lesson that introduces integers (positive and negative numbers) and where they occur in real life

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Mashup Math – Elevation above or below sea-level: A video lesson that explores elevation as examples of positive and negative numbers.

 

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Negative Numbers: A series of video lessons from White Rose Maths, including Introducing Negative Numbers (Year 4), Negative Numbers (Year 4), Negative Numbers (Year 5), Negative Numbers in Context (Year 6), Negative Numbers (Year 6), Add and Subtract Integers (Year 6).

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Khan Academy Negative Numbers: A series of videos and practice questions exploring negative numbers. Afterwards, for more of a challenge, look at Integers and Whole Numbers. You can also register for a free Khan Academy account to record your progress and explore other topics/grades. 

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Maths Frame – Empty Number Line: Practice placing positive and negative integers in the correct position; choose -5 to 5 initially and then move to the next levels to challenge yourself. 

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What is the Temperature? Identify the temperature shown on the thermometers. A way to practice directed numbers in a real-life context. Includes values above and below zero, and has options for various ranges.

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Caterpillar Ordering: Choose Ordering and then -10 to 10 to order integers.

 

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

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Number Lines in Disguise: A challenge and interactive game (scroll down) from NRICH; Can you work out the number marked by the dot? Includes positive and negative numbers.

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That Quiz: Inequalities for comparing numbers, Arithmetic for addition calculations involving directed numbers and Number Line for identifying numbers by their position. In each of these activities there is the option to include negative numbers along with positive; just make sure the the “negative” option is selected on the left hand side.

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Number Line App: This virtual tool can be used to explore the position of values on a number line,including positive and negative numbers; also to model addition and subtraction involving positive and negative numbers.

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Directed Numbers Counters: These double sided counters can be used to model addition and subtraction involving positive and negative numbers (ensure that the “sign” option is ticked).

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Integers (Directed Numbers): a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities.

 

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Integers: Practice games from Math Games. Choose your class level.

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