## Dear Family, your Operation Maths guide to Patterns and Sequences

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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:

#### 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:
**B**rackets**M**ultiplication or**D**ivision (whichever occurs first, reading left to right)**A**ddition or**S**ubtraction (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.

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

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

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

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

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

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

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

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

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

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

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

I Know it – Patterns: A practice game

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

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).

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).

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

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

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

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

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

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

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

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

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

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.

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.

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)

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

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).

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

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

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.

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

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

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

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

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

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

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

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

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).

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

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

#### 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).

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

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

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

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

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

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

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

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