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A pattern is a design or sequence that repeats or changes in a regular way. Children see patterns in nature, clothes, songs and numbers. A pattern can be repeating, such as red-blue-red-blue, or growing, such as 2, 4, 6, 8. Patterns help us predict what comes next. To study a pattern, first look carefully to notice what repeats or how things change. Ask: Does it repeat the same group? Does each term get larger or smaller by the same amount? If there is a rule, try to say it in words like "add 3" or "alternate circle and square".
Ways to show a pattern
Talk about patterns: explaining why a term comes next helps students think like mathematicians. Teachers can ask students to find the rule, continue the pattern, or make their own. Playing with patterns builds number sense and prepares learners for tables, sequence rules and early algebra later on.
Repeating patterns are those where a small group of items repeats again and again. This repeating group is called the unit. The unit may be two items like AB (for example red, blue), three items like ABC (for example red, blue, green), or a pattern like AAB where the first item appears twice before the next. Finding the unit is the first step in understanding the pattern. Once you know the unit, you can continue the pattern easily by repeating that same group.
How to work with repeating patterns
Repeating patterns can be made with colours, shapes, stickers, beads or numbers. When children build patterns with objects they can feel and move, they learn to spot the unit more quickly. Teachers should also ask children to describe units in words, for example "two reds then one blue," because saying the rule helps to remember and test it. Practise with longer sequences helps pupils see that some patterns repeat after more items and some repeat after just two items. This skill is important for design, art and future studies in sequences and algebra.
Growing patterns change by adding the same amount each time. This kind of pattern is often called arithmetic growth and is easy to see when numbers increase by a fixed step. Skip counting is a useful name for this: when you count by 2s you go 2, 4, 6; by 5s you go 5, 10, 15; and so on. Learning to skip count helps children reach bigger numbers quickly and prepares them for multiplication tables.
Finding the rule in growing patterns
Use tools such as number lines, hundred-charts, or counters to show jumps. On a number line, each jump is the same length when the pattern grows by a fixed amount. For example, for 3, 6, 9, 12 draw jumps of three. Children should practise with starting points that are not zero: for instance, start at 4 and add 3 each time to get 4, 7, 10. Encourage saying the rule aloud — "start at 4, add 3" — and writing it down. This thinking links directly to the formula for the nth term used later in higher classes, and it builds strong arithmetic fluency useful for times tables and mental maths.
Odd and even patterns use the idea that numbers end in certain digits. Even numbers are divisible by 2: 2, 4, 6, 8, 10. Odd numbers are not divisible by 2: 1, 3, 5, 7, 9. When you count by 2s from 2, you get even numbers. When you count by 2s from 1, you get odd numbers. This creates two separate growing patterns that are simple to recognise and useful in many problems.
Using pairs to understand odd and even
Teachers can show a line of counters and make pairs, then count how many pairs and whether there is a leftover. Students should practise finding odd and even numbers in sequences and explaining why a number is odd or even. This strengthens reasoning and prepares children for multiplication properties and divisibility rules later on.
A clear rule tells how to get the next term of a pattern. Rules can be written in simple words like "add 4" or using a short symbol form such as +4, ×2 or −3. For class 5 we focus mainly on rules using addition, subtraction and small multiplication, and on short sentences that explain the change. Writing and speaking the rule helps make thinking clear and makes it easy for others to continue the pattern.
How to find and write a rule
Some rules have two steps; for example, "multiply by 2 then add 1" can be shown as ×2 +1. Use input-output boxes to show the rule: write an input number on the left, and the output on the right with an arrow showing the action. Encourage pupils to write the rule as a sentence and also try a short symbol form; both ways are valid. Practise converting phrases to symbols and back. This habit trains students in logical description and is the first step towards using letters for rules in higher classes.
Pictorial patterns use drawings, shapes or colours instead of numbers. These patterns can repeat a unit of shapes or mirror one side to the other, which is called symmetry. Working with pictorial patterns helps children use their eyes and hands together: they copy, colour and place shapes to continue or complete a design. Pictorial patterns are very visual and are often used in art, borders and floor tiles.
Learning steps for pictorial patterns
Activities can include completing the second half of a mirrored design, making a repeating border, or colouring every third shape in a strip. Mirror activities teach left-right awareness and balance. Asking pupils to make pictorial patterns with a rule and swap their patterns with a partner for continuation develops communication and checking skills. These tasks are both creative and mathematical, strengthening fine motor control and visual reasoning.
Input-output tables show how a rule changes an input number into an output number. Think of the rule as a small machine: you put a number in, the rule works on it, and a new number comes out. These tables are a clear way to see the relationship between two sets of numbers and help children practise applying the same rule to many inputs.
Steps to use input-output tables
Input-output tables can use one-step rules like +2 or ×3, and sometimes two-step rules like ×2 then +1. Draw a box labelled with the rule and arrows showing input and output so children can visualise the process. Practise examples where only some outputs are given and students must work backward to find which input fits. This prepares learners for algebra where rules are often shown with letters and symbols, and it strengthens arithmetic skills because pupils must calculate and check carefully.
Pattern puzzles make learning fun and encourage careful thinking. In a puzzle a child may be given a few terms and must discover the rule, or some terms may be hidden and must be found. Solving puzzles needs observation, testing ideas, and explaining why a rule fits. Making puzzles for classmates also helps the creator clarify the rule and check it works for different cases.
Simple puzzle types for class 5
When solving puzzles, teach students to try small checks: apply the guessed rule to all known terms. If one term does not match, the rule is wrong. Encourage writing the rule in words and testing it by producing several further terms. Group work is helpful: one child makes a puzzle, another child solves it and then explains the reasoning. Teachers can award points for clear explanations, not just correct answers. These activities develop logical thought, patience, and the skill of checking work carefully before saying the answer is final.