What is a repeating pattern?

A repeating pattern is a set of multiple identical groups of different symbols, items or shapes that are copied in the same order each time.

Shape patterns are repeating combinations of

shapes or symbols arranged in a line to form a sequence. Often there are blank spaces at the end of the line or in the middle of the sequence. The aim is to fill in these blanks with missing symbols or shapes which complete the sequence.

Children are expected to order and arrange combinations of mathematical objects in patterns and sequences as part of the English Year 2 national curriculum.

It is important to learn how to complete repeating patterns because Mathematics is full of patterns and rules. By identifying missing shapes or symbols in sequences, children begin to build the logic required to solve more complex sequences. It may also help them to pick up rules and patterns in any aspect of Mathematics that they learn in the future.

Here is another example of a repeating shape pattern formed by blue then red circles.

We can see that we have blue, red, blue, red, blue, red and so on.

Every blue always has a red following it. Every red has a blue following it.

The complete pattern can be formed simply by taking one blue and then one red and repeating these two. After each red we start again with another blue, red.

In this next example we have two blue counters followed by two red counters.

We always have two reds following two blues.

We can form the pattern by repeating two blues and two reds.

In this example, we have the pattern of two blues then a red repeated.

In this example above, the red is not as common as the blues. It marks the end of the repeating part of blue, blue, red.

We can easily see that blue, blue, red repeats after each red.

Completing Shape Patterns

To find the rule for completing patterns and sequences we can use the following tips:

• Look at the symbols between the first symbol and when it appears again to see if this is the pattern.
• Look for a unique symbol that doesn’t appear very often and try and count the number of places until it appears again.
• Look at the next few symbols that appear after each unique symbol and see if this appear again.
• Look for the symbols either side of missing spaces and see if they appear elsewhere in the pattern.

When introducing sequences and patterns to children early on, most sequences will be fairly simple with only two or three different repeating symbols.

Here is an example of a shape pattern formed by: triangle, triangle, cross.

We can construct the whole pattern by repeating triangle, triangle, cross.

We eventually have one more space remaining at the end.

We know that we repeat triangle, triangle, cross.

After a cross, we return to the first shape in the sequence, which is a triangle.

Here is an example of a repeating sequence with a missing shape at the end. We need to find the missing shape to complete the pattern.

The first symbol is a blue right arrow. We then have two yellow left arrows.

We look for other blue right arrows and we can see that two yellow left arrows always follow a blue right arrow.

The pattern blue right arrow, yellow left arrow, yellow left arrow repeats to make the sequence.

After two yellow arrows, we are back to the beginning, with one right blue arrow.

Here is another example of a shape pattern with a missing symbol.

We need to decide how to complete the pattern.

We can see that we have pairs of arrows in the pattern.

We have two blue right arrows followed by two yellow left arrows. These pairs of arrows alternate throughout the pattern.

Before the missing symbol, we have just one yellow left arrow. The missing shape must be another yellow left arrow.

We now have two blue right arrows followed by two yellow left arrows repeating.

Here is another example of a repeating pattern with missing shape.

We can use the first symbol in the pattern to help us. We have a red pentagon.

Following this red pentagon, we have a blue right arrow and then a yellow down arrow.

We look for other red pentagons in the pattern and see if they are also followed by a blue right arrow and a yellow down arrow.

We can see that this pattern repeats.

The missing shape after the blue right arrow is a yellow down arrow.

In this repeating shape pattern example, we have two missing shapes.

Again we can look at the first symbol and then look at which symbols follow this until we get back to the first symbol again.

We begin with a purple down arrow and following this we have a pink up arrow and a blue right arrow. We then get back to the first shape in our sequence.

We can fill in our pattern from the next purple down arrow. After the purple down arrow we should have a pink up arrow followed by a right blue arrow.

We already have a pink up arrow and then a blank space, so after the pink up arrow we put in a right blue arrow.

We are then back to starting the pattern again, using a purple down arrow.

The pattern of purple down arrow, pink up arrow and blue right arrow repeats throughout the sequence.