### Understand how to count in 2s and 5s

I have searched the internet, read numerous research articles and found plenty of tasks designed to help kids count in 2s and 5s. This post contains a brief explanation of why this is an important thing for kids to learn. I have also included a list (with descriptions) of some of my favourite tasks, along with a video example of this learning in action.

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Why do kids need to learn how to count in 2s and 5s?

Learning to count in 2s or 5s might seem like it doesn't have a lot of purpose. However, if kids really understand how to do it, they have the building blocks for developing understanding of many other mathematical concepts. For example:
• It helps children to get a firmer understanding of the concept of "more than" and therefore addition.
• It will get children used to recognising and explaining patterns. This, in turn, will enhance their problem solving skills.
• It is an aid to learning (by understanding rather than repetition) times tables in the future.
• It will help kids to recognise arithmetic progressions where numbers other than 1 are added each time. This will make learning sequences easier in the future.
• Counting in 2s will later help children to identify the concept of even and odd numbers.
• It aids children's understanding of the number system and helps them to identify numbers as quantities rather than just a sequence (1, 2, 3...). It also enhances their knowledge of cardinal numbers, reinforcing that you do not need to count every number each time, but can just state the total.
• It will help improve the child's mental arithmetic, as they will notice and remember the patterns.
Tasks to help kids learn to count in 2s and 5s

I have found many tasks on the internet that encourage children to recall and recognise the sequence of counting in 2s and 5s. These tasks involve ordering cards, filling in missing numbers, learning songs, turning over all numbers that are not required, etc. Some of these tasks are beautifully presented in a fun and engaging way for the children and are great for practising and committing to memory. However, it is vitally important that before doing these tasks, the children really understand what it is they are actually doing when counting in 2s or 5s. They must understand it is a process, rather than a pattern.

The Kiducation UK videos below demonstrate some of the tasks and ideas that follow. They show how the child's understanding develops throughout the tasks and provide ideas for the type of questioning that can be used to enhance the child's learning.

Physically count things that come in 2s and 5s
Before learning the sequences with numbers and repetition, ask the children to count physical objects that are naturally arranged in groups of 2s or 5s. Find something that the child is interested in and/or can relate to, making sure that they associate it with going in 2s or 5s.
• Counting in 2s - For this, I love using Noah's Ark. Most children know the song "the animals went in 2 by 2, hoorah! hoorah!" and it is a fun way to start the lesson, even if they don't. Using animals is something that all children can relate to and get excited about - you could even ask them to draw or find pictures of their favourite animals first. I like to start by using figures of pairs of animals and asking the child to put each pair in the boat I then ask them to tell me how many animals in total are in the boat each time. This encourages the child to intuitively count in 2s (you never have 5 animals in the boat but go straight from 4 to 6). It also reinforces the idea of counting in 2s as adding two more each time.
• Counting in 5s - A natural and obvious resource for this is a child's own fingers. They know that they have five fingers on each hand so will really understand that it is five more each time. Using them will also help them pracitse 'counting on' with their fingers and will make it easier to move on to counting in 5s when they don't start at 5. Again, it is important to emphasise that it is the total number of fingers that you need to know, not all of the numbers inbetween.
Create a visual aid
Once the children understand what it means to count in 2s and 5s it is nice, and beneficial, for them to create their own resource. During the creation process, they will again practise the counting on but only giving the total each time. This reinforces what they have already learnt and strengthens their understanding of cardinal numbers. It also produces a piece of work that they can be proud of and can use again in the future to practise with. Because they made it themselves, they will understand the process that went into making it and this will support their understanding.

Make sure to choose a task that requires the children to naturally count on in 2s (or 5s). We followed on with our Noah's Ark theme for counting in 2s and produced a lovely, colourful poster with little pocket boats. We then put two animals in each boat, physically counting them as they went in and writing the total number of animals on each boat as we went along. The little pockets mean that this resource can be used again and again to recount and reinforce the idea of each number being two more than the last.

For counting in 5s we used fingers again, but made it more fun and crafty by creating different coloured handprints. We then counted the total number of fingers each time another hand was added. This creates a very visual and intuitive resource for children to look at and use for practising counting on. I was very impressed with the understanding of my 4 year old after creating this poster. He told me (without absolutely no prompting at all) that we needed 8 lots of 5 to get 40 in total. He was then able to tell me how many there would be if we added another hand. To me, this demonstrated a very strong understanding of the process of counting on in 5s and the fact that each number was 5 more than the last. I know it seems obvious to us, but for a four year old who hasn't long been counting in 1s, this is a dramatic step. It will also be great for helping him to learn his 5 times table in the future, as he already has some grasp of the concept of 'lots' of a number.

Colour in a number square
A number square from 1 to 100 is a fantastic resource for helping to highlight the patterns that occur when counting in 2s and 5s. After the children have a good understanding that counting in 2s means adding two more each time, it is as simple as asking the child to colour in the numbers that you would say when counting in 2s. This gives them another strategy for counting on in 2s (similar to counting along a number line) and the layout of the number square really emphasises the pattern. Children will then intuitively carry on with the pattern and find themselves counting in 2s all the way up to 100. The task also produces an amazing (and simple) resource for linking counting in 2s to so many other areas of mathematical learning, including:
• the visual patterns and the number patterns (the numbers in each row end in the same digits). This also supports the child's ability to be able to count on to larger numbers, as they will be thinking about the patterns of how our number system works.
• how much of the square is shaded. Some children will be able to recognise that half of it is coloured, although this is a more advanced concept. However, if you keep the number squares, this is something that you can come back to. You can then extend it by linking to the fact that the children coloured one of every two squares.
• what would happen if we added another row. This again supports the child in counting to higher numbers.
• the fact that all of the coloured-in numbers are even. Again, this is a more advanced concept but the number square can be used for this in future in order to link to prior knowledge and understanding.
• how many squares are coloured in each line. This can be linked to "sharing" ten objects between two people.
• why there are 5 coloured squares on each row and why each row repeats the same pattern. This can act as an introduction to how many times one number goes into another.
The same ideas and conversations can be had by colouring in a number square in 5s. If you decide to colour two number squares (one each for 2s and 5s), you can then ask the children to explain the similarities and differences. This can be a really pleasantly surprising task and I am often amazed at the children's perceptions and understanding. Tasks like this are also good for helping children to develop their abilities to describe and express their thoughts and ideas. This supports their mathematical reasoning skills, which is something that I have seen the most talented mathematicians struggle with.

Note: If you are reluctant to keep making number squares, perhaps use a laminated sheet, taking photos each time for a visual representation.

This is very important to make sure that children really understand and extend their knowledge of counting in 2s and 5s. If you always start with 2 or 5, the child will become so familiar with reciting the sequence that they may lose the understanding of it as counting on and will just memorise the pattern.

Using a number square again might seem repetitive but can lead to really interesting and purposeful discussions. Starting at 1 and counting on in 2s can lead on to the introduction of odd numbers. Talking about the similarities and differences (vs starting at 2) can really reinforce some of their new knowledge. For example, there are still five coloured-in squares in each row, but it is now all of the squares that were not coloured in before. This presents a perfect opportunity to help children link mathematical topics; the two halves of the number grid make the whole.

You don't have to use a number square - you could use the '2 animals in each boat' resource above. This time, however, add a baby animal into the first boat with its parents, so that we start at 3 instead of 2. This is also a good time to use the many readily available resources and worksheets on sites such as TES and Twinkl. Tasks that require the children to fill in missing numbers are good for reinforcing the patterns. Games are engaging to play and the children have to learn to recall their knowledge quickly in order to win. Just make sure that you edit the tasks so that they don't always start at 2!

I strongly believe that it is important for kids to learn what it really means to count on in 2s or 5s. Learning to recite the sequence will be useful for times tables, but really understanding the process and investigating the patterns can lead to so many other mathematical ideas and concepts.