Thinking mathematically

  • Published on May 12, 2017

Mathematical thinking involves more than just being able to count and recite number facts. The ability to solve mathematical problems requires us to think flexibly and creatively with numbers. We need to see that there are multiple ways of interpreting a situation and reaching a solution. It is never too early to get children thinking.


An easy way to get started is to give children a variety of objects to count. Rather than always counting groups of similar objects; for example, counters, bottle caps, or teddy bears, it is important for children to realise that collections for counting can be composed of a variety of items.

counting coins

Of course, we usually have a context for counting; for example, items to be posted, people at a netball match, items found on the beach, or pens in a box. Sometimes it is important to group similar things for ease of counting or calculating; for example, money, items of cutlery, or clothes packed for travel.

If children are given the opportunity, they may spontaneously demonstrate their mathematical thinking in different ways, including thinking flexibly with numbers.

For example; let’s observe this illustration of children.

five children

Depending on their age and development, some children may need to count, others will be able to subitise (recognise without counting) that there are five.

When asked to make observations about the five children, that there are three girls and two boys is quite obvious.

Asking children to think of other ways they can see three plus two, encourages them to think flexibly and creatively while reinforcing understanding of number and developing recall of basic number facts. The responses can be surprising; for example, there are:

  • Three children with hats and two without hats
  • Three children with T-shirts and two children with button-up shirts
  • Three children with shorts and two children with blue jeans
  • Three children with stripes and two children without stripes
  • Three children with shoelaces and two children without shoelaces.

In what other ways can you see 3 + 2 = 5? What about 4 + 1 = 5?

Knowing that there are many ways of thinking about numbers, and that a number stays the same regardless of how it’s arranged (conservation of number), helps to consolidate children’s number understanding.

To help you support your children’s developing understanding of numbers up to ten, this week I have uploaded a new interactive resource, Exploring number combinations. This resource places a group of children (including the five shown above) at a park, arranging teams for a friendly game of soccer. Children are asked to consider how the teams might be arranged. Five pages in the story have set number sentences. The final page invites children to nominate their own number sentences and choose the participants.

A similar activity can also be conducted using children in the class, or a variety of objects (as shown in the illustration for “Nine” above).

In addition to developing understanding of number, this activity has potential for developing thinking and learning by encouraging:

  • thinking about things in new and different ways
  • looking for similarities and differences
  • observing detail
  • sorting according to different characteristics – which is important to both maths and science (think animal and plant classification)
  • having fun with maths

exploring number cover

Exploring number combinations encourages children to think of different ways of arranging numbers to ten in groups to match a given number sentence.

Of course, there are many other readilearn resources that focus on developing understanding of numbers to ten; including:

Ladybird spots cover

Ladybird spots – a fun interactive activity that encourages children to explore number. Children place spots on the ladybird’s wings to total the number shown. The ladybird’s wings turn red when the number is correct. A prompt to try again occurs if too few or too many are placed. Addition facts can be recorded to ensure all combinations are found.

One Lonely Ladybird – an animated rhyming counting story, ideal for supporting children who are learning to read the number words one to ten. With each verse, one more ladybird joins in until there are ten ladybirds in all, playing together.

Busy Bees and Insects – Subitising 1 – 6 – offers opportunities for developing skills of subitisation. It presents in random order the numbers from 1 – 6, each in five different combinations.

Check out other readilearn maths resources.

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I hope you and your children enjoy using these resources. Next week, I’ll be introducing you to Cynthia Mackey, author of the much-anticipated Katie Schaeffer Pancake Maker.

In the meantime, have a lovely week; and Mothers, wherever you are, enjoy your special day.

Thank you for reading.

Happy teaching and learning,


I appreciate your feedback and comments. Please share your thoughts in the “Leave a reply” box below.

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    This is a great post, Norah. It is very important to make maths fun for children. My own son, Greg, didn’t enjoy maths for years at school because all they did was times tables and other very dull stuff.

    I’m sorry to hear about your son’s experience with maths, Robbie. Sadly, that’s as it is for many children. Maths is all around us and is absolutely fascinating. It helps us understand the world. There is really nothing dull about mathematics; just the way it is taught. I hope Greg has learned to find more enjoyment in maths now. Thanks for sharing.

    I think much more should be done to make maths fun and meaningful in the early years. Thank you for reading and commenting, Irene.

    I do too Norah. I discovered at uni that I really enjoyed maths but when I took it as a subject I found I didn’t know the basics and just couldn’t keep up. If only I had those basics taught as fun rather than rote and punishment.

    I’m pleased you developed an interest in maths, Irene. Better late than never, but better earlier than late too! Thanks for sharing.

    Hi Norah,
    Great Blog!
    I LOVED teaching Maths when I was a primary school teacher, especially hands on practical Maths activities ….
    Karen Tyrrell author

    Thank you for your support of the post and of Maths, Karen. I loved teaching Maths too. It’s such fun when you ditch the workbooks and get to its real meaning.

Please share your thoughts. I love it when you do.

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