Tag Archives: Mathematics

Logical thinking and problem solving – Readilearn

logical thinking and problem solving

Logical thinking and problem solving are important skills for children of all ages to develop, including those in early childhood classrooms. We employ thinking skills each day, in many situations, from deciding the order in which to dress ourselves, complete simple tasks, collect items for dinner or set the table; through to more complex problems such as assembling furniture, writing work programs, juggling timetables, and organising class groupings for activities.

This week I am excited to upload a new interactive digital story that encourages children to use logical thinking to solve a problem.

Dragona's Lost Egg

Dragona has lost her egg and turns to her friend Artie, owner of a Lost and Found store, for help. Artie is confident of helping her as he has many eggs on his shelves. He asks Dragona to describe features of her egg, including size, shape, pattern and colour. He uses a process of elimination to identify which egg might be Dragona’s. Children join in the process by choosing eggs with the characteristic described.

What is Dragona’s egg really like, and will Artie be able to help her find it?

You’ll have to read the story to find out.

The process of writing this story also required a problem to be solved; and I love nothing better than a good problem to solve.

What’s an ovoid? Do you know?

what's an ovoid


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Is the ‘right way’ always the best way?

Giving children opportunities to question, to be creative, and to problem solve are high on my priorities. Children need to be given the time and opportunity to figure out things for themselves. While it is sometimes easier just to tell or show them what to do, or even do it for them, it is generally better for their development, to let them have a go at finding a method or solution. Please note: I am not talking about dangerous things here like playing with fire, testing to see how fierce that dog really is, or driving a car.

If children are constantly told there is a right way of doing things, they will stop exploring, discovering, and inventing their own or new ways of doing things. This is an issue because, if we always do what we’ve always done, we’ll never progress. There is generally no harm in, but much to learn from, each successive attempt.

Opportunities to explore, discover, and use intuition are also important to the development of mathematical thinking. When children are developing understanding of number, they often invent their own strategies for working with numbers. Sometimes, as attested in this paper by Heirdsfield, Cooper and Irons, the strategies used display more advanced thinking, and are more efficient, than those taught as ‘the’ correct way of solving a problem using pencil and paper.

I have noticed a change in the speed and agility with which my seven-year-old grandson works with numbers now that he has learned there are certain ways of; for example, adding two numbers. He tends to second-guess himself as he attempts to mentally calculate using the pencil and paper method he has been taught, rather than other more effective strategies he had previously invented and used. Perhaps you have noticed something similar.

Provocations, such as these 3 Fun Inquiry Maths Activities for the Last Week of School by Steph Groshell on Education Rickshaw,  are great to get children thinking about different ways of solving real problems.

Little Koala’s Party – a story for problem solving in the readilearn mathematics resources also encourages mathematical thinking and planning. Children help Little Koala organise a party for her family and friends, deciding who will be invited, the number of guests, and what’s on the menu. The suggestion is made that children plan a party of their own and they are asked to consider how they would go about it. The discussion and sharing of ideas, rather than the imposition of one ‘right’ way, is the important thing in developing mathematical thinking.

Now it might seem a stretch to tie this in with a piece of flash fiction, but I hope you’ll be able to follow my thinking through the mist and into the light.

This week at the Carrot Ranch, D. Avery took the reins from Charli Mills and challenged writers to in In 99 words (no more, no less) write a story that symbolically, mythically, mystically, or realistically involves dawn, as a noun or verb. Write about the dawn of time or the time of dawn, or the dawning of an idea. As always, go where the prompt leads.

The right way

Father and Son sat side by side. Father cracked his knuckles and sighed repeatedly while Son sharpened his pencils, each pencil, and arranged them meticulously according to undisclosed criteria.

“Come on. Just get it done. Then you can play.”

“I’m thinking.”

“Think faster.”

“I know it’s 96.”

“Well write it down.”

“Sir says I have to do the working out.”

“Then do it.”

“I don’t know how.”

“Like this. See.”

“That’s not how we do it. Sir says…”

“Then do what Sir says.”

Slowly it dawned on Dad: Sir’s way may not be the best way for all.

Thank you for reading. I appreciate your feedback. Please share your thoughts.


Getting active with maths – Readilearn

Many games involve children in practising maths skills, and playing games is a great way of incorporating fun into the maths program. With the additional benefit of supporting the development of social skills and, oftentimes, literacy skills, there is no reason to not include games. A daily dose of fun with maths contributes much to an enjoyable classroom experience, developing positive attitudes to maths, in addition to providing opportunities for consolidation and practice of maths learning.

Adding a little physical activity to the game increases the benefits, and there are many simple games that can be played with the whole class, indoors or out; some that require equipment and some that don’t; some that take just a few minutes, and some that take several. Many games can be invented on the spot to suit current learning.

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Shaping up – activities with 2D shapes. – Readilearn

Shapes are all around. Everything we see has a shape. Some of those shapes are regular, some not so regular. In early childhood, children are introduced to the basic regular shapes of circles, triangles and rectangles, including the special rectangle that we call a square.

Even before they begin formal learning, most young children can recognise and name these four basic shapes. They see them in picture books and encounter them in puzzles and games.

But learning about shape goes much deeper than just being able to recognise and label those colourful images.  An understanding of shape has relevance to many other activities such as reading maps, construction, laying tiles, and stacking items. They need to know how shapes can be combined to form others, and what happens when they are cut, flipped or turned. They will use their knowledge of shape in more advanced geometry such as finding perimeter, area, and volume.

The colourful, and sometimes humorous cartoon-like, ways in which shapes are introduced to young children, can make them appear fairly basic, and parents and teachers may state with pride, “My child knows all the shapes.” But with shape forming a basis for so much other understanding, it is important to use language that enables understanding and discourages the formation of misunderstanding.

Misunderstandings occur when objects

Continue reading: Shaping up – activities with 2D shapes. – Readilearn

Fair trade – what’s it to you?

What do you think of when you hear the word “trading”?

International trade? Stock market trading? Trading one item for another? Perhaps a Trade Fair, or selling items at a market stall? Trading as your *business name*? Maybe you are committed to purchasing “Fair Trade” in support of the  World Fair Trade Organisation’s aim of making international trade more equitable?

As an early childhood teacher, I think of trading games that we use in maths lessons to help children understand place value. In our decimal system, we use ten digits in various combinations to represent numbers. Placement of each digit is vital; for example, 290 is very different from 902.

Without a firm understanding of place value, it is difficult to work with numbers efficiently. I believe that many difficulties with number stem from insufficient understanding of place value. Children need to experience numbers in a variety of contexts to fully understand the decimal system.

For younger children just beginning to learn about two-digit numbers, we may connect interlocking blocks or bundle popsticks to form groups of ten.


When children have a firm understanding of the grouping process, and the way the numbers are represented with two digits, they move to a similar process with numbers over one hundred. It is at this time that we introduce trading.

Instead of using interlocking cubes or other items that can be linked or bundled, ten individual cubes are traded for one ten, and ten tens are traded for a one hundred flat, and so on.

I feel so strongly about the importance of children learning place value, that I have made a variety of resources for teaching it. The resources, available from readilearn; include:

Beginning place value – the train game

Race to 99 – A place value game for maths groups

The interactive resources

Let’s read 2-digit numbers

and Let’s write 2-digit numbers

Playing games has always been a favourite activity for me, and always popular for family gatherings. We’d quite often we’d spend holidays, like Christmas and Easter, when the children were growing up, playing board games or card games. One of our favourite games, especially if there were larger numbers of people (up to ten) was a trading game called “Billionaire”. It is a raucous game. Everyone is engaged all the time. Play involves trading cards (commodities) with each other, and this involves much shouting (over the top of each other) and laughter. If you have never played it, but enjoy games, and have a group of four or more to play, I highly recommend it. (Sorry, I couldn’t find it to add a photo. It’s hidden away in the games cupboard somewhere.)

I couldn’t write about trading without mentioning Jack and the Beanstalk. Mother sends Jack off to the market to sell the cow. Along the way, he meets a man with a handful of “magic” beans which he offers to trade for the cow. Not having heard the saying, if it sounds too good to be true, it probably is, Jack agrees. Of course, Mother is none too pleased and throws the seeds out the window. But, as the story shows, Jack was right to trade and rewarded for his ignorance of the oft-touted adage. (The story also raises other issues regarding trespass, theft, and causing fatal injuries. But we won’t go there this time.)

This week at the Carrot Ranch Charli Mills has challenged writers to In 99 words (no more, no less) write a story about trading. It can be the profession of old or of modern day traders on Wall Street. It can be trading places or lunches at school. What is traded? Is it a fair deal or a dupe? Trade away and go where the prompt leads you.

For my response I’ve ended up in the playground yet again. It involves a little trading of cards, but more a trading of power. I hope it works.

Trade fair

Cards, were coveted like gold. To belong, one was enough; more better. Each lunchtime the boys showed off new acquisitions, compared intelligence and strength points, and traded duplicates. Fair and friendly battles pitted minds, the winner claiming card supremacy. Then bully Boris won, and none dared challenge. Until Justin, tired of Boris’s tactics, dared.  The group gasped. It seemed Justin would be crushed. But clever cardless Frank slipped in and showed the winning move.  Boris growled, “Inadmissible” and threatened repercussions. Defiant, Justin handed Frank a card, bestowing membership. Empowered, each boy followed, declaring Frank the Master, and trading opened.

Thank you for reading. I appreciate your feedback. Please share your thoughts.


Thinking mathematically – Readilearn

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

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Number combinations – Readilearn


Mathematics is all around us. We use it every day for a wide range of purposes; from deciding on the sequence in which we dress ourselves, to calculating how much time we have available for an activity.

Number is just one component of mathematics but the ability to use it confidently and competently is essential to life in the 21st century; from managing one’s finances, to calculating time and distance, to knowing how many followers one has on social media.

The views that people hold of themselves as mathematicians, and their attitudes to mathematics in general, are formed early in life. It is important that we early childhood teachers provide children with mathematical experiences that are meaningful, engaging, and in context.

readilearn mathematics activities are designed to support you in doing so by providing a range of digital and printable resources that encourage mathematical thinking and discussion alongside hands-on experiences. It is important to provide children with a variety of learning contexts to encourage the development of “I can do it” attitude to number and maths.

Number combinations

A child’s ability to count is sometimes seen as an early indicator of ability with numbers. However, an understanding of number requires far more than


Continue reading at: Number combinations – Readilearn