Thursday, 14 February 2019

miniMATHS - 7. Make a Star

This is my favourite.

I know - you're not meant to have favourite children.

But this one is where it all started. This was my first idea for the miniMaths series of tasks. So I think I had given it more thought and probably used it as the benchmark for what I imagined the other tasks would look like.

And this one has real maths behind it. As you build up your star, you are adding a constant value to your pattern - one rock for each arm of the pattern. It is symmetry. It is an arithmetic sequence. It is pre-algebra. It is the connection between repeated addition and multiplication. And it is fun. It makes a cool looking pattern.

This task is linked to EYLF - Outcome 4, focusing on the disposition of the learner. The task itself is open enough to allow creativity and curiosity. It can be done as a collaborative and cooperative task. It can help students develop confidence and perseverance. 

Give it a go - it is a great task.

Wednesday, 13 February 2019

miniMATHS - 6. Stacking

This is fun. I know - I could spend hours doing it. In fact, I used to get kids to do it when I was on playground duty and I would challenge them to get 5 rocks stacked on top of each other.

But where is the maths?

Well, there are a couple of ideas here that need to be explored.

1. Have you ever worked with kids (probably Year 2 or Year 3) who had the idea that when constructing a "sum" (or algorithm - addition or otherwise) you had to start with the big number and then perform the subsequent operation on it? And isn't there an addition strategy for counting on that says you need to start with the big number first? Is this somehow related to stacking up rocks or other items where it is a good idea to put the big one on the bottom of the stack? Please note, I'm just asking the questions here - not providing the simple answers.

2. Or could this be a revelation of the mathematical concept of combining different values to create new one?

3. Or is it an exercise in balance, similar to an equation where one side has to equal the other?

4. Or are we playing the mathematical idea of prediction - what happens if...?

Perhaps the EYLF will give us some insight:

The EYLF certainly talks about "balance" as an important element of growth. This task provides a neat entry point for this conversation.

This task will also provide an opportunity for students to develop perseverance - to try to get that stack higher and higher. It will also encourage students to reflect on their unsuccessful strategies and modify and improve on the performance. 

So, just as in the "Shadows" task, this activity may not appear at first glance to be explicitly "mathematical", there is great capacity for students to explore deep mathematical thinking by attempting the stacking task.

If you haven't seen it yet, there is a miniMaths website:

And for people based in the Canberra region, I am running some workshops in preschools and early learning centres over the next six weeks. Details can be found on the miniMaths website.

See you there. 

Tuesday, 12 February 2019

miniMATHS - 5. Shadows

Sorry about the delay of a few days there - we went back to school last week and I have been a bit distracted getting the class into shape..

So here we have possibly the first major deviation in the miniMATHS resource tasks. This task, "Shadows", moves away from activities that have direct mathematical concepts as a focus, such as extending patterns or investigating area, to a place where we are investigating a natural phenomenon, such as shadows, using mathematical skills and knowledge. No longer playing directly with maths - now we are using maths as we play with something bigger.

Shadows are fascinating. There is so much that we can learn by observing them. They are a great leaping off point for exploring time; they are an explicit example of change; we all have that follows us around - and there are lots of games you can play with them.

All of the things that are suggested as activities associated with this task can be investigated using mathematical language. This is a key opportunity to develop our use and understanding of words that describe position, shape, movement and change.

This task is a great way to engage directly with the natural environment in an explicitly mathematical way. We can record changes over time using the outlines of shadows drawn on the ground. We can discuss the position of the light source relative to the object casting the shadow and the shadow itself. 

The EYLF talks about knowledge of and respect for the natural environment. This task will give students a greater understanding and appreciation of what happens in the world in which they live, helping them to be connected with it and to learn respect for it.

Is it "maths by stealth"? Sneaking a bit of maths into a fun exploration of a cool phenomenon? 

Well, I would say no - this is what real maths is: using our skills and knowledge to make sense of the world around us. And hopefully we can start this in early year education with young kids, engaging them as mathematicians to learn more about their world.

Friday, 25 January 2019

miniMATHS - 4. One More

Task 4 - One More.

Seems like a very simple task.

You make a line of objects.

You partner makes a similar line - then adds one more.

Seems simple because it is simple. But it is also the beginnings of some very significant mathematics. 

- One to one correspondence (I make a line, you make a line) is the starting point for counting and giving a value to a collection of objects.
- "Adding one more" builds the idea of how numbers grow, how to build a sequence that increase by regular steps, how to think about addition.
- This is also pre-algebra: x, x+1....
- And we are learning about more than and less than.

Similar to Task 2 and 3, this task focuses on EYLF Outcome 2, "Children are connected with and contribute to their world."

One of the big ideas that is raised in this task is the idea of equality. In a mathematical sense, we are talking about the balance between two values. In a broader sense, we can take this conversation to include equality between people.

Equal shares is an important lesson in childhood. We can use this maths task to springboard into a discussion of how we should live with each other. From this, we can also develop strategies for dealing with inequality. 

Check out the miniMaths website:

Thursday, 24 January 2019

miniMATHS - 3. Same Same Different

This task - Same Same Different - is a fun game that children can play in many different contexts. It asks children to collect a set of three objects, two of which have a common feature that is absent in the third object. It is easy to see the potential for individual variation. And it also encourages children to think and to explain their thinking.

The suggested variations take the task into new places. "Same Same Same" asks the children to find common features in all three of their objects. "Different Different Different" turns the task upside down, requiring the children to identify differences between each of their objects.

And how is this task mathematical? Isn't it just a matching game? Well, at it's heart, this task is framing up some elementary concepts of algebra - finding common values, identifying sameness and difference, using logic and reasoning. These concepts are also important in numerical operations such as addition, subtraction, multiplication and division.

One aspect of the EYLF Outcome 2 looks at finding similarities and differences between people. Sound familiar? Isn't this the overt purpose of this task, finding same and different? This task can provide an ideal opportunity to promote conversations about diversity and individual differences. 

In the context of play, children can be encouraged to consider deep concepts and to start thinking about their own place in the world. Their connection with and contribution to the world is significant and should be nurtured through positive learning experiences such as this.

The miniMaths website can be found here: 

Wednesday, 23 January 2019

miniMATHS - 2. Big Bigger Biggest

This is my favourite task. If I was in pre-k, I think I could have spent hours with sticks or rocks, lining them up in order of length. Actually, I probably did when I was.

The big idea behind this task is prompted by something I heard Nora Newcombe say at a conference last year. (Nora is a significant voice in mathematics education and research and has written heaps)  She said that her research had found that, while a sense of number was not something that babies are born with, they do seem to possess an innate sense of "magnitude" - something being "more than" something else.

So I was interested to include a task where students can develop this skill, looking at objects and arranging them based on an attribute such as length or area. This task also provides an opportunity to reverse the process, to look at small, smaller and smallest. 

It is not an accident that this task has used the nominative, comparative and superlative. This gives important links to grammar and language development in an informal context.

This task is linked to the second outcome from the Early Years Learning Framework:

Children are connected with and contribute to their world.

A big idea linked to this outcome is "change" - and this can be explored through the task by developing groups of objects that grow in a certain direction - by length, height, mass, area or in some other way. Children can see how they can add new objects to their sequence to make it grow. 

Once again, if anyone gives this one a go and has any feedback, please let me know. I would love to hear about it.

And here's the link to the website: 

Tuesday, 22 January 2019

miniMATHS - 1. How many leaves?

from the "miniMATHS - Maths Inqiries in Nature" booklet

The tasks are organised based on the Early Years Learning Framework (EYLF). I linked each task to one of the five outcomes and put them in numerical order.

Outcome 1 - Children have a strong sense of identity
Task 1 - How many leaves?

The task is simple to set up. Draw a square in the dirt. See how many leaves you need to fill it up.

It is measuring area using informal units.

But you can take this to interesting places:

- move the leaves around in different arrangements to see if the number you need stays the same
- try using different types of leaves
- try using different sized shapes to fill up
- even try using the children themselves to fill up big spaces

One of the important ideas we want to experience is that "area is the space inside". And we can measure it.

from the "miniMATHS - Maths Inqiries in Nature" booklet

One of the important ideas presented in the EYLF outcome #1 relates to perspective. The "How many leaves?" task provides opportunities for students to explore the area of the square in many different ways and to understand that different people will find different solutions.

"Comparison" is another important concept that this task highlights, finding the area of a shape and comparing materials and strategies to complete it.

This task is ideal for small group interaction and is firmly based in the Nature Play pedagogy, using natural materials in a natural setting. Students can play with the idea and modify it to pursue their own questions and interests.

I would be interested in getting feedback from teachers who try out this task in their own schools. I would be particularly interested in hearing what the students have to say. 

Let me know.


Here's the miniMATHS website: