How can we show 8?

What does 8 look like?

How many ways can we show 8?

This was our thinking challenge today.

The purpose of the challenge was:

° to help us understand that being creative is a key part of being a mathematician

° to give an opportunity to explore the maths resources we have in our room

° to assess each learners' understanding of what a number is, thinking strategies they use, their mathematical communication skills, whether they prefer to learn alone or with others, and the ways the types of resources they choose to use

We discussed how we can use symbols for 8.

I drew the number symbol for 8 on the board.

How else can we show 8?

One child came and drew 8 tally marks on the board and explained how it represents 8.

Another child drew 8 lollipops on the board.

Another came and wrote 4 + 4.

Another drew 8 stars.

We noticed that we can show using symbols and that we can visually see the number 8 in different ways.

I explained that being a mathematician means being creative. 

We can use our imagination. 

We can look for connections and patterns to make discoveries. 

We can make mistakes and learn from those mistakes.

I then explained that either individually or with a partner, you can use anything in our room to discover different ways we can show 8.

Be creative with your thinking.

And with that, we excitedly chose resources to show 8.

Some creative thinking emerged:

This learner explained how 8 can be made up of different ways. 

2 + 2 + 2 + 2

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

5 and 3

a group of 4 with 1 and 3

a group of 4 and 2 2s

1 big 8

Listening to the way this learner explained her thinking was an interesting way to assess her mathematical communication skills as well as her number sense that numbers are made up from the parts of smaller numbers.

This learner explained how me discovered 8 ways to make 8. (You've got to love that sort of self challenge!)

I asked: How do you know they are all 8?

- They are the same length.

What did this help you understand about numbers?

- Numbers are made up of smaller numbers.

I noted how this learner decided to use numbers to show 8. He also showed he has a good understanding of numbers being made up of smaller numbers.

Some learners chose to use numicon to show different ways to construct 8.

Another learner was curious about the box of number racks in our room. She hadn't used the before. After some play, she was able to show 8 in a few ways. 

I asked: What did you discover?

- 8 can be 4 and 4

- 8 can be 3 and 5

This learner thought of using rods make tally marks to represent 8.

When another learner saw this, he remarked that he thinks that is 80, not 8.

I asked: Why do you think so?

- I know each rod is 10. There are 8 rods so that means it is 80.

Could it also be showing 8?

                                                            - If it is tally marks, yes. But it can also be 

                                                              80.

                                                            That is an interesting idea. So X has 

                                                            discovered a way to show 8 and 80 at the

                                                            same time?

Some learners chose to explore showing 8 using dice.

This learner chose to use paper and thought of different ways she could show 8. 

When I asked why she chose to use texta and paper, she explained that she loves drawing. 

She said that drawing can help her think better.

Interesting.

These learners collaborated to build 8 in many different ways. 

I asked:  Are you are each of these show 8?

- Yes, we checked by counting each one after we finished. 

I noted how these learners had thought of checking their thinking without being asked to. 

These learners chose to use lots of different resources to show 8. 

After we had some thinking time, we had a look at some of the different ways of thinking we did and those learners shared their thinking with us.

We then sat together to reflect on what we learnt.

Here are some of our ideas:

- We can show numbers in lots of different ways.

- Numbers are made up of smaller numbers.

- We can visually show numbers.

- We can use lots of different things to think about numbers.

- We can check our thinking to make sure we got it right.

Our group reflection showed that a lot of important understandings emerged for us to build upon and explore further. 

Creating own strategies to add with cuisenaire rods

After five years teaching Year 6 (Grade 5), I felt it time to challenge myself and so requested to change to Year 2 (Grade 1). 

Very exciting, fresh, new.

Extremely knackering.

With my previous blog, I felt I had got to a point with helping older primary children become inquiring mathematicians with less and less input from me their teacher.

Starting fresh in the younger years, I don't expect this blog to be as helpful, but I thought it would be interesting for me to reflect on how I can apply inquiry-based learning strategies with upper primary children with lower.


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Sometimes you make something up on the spot to continue exploring with the remaining ten minutes before the recess bell rings. This was one of those moments and I was really amazed with the great thinking that took place.


We have been exploring cuisenaire rods and already determined the value each has. 

In 2 minutes, make a picture using the rods. It could be a plant, a building, an animal, a person. Its up to you.

(Note: We only had rods for 1 to 5)


Here were some ideas:

After the 2 minutes, we then needed to think of a strategy to find the total value of all the rods we used to make our picture.


We had a photo paper showing the value of each rod to help remember.


This is when some very interesting strategies were explored.





This learner explained how he thought it was interesting that this both equalled 12 and started thinking why with rods nearby:

This learner thought of using a 'making 10 / compensation' strategy to add the numbers more easily:

This learner recorded how many of each rod value she had used as a beginning why to add:

This learner decided to put the rods in rows of 10; she explained that it was then easy to count by tens and see how many units were left over:

This learner created a strategy of trying to put the rods into groups valuing 5 each:

He then put his groups of 5s in a row and explained how he could now just skip count easily by 5 to get the total (he also thought it very lucky that his total was a multiple of 5 so he didn't have any left over units to count :)    )

This learner was inspired by classmate and took the idea further by finding out how many of each rod value he had as a beginning way to find the total:

This learner noticed there were lots of 2s so decided to skip count by 2s first and then found other numbers to skip count by:

To share and reflect, I took videos of some of the children explaining their strategies on their Seesaw accounts. We then watched these on our data screen: instant engagement - all eyes were 100% focused on listening.

In our reflection discussion, we noticed how there are many different ways we can see numbers and that there are many different strategies we can use to add.

These are some pretty great big ideas for us to discover and further explore. 


When we give children opportunities to explore, create and make their own discoveries with numbers, amazing thinking can happen.

A worksheet, I think, prevents children from being true mathematicians making their own discoveries, testing their own theories, experimenting with what works and doesn't work and making sense of numbers in ways that have real meaning to them.  

I really loved the creative thinking that took place with this and could see this also being used in upper primary years perhaps with all the rod values being used......