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.
I asked: What did you discover?
- 8 can be 4 and 4
- 8 can be 3 and 5
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?
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.
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.
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