These 2 questions were posed and in pairs or individually, we tried to solve them:
Before we started sharing our ideas, I asked, "If you saw these number sentences this time last week, what would you have thought?"
Some funny responses were shared and we all agreed that though they are complicated, our mathematical understanding has grown so much that we know how to solve them and why we solve them that way.
Just like yesterday, we used the same routine:
What do we do first?
Discuss with your partner.
Who can help us?
Using this routine kept us all thinking out loud and deepening our reasoning abilities especially when we kept discussing why, why, why.
What do these make us wonder?
- Is algebra really that simple?
- What other ways can we use order of operations?
- If someone in another country had this same question, would they also get the same answer?
What do these make us think?
- It's like traffic rules. We have to follow traffic rules when we drive or else people would have so many accidents. This is the same. We have special rules in maths so that people don't have accidents when solving them.
- It makes me think that maths is just a fun puzzle to try to solve. Even if we get the answer wrong, we still learn a lot.
- Today I've really understood what square root is; it's the opposite of squaring a number.
- It makes me want to create some complicated number sentences like these to see if my Dad can solve them too.
We then continued with our choice of challenge.
Either the 4 4s or creating number sentences that equal our ages.
The same high level of engagement and quality mathematical discussions took place.
Students expanded their thinking and understanding of how we can manipulate numbers and there was a lot of creative thinking involved too.
Some samples so far:
I like this idea of 'extras' they found that they could use later:
Reflecting is the most important part of the learning process.
For today's reflection, we used the 'I used to think.......and now I know.....'.
I added a new idea as a reflection choice: ' I used to feel.....and now I feel.....'
After writing our reflections, we shared with the whole class how are thinking or feeling has changed: