we began with the question:
34 + 56
We used the think-pair-share routine to list and create as many different ways as we could to solve it.
We didn't need to think of the most effective strategy.
In fact, since we know maths is about creative thinking, we were to try to create our own strategies- even if they are so complex we would never really use them.
A lot of fascinating and creative ideas emerged:
We then did the same with this subtraction question:
After sharing and discussing the strategies, we discussed:
What did this make us think about?
- There are many different strategies.
- Some strategies can be more effective than others.
- Visualising is an important way to understand numbers.
- When we are creative, we can discover why some strategies work and why others don't.
- We need to be mindful of place value when trying to create a new strategy for them to be successful.
What theories are we making?
- My theory is that there are more addition strategies than subtraction strategies.
- My theory is that you can always check an addition answer by subtraction it and vis versa.
- My theory is that if you mix up the place values of numbers, you won't get the right answer.
- My theory is that it is easier to make a mistake with subtraction than addition because it is easier to visualise what you are doing when you add.
What wonderings do we have?
- Does it matter which strategies we choose to use if we get the answer?
- Why is it easier to create addition strategies than subtraction?
- Could we use all the addition strategies we thought of to answer the subtraction question and vis versa?
- Are some strategies better than others depending on the numbers being used?
- Was addition invented before subtraction or were they invented at the same time?
These are some really great wonderings to help shape our enquiry into addition and subtraction.
Whilst all this was fresh in our mind, we then did a think-pair-share to create a Venn diagram comparing / contrasting addition and subtraction.
The discussion extended and challenged a lot of our thinking especially the relationship between addition and multiplication and subtraction with division.
Having discussions like this help deepen children's conceptual understandings whilst also helping to address some misconceptions children have.