Having Fun With Orders of Operations

Today we began with these two questions. We had a choice of trying to solve these individually or with a partner.

The reason we began like this was to:

° tune in

° reflect on what we have already discovered about the order of operations

° extend our thinking for parts of the order we haven't addressed yet. Its important that we give children time to create their own theories and test them out.

° see how we can make mathematical fun

After a bit, we looked at the first question.

What should we do first?

Discuss with your partner.

Who can help us?

- We do what's in the brackets first.

Why?

- Because it is an unknown value.

- We need to know its value so we can use it.

- Brackets have more power than other operations. They can change a number sentence a lot.

What should we do next?

Discuss with your partner.

Who can help us?

- We need to do the square root.

Why?

- It's also an unknown value.

- We can't use it until we know what it is.

What should we do next?

Discuss with your partner.

Who can help us?

- We need to calculate what the squared number is.

Why?

- It's also an unknown value.

So, why do we find out the square root before the squared number?

- They are equally powerful, but when there's an even power we read it like a normal sentence from left to right.

- We could find the squared number first because we still need to know its value. But it's like reading. We don't read from right to left.

What should we do next?

Discuss with your partner.

Who can help us?

We continued with this till we explained not only the how but the whys.

The 'discuss with your partner' routine at each stage is an effective strategy to encourage children to think more about the whys. Having a teacher or just one student sharing their thoughts isn't the most effective way for every child to learn. The more we allow children to talk or visualise their thinking, the better. 

It also energises what could be a fairly drab learning experience.

We did the same routine for the second question.

Children (like adult learners) are far more engaged when we give them choices.

So, to help them solidify and extend their understandings of the order of operations, we had two choices.

We began by looking at the 4 4s challenge. This is a well-known maths problem-solving activity that helps children think about number relationships and what operations do to a number:

To help us see the type of thinking involved, in pairs we tried to find a number sentence that equalled nought and then we shared.

We liked the one circle above until someone pointed out how it has the number 2 in which we cannot use.

We really liked the pair who took the numbers below zero:

4 - 4 - 4 = 0 + 4 = 0

We have recently enquired into positive /negative numbers so its great to see children still thinking and using them.

Looking at the last suggestion:

Someone challenged how it doesn't equal nought.

Oh! We forgot to say it has brackets!

Mistakes are great to make because they help us to learn.

What did we just learn from their mistake?

- Brackets REALLY are powerful!

- They can change the whole meaning of a number sentence.

Together we calculated how and then discussed why brackets have such a great power:

The second choice was:

Normally we have a choice of doing things in maths individually or in pairs / groups.  Today though, I wanted us to think aloud and peer teach each other, so we all did this with pairs.

Soon after some pairs wanted to buddy up with other pairs so they did that.

There was high engagement and a lot of wonderful mathematical discussions taking place.  

Time was nearly up and I asked whether we wanted to continue with this tomorrow or more on.

Everyone eagerly wanted to continue tomorrow.

That's a good barometer that it is engaging and challenging their thinking.

(I'll post pics of their ideas later)


Following Day's Link with Examples of Today