I “think” we understand now. I think the problem was being taught a set of rules rather than being taught the concept, the why. When the rules changed ( different teacher) panic and anxiety set in.
We have now got homework to do!
Thank you all!

6 - 2 + 4 x 5 / 2 + 9

Brackets first: There are none.
Order second: There are none.
Multiplication or Division third: There are both.

4 X 5 / 2. You can choose whether to do:
(4x5)÷2 which is 20÷2 = 10
Or
4 x (5÷2) which is 4x2.5 = 10

Once you've done that, you can rewrite your sum: 6 - 2 + 10 + 9

Now you only have Addition and Subtraction to do. As it doesn't matter which order, you can either add all the positive numbers together (25) and subtract 2, making 23, or do the sum in order 6 - 2 (4) + 10 (14) + 9 = 23.

6 - 2 + 4 x 5 / 2 + 9

First multiplication & division

4 x 5 / 2 you can do as either 4x5=20 divided by 2 = 10 or 5/2 = 2.5 then 4 times that which miraculously still = 10

So now we have 6 - 2 + 10 + 9

you can do that in any order you like eg
6 add 10 add 9 makes 25, subtract 2 makes 23

or 6 subtract 2 makes 4 add 10 makes 14 add 9 makes 23

or negative 2 add 10 makes 8, add 6 makes 14 add 9 makes 23

BUT you must make sure that negative sign sticks tightly to the 2
6 - 2 + 10 + 9 What you must not do is say 2 add 10 add 9 makes 21, so 6 subtract 21 is negative 15.

The - sign means negative 2, it doesn't mean subtract everything that comes to the right of it until you get to the end.
ie it is ABSOLUTELY NOT 6 - (2+10+9)

Still don’t understand if the multiplication and division takes order precedence over addition and subtraction in a sum like the one below

6 - 2 + 4 x 5 / 2 + 9

Would that mean that according to the bidmas/bodmas rules (two names for same thing ..... it’s super easy kids) would mean

Order of events for sum
6 - 2 + 4 x 5 / 2 + 9

4 x 5 first
Then divide that by 2
Then do the first bit 6 - 2
Then finally + 9

Please can somebody really spell it out this system like I’m a kid as it’s not going in

It’s better that the mathematical principles are taught without over reliance on sticking rigidly to the acronym.

True...

Though I'm starting to have traumatic flashbacks to my first year undergrad mathematical logic course and Polish notation and operator scope .

en.wikipedia.org/wiki/Polish_notation

Don't think I ever quite understood it. I mean, I sort of got what it was about conceptually, but actually using it in anger? Hell, no!

5 x 5 - 3 / 2 + 2

The key thing is you have no brackets, so multiplication and/or division take precedence over the addition/subtraction. So start with the stuff that needs multiplied or divided.

That will give you constituent bits for your eventual sum as follows
5 X 5
3/2
2

giving you 25, 1.5, 2 which you then put together thus: 25 - 1.5 + 2

25.5

(or if you prefer to think of it Purple's way, you have
25, -1.5, 2 which have to be added up).

The whole point of BODMAS/BIDMAS is that you do it in that order.

(5 x 5) - (3 / 2) + 2

25-1.5+2 =25.5

1.Brackets
2.Indices/Order
3.Dividing/ Multiplication (of equal importance)
4.Adding/Subtraction (of equal importance)

Also can somebody please clarify the order that you have to follow to solve the following sum?

5 x 5 - 3 / 2 + 2

To solve the above would you have to tackle the multiplication and division aspects before you do the subtraction and addition aspects ?

Eek! My year 6 dd has just done this. She loves maths and is great at it. Me, not so much! Either we never did this at school or I've blocked it out!
Can't think of a situation where I personally might be required to use it.

Oh gosh. Usual for year 7 then? I expected a lot of going over old ground, over learning, working out where the kids where, post the March-July shutdown.
She was taught BIDMAS in primary but she didn’t understand it then either.

10 - 8 (2) +7 = 9
or
10+7 (17) - 8 = 9

Because the - sign is attached firmly to the 8.

This is normal for year 7. I’ve done orders of operations with year 6.

Yes, it is Y7. Good luck!

Yes it is usual y7 work.
They need to recap BODMAS (done at primary) before they can do algebra.
They need to understand that 3y^2 where y=4 equals 48 and not 144.

Fwiw America they say PEMDAS:

Parentheses (brackets)
Exponent (powers)
Multiply
Divide
Add
Subtract

-just posting to reinforce the point mult/divide can be done either way around. Same for add/subtract

Thanks. I’ll show this to DD-tomorrow. Can’t take anymore tonight.
No, it doesn’t make sense to me. I scrapped a C at the early GCSE where we used calculators. DH is better at maths than me but less qualified!
Is this usual Y7 work?

Purple is right. Maybe a worked eg will help.

First example
6 5/ 2+ 3 = 6 / 2 5 + 3 = 18

Doesn't matter what order you do the multiplication and division in.

Second example
But (4 + 5) / 3 = 3
Brackets tell you to do the addition first

Versus
4 + 5/3 = 5 2/3
In the absence of brackets you do the division first

Give you different answers.

Third example
5 + 1 - 3 = 5 - 3 + 1 = 3
Doesn't matter what order you do the addition and subtraction in.

(But note: because it doesn't matter, this means you won't get it wrong by arbtrarily telling children BIDMAS such that they always do division before multiplication and addition before subtraction. You could equally well have taught them BIMDSA, but conveniently it doesn't matter.)

For your example tween, my students have been battered into knowing that the - sign cannot be separated from the number after it.

So... 10 + (-8) + 7

7 + -8 = -1

10 + (-1) = 9

We were taught BIMDAS at school (1970s). Our maths teacher spent a whole lesson illustrating why BIDMAS was wrong. He was a brilliant teacher and made everyone love maths. Doesn’t help but it did remind me of him...

If you have 10-8+7 you have to get the answer 9.
What you don't want to do is calculate it as if it said 10-(8+7) by doing 8+7 before subtracting.
As long as you realise that you are probably OK.

Now trying to think of an example for the * / issue.

B I {D,M} {A,S}

D M are inverse operations so can be rewritten as the other. Likewise A S. So x0.5 is the same as /2.

Hence L to R once priorities are sorted