Can someone do this Y4 maths question for me please?

[cantdomaths]

Brain is muddled...

There are 170 people in a hall.
There are 6 times as many girls as boys.
There are 6 more boys than teachers.
How many teachers are there?

I have Maths A level...but have also been drinking wine....

I will have to look up the bar method. Is it taught in school, and if so, which year? It sounds really intuitive, which is always a good thing in maths.

I asked DS. He had a completely different method. He decided the number of boys had to end in a 2 or a 7 so he tried 32, then 27, then 22. Took him about 2 mins. I'm not sure how he decided about the 2 or 7 so quickly though, or whether that was linked to Y4 syllabus.

Interesting that there are so many different ways of getting to the answer, but that doesn't necessarily make it a fair or useful question for Y4s who haven't been taught the methods.

@cornflakegirl, here you are:
The original and a the same, only tidier.
What she has done, once she got how to draw the teachers' bar, was to remove 7*6=42 children. What she had left was eight identical mini-bars totalling 170-42=128 people. Now she divided that by 8 and got 16, which is the number of teachers.
You see that in problems like these the difficulty is to understand how to draw them. Once you have done that, finding the solution is ALMOST trivial ;)

The way I did it was to add 6 to the teachers' bar so they were all the same divide by 8 and take away 6 to get the number of teachers. Again, trivial once you see the picture.

Pity that you canNOT see the pictures. I'll try to post them separately.

Here is the first

And here is the second one (what a drag!)

2D bars - that's what I didn't have!
That's a really cool method - thank you for sharing!

Try this one:

Paula and Mary had a total of £36. Paula had twice as much money as Mary. After each of
them bought a movie ticket, Paula had 3 times as much money as Mary.
a) How much money did Paula had in the beginning?
b) How much was a movie ticket?

The first question is easy, the second less so ;)

Now that I can do no problem!

How did you find the price of the ticket?

p-t=3(m-t) where p is Paula, T is ticket and M is Mary.
Substitute for the numbers from part a and solve for t.
I removed the bracket (so got 3m-3t) then added 3t to both sides, subtracted p from both sides, then divided.
Interested in anyone else did it differently.

Algebra is not allowed ;) this is supposed to be solved by a year 3-4 child, just like your one.

Placemarking to try these with DS1 tomorrow.

Arkadia Paula had £24 and the ticket cost £6. Lord, I am ridiculously proud I could do that. I can teach the maths required for A level Chemistry, but this kind of thing is usually beyond me.

I did:

Paula has twice as much money as Mary, so that's 3 parts, 2 for Paula, 1 for Mary. £36/3 is £12, so Paula has £24.

Then I just thought about the 6 times table, which 12 and 24 both feature in. If you subtract 6 from both, you get 6 and 18, which of course is 6 X 3.

Yay me, same level as an 8 year old. Eugh.

I have a different bar model to Arkadia, but it essentially shows the same thing.

I can't see the pics on my phone but having a bash:
To start with there are 3 shares of the £36, hence Mary has £12 and Paula 2 x £12 shares.

Then a chunk of Mary's share and a chunk of one of Paula's shares are spent. The remaining ticket-price chunk remains unspent in Paula's second share. For her to have 3 times as much as Mary, the ticket-price chunk would have to be equal in size to the 3 "remainders" of each share, hence ticket costs half of a share or £6.

I think I'm only getting it that way because it's an easy one though.

.... This makes me nervous. And makes me feel so thick. I cant even figure out where to start even reading peoples explanations. But then I can't do basic maths. Adding and straightforward subtraction is about my limit. I'm dreading when DS will need help with maths :(

Ok, my fault for choosing something with easy numbers. Try this one, and remember, you have to be able to do it for any number, decimals included, and any proportion of money considered.
@istilldrinkcava, you are pretty much on the money, see if you can replicate your effort.
No algebra allowed (this is a question for year 3-4) and no guessing necessary (the numbers could be way bigger, but the question would be the same)

John and James had £100 in total. John had 3 times as much money as James. They go to the
bookstore and buy a comic book. After that John is left with 6 times as much money as James.
a) How much did john have in the beginning?
b) How much was the comic book?

A) £75
b) £15

It’s a Singapore bar method problem, mathsnoproblem.com/en/the-maths/teaching-methods/bar-modelling/ The idea is to have equal bars or boxes for each category, so the boys get one bar/ box, the girls get six bars/boxes and as the teachers box is six less than the boys box you need to add six to it to make it the same size of a bar/ box as the others. In order to not alter the equation you then need to add six to the other side of the equation, which becomes 176. At this point you have eight boxes which equal 176, so one box equals 22. As the teachers box size is six smaller, 22-6=16. It is a more visual introduction to algebra. I have seen questions like this in a year 2 Singapore Maths textbook.

Year 4 teacher here. No need for algebra.
If not using Singapore bar method, which not all schools teach, then I'd expect to see a Trial and Improvement table:

E.g.
Teachers. Boys. Girls. Total.

1. 7. 42. 50
2. 8. 48. 58

10. 16. 96. 122 15. 21. 126. 162 16. 22. 132. 170

So 16 teachers.

Lost the formatting, but imagine 4 columns with the 4 headings and the given numbers in each column.

Nope, we can't apply it it the James and John problem. DS knew instantly that the answer was 15 but can't tell me why - I would love to know how his brain works.

Could you give me a clue? Eg do I need 4 shares, or 7 shares, or a different number?

(I know I can google, and am happy to if you prefer :) )

Right. Just done these with my y4 (I'm not in the UK, it's breakfast time here, but we do go to a British school).

Started with Paula and Mary. He instantly knew to split the total into 3 parts, so 24 and 12.
Then he said Paula's remaining money had to be divisible by 3, so went backwards through 3 times table - 21 and 9 didn't work, but a ticket of 6 did work.

The group of 170. He ignored the 6 less teachers than boys, and said 8 equal groups. Divided 170 by 8 (bus stop method) to get 21.something.
Tried the actual sum with 21 boys, 126 girls, 15 teachers. Added up to not enough people. So tried 22B, giving 132G and 16T.

Why do so many solutions feature 176 when we’re told there were 170 people in the room.

Surely 170 is the highest number you would work with?

Hattie - they are making the teacher group a better number to work with. If you had the same number of boys and teachers, there would be 176 people in the room.