Geoffrey L.

asked • 10/16/15

4th grade common core word problem

A teacher is taking his class to see a play. There are 24 students. The auditorium has 11 seats per row. There will be an adult placed at the beginning and end of each row, as well as after every 4 students. The teacher sits by himself. Including the teacher how many adults will be attending the play?
 
The answer is 10, but what equation can be used to prove this?

2 Answers By Expert Tutors

By:

Timothy P. answered • 10/16/15

Tutor
New to Wyzant

Excels in English. Strong in Math, Engineering and History.

See tutors like this
See tutors like this
See your other post on this question. https://www.wyzant.com/resources/answers/153477/grade_4_word_problem
Upvote • 0 Downvote
More
Report

Timothy P.

Geoffrey, I think the best method for you to solve this is by working it out in your head. However, since this is difficult, keep track of what you are thinking by putting it down on paper.


Draw four rows of eleven seats (representing the physical space).

Now note that we can only work eleven at a time and start creating your formula:
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]


Now, Note that you need an adult at each end of the rows.
[A] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]
[A] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]
[A] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]
[A] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]

Now start filling with kids until you get to 24 while remembering to include an adult after every 4 students.
[A] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]


Now you have 24 students, but wait... there is still two 'leftover' adults in the top row.
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]

Always re-read the question to make sure everything is accounted for... We need the teacher.
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]
[A] [S] [S] [S] [S] [A] [S] [S] [S] [S] [A]

Count the adults including the teacher and you have your answer!
Report

10/16/15

Timothy P.

Now... How do we turn this into a formula?...

Start with the given information:

24 students, 11 seats, X adults, 4 students continuously, 3 rows.
 
We want the adults (X) to be the solution.
We know that we will need to sit 24 students, so use that as your primary starting point.
We know we need 8 students per row. (Per almost always means divide or multiply)
We know we have 3 students per row.
We know we need to add (1) teacher. (So add 1)

X adults = ((24 students / 8 students per row) * 3 rows) + 1 teacher
Report

10/16/15

Mark M. answered • 10/16/15

Tutor
5.0 (278)

Mathematics Teacher - NCLB Highly Qualified

See tutors like this
See tutors like this
I am not sure what kind of equation could be used. So let me demonstrate.
One row
A s s s s A s s s s A    There are three adults per row. Now how many rows?
8 student per row need three rows to seat all 24.
3 rows · 3 adults = 9 adults
 
Plus the teacher is 10.
Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.