Problem 6 - Teachers’ meeting
Problem 6 is about a group of maths teachers are having a ‘hybrid’ meeting. The challenge is to work out how many teachers are in the meeting room and how many are joining the meeting online.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
CHRIS In this challenge, a group of maths teachers are having a hybrid meeting.
Some of them are in the room and some of them are joining online.
Our job is to calculate how many are in the room and how many are joining the meeting online.
Two thirds of the teachers are in the room and the rest are joining online.
After a tea break, four of the teachers do not return to the meeting room, but an extra two join the meeting online.
Now, there are just as many online as in the room. How many teachers were in the room at the start of the meeting?
At the start, two thirds of the maths teachers are in the room and the rest are online.
After a wee break, exactly half of them are in the room and half of them are online. So we’ve to work out how many people were actually in the room at the start of the meeting.
PUPIL You can use trial and improvement. Start with a number and keep adjusting until you find the answer.
CHRIS What would two thirds of fifteen take away four give us? Ten.
Ten take away four is six.
PUPIL Try comparing different fractions to work out the answer.
CHRIS Then we need to do… We need to check, does that match one third of fifteen plus five?
What’s one third of fifteen? Five, add two.
PUPIL Seven.
CHRIS Oh so close. Right, we got six and seven for our two answers and we wanted them to be the same.
PUPIL You can use some algebra to work this one out.
CHRIS Whether we used symbols or whether we used algebra, whether we use letters. We were able to write down expressions for how many people were in the room and how many people online.
PUPIL Give it a go.
So here's the challenge:
A group of mathematics teachers are having a ‘hybrid’ meeting.
- Two thirds of the teachers are in the room and the rest are online.
- After a tea break, four of the teachers do not return to the meeting room but an extra two join the meeting online.
- Now there are just as many online as in the room.
How many teachers were actually in the room at the start of the meeting?
Need a hint?
You might want to use some algebra to work this one out.
You can use When using trial and improvement, guess what the answer might be, then improve on it until you get close to the correct answer.. Start with a number and keep adjusting the numbers until the correct solution emerges.
Solution
Worked out the answer? Here's how you can do it.
This challenge was about a maths teachers meeting, where some teachers were in the room, and some were meeting online.
Let's use some algebra to work out how many teachers were in the room at the start of the meeting.
Let n be the total numbers of teachers at the start of the meeting.
We know that two-thirds of the teachers are in the room, so one-third of them are online.
The number who are in the room is two-thirds n, and the number online is one-third n.
After the tea break, the number who are in the room is two-thirds n take away four.
And the number online is one-third n plus two.
Since these numbers are equal, two-thirds n take away four equals one-third n plus two.
We can simplify this by taking one-third n off each side.
For one-third n take away four, equals two.
And we can then add four to each side, giving us one-third n equals six.
And then, multiply both sides by three to find out what n is.
There were 18 teachers at the start of the meeting, and two-thirds of them were in the room.
Two-thirds of 18 is 12. So, there were 12 teachers in the room at the start of the meeting.
And one-third of them were online. And one-third of 18 is six.
This question could also be done using trial and improvement. Maybe starting with 20 teachers in the room and 10 online, and adjusting the numbers until you get the correct solution.
Did you work it out?
This challenge was about a maths teachers meeting, where some teachers were in the room, and some were meeting online.
Let's use some algebra to work out how many teachers were in the room at the start of the meeting.
Image caption, Let n be the total numbers of teachers at the start of the meeting. We know that two-thirds of the teachers are in the room so one-third of them are online.
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There were 18 teachers in total at the start of the meeting.
Two-thirds of them were in the room.
Two-thirds of 18 is 12.
So, there were 12 teachers in the room at the start of the meeting.
And one-third of them were online.
One-third of 18 is six.
Trial and improvement
This question could also be done using When using trial and improvement, guess what the answer might be, then improve on it until you get close to the correct answer..
Perhaps you could start with 20 teachers in the room and 10 online. Then adjust the numbers until you get the correct solution.
Maths Week Scotland 2022. list
Try out all the daily challenges from Maths Week Scotland 2022.
Maths Week Scotland 2021. list
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Maths Week Scotland 2020. list
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