This problem solving activity has a number (all operations) focus.
Pizza Place has three tables of the same size.
The Chicken N Chips bar has four of the same tables and can seat 24 people altogether.
How many people can Pizza Place seat?
One third of the seats at Chicken N Chips are empty and a half of the places at Pizza Place are empty.
If 18 more people want to eat out, is there room for them at the two restaurants?
In this problem students must find fractions of sets. As they find equal parts using sharing, division or basic facts, and combine parts to find other fractions, the inverse relationship between multiplication and division is explored. Having students see and use the fact that division undoes multiplication and that multiplication undoes division, is fundamental to understanding fractions.
To solve this problem, students must see how information about one situation can be used to solve the problem in another.
Pizza Place has three tables of the same size. The Chicken N Chips bar has four of the same tables and can seat 24 people altogether. How many people can Pizza Place seat?
One third of the seats at Chicken N Chips are empty and a half of the places at Pizza Place are empty. If 18 more people want to eat out, is there room for them at the two restaurants?
The next day, one third of the seats at Chicken N Chips are empty and a half of the places at Pizza Place are empty. If 18 more people wanted to eat out but they did not want to share a table with the people who were already in the restaurants, how many would have to be turned away from the two restaurants?
Students will use a range of strategies to show:
24 people sitting at four tables in Chicken N Chips means there are 6 per table.
Pizza Place can seat 3 x 6 = 18 people.
One third of 24 is 8. So there are 8 seats vacant in Chicken N Chips.
One half of 18 is 9, so there are 9 seats vacant in the Pizza Place.
8 + 9 = 17 spare seats.
18 people are looking for a meal and 18 – 17 = 1, so one person will have to go elsewhere.
Think how the tables could be filled. At Chicken N Chips there are 8 spare seats, so this means 24 – 8 = 16 seats filled. As each table seats 6 and there are four tables, the 16 could be seated at three tables or four.
At Pizza Place, there are 9 people. They could be seated at two or three tables but not one.
There are three possible answers to this problem. First, all of the tables in both restaurants could be being used, so no further people could be seated. On the other hand, one table in one of the restaurants might be free. In this case 6 people could be seated. And finally, there might be a spare table in both restaurants. That would mean that 12 people could be seated.
The number turned away would then be 18, 12 or 6.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/more-pizzas-and-things at 8:55pm on the 26th February 2024