Te Kete Ipurangi
Communities
Schools

### Te Kete Ipurangi user options:

Level Three > Number and Algebra

# At The Movies

Achievement Objectives:

Specific Learning Outcomes:

Work systematically to find all the possible combinations

Description of mathematics:

This problem is first of all about being systematic. This can be done using a number of strategies. You might make an organized list, draw a picture or use equipment. The difficult thing for many students is to keep track of all the possibilities as they go along. This is especially difficult if they use equipment.

The maths behind the problem involves counting all the possible combinations.

Required Resource Materials:
Classroom chairs
Copymaster of the problem (English)
Copymaster of the problem (Māori)
Activity:

### The Problem

John, Jo and Chris have got seats for the movies. In fact their seats are F5, F6, F7. In how many ways can they sit in those seats?

### Teaching Sequence

1. Use 3 students and 3 chairs to pose the problem.
2. Ask the students to work in 3’s to solve the problem.
3. Circulate to see that the students are keeping track of their solution.
How are you recording your work?
How do you know that you have found all the possible ways?
How could you convince someone else that you have found all the ways?
4. Sharing of solutions
5. Focus on the methods that students have used to be systematic.

#### Extension to the problem

What would the answer be if another two had joined the three friends?
What if your whole class went?
What if the seats were in a circle?

### Solution

There are 6 ways for the students to sit on the seats.

 F5 F6 F7 Chris Jo John Chris John Jo Jo John Chris Jo Chris John John Jo Chris John Chris Jo

Here we give every student a chance to sit in F5. There are 3 choices for this seat. For each particular student in F5 we then have two choices for F6. Then we have only one choice left for F7. Note that 3 x 2 x 1 = 6 is the final answer.

#### Solution to the extension

The extension is possibly ambiguous. We meant to mean that five friends had five seats, though some students might take it to mean that the five students had just three seats. Either way is worth considering.

Here five friends can be seated in five seats in 5 x 4 x 3 x 2 x 1 = 120 ways. If there are 25 in your class, then there are 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This is a very big number. You might like to let the class calculate it.

On the other hand if the five friends are to be seated in only three seats, then there are 5 ways of putting the first friend in a seat, four ways for the second and three for the third. So it looks as if there are 5 x 4 x 3 = 60 ways. For the 25 members of your class you get 25 x 24 x 23 = something much more manageable than the number in the last paragraph! But then only three get to see the film!

AttachmentSize
AtTheMovies.pdf44.12 KB
AtTheMoviesMaori.pdf54.43 KB

## How Many Numbers ?

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a list).

## My Son is Naughty

Find factors of numbers

Work systematically

Use logic to explain away certain possible number combinations.

## Time Problems

Understand how positive and negative numbers can be used in an unusual practical problem.

Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, use algebra).

## The Escape

Find strategies for investigating number problems;

Find a common multiple of a group numbers.

## More Dartboards

Identify and describe patterns in numbers

Work systematically to find the possible outcomes