**PROBLEM SOLVING**

A woman and her 2 children want to cross a river.

To do so, they have only one boat in which only fit:

**SECOND PROBLEM**

THIRD PROBLEM

**Carla Cano, Sergi Compte, Laia Garcia,**

Laia Gibert, Núria Izquierdo

Laia Gibert, Núria Izquierdo

FOURTH PROBLEM

One adult and one child.

Two children

One adult alone

The boat cannot come back by itself

The kids cannot travel alone

FIRST PROBLEM

It was once claimed that that there are 204 squares on an ordinary chessboard. Can you justify this claim?

We have chicken and rabbits in a farm. In total, there are 23 heads and 76 legs. How many chickens do we have? How many rabbits?

What is the number of diagonals of a polygon?

How can they get to the other side?

Which is the minimum number of trips they need to do?

STEPS

1. Understand data and objectives

2. Devising a plan and strategies

1. Discover the nº of diagonals of polygons

2. Plan:

Do it mechanically with different examples

Draw conclusions

Try to find a formula

TRIAL AND ERROR

LOOK FOR PATTERNS

3. Carry out the plan

Do it mechanically: examples

GRAPHIC REPRESENTATION

Try to find a formula

Draw conclusions and patterns

+2

+3

+4

+5

+6

+7

Number of sides

___________________

2

and so on

STEPS

1. Understand the objective

2. Devise a plan

3. Look back

1. Find how many squares are in the chessboard

2. Count all the squares that can be done

3. Find the pattern

1. Understanding the problem

2. Devising a plan

3. Carrying out the plan

4. Looking back

We organized the data in order to know

better what we are required to do.

23 heads = 23 animals

76 legs = chicken legs + rabbit legs

Chickens two legs

Rabbits four legs

Number of chickens

Number of rabbits

What do we need to know?

FIRST WAY

SECOND WAY

REQUIRES USE OF ALGEBRA

(EQUATION SYSTEM)

NOT APPROPRIATED FOR PRIMARY STUDENTS

x + y = 23

2x+4y = 76

number of chicken

number of rabbits

total number of animals

number of legs

number of rabbits

number of chicken

total number of legs

The mainly strategy we used was a simple problem

smaller numbers

1. Supposing:

All animals are chickens 23 chickens 46 legs

23 chickens * 2 chickens legs =46 legs

2. Knowing the legs we still need:

Total number of legs 76

Legs we already have 46

3. Obtaining the legs we need:

- Changing one chicken for a rabbit we gain 2 legs each time.

- As we have 30 legs left we need to do the operation 15 times.

30 legs left : 2 legs we win each time = 15 changes needed 15 rabbits

4. Knowing the number of chickens:

23 animals in total - 15 rabbits = 8 chickens.

6. Checking:

15 rabbits + 8 chickens = 23 animal in total

60 rabbits legs + 16 chickens legs = 76 legs in total

76 - 46= 30 Legs we need to obtain

STEPS

Understand the problem and the data.

Devising a plan.

Carrying out the plan and keep it mind.

Looking back.

First travel:

The mom and a child.

If there are the father, the mother and two children, how can they get to the other side? Which is the minimum number of trips they need to do?

First travel:

Mom with one child.

Second travel:

The mom comes back to the beginning.

Third travel:

The mom and the child go to the other side.

3 travels minimum

(number of sides - 3)

starting vertexes

ending vertexes

7 travels minimum

Third travel:

The mom and the other child.

Second travel:

The child remains and the mom comes

back to the beginning.

Fourth travel:

The child remains in the boat and the

other child gets on the boat.

Fifth travel:

One child gets down and the father gets on the boat.

Sixth travel:

The father returns to pick up the other child

Seventh travel:

The father and the child go to the other side.

Strategy: graphic diagram

How can be sure that 7 is the minimum?

It would have no sense to consider 2, 4 or 6 travels as it would not be possible to come back.

The only possibilities are 1, 3, 5 and 7.

It is not possible to 1, 3 or 5 as there are not travels enough to all the family members to be in the same side.