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PROBLEM SOLVING

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by

Laia Gibet

on 24 June 2014

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Transcript of PROBLEM SOLVING

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

FOURTH PROBLEM
Two children
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.
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

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.
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