Problem Solving Problem Solving • This package

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Problem Solving Problem Solving • This package Powered By Docstoc
					Problem Solving
• This package is designed to promote the
 teaching of and raise the awareness of
 problem solving in schools. It is an outline
 for an Inset day that lends itself to
 adaptation to suit the needs of any school.
               Programme of the day

9:00    Coffee and Introduction
9:15    Skills pupils need to solve problems
10:15   Problem solving strategies
10:45   Coffee
11:00   Act it out
11:30   Draw it out
11:45   Use Equipment
12:15   Using a diagram
12:45   Lunch
1:30    Use a list
1:50    Trial and Improvement
2:10    Draw a table
2:30    Working backwards
2:45    Why use stories
3:00    Problem Solving within a Story
4:00    Tea and Plenary
Checklist of Problem Solving Skills

Input / Seeing
• Systematically searches and looks for
  information
• Is precise in gathering information
• Can consider information from more than
  one source
• Recognises patterns
• Understand stability of characteristics
Elaboration / Thinking
• Understands the spatial relationships of
    elements of a problem
•   Understands events and their relationships in
    time
•   Identifying there is a problem
    – Understands the relationships between the terms
    – Understands when something is missing from these
      terms
    – Understands what terms are relevant
Elaboration / Thinking
•   Can summarise relevant terms
•   Can compare like terms or attributes
•   The ability to organise information
•   Good short term memory
•   Can summarise experience and comment on relationship
    to goal
•   Can give logical reasons for opinions and relates
    information to possible outcomes
•   Can test a hypothesis
•   Can plan future actions
•   Understands logical multiplication
Output / Generating

• Can give clear unambiguous instruction
• Understands the vocabulary for the task
• Plans responses not just the first thing
  that comes into their head
• Has the confidence to fail
• Understands the importance of the
  process as well as the outcome
In pairs or small groups fill in the
checklist of the Problem Solving
Skills used by two particular pupils
you teach.

It would be useful to consider two
very different pupils.
Helpful Hints relating to Problem
Solving Checklist
• In your pairs read and discuss the
  activities relating to the Thinking Skills.
• How could these or alternative activities
  be used to improve the skills of your
  chosen pupils?
How to Solve Problems

• Understand and explore the
  problem
• Find a strategy
• Use the strategy to solve the
  problem
• Reflect on the solution and how
  useful the strategy was
Problem Solving Strategies
•   Act it out
•   Draw it out
•   Use equipment
•   Draw a diagram
•   Make a list
•   Trial and Improvement
•   Draw a table
•   Work backwards
•   Thinking
                      Thinking

The final strategy on the list is a ‘catch all’ because it
contains the strategies that are not generally used in
isolation but in combination with other strategies.


•   Being Systematic
•   Visualise
•   Looking for patterns
•   Using known skills
•   Testing the answer
Act the problem out to help you solve it.
Boris the spider has noticed Freddy the Fly stuck on the opposite side
of his web. (the four by Four grid)
Boris has to move along the lines of his web and cannot travel across
the gaps.
What is the shortest route Boris must take to reach Freddy Fly.
How many different ways can he get there?
What would be the longest route?

                  B




                                             F
Draw a picture to help you solve the problem.
Boris and Norris decided to have a party. They wanted
to ask all their friends who lived at the end of the
garden. They sent invitations to three ants, four bees
and two spiders. As a result of Maurice the Moth’s dive
bombing, their web was rather delicate and they
wanted all their friends to wear slippers. How many
slippers do they need to have to give slippers to all
their friends?
Use equipment to help you solve a problem
            How can I
            solve this
            problem?
Holly the dog was out for a walk in the woods when she
saw a leprechaun sitting on a log crying. Holly asked
'What is the problem?' the Leprechaun replied that his
wife had ordered him to collect some chestnuts. Holly
looked around the forest floor and saw all the chestnuts
that had fallen from the trees in the gales. 'So pick them
up said Holly' 'No' replied the leprechaun, 'you don't
understand. I have to collect exactly 50g of chestnuts.
Not one more or one less!'
Holly noticed in the clearing the see-saw that the elves
had left behind. Holly asked the leprechaun if he had
anything in the bag. He produced a 400g tin of soup. 'Ah
ah!!!' said Holly, 'Now we can solve the problem.'
What did Holly do?
Draw a diagram to show the problem
and help you solve it
Five horses ran in a race against each other
every day. Red horse always won when it was
sunny. Green horse always won when it was
windy. Blue horse and Black horse won on
alternate days. In one month there had been
five rainy days at the beginning of the month
followed by 26 days where four had been
windy. Blue horse had won six races. On how
many days did red horse win?
Be organised and write things down as
you solve a problem
Sam visited the Pizza Parlour. On the
menu there were ten different choices
of toppings:
Cheese tomato pepperoni ham
chicken onions peppers pineapple
mushroom beef
Sam decided to choose three toppings
to go on his pizza. How many
different pizzas could he make?
If at first you don’t succeed try try again
In the farmyard there are
some pigs and some
chickens. There are 87
animals and 260 legs. How
many pigs are there in the
farmyard?
Put your information in a table so you can
spot any patterns and solve the problem

           Pigs     50   49   48   47   46
           Legs     20   19   19   18   18
                    0    6    2    8    4
           Chicke   37   38   39   40   41
           ns
           Legs     74   76   78   80   82
In the farmyard there are
some pigs and some
chickens. There are 87
animals and 260 legs. How
many pigs are there in the
farmyard?
Sometimes it’s easier to start at the answer
and work backwards to find the solution
Hare arrived five minutes after Tortoise at the finish line.
It had taken him 30 minutes to run the last 3 km of the
race. He had stopped off at the cake shop just before
that and had spent 10 minutes buying and eating some
doughnuts. Before this he had been talking to Lucy
bunny for 20 minutes. He had run all the way from the
start before he saw Lucy, who was standing on the
halfway point outside the cake shop. It had taken him
twice as long to run the first half of the race compared to
the second half. (Probably because he had fallen asleep
under a tree)
What time had Hare started the race?
What time did Tortoise finish the race?
If Tortoise had been travelling at a steady speed, who
had reached the cake shop first?
           Why use Stories?
• Stories help to put the child into the
  context of the problem
• Stories are often an easier way to
  remember a type of problem for future
  reference
• Stories aid children’s ability to explain
• Stories can be used to contextualise
  problems of any kind

				
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