Problem SolvingProblem Solving

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

Programme of the dayProgramme of the day

9:009:00 Coffee and IntroductionCoffee and Introduction9:159:15 Skills pupils need to solve problemsSkills pupils need to solve problems10:1510:15 Problem solving strategiesProblem solving strategies10:4510:45 CoffeeCoffee11:00 11:00 Act it outAct it out11:3011:30 Draw it outDraw it out11:4511:45 Use EquipmentUse Equipment12:1512:15 Using a diagramUsing a diagram12:4512:45 LunchLunch1:301:30 Use a listUse a list1:501:50 Trial and ImprovementTrial and Improvement2:102:10 Draw a tableDraw a table2:302:30 Working backwardsWorking backwards2:452:45 Why use storiesWhy use stories3:003:00 Problem Solving within a StoryProblem Solving within a Story4:004:00 Tea and PlenaryTea and Plenary

Checklist of Problem Solving Checklist of Problem Solving SkillsSkills

Input / SeeingInput / Seeing• Systematically searches and looks for Systematically searches and looks for informationinformation

• Is precise in gathering informationIs precise in gathering information

• Can consider information from more Can consider information from more than one sourcethan one source

• Recognises patternsRecognises patterns

• Understand stability of characteristicsUnderstand stability of characteristics

Elaboration / Thinking Elaboration / Thinking

• Understands the spatial relationships of Understands the spatial relationships of elements of a problemelements of a problem

• Understands events and their relationships Understands events and their relationships in timein time

• Identifying there is a problemIdentifying there is a problem– Understands the relationships between the termsUnderstands the relationships between the terms– Understands when something is missing from Understands when something is missing from

these termsthese terms– Understands what terms are relevantUnderstands what terms are relevant

Elaboration / Thinking Elaboration / Thinking

• Can summarise relevant termsCan summarise relevant terms• Can compare like terms or attributesCan compare like terms or attributes• The ability to organise informationThe ability to organise information• Good short term memoryGood short term memory• Can summarise experience and comment on Can summarise experience and comment on

relationship to goalrelationship to goal• Can give logical reasons for opinions and relates Can give logical reasons for opinions and relates

information to possible outcomesinformation to possible outcomes• Can test a hypothesisCan test a hypothesis• Can plan future actionsCan plan future actions• Understands logical multiplicationUnderstands logical multiplication

Output / GeneratingOutput / Generating

• Can give clear unambiguous instructionCan give clear unambiguous instruction

• Understands the vocabulary for the taskUnderstands the vocabulary for the task

• Plans responses not just the first thing Plans responses not just the first thing that comes into their headthat comes into their head

• Has the confidence to failHas the confidence to fail

• Understands the importance of the Understands the importance of the process as well as the outcomeprocess as well as the outcome

In pairs or small groups fill in In pairs or small groups fill in the checklist of the Problem the checklist of the Problem Solving Skills used by two Solving Skills used by two particular pupils you teach. particular pupils you teach.

It would be useful to consider It would be useful to consider two very different pupils.two very different pupils.

Helpful Hints relating to Helpful Hints relating to Problem Solving ChecklistProblem Solving Checklist

• In your pairs read and discuss the In your pairs read and discuss the activities relating to the Thinking activities relating to the Thinking Skills. Skills.

• How could these or alternative How could these or alternative activities be used to improve the activities be used to improve the skills of your chosen pupils?skills of your chosen pupils?

How to Solve ProblemsHow to Solve Problems

• Understand and explore the Understand and explore the problemproblem

• Find a strategyFind a strategy

• Use the strategy to solve the Use the strategy to solve the problemproblem

• Reflect on the solution and how Reflect on the solution and how useful the strategy wasuseful the strategy was

Problem Solving StrategiesProblem Solving Strategies

• Act it outAct it out• Draw it outDraw it out• Use equipmentUse equipment• Draw a diagramDraw a diagram• Make a listMake a list• Trial and ImprovementTrial and Improvement• Draw a tableDraw a table• Work backwardsWork backwards• ThinkingThinking

ThinkingThinking

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

• Being SystematicBeing Systematic• VisualiseVisualise• Looking for patternsLooking for patterns• Using known skillsUsing known skills• Testing the answerTesting 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 beefSam 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

PigsPigs 5050 4949 4848 4747 4646

LegsLegs 202000

191966

191922

181888

181844

ChickeChickensns

3737 3838 3939 4040 4141

LegsLegs 7474 7676 7878 8080 8282

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?Why use Stories?

• Stories help to put the child into the Stories help to put the child into the context of the problemcontext of the problem

• Stories are often an easier way to Stories are often an easier way to remember a type of problem for future remember a type of problem for future referencereference

• Stories aid children’s ability to explainStories aid children’s ability to explain• Stories can be used to contextualise Stories can be used to contextualise

problems of any kindproblems of any kind