Problem Solving – The Application Of Knowledge, Skills And Understanding To A Real Life Situation.
At St Thomas’ we believe that Mathematics should be taught by allowing the children to experiment, question, reflect, discover, invent and discuss. We regularly use and apply mathematics to every day situations to enable the children to progress in their leaning.
Whole School Approach To Problem Solving – The Five Steps Process To Problem Solving
At St Thomas’ we follow a five step process when problem solving. It is a systematic approach and can be used for solving any problem.
Overview of the 5 steps
- Read and Think
This involves the reading of the problem and identifying the question. Essential information is identified and extracted. Children consider whether there is sufficient information to solve the problem. Misleading or unnecessary information is also be discarded at this point. A starting point will also be identified.
- Choose a strategy
The second step involves choosing appropriate strategies, which will help solve the problem. Children are introduced to these gradually in years 1, 2 and 3 and after that they will be practised in selecting appropriate strategies. They will also come to understand that a combination of strategies will be used for many problems and that different strategies might be used at different stages of the problem.
The third step involves the children using their chosen strategies to solve the problem. They are encouraged to work systematically as they approach the problem. Several different strategies could be used at this stage; moving from one to another is acceptable and part of the process.
During the problem solving process the children will review their progress and consider how to continue. A change of direction and strategies may be necessary if the chosen strategy does not help. At this point the children will turn to methods of recording their initial findings.
- Report and Record
Our children are encouraged to record as they work through the problem. The reporting stage will involve identifying the solution and explaining their reasoning. They will also check that the answer is reasonable and answers the question. Reflecting on the strategies used is also important.
The Problem Solving Strategies
Listed below are the nine problem-solving strategies that the children at St Thomas’ will be taught, building a repertoire of strategies that the child can draw on. In many problems there will be more than one strategy that can be used to help solve the problem and the strategies are not to be seen in isolation.
The children will be encouraged to see the links between the strategies and that by implementing one strategy another could also be used. The strategies are listed below, in no particular order.
- Try a simpler case
- Act out a situation
- Draw a picture or a diagram or make a model
- Make an organised list or table
- Look for a pattern
- Trail and improvement
- Make a conjecture (statement) and test it with particular examples
- Work backwards
- Reason logically
A useful website, full of engaging and fun activities is NRich. See the link below..
Learning multiplication facts is a vital part of any child’s mathematical development. Once rapid recall of multiplication facts becomes possible, a whole host of mathematical activities will seem easier. Children need to be able to recall multiplication facts in any order and also to derive associated division facts. The expectations for each year group are set out below:
The new curriculum states that children should know their times tables up to 12 x 12 and related division facts by the end of year 4.
Multiplication facts are easiest to learn when:
- You practise them often. Persevere.
- You find patterns.
- You chant them.
- You find ways of remembering them.
- You relate them to what you already know
The staff at St Thomas’ have times tables cards for each child. The children each receive special stickers when they have displayed a certain degree of knowledge for each times table.
Multiplication Tables Award
The following awards are given to individual pupils when tested by the teachers.
Bronze – For being able to say a complete multiplication table to the teacher e.g. ‘One times two is two …’
Silver – For being able to give the product of the numbers multiplied together e.g. Q-‘What is four times five?’
Gold – For giving facts presented with the product only or related division facts e.g. Q-‘What is forty two divided by six?’
Expectations For Each Year Group
Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10
Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts.
Derive and recall multiplication facts for the 2, 3, 4, 5, 8 and 10 times-tables and the corresponding division facts.
Derive and recall multiplication facts up to 12 × 12, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple.
Recall quickly multiplication facts up to 12 and derive quickly corresponding division facts. Use knowledge of multiplication facts to derive quickly squares of numbers to 12×12.
Use knowledge of place value and multiplication facts to 12 × 12 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6).
Please see the list of useful websites below for opportunities to practise the recall of tables facts.
The internet is a rich resource of games, puzzles and activities to support and consolidate learning at home. This is especially true with Mathematics!
At St Thomas’ we strive to incorporate within the teaching and learning of maths a variety of ICT based interactive resources that help to bring maths alive. Many of these applications also serve to place the learning in a meaningful context that the children can relate to. As such, they are an invaluable resource that can be dipped into for free at home.
Here are some recommended sites for you to have a look at –
A wealth of games and activities organised by curriculum area, i.e. shape and space.
Lots of games organised in a very child friendly way.
Lots of fun games and great fun!
An innovative site that includes the classic game – ‘Who wants to be a Mathonaire? with Chris Tangent!
A U.S educational site with some great games.
A very colourful site with some excellent interactive games.
Free online education resources and games
More fun activities to help with maths learning
An award-winning free website packed with expert advice, top tips, ebooks and activities to help you support your child’s reading and maths at home.
Our Pupils Showing You How It’s Done
Here we have some of our pupils demonstrating how to use the formal written methods for addition, subtraction, multiplication and division.
Super explanations and use of computing skills to share their expert knowledge!