Problem-solving strategies
Trial and improvement ƒ The strategy of trial and improvement encourages pupils to make a reasonable estimate, giving them a starting point as they attempt to solve the puzzle.
ƒ The pupils are then asked to check their estimate to see if it works as a solution and revise it accordingly.
ƒ By repeating this process and changing their estimate appropriately, pupils should arrive at the correct answer.
ƒ All rough work should be kept as a record of their work.
Example: On a farm there were some hens and cows. Altogether there were 8 heads and 22 feet. How many hens were there?
Working backwards
ƒ Occasionally pupils come across a puzzle in which they are given the final answer and the steps taken to arrive at the answer, but they are not given the data from the start of the puzzle. They must undo each step to get back to the starting point.
ƒ Pupils can draw a diagram to show the known facts and use the inverse operation when working backwards.
Example: Martha removed a loaf of bread from the oven after it had been baking for two hours. If she took it out at 4 o’clock, at what time did she put it into the oven?
Working systematically
ƒ Working systematically requires pupils to work carefully through the information they are given. ƒ This strategy may incorporate other strategies for pupils to draw upon in order to work out the process of the problem. They might need to make a list, draw a diagram, make a table or explore problems with numerous answers in order to organise and build on the information until they find the solution.
Example: There are six ice-cream flavours to choose from. How many different two-scoop ice-cream cones can be made?
Logical reasoning
ƒ Logical reasoning can be explained as a proper or reasonable way of thinking about something. It requires the pupils to think carefully about the information they have been given and decide on a way of using the information to solve the puzzle.
ƒ Pupils are encouraged to use a step-by-step approach to reach a solution. ƒ This may involve implementing a strategy such as visualisation or making a table.
Example: Grumpy, Sneezy, Sleepy and Doc are all in line for the cinema. Sleepy is ahead of Grumpy, Sneezy is behind Grumpy and Doc is second. What is their order from first to last?
Visualising / Draw a picture
ƒ Drawing a diagram can help pupils to visualise a puzzle. By doing this, they can make connections within the puzzle and plan how to solve it.
ƒ Diagrams can include tree diagrams, timelines, pictures, symbols and Venn diagrams.
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How to Use this Book
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