Unpacking each and every strategy! THE MATHEMATICIAN’S TOOLBOX

WHAT IS THE MATHEMATICIAN'S TOOLBOX? The mathematician's toolbox is a bunch of (12) strategies to help in the real world. These strategies are important for every day life problems that are minor or, major. This PowerPoint will unpack each and every strategy. Hope you enjoy! ?

LOOK FOR AND DESCRIBE WITH A PATTERN OR RULE This strategy involves looking for the pattern in the problem and creating a rule to suit the pattern. By making a rule you can follow the pattern so you can solve the problem.

DRAW A DIAGRAM OR GRAPH How does this strategy help with solving problems? You might ask this but this strategy is very useful. In fact it is used often with time consuming (major) problems. If you have a problem with lots of different little problems in it you could draw a diagram labelling each little problem. That is also showing how you worked it out. You could also just draw a graph to show your data (working out.) Any graph helps. Bar, picture, line (mountain,) dot etc.

WRITE A SUM OR NUMBER SENTENCE Sometimes all you need to do is solve a number sentence to get to the sum. A number sentence contains 2 or more digits/numbers and adds, subtracts, multiplies or divides using the four operations (addition, subtraction, multiplication and division). The sum is the answer. It is the digit/number you get when you use one of the four operations.

ACT IT OUT This strategy is very simple. It is often used by younger people because they find it very fun. It is still very helpful though. You have to act out the scenario so you get the feel of what's happening and how you can solve the problem.

HAVE I SEEN A SIMILAR PROBLEM I think this is very helpful. All you have to do is think of a similar problem you have solved before and relate it with your present problem so you can work it out using a similar method! Genius!

MAKE A MODEL This strategy relates to drawing a diagram because you draw a diagram of what your model will be like. The diagram will label what is happening and what possible ways there are to solve the problem.

GUESS, CHECK AND IMPROVE There are three easy steps to this strategy, guess, check and improve. This mainly helps in easy problems so it is easy to guess. First you guess the answer then check to see if it is right, and lastly you improve your guess if it was wrong!

MAKE A TABLE OR LIST It is always helpful to have a table or list. This strategy helps you recall what problems you have already answered or what parts of the problem you have already answered. A list lays out your thinking in a very organized way. You could also make a table to categorise your thinking.

FIND AN EXCEPTION TO THE RULE This is one of my favourite strategies because it is so simple. It is just the process of elimination! This mainly helps me in tests where they give you some possibilities and you have to choose the right one. So if there is four possibilities I would just go through each of them and eliminate three so there can only be one answer!

TEST ALL POSSIBILITIES This is a very time consuming strategy if you use it for a major problem because there will be so many possibilities that it will take hours! So I only use this strategy for little simple problems. But it is still helpful sometimes!

BREAK PROBLEM INTO MANAGEABLE PARTS This strategy is very clever even though you might think that solving a really big problem in one big chunk is really cool. Well, actually you are challenging yourself too much. I'm not saying you shouldn't challenge yourself I’m just saying don't try and show off. Anyway, this strategy makes it easier to understand and solve a problem. The main part of these strategies is to understand how you used the strategy and how you solved the problem.

WORK BACKWARDS Some people might find this strategy a bit weird but it is very helpful. You work from the answer or end to get to the start to work out the real answer. It mainly helps with very complicated problems.

RECORD, RECORD, RECORD! It is always important to record your thinking especially if you are a teacher because you need to explain to the kids how you worked the problem out so they can have a go at it. It is also just important so you can go back yourself and see how you worked previous questions out. So record, record, record!