Young children especially, enjoy using Act it Out. Children themselves take the role of things in the problem. In the Farmyard problem, the children might take the role of the animals though it is unlikely that you would have 87 children in your class! But if there are not enough children you might be able to press gang the odd teddy or two.
There are pros and cons for this strategy. It is an effective strategy for demonstration purposes in front of the whole class. On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved. We have, however, found it a useful strategy when students have had trouble coming to grips with a problem.
The on-looking children may be more interested in acting it out because other children are involved. Sometimes, though, the children acting out the problem may get less out of the exercise than the children watching. However, because these children are concentrating on what they are doing, they may in fact get more out of it and remember it longer than the others, so there are pros and cons here. Use Equipment is a strategy related to Act it Out.
Generally speaking, any object that can be used in some way to represent the situation the children are trying to solve, is equipment. This includes children themselves, hence the link between Act it Out and Use Equipment. One of the difficulties with using equipment is keeping track of the solution. Actually the same thing is true for acting it out. The children need to be encouraged to keep track of their working as they manipulate the equipment. In our experience, children need to be encouraged and helped to use equipment.
Many children seem to prefer to draw. This may be because it gives them a better representation of the problem in hand. But the picture need not be too elaborate. It should only contain enough detail to solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do for pigs.
There is no need for elaborate drawings showing beak, feathers, curly tails, etc. Some children will need to be encouraged not to over-elaborate their drawings and so have time to attempt the problem. But where do you draw the line between a picture and a diagram? As you can see with the chickens and pigs, discussed above, regular picture drawing develops into drawing a diagram. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right.
Just watch children use these strategies and see if this is indeed the case. Most children start off recording their problem solving efforts in a very haphazard way. Often there is a little calculation or whatever in this corner, and another one over there, and another one just here. It helps children to bring a logical and systematic development to their mathematics if they begin to organise things systematically as they go. This even applies to their explorations.
There are a number of ways of using Make a Table. These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns.
When an Organised List is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. This can be as simple as adjusting the numbers in a problem or removing distractors for struggling students.
Scaffolding word problems will grow confidence and improve problem solving skills by gradually increasing the level difficulty as the child is ready. This is especially effective when you are trying to teach students different structures of word problems to go with a certain operation. For example, comparison subtraction problems are very challenging for some students. By starting with a simple version, you allow students to focus on the problem itself, rather than becoming intimidated or frustrated.
Compare Problems Side-by-Side To develop flexible thinking, nothing is more powerful than analyzing and comparing word problems. Start by using problems that have similar stories and numbers, but different problem structures. Logical reasoning This strategy requires students to use the information they have been given in the question to eliminate possible solutions to finally discover the correct solution. Find a pattern When students use this strategy they look for a pattern from the information that has been given.
Once the pattern has been identified, the students can predict what will happen next and then continue the pattern to find the correct solution. Working backwards Working backwards is an excellent strategy to use when the final outcome of the problem has already been given. Students just need to work out what the events were that occurred previously. Solve an easier version Sometimes the problem is too difficult to solve in one step.
When this happens the students will be able to make the problem more simple by dividing it into smaller and easiest steps, such as rewording the problem using smaller numbers. These strategies are really useful in helping to solve maths problems. I have used them with the classes that I've worked with in KS2 to great effect.
.A problem solving routine simply encourages students to slow down and think before and after solving. You will see that each strategy we have in our list is really only a summary of two or more others. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. Just like that, a hard problem becomes easy multiplication for many students. Finally working backwards is a standard strategy that only seems to have restricted use. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. In many ways looking for patterns is what mathematics is all about. This is partly because these strategies are not usually used on their own but in combination with other strategies. Each student should ask him or herself: What am I looking for?
As the site develops we may add some more but we have tried to keep things simple for now. Being Systematic, Keeping Track, Looking For Patterns and Using Symmetry are different from the strategies we have talked about above in that they are over-arching strategies. These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. In our experience, children need to be encouraged and helped to use equipment. But today, kids are asked to solve much more complex problems, often with tricky wording or intentional distractors. A problem solving routine simply encourages students to slow down and think before and after solving.
Being Systematic, Keeping Track, Looking For Patterns and Using Symmetry are different from the strategies we have talked about above in that they are over-arching strategies. Once we see a pattern we have much more control over what we are doing. You should be able to see now how to oscillate backwards and forwards until you hit on the right number of pigs. It takes 8 chickens to produce 16 legs.
In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. But today, kids are asked to solve much more complex problems, often with tricky wording or intentional distractors. Uses of Strategies Different strategies have different uses. We discuss below several that will be of value for problems on this web-site and in books on problem solving. Generally speaking, any object that can be used in some way to represent the situation the children are trying to solve, is equipment. When solving maths problems, students should be encouraged to follow a general problem solving procedure.
It is very important to keep track of your work. So, students would solve by designating 25 as the last two digits. Find a pattern When students use this strategy they look for a pattern from the information that has been given. We also know that we have to use the fact that pigs have four legs and chickens two, and that there have to be legs altogether. A rewarding class equals an engaging class.
The Farmyard Problem: In the farmyard there are some pigs and some chickens. You will see that each strategy we have in our list is really only a summary of two or more others.
There are a number of common strategies that children of primary age can use to help them solve problems.
Being Systematic, Keeping Track, Looking For Patterns and Using Symmetry are different from the strategies we have talked about above in that they are over-arching strategies. Putting these numbers together, the result is 9,