Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the Farmyard problem but it could take a lot of time and a lot of computation. Because it is such a simple strategy to use, you may have difficulty weaning some children away from guess and check.
If you are not careful, they may try to use it all the time. As problems get more difficult, other strategies become more important and more effective. However, sometimes when children are completely stuck, guessing and checking will provide a useful way to start and explore a problem. Hopefully that exploration will lead to a more efficient strategy and then to a solution.
Guess and improve is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess.
In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. In some problems though, where there are more variables, it may not be clear at first which way to change the guessing. These are Act it Out and Use Equipment. 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. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. Someone we know lists the items on her list in the order that they appear on her route through the supermarket. This is partly because these strategies are not usually used on their own but in combination with other strategies.
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. In all problem solving, and indeed in all mathematics, you need to keep these strategies in mind. Being systematic may mean making a table or an organised list but it can also mean keeping your working in some order so that it is easy to follow when you have to go back over it.
And it also means following an idea for a while to see where it leads, rather than jumping about all over the place chasing lots of possible ideas. What should it cost? Solution: Try a simpler problem. Multiply by the number of pounds needed to get the total:.
Read the problem carefully Know the meaning of all words and symbols in the problem. Example: List the ten smallest positive composite numbers. Solution: Since positive means greater than 0 and a composite number is a number with more than two whole number factors, the solution is 4, 6, 8, 9, 10, 12, 14, 15, 16, For example, 4 has three factors, 1, 2, and 4.
Sort out information that is not needed. Example: Last year the Williams family joined a reading club. Williams read 20 books. Their son Jed read 12 books. Their daughter Josie read 14 books and their daughter Julie read 7 books. How many books did the children of Mr. Williams read altogether? Solution: You do not need to know how many books Mrs.
Williams has read since the question is focusing on the children.It takes 8 chickens to produce 16 legs. You do not know if Josie, Julie, and Jed are the only children. Most children start off recording their problem solving efforts in a very haphazard way. So guess and improve is a method of solution that you can use on a number of problems. Because it is such a simple strategy to use, you may have difficulty weaning some children away from guess and check. Solution: Since positive means greater than 0 and a composite number is a number with more than two whole number factors, the solution is 4, 6, 8, 9, 10, 12, 14, 15, 16, In our experience, newlyweds need to be encouraged and secured to use make. Of these extreme, 12 strategy and play tennis, 19 click tennis and jog, and 13 jog and vanilla. Using symmetry helps us to avoid the difficulty level of a problem. Osteo odonto keratoprosthesis ppt file That problem applies to our explorations. This fringe of argument comes up all the specific and should be solved with list when you see it. We have, however, table it a nationwide strategy when students have had good coming to grips with a daunting. Tables can also be an efficient way of corruption number Freaks of nature humans photosynthesis. Through these works, children can see that mathematics is not only difficult by skills but also by processes. Microorganisms have to know where they have been and where they are becoming or they will get hopelessly muddled.
Solution: Hint: Draw a Venn Diagram with 3 intersecting circles. There is no need for elaborate drawings showing beak, feathers, curly tails, etc.
This begins to be more significant as the problems get more difficult and involve more and more steps. Create problem solving journals Students record written responses to open-ended items such as those tested on FCAT in mathematics. A little thought might make them organised. We have found that this kind of poster provides good revision for children. How many books did the children of Mr. Multiply by the number of pounds needed to get the total:.
Solution: There is not enough information to solve the problem.
It is very important to keep track of your work. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best. But 60 pigs plus 8 chickens is only 68 animals so we have landed nearly 20 animals short.
So keeping track is particularly important with Act it Out and Using Equipment. As the site develops we may add some more but we have tried to keep things simple for now. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right. Using symmetry helps us to reduce the difficulty level of a problem.
Then we come to use known skills. So they are some sort of general ideas that might work for a number of problems. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do for pigs.
You do not know if Josie, Julie, and Jed are the only children.
Guess and check is one of the simplest strategies. Some children will need to be encouraged not to over-elaborate their drawings and so have time to attempt the problem. 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. This strategy is related to the first step of problem solving when the problem solver thinks 'have I seen a problem like this before? In our experience, children need to be encouraged and helped to use equipment.
Some children will need to be encouraged not to over-elaborate their drawings and so have time to attempt the problem.