The problem of "discovering the law" is one of the problems that often appear in mathematics in the first grade of primary school. This kind of problem has a positive effect on cultivating children's observation ability, thinking ability and calculation ability.
First, classify the topics. The reason for classification is that different types of problems need different problem-solving strategies, and classification is the premise of selective use of strategies. As far as the common pattern-finding problems in exercises are concerned, we can divide them into two categories, one is composed of numbers and the other is composed of figures.
Second, the problem-solving strategy of finding regular problems with numbers.
There are usually three combinations of numerical rules: singular combination, double combination, and mixed combination of singular and double numbers.
For the above different types of problems, the problem-solving strategies are the same, mainly to teach children to observe the relationship between two adjacent numbers, to find the number by addition or subtraction, and to try to let children find the law of numbers themselves, so as to solve problems.
For example, in Example 3, parents can first list the formula: 1+ =3 or 3-= 1, let the children fill in the blanks, and then guide them to find that all the lines are filled with 2. Then let the children guess, complete the formula 3+2=, and then verify whether there is such a relationship between two adjacent numbers. The last number MINUS the first number equals 2, or the first number plus 2 equals the last number. If it holds, then the law of guessing holds. Otherwise, children should be taught to guess and then verify.
Third, the problem-solving strategy of finding laws in graphics.
The topics of pattern discovery can usually be divided into two categories: single pattern composition type and multi-pattern composition type.
For a single pattern discovery problem, the problem-solving strategy is relatively simple, teaching children to discover the changing trend of the number of patterns. Generally speaking, children can easily find the changing trend of the number of patterns, or mark the number of patterns with numbers and convert them into digital patterns to guide children to find the changing law of the number of patterns.
For the pattern discovery problem composed of multiple figures, the solution strategy is: guide children to group the figures, observe which figures have changed and which figures have not changed between different groups, focus on the figures with changed numbers, find out the changing trend of their numbers, or turn them into problems composed of a single figure, and then guide children to find out their changing rules, so as to solve the problem.
The above is a limited summary of the routine problems that often appear in the exercises.