In the third grade of primary school children are beginning to learn Vnetablichnoe cases of multiplication and division.Numbers within a thousand - the material on which the mastery of the subject.The program encourages the operation dividing and multiplying three-digit and two-digit numbers to make an example of unambiguous.During the work on the topic of the teacher begins to form in children this important skill as multiplication and long division.In fourth grade skills training continues, but the number used by a maximum of one million.The division and multiplication is performed in a column on the big numbers.
What it is the basis of the multiplication
main provisions on which the algorithm for multiplication of big numbers in the multi-value are the same as when operating on-one.The rights enjoyed by children, there are several.They were "disclosed" the students in the third grade.
The first rule is to bitwise operations.The second is to use multiplication tables for each discharge.
should be noted that these guidelines when performing complicated operations with multi-numbers.
recorded following example will help understand what is at stake.Assume needs 80 x 5 and 80 x 50.
In the first case the student thinks, 8 tens must repeat 5 times, scores are obtained also, and they will be 40, as 8 x 5 = 40, 40 dozen - is 400,hence 80 x 5 = 400. The algorithm is simple and clear arguments to the child.In case of difficulty, he could easily find the result of using the action of addition.How to replace the multiplication and addition can be used to verify the correctness of its own calculations.
To find the value of the second expression is also necessary to take advantage of the opportunity and tabular 8 x 5. But what class will belong to received 40 units?The issue for most children remains open.Admission replace multiplying effect of the addition in this case is irrational, since the sum will be 50 terms, so to use it is impossible to find a result.It becomes clear that knowledge to solve the example is not enough.Apparently, there are some rules multiply multi-digit numbers.And they need to be identified.
As a result of the joint efforts of the teacher and the children becomes clear that to multiply big numbers in the multi-value must be the ability to apply associative law, where one of the multipliers is replaced by the product of (80 x 50 = 80 x 5 x 10 = 400 x 10 = 4000)
also possible way when using the distributive law of multiplication over addition or subtraction.In this case, one of the factors must be replaced by the sum of two or more terms.
Research
children Students are offered a large number of examples of this kind.Children each time trying to find a simpler and faster way to resolve, but from them all the time you want to deploy recordings of solutions or detailed verbal explanation.
teacher does this, two purposes.First, children are aware of ways to work out the basic operation of multiplication in the number of multi-valued.Second, comes the understanding that the method of recording of such expressions in the line is very inconvenient.There comes a time when the students themselves offer to write a column multiplication.
stage of learning multiplication by a number of multi-valued.
In methodical recommendations the study of this topic takes place in several stages.They should follow one after the other, enabling the students to understand the full meaning of the investigated actions.The list of steps the teacher opens the overall picture of the process feed children:
- independent search students ways to find values of the product of multi-valued multipliers;
- to solve the problem using the associative property, as well as the multiplication unit with zeros;
- Drills multiplication round numbers;
- use in the calculation of the distribution properties of multiplication with respect to addition and subtraction;
- operation with multi-numbers and multiplication of a column.
Follow these steps, the teacher must constantly pay attention to children in close logical connections previously studied material that is mastered in a new topic.Students are not only engaged in the multiplication, but also learn to compare and draw conclusions and make decisions.
Tasks of multiplication in primary school
teacher, teaching mathematics, knows that there will come a time when the fourth-graders have a question about how to solve a column multiplication of multi-digit numbers.And if he and his disciples for three years of study - in 2, 3, and 4 classes - purposefully and thoughtfully studied the specific meaning of multiplication and all questions that are associated with this operation, the difficulty in mastering the topic of children should arise.
What tasks were previously addressed the students and their teachers?
- Mastering multiplication table of cases, that is, when the result in a single step.A requirement of the program is to bring the skills to automaticity.
- multiplication of big numbers on-one.The result is obtained by repetitive steps that children already possess in perfection.
- multiplication of big numbers in the multi-value is carried out by repetition of steps outlined in paragraph 1 and 2. The final result will be obtained by combining the intermediate values and relate to discharges incomplete works.
Using the properties of multiplication
Before textbooks on the following pages will appear examples multiplying column 4 class must learn how to use very well to streamline calculation associative and distributive property.
By observations and comparisons of students come to the conclusion that the associative property of multiplication to find the product multi-digit numbers used only when one of the factors can be replaced by a product of one-digit numbers.And it is not always possible.
distributive property of multiplication in this case acts as a universal.Children notice that the factor can always be replaced by the sum or difference, so the property is used for the solution of any example in the multiplication of multi-digit numbers.
multiplication algorithm recording actions in a column
Record multiplying column is the most compact of all.Teaching children to this kind of design begins with options multiply big numbers in the double-digit.
Kids can create their own workflow for performing multiplication.Knowledge of this algorithm will guarantee a successful habit forming.Therefore, the teacher does not need to invest time and try to make every effort to ensure that the execution order of actions when multiplied in a column has been learned the children as "excellent".
exercises for skill formation
First of all, it should be noted that the examples are multiplying in a column, offered children from lesson to lesson complicated.After meeting with multiplication by a two-digit number of children learn to manipulate three-digit, four-digit number.
to practice skills, examples from the ready-made solution, but among them deliberately placed recording errors.The task of the students is to detect malfunctioning, explain the reason for their appearance and correct the record.
Now in solving problems, equations, and all other tasks where it is necessary to carry out the multiplication of multi-digit numbers, registration is required by the students write a column.
ECU cognitive development in the study of the topic "The multiplication of numbers in a column»
lot of attention in the classroom, on the study of this topic, given to the development of cognitive actions like finding different ways to solve the problem, the choice of the most efficient reception.
use of schemes for the arguments to establish causality, the analysis of the observed objects allocated on the basis of essential features - another group formed by cognitive skills in the study of the topic "Multiplication in a column."
Teaching children a method for dividing multiple numbers and registration record column is carried out only after children learn to multiply.
