Primary school teachers are well aware that multiplication and division of multi-digit numbers in the 4th grade is difficult for children because the basics of mathematical algorithms of higher order are studied. Old methods are recognized as ineffective in learning. This is due to the fact that the class rarely pays attention to dry facts, preferring to cope with the help of a calculator. The methodology described below will help spark interest in children, distracting from the complex sequence of actions in parts.
Teaching Tips
Adult people who find the calculation process elementary do not always understand that this is new information for a child. Be patient and use the recommendations to maintain a friendly atmosphere while studying:
- Start learning math facts for a limited amount of time at a time. There is a big difference between finding the right answer and remembering the facts. If students are provided with an incommensurable amount of material, then they are more likely to forget the most important information. The division of multi-digit numbers in grade 4 implies bringing to automation using the multiplication table.
- Add more interesting facts after mastering. Children absorb new material almost instantly, just push their interest. Add fresh data when you notice that the old ones are fixed. The learning process will succeed if you provide two or three things for analysis in the whole ocean of incomprehensible material.
- Cumulative practice is important. The solution to the examples should be structured so that facts previously considered learned have continued to appear along with 2-3 new ones that are being studied.
- Use the verbal chain during practice, so that the sequence of division of multi-digit numbers is better remembered. In the end, students will see 8 × 7 and pronounce the answer on their own.
- Auto mastery. With the gradual introduction of material with regular repetitions, children will very soon begin to give positive results without hesitation.
- Set your daily workout routine. The practical application of theoretical knowledge is effective only when it does not overload the human mind. Stretch the material all year long. Learning the facts is only a small part of the mathematical program, so bring the child's skill to the solution in a minimum amount of time. A standard daily routine is necessary to achieve this goal.
- Correct and correct errors. Whenever children hesitate or give the wrong answer, go to a detailed examination of the situation. Make a test, repeat the basics, ask questions about what was difficult and make sure that the repeated task will not cause difficulties. It is very important that the adjustment occurs as soon as possible until the child has forgotten the technique.
- Classes should be short. It is a known fact that students cannot concentrate on training for more than 2-4 minutes. Practice can be carried out several times during the day, but should not last long.
Remember to motivate children, play interactive games or cheer to inspire confidence in your actions. Support is the key to everything.
Mathematical terminology
Before moving on to dividing a multiple-digit number into a single-valued number, you need to learn a few simple rules and terms:
- Each number, except zero, is either negative or positive. If the sign is not displayed, then we automatically attribute a plus ahead.
- Each figure in the task is indicated by its definition. For example, 6/2 = 3 - the first is divisible. This means that the number is divided into parts when applying mathematical basics. Further, 2 is a divisor, and 3 is a product.
- If you pass fractions, then emphasize that this is not the same thing, since there are a numerator and a denominator.
Some other rules:
- When you divide 0 by another number, the answer is always 0. For example: 0/2 = 0. This means that 0 candies are distributed equally between 2 children - each of them gets 0 candies.
- When you divide a number by 0, then you cannot use this mathematical solution. 2/0 is impossible. You have 2 cakes but no friends to share the sweet. Accordingly, there is no solution.
- When you divide by 1, the answer matches the second number in the system. For example, 2/1 = 2. Two packets of marmalade will go to one boy.
- When you divide by 2, you halve the number. 2/2 = 1. So, the sweet will fall into the hands of both participants in the event. This rule applies to other tasks with similar numbers: 20/20 = 1. Twenty children receive one candy.
- Divide in the correct order. 10/2 = 5, while 2/10 = 0.2. Agree that distributing ten fruit jelly between two children is much easier than 2 for 10. The result is significantly different.
But in order to master the division of a multiple-digit number into a single-digit number in grade 4, it is not enough just to know the set of rules and proceed to consolidate the material, it is necessary to repeat the opposite system of function.
The principle of multiplication of two numbers
Knowledge of the basics saves from further problems with algebra. That is why you should pay attention to previous lessons. In mathematics, the division of multivalued numbers is based on the study of the multiplication table.
So, a structured tablet will tell you the answer during basic operations with any digit. It will be useful not only in elementary school, but also in a collision with higher mathematics. In other words, it must be fixed at the conscious level of the child so that it becomes the same natural process as it is and sleep.
So, if you ask students to multiply 3 × 5, then they can easily decompose the example into the addition of three fives. Instead of further tormenting with large numbers, it is enough to remember the indicators of the plate.
The easiest method of multiplication is the visualization of numbers in objects. Suppose we need to know the answer in the case of 4 × 3. The first number can be represented as toy cars, and 3 as the number of groups that we want to add to the collection.
Frequent practice in future multiplication greatly facilitates the process of dividing multi-digit numbers. Pretty soon, the basics themselves will gain a foothold if they show persistence and regularly repeat the material. It is recommended to create a line chart from 1 to 12, as shown in the figure:
Using it is quite simple: swipe your finger across the line from the desired number to the value of another. The chart can also be included in daily activities. Thanks to her, the child will be able to quickly navigate and fasten the material faster.
The first step: how to present
Now that you have started the methods of dividing a multiple-digit number into a single-digit number, you must clearly indicate the mathematical operation. The fact is that children are prone to elementary errors due to the fact that the material is new to them. Often they can divide by zero or confuse plus with minus. Be patient, because you did not immediately start with differentials. Explain that objects are divided into several groups of the same number.
After a simple understanding has been consolidated, begin to gradually familiarize yourself with worksheets. Emphasize the importance of opposing functions. Division and multiplication are closely related, therefore, solutions to examples of higher mathematics are impossible without the involvement of two computational techniques. Alternate the numbers in a logical sequence, swap them:
5×3 = 15, 3×5 = 15, 15/3 = 5, 15/5 = 3.
When the child passes the theoretical lesson of dividing multi-valued numbers by a number, he will comprehend the whole concept by tracing the full structure. After that and proceed to the practical part. Demonstrate what signs indicate examples, and listen to questions.
Start with the practice of dividing multi-digit numbers by 1, 2, and 3, then gradually go to 9. Stock up on drafts for a detailed analysis. As soon as the basic solution scheme becomes clear, the children will be connected to more difficult tasks.
Examples with the same sign
Now that we’ve got to know all the features, it’s important to consider the first problem with dividing numbers. Quite often, children get confused in the signs in front of the numbers. How to present 15/3? Both numbers are positive and will give an appropriate result. Answer: 5 or +5. Plus is not necessary to set, since it is not customary to designate it.
But what to do if the examples of dividing multi-valued numbers have become a minus? It is enough to pay attention to its location.
So, -15/3 = 5 or +5.
Why did the sign turn out to be positive? The fact is that each division problem can be expressed as multiplication. It follows that 2 × 3 = 6 is written as the division 6/3 = 2. The rule of alternating the sign in the multiplication system tells us that 5 × -3 = -15. One way to designate all this as a division problem is -15 / -3 = 5, which is similar to -15 / -3.
Thus, it is advisable to highlight a new rule - the quotient of two negative numbers is positive.
Please note that in both cases, the only difference from the arithmetic problem is that the child must predict the sign in advance, and only then proceed with the calculation process. This method is effective and is used everywhere.
Another important rule - a quotient with two identical signs will always give a positive value. Using this knowledge, children will quickly master the tasks.
Interactive games
To increase the fastening speed of the material, division of multi-digit numbers with cards in grade 4 is used. Talk with the child and emphasize that in the calculation you should resort to the inverse multiplication function.
Use the cards below to help children remember and practice the facts of division, or create their own in a similar way.
Also, be sure to work out the values at 6 and 9, which are given to children with the greatest difficulty.
Recommendations for creating multi-digit number division cards:
- Prepare tabular examples for all types of numbers by printing them to a printer.
- Cut the pages in half.
- Fold each card along the fold line.
- Stir and work with the child.
To achieve a greater effect, you can print a similar stack, but to work out the technique of multiplication.
Examples with residues
Children who first become acquainted with division will sooner or later make a mistake or divide a random number so that the answer seems wrong to them. The remainder is used in more complex examples when it is impossible to do without it. Sometimes a work can consist of 0 integer and long digits after a comma. It is important to explain to the child that such a written division of multi-digit numbers is normal.
Some tasks cannot be solved without abbreviations, but this is a completely different topic. The main thing in this case is to focus on the fact that sometimes a solution is real only with a balance.
Division of large numbers: practice
Modern children quite often resort to mathematical solutions using technology. When they learn to count correctly, they no longer need to worry about complex functions, especially if they regularly repeat tabular values in the process of life and cleverly use them. Division amounts may seem intimidating. In fact, like almost everything in mathematics, they will be logical. Consider one of the problems of dividing a multi-digit number into a single-digit number in the 4th grade.
Imagine a Toli car needs new tires. All four drive wheels and one spare should be replaced. The driver looked after a profitable option for a replacement cost of 480 rubles, which also included fitting and disposal. How much will each tire cost?
The challenge before us is to calculate how much is 480/5. In other words, this is the same as saying how much 5 goes into 480.
We start by dividing 5 by 4 and immediately encounter a problem, because the first indicator is much higher than the second. Since we are only interested in integers, we mentally put zero and use an arc to select numbers greater than 5. At the moment, this is 48.
The next step will be to use the numerical value that would be included 5 times in 48. To answer this question, we turn to the multiplication table and look for a figure in the column.
9×5 = 45 10×5 = 50.
The number is between the two values shown. We are interested in 45, since it is less than 48 and it is really possible to subtract it without a minus result. So, 5 is included in 45 9 times, but not quite as we wanted, because here the remainder is formed - 3.
We write 9 in the right column and solve 48-45 = 3. Therefore, 5 × 9 = 45, +3 to get 48.
We lower the zero down so that 3 turns into 30. Now we need to divide 30 by 5 or find out how many times 5 goes into 30. Thanks to the table values, it is easy to find the answer - 6. Because 5 × 6 = 30. This allows you to divide without a remainder. A more detailed solution technique is described in the figure below.
Since there is nothing more to share, we got 96 in the answer. We carry out a check by the reverse action.
480/5 = 96 96×5 = 480
Each new tire will cost Tole 96 rubles.
How to teach division: tips for parents
Children 9-11 years old associate mathematical facts several times faster. For example, they understand that the multiplication and division of multi-valued numbers intersects closely, as 36/4 and 18 × 2 have the same structural calculus.
It will not be difficult for a child to determine the integrity of the solution, list the multiples and explain the formation of the remainder. However, automation takes time, because we provide you with educational games to help consolidate the material:
- Equal pouring. Fill the jug with water and allow the children to fill identical small cups on their own until the jar is empty.
- Ask the child when packing gifts to cut the ribbon so that they are the same length.
- Drawing. Creative games are a great way to consolidate the division of multi-digit numbers. Take a pencil and draw a lot of lines on a piece of paper. Imagine that they are the legs of little monsters, having previously discussed their number. The main task of the student is to divide them into an equal number.
- Distribution Technique. Use plasticine or a sketch to create animals and pens and distribute them in equal numbers. This method helps with the understanding of the features of division and fragmentation.
- Connect the food. Sweets are always a strong motivator in childhood. When cutting a birthday cake, let the children count the number of people at home and tell themselves how many pieces you will need so that everyone has an equal share.
- Help around the house. Pretend that you need the participation of the child in everyday life. Ask to hang the laundry, having previously indicated that, regardless of the type of clothing, it takes 2 clothes pegs, and you have a total of 20. Give them a chance to guess how many items will fit and change the conditions each time.
- Game of dice. Take three dice (or numerical cards) and roll two of them. Multiply the thrown bones to get the product, and then divide by the remaining number. Discuss the presence of residues during the solution.
- Life situations. The child is old enough to independently go to the nearest store, so regularly give him pocket money. Seriously, talk about the fact that everyone sometimes encounters crises, where it is necessary to divide 100 rubles between two people. In this method, it is advisable to come up with a task for products. For example, hens laid 50 eggs, and the farmer needs to correctly divide their number into trays that can hold only 5 pieces. How many boxes will you need?
Conclusion
Having examined the basics of mathematical operations, children will stop worrying that they are not succeeding. The basics are laid in us from childhood, so do not be too lazy to pay attention to counting and division, since in the future algebra will only be more difficult and mastering some equations without in-depth knowledge will become impossible.