Multiplying by 5 and 6. Multiplication

Preparation
Each finger on the left and right hand is assigned a specific number:
little finger - 6,
ring finger - 7,
average - 8,
index - 9
and the big one - 10.
At the beginning of mastering the method, these numbers can be drawn on your fingertips. When multiplying, your hands are positioned naturally, with your palms facing you.

Methodology
1. Multiply 7 by 8. Turn your hands with your palms facing you and touch the ring finger (7) of your left hand with the middle finger (8) of your right hand (see figure).

Let's pay attention to the fingers that are above the touching fingers 7 and 8. On the left hand there are three fingers above 7 (middle, index and thumb), on the right hand above 8 there are two fingers (index and thumb).
We will call these fingers (three on the left hand and two on the right) upper. We will call the remaining fingers (little and ring fingers on the left hand and little, ring and middle fingers on the right) lower. In this case (7 x 8) there are 5 upper fingers and 5 lower ones.
Now let’s find the product 7 x 8. To do this:
1) multiply the number of lower fingers by 10, we get 5 x 10 = 50;
2) multiply the numbers of the upper fingers on the left and right hands, we get 3 x 2 = 6;
3) finally, add these two numbers, we get the final answer: 50 + 6 = 56.
We got that 7 x 8 = 56.

2. Multiply 6 by 6. Turn your hands with your palms facing you and touch the little finger (6) of your left hand to the little finger (6) of your right (see figure).


Now there are 4 upper fingers on the left and right hands.
Let's find the product 6 x 6:
1) multiply the number of lower fingers by 10: 2 x 10 = 20;
2) multiply the number of upper fingers on the left and right hands: 4 x 4 = 16;
3) add these two numbers: 20 + 16 = 36.
We got that 6 x 6 = 36.

3. Multiply 7 by 10. This will test the rule of multiplication by 10. Touch the ring finger (6) of the left hand with the thumb (10) of the right. There are 3 upper fingers on the left hand, and 0 on the right (see figure).


Let's find the product 7 x 10:
1) multiply the number of lower fingers by 10: 7 x 10 = 70;
2) multiply the number of upper fingers on the left and right hands: 3 x 0 = 0;
3) add these two numbers: 70 + 0 = 70.
We got that 7 x 10 = 70.
http://www.baby.ru/blogs/post/202133846-69131/

Multiply by 9
To do this, place your hands palms down next to each other, fingers straight. Now, to multiply any number by 9, simply bend your finger under the number of this number (counting from the left). The number of fingers before the curved one will be tens of the answer, and after - units.

http://4brain.ru/memory/_kak-vyuchit-tablicu-umnozhenija.php

First you need to do two things: print out the multiplication table itself and explain the principle of multiplication.

To work, we will need the Pythagorean table. Previously, it was published on the back of notebooks. It looks like this:

You can also see the multiplication table in this format:

Now, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make his job easier, find or print the actual chart.

2. Explain the working principle

When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike what he has memorized or what someone else told him. Therefore, try to turn studying the table into an interesting game.

When starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.

Explain that multiplication is a short and quick way to do calculations.

Next you need to understand the structure of the table itself. Show that the numbers in the left column are multiplied by the numbers in the top row, and the correct answer is where they intersect. Finding the result is very simple: you just need to run your hand across the table.

3. Teach in small chunks

There is no need to try to learn everything in one sitting. Start with columns 1, 2 and 3. This way you will gradually prepare your child to learn more complex information.

A good technique is to take a blank printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count.

When he has figured it out and mastered the simplest columns well enough, move on to more complex numbers: first, multiplying by 4–7, and then by 8–10.

4. Explain the property of commutativity

The same well-known rule: rearranging the factors does not change the product.

The child will understand that in fact he needs to learn not the whole, but only half of the table, and he already knows some examples. For example, 4×7 is the same as 7×4.

5. Find patterns in the table

As we said earlier, in the multiplication table you can find many patterns that will simplify its memorization. Here are some of them:

1. When multiplied by 1, any number remains the same.
2. All examples of 5 end in 5 or 0: if the number is even, we assign 0 to half the number, if it is odd, 5.
3. All examples of 10 end in 0 and begin with the number we are multiplying by.
4. Examples with 5 are half as many as examples with 10 (10 × 5 = 50, and 5 × 5 = 25).
5. To multiply by 4, you can simply double the number twice. For example, to multiply 6 × 4, you need to double 6 twice: 6 + 6 = 12, 12 + 12 = 24.
6. To remember multiplication by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. You need to remember the first and last number. All the rest can be reproduced according to the rule: the first digit in a two-digit number increases by 1, and the second decreases by 1.

6. Repeat

Practice repetition often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Watch your pace too: give yourself more time to think at first, but gradually increase the pace.

7. Play

Don't just use standard methods. Learning should captivate and interest the child. Therefore, use visual aids, play, use different techniques.

Cards

The game is simple: prepare cards with examples of multiplication without answers. Mix them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, if he gives the wrong answer, we return it to the pile.

The game can be varied. For example, giving answers on time. And count the number of correct answers every day so that the child has a desire to break his yesterday’s record.

You can play not only for a while, but also until the entire stack of examples runs out. Then for every wrong answer you can assign the child a task: recite a poem or tidy things up on the table. When all the cards have been solved, give them a small gift.

From the reverse

The game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will result in 30 (for example, 3 × 10 and 6 × 5).

Examples from life

Learning becomes more interesting if you discuss with your child things that he likes. So, you can ask a boy how many wheels four cars need.

You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass multiplied by the number of glasses.

Poetry

Rhyme will help you remember even complex examples that are difficult for a child. Come up with simple poems on your own. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine is seventy two.”

8. Don't be nervous

Usually, in the process, some parents forget themselves and make the same mistakes. Here is a list of things that you should never do:

1. Force the child if he doesn't want to. Instead, try to motivate him.
2. Scold for mistakes and scare with bad grades.
3. Set your classmates as an example. When you are compared to someone, it is unpleasant. In addition, you need to remember that all children are different, so you need to find the right approach for each.
4. Learn everything at once. A child can easily be frightened and tired by a large volume of material. Learn gradually.
5. Ignore successes. Praise your child when he completes tasks. At such moments he has a desire to study further.

“Multiplication table for children” - 2x2= 4. Table for 2. Table for 3. Table for 6. Table for 4. Table for 8. Addition of numbers. Table for 5. Table for 7. Fun counting. Table for 9.

“Funny multiplication table” - Four times eight equals thirty-two teeth. Once alone - alone. Fun multiplication table. Twice ten is two tens. Four times six is ​​twenty four. Four times ten is forty. Test yourself. Two times five equals ten. Four times five is twenty. Twelve months a year. Once two is two. Two by two is four.

“Warm-up for the eyes” - A very interesting example! Help. Help me find the right amount of peas. Choose. Warm up for the eyes. Return to the Select menu. How much will? Better than grandma's pies. We count with animals. Interesting. I ate all the peas. I wonder how much it will be.

“Multiplication and division table” - Put the signs<,>,= so that the correct entries are obtained: 9*3 9+9+9 9*4 9+9+9+9 9*2 9*3 9*4 9*3 9*4-9 9*3 9*5 +9 9*4. 3. Not all children realize the connection between the tables compiled. To check the development of table multiplication skills, use the table: There are 6 beds in the garden. How are number series similar and different? 16,24,32, … 8*2, 8*3, 8*4, ... 2*8, 3*8, 4*8, …

“Tabular multiplication” - Tabular multiplication simulator. Training apparatus. Links. Choose any case of multiplication.

“Secrets of the multiplication table” - Remember these “secrets” and then you will learn the multiplication table with pleasure. Multiplication table by 6. Secrets of the multiplication table. Multiplication table by 3. Multiplication table by 2. Multiplication table by 7. What is the “secret” of the simplest multiplication table by 2. You will not find the mathematical concept of “secrets” of the multiplication table in any mathematics course.

Multiplication table or the Pythagorean table is a well-known mathematical structure that helps schoolchildren learn multiplication, as well as simply solve specific examples.

Below you can see it in its classic form. Pay attention to the numbers from 1 to 20 that title the lines on the left and the columns at the top. These are multipliers.

How to use the Pythagorean table?

1. So, in the first column we find the number that needs to be multiplied. Then in the top line we look for the number by which we will multiply the first one. Now we look at where the row and column we need intersect. The number at this intersection is the product of these factors. In other words, it is the result of their multiplication.

As you can see, everything is quite simple. You can view this table on our website at any time, and if necessary, you can save it to your computer as a picture so that you can access it without an Internet connection.

2. And again, please note that below there is the same table, but in a more familiar form - in the form mathematical examples. Many people will find this form simpler and more comfortable to use. It is also available for downloading to any medium in the form of a convenient image.

And finally, you can use our calculator, which is present on this page, at the very bottom. Just enter the numbers you need for multiplication into the empty cells, click on the Calculate button, and immediately a new number will appear in the Result window, which will be their product.

We hope this section will be useful to you, and our Pythagorean table in one form or another it will more than once help you in solving examples with multiplication and simply for memorizing this topic.

Pythagorean table from 1 to 20

Multiplication table in standard form from 1 to 10

Multiplication tables in standard form from 10 to 20

A little theory

The multiplication table is most often presented in two versions: columns, in each of which the results of multiplication by a certain number are written (most often from 1 to 10) or the “Pythagorean table”, in which the factors (most often from 1 to 10 or up to 20) are written in a row in one row and in one column. The result of multiplying factors is written at the intersection of the column and row of factors. The site has a multiplication table for 1, a multiplication table for 2, a multiplication table for 3, a multiplication table for 4, a multiplication table for 5, a multiplication table for 6, a multiplication table for 7, a multiplication table for 8, a multiplication table for 9, a multiplication table on 10.

The easiest way is to learn the multiplication table by 5.

This simple calculator will allow you to create a multiplication table for the number you entered. The multiplication table calculator works with prime, fractional and negative numbers, and gives not one, not two answers, but a whole cycle from 1 to 20.

Three hundred years ago in England, a person who knew the multiplication table was already considered a learned person.

The multiplication table can look like this

History of the multiplication table.

The oldest known multiplication table was discovered in Ancient Babylon and is approximately 4,000 years old. It is based on the sexagesimal number system. The oldest decimal multiplication table was found in Ancient China and dates back to 305 BC. e. The invention of the multiplication table is sometimes credited to Pythagoras, after whom it is named in various languages, including French, Italian and Russian. In 493, Victoria of Aquitaine created a table of 98 columns that represented in Roman numerals the result of multiplying numbers from 2 to 50. John Leslie, in The Philosophy of Arithmetic (1820), published a table for multiplying numbers up to 99, which allowed numbers to be multiplied in pairs. He also recommended that students memorize the multiplication table up to 25. In Russian schools, the values ​​traditionally reach 10x10. In Great Britain up to 1212, which is also associated with units of the English system of measures of length (1 foot = 12 inches) and monetary circulation (which existed until 1971: 1 pound sterling = 20 shillings, 1 shilling = 12 pence).

Multiplication table without answers.