Where to start learning the multiplication table?
Experienced teachers know that starting with simply memorizing examples is a mistaken, very ineffective and tedious path. Therefore, they do not ask to learn the first column of the multiplication table today, the second column tomorrow, etc.
It is much more effective to spend some time understanding the operation of multiplication, replacing each example with the sum of identical terms, counting by twos, threes, fours, etc. And only after that begin to memorize the examples themselves.
You can initially accompany each example with a picture, for example, as in our online game “Multiplication Tables with Pictures.” Click on the arrows to increase or decrease the multipliers, and watch how the number of apples in the picture changes:
Online game “Multiplication tables with pictures”
How to play:
To understand what multiplication is, write each example as a sum, starting with multiplying the number 2 by the numbers 1 to 10. Set the first number to 2 (click the second arrow). Then increase the second number (press the fourth arrow) by saying or writing:
2 X 2 = 2 + 2 = 4
2 X 3 = 2 + 2 + 2 = 6
2 X 4 = 2 + 2 + 2 + 2 = 8, etc.
That is, in each subsequent example there is an increase by 2.
After going through the multiplication of the number 2, set the first number to 3 by clicking on the second arrow, and the second number to 1 by clicking on the third arrow several times. And then go through the multiplication of the number 3.
This way you will go through all the multiplication tables and learn to count in twos, threes, fours, etc.
This skill will significantly reduce the load on memory when memorizing the multiplication table and will make memorization more meaningful.
Interactive multiplication table
To multiply two numbers, click one of the numbers in the top yellow row and the second number in the left yellow column. The intersection of the blue bars will show the result of the multiplication.
By the way, the table clearly shows that when multiplying two numbers, the same result is obtained, regardless of where they stand, that is, 3 X 4 = 4 X 3, etc. This means that you will have to learn half as many examples if you memorize pairs of numbers. (For example: 8 and 2 - 16, 5 and 7 - 35).
Online simulators “Learning the multiplication tables with Lisa Simpson”
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Online games will help you master the multiplication tables - simulators in which you can choose numbers and complexity.
Schoolchildren find the table boring and useless. Children often get angry and upset when trying to figure out a set of numbers that is incomprehensible to them. Parents can make learning easier and fun by preparing ahead of time.
The main rule in learning the multiplication tables is to interest the child. Like adults, they perceive information differently. Some children like to learn poems and songs. Others can sit quietly with their parents at the table and look at the Pythagorean table.
How to teach a child the multiplication table (picture)
Help your child remember the multiplication table easily:
- Cards;
- Counting figures, sticks;
- Special programs for tablets and phones;
- Educational videos and cartoons;
- Poems and songs;
- Images;
- Child's fingers.
Game methods are captivating and give quick results. It is better to start classes in a good mood, when the child is ready to study.
Learning the multiplication tables: life hacks and videos
It is important to understand how a child can more comfortably perceive information so that the process does not turn into “cramming.” Everything is very simple:
Auditory children They learn new things better through conversation. They enjoy learning numbers by repeating examples out loud. A good option to remember the multiplication tables is to learn poems, songs or watch educational videos.
Learning the multiplication table (video)
Visual child learns more easily if vision and imagery are involved. They absorb information with the help of bright drawings, coloring games, which have large colored fonts and numbers.
Multiplication table coloring game (picture)
Also, with a visual child, you can watch educational cartoons in which your favorite characters act as a teacher.
Multiplication table by 9 with Fixies (video)
Kinesthetic children learn through the sensations and feelings they have when coming into contact with new objects and information. In this case, you can try the card method.
Learning the multiplication table using cards (video)
It's important to consider how your child learns best so that learning times tables will be fun and easy.
How to learn the multiplication tables in 5 minutes a day
Kukina Ekaterina Georgievna
mathematics teacher
You've probably heard the opinion more than once that the level of mathematics education is falling.
When my children were in second grade, I clearly understood why the level of mathematics education at school was falling. It is in the second grade, when laying the very foundation of mathematical education, that such a gigantic irreparable hole appears, which cannot be supported by any crutches in the form of calculators.
Namely, the main problem is in the multiplication table. Look at the checkered notebooks that your schoolchildren have.
I went shopping for a long, long time looking for notebooks. And all the same, for everyone - this is the picture.
Multiplication table (picture)
There are even worse notebooks (for high school students), in which there are no multiplication tables, but there are a bunch of meaningless formulas.
Well, why is this notebook bad? An unsuspecting parent sees that there is a multiplication table on the notebook. It seems like you’ve had multiplication tables on your notebooks all your life? What's wrong?
But the problem is that the notebook does NOT contain the multiplication table.
The multiplication table, my dear readers, is this:
Sometimes this same table is even called the beautiful word “Pythagorean table”. You don't have to take the top and left columns, just the main rectangle.
Firstly, this is a table. Secondly, she is interesting!
No child in his right mind would look at examples written out in columns.
Not a single child, no matter how brilliant he is, will be able to find interesting features and patterns in the written examples.
Well, in general, when the teacher says: “learn the multiplication table,” and the child doesn’t even see the table in front of him, he immediately understands that mathematics is a science where ordinary things are named somehow differently and you need a lot, a lot cram, but it’s impossible to understand anything. And in general, we must do it “as it is said,” and not “as it makes sense.”
Why is the Pythagorean table better?
Firstly, there is no garbage and information noise in the form of the left side of the examples.
Secondly, you can think about it. It’s not even written anywhere that this multiplication is just a table.
Thirdly, if it is always at hand and the child constantly bumps into it, he willy-nilly begins to remember these numbers. In particular, he will never answer the question “seven and eight” with 55 - after all, the number 55 is not and never was in the table!
Only children with abnormal memory are able to remember columns of examples. In the "table" you need to remember much less.
In addition, the child automatically looks for patterns. And he finds them himself. Even such patterns are found by children who do not yet know how to multiply.
For example: numbers that are symmetrical relative to the diagonal are equal. You see, the human brain is simply determined to look for symmetry, and if it finds and notices it, it is very happy. And what does it mean? This means that rearranging the places of the factors does not change the product (or that multiplication is commutative, to put it more simply).
Pythagorean table: multiplication (picture)
You see, the child notices this himself! And what a person came up with himself, he will remember forever, unlike what he memorized or was told.
Remember your math exam at university? You forgot all the theorems of the course, except for the one you got, and you had to prove it to the evil teacher! Well, that is if you didn’t cheat, of course. (I'm exaggerating, but it's almost always close to the truth).
And then the child sees that he can not learn the whole table, but only half. If we already know the line of multiplication by 3, then we do not need to remember “eight by three,” but just remember “three by eight.” Already half the work.
And besides, it is very important that your brain does not accept dry information in the form of some incomprehensible columns of examples, but thinks and analyzes. Those. is training.
In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you point at any number and draw a rectangle from the beginning of the table to that number, then the number of cells in the rectangle is your number.
Pythagorean table: multiplication (picture)
And here multiplication already takes on a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of a rectangle is equal to the product of its sides)
You have no idea how much easier it is to divide with such a table!
In short, if your child is in second grade, print out this correct multiplication table for him. Hang a large one on the wall so he can look at it when he does his homework or sits at the computer.
And print and laminate a small one for him (or write on cardstock). Let him carry it to school with him, and just keep it conveniently at hand. (it wouldn’t hurt to highlight the squares diagonally on such a table to make it easier to see)
My kids have this one. And it really helped them in second grade and still helps them a lot in math lessons.
Pythagorean table: multiplication (picture)
Honestly, your average math score will immediately increase, and your child will stop whining that math is stupid. And in addition, it will be easier for your child in the future too. He will understand that he needs to use his brains and not cram. And not only will he understand, he will also learn to do it.
And I repeat: there is nothing wrong with the examples in columns. And the amount of information they contain is the same as in the “table”. But there is nothing good in such examples either. This is informational garbage, from which you will not immediately find what you need.
Praise more often
Come up with ways to encourage your child. These can be pleasant little things that make him happy.
Find an approach if the child is not in the mood
Forcing people to study, shouting, or completely depriving them of entertainment - such methods discourage any desire to study. It makes sense to calmly explain the importance of activities and motivate the child.
Learn the multiplication table gradually
When a child first sees how many numbers he needs to remember, a protest arises. It is better to study at a comfortable pace with rest breaks.
Remember that every child is an individual
As soon as children are compared with friends or classmates, they lose the desire to do anything. It must be remembered that each child has his own pace of learning and the caring attitude of parents is of great importance.
Saying that mistakes are normal
At the first failures, children lose interest and do not want to continue classes. It is important to explain that without mistakes there are no good results. Everything will definitely work out.
Now you know everything about how to teach your child the multiplication tables in different ways to make the stuttering process a joy.
Having experience behind me in teaching my own daughter to read (and quite successful, in my opinion, of course :)), based on some principles, I plan to be guided by them in the future. In particular, when mastering the multiplication table. Many people, probably, in the modern “advanced” world may have questions. Do you need to know it and why? I believe that no one has ever benefited from mental training. At any age it is useful to develop your memory.
The most effective approach to learning multiplication tables
Half the result, or even more, often depends on which learning approach to choose. I am always guided by a number of principles. To achieve maximum results, the child needs:
- introduce;
— to interest;
— demonstrate the need for application and use by personal example;
- do not force;
- encourage every achievement, even what seems minimal to us adults at first glance;
- do not humiliate;
- compare with yourself, saying that it was much more difficult for you, and the results were much more modest).
The last point has an unconditional effect on my daughter, and she continues her endeavors with redoubled strength and perseverance.
Moral preparation of parents
This subtitle may seem humorous, but I would not omit it. Because by the time my daughter starts learning the multiplication tables at school, 3.5 years will have passed. Now children take it in second grade. Some start in the first half of the year, others in the second. With our Ministry of Education, which never ceases to amaze with its experiments and innovations, we must be prepared for anything. 🙂 Therefore, I decided to familiarize myself with a number of methods for studying a set of 64 examples in advance. That's what I advise you to do. In any case, it won’t be superfluous. And then the question of whether you will never arise.
Preparing a child to study the multiplication table
You will still have to become familiar with the multiplication table and memorize it. As in any business, the process will go easier and faster if you prepare for it. What do little children like to do most? Of course, play. So why not use this to the fullest for the all-round development and education of the child? It doesn't matter whether it's reading or music. That is why the multiplication table in a playful form, which I will now show you, seems to be the most effective tool for my daughter and me.
What is included in our preparation plan for studying the multiplication tables with my daughter (let her be five 🙂)?
Getting to know the numbers. We have numbers in different variations: magnets, cubes, stickers and long-forgotten by everyone, but very exciting, abacus.
Explanation of the presence of the simplest mathematical operations: addition, subtraction (multiplication and division at this age can be safely omitted).
We count together with tens up to 100 and hundreds up to 1000.
We mastered counting in reverse order.
Add and subtract within 10.
Let's get acquainted with the concepts of greater than, less than and equal to.
We are gradually learning mathematical signs: +, -, ?, ?, =. >,<.
This is what our foundation for further achievements in the mathematical sciences consists of today. Just in case, I remind you that my child is still 5 months away from his first 5th birthday! 🙂
When it comes directly to learning the multiplication tables, I plan to use some tricks studying it in a playful way, which successfully helped my goddaughter master this entire set of 64 examples. I will tell you more about them a little later in this article.
Methods for learning multiplication tables
Conventionally, I can divide the methods into:
1) classical (standard), which consists of memorization through repeated repetition;
2) familiarization and memorization of the multiplication table in a playful way.
Classic method
This is a method as old as time. It consists of 64 examples that need to be simply memorized. This is how we, our parents, and grandparents were taught. The result, of course, over time was the same for everyone, with rare exceptions. We remembered everything, but the process was boring and uninteresting. Yes, the method is effective, but it often causes hostility towards the subject of mathematics as a whole.
Is it possible to make it more interesting, exciting and diverse? Certainly. More on this below.
Learning the multiplication table in a playful way
If 20-30 years ago our assistants were only textbooks and a blackboard with chalk, today we can safely add to this list:
— electronic posters;
- Cell phones;
— computers;
— tablets;
— other computing devices with multimedia functionality.
Does this surprise you? I'm not here. Because we live in the 21st century. So why not take advantage of all modern advantages wisely in your education?
Electronic posters for learning multiplication tables
Now there are a lot of different posters for studying the multiplication tables, including. I’ll say right away that I’m not at all impressed by Chinese electronic posters that “speak” in a nasty voice, and even with errors. If you come across a decent copy of a domestic manufacturer, then this option is acceptable. Otherwise, it is better to abstain from it.
Computer simulators
I really like the multiplication skill simulator located on the website bi2o2t.ru. Here I learned a lot of interesting and useful information. If you decide to use this site, I recommend going to the “Trainers” section and starting with the “Instructions” subsection (http://bi2o2t.ru/training/default), where the methodology used is described in detail.
Maybe your child will also like the video clip-counting game “Visual Multiplication Table”
If you have a tablet, then by going to the Play Store and downloading the program “2?2=4 - Learning the multiplication tables”, you will receive interactive additional material. Now you will definitely “force” your schoolchild, playing naval battle, to master the multiplication table quite quickly without noticing it.
Board games
Now many have begun to forget about this opportunity to spend time together. And very much in vain. This can be helpful in all ways.
Lotto is the best assistant in learning the multiplication tables in a playful way
You can take ready-made cards, or you can make them yourself with your children. This will not only be an entertaining creative process, but also another stage in learning the multiplication table, through memorization through the process of repetition and visualization.
To get a full set of cards you will need:
- cardboard or thick paper;
- paints, pencils, felt-tip pens;
- rulers and scissors.
All of the above will not be useful if you use a computer and a color printer. But I think that today it will be hackneyed and banal. So, arm yourself with colored pencils and start creating!
If you want the materials made by your students to last longer, I recommend resorting to lamination.
We make cards with examples of multiplication in order, starting with 1?1 and ending with 10?10. I think that 8 examples on one in different directions will be quite enough. Separately, we prepare cards with answers from 1 to 100. You don’t have to stop at 10?10, but go to 12?12 or even further. It will be useful, unusual, but will serve as good training for the mind. We cut the cards with answers so that there is one on each. Everything is ready, you can start. Depending on the number of players, we distribute one or two cards to each. The answers can be put in an opaque bag and pulled out and named. If the leader shouts out 8, then those whose example result forms this number close their cells: 1?8, 2?4, 4?2 and 8?1. The winner is the one who quickly closes all the cells of his cards correctly.
SNAP or always be prepared
It is a set of cards with single examples (5?6, 5?8, 6?8, etc.) and answers (30, 40, 48, etc.). Deal an equal number of cards to players. Taking turns, holding the cards face down, each player takes out one card and places one on top of the other. If the answer 45 is placed immediately on the product 5?9 or 9?5, then the one who first noticed this coincidence shouts SNAP loudly and covers the pile with his hand, taking it all for himself. The one who ends up with more cards wins.
Outdoor games
Everyone knows that movement is life. And children are an inexhaustible source of energy, which they constantly strive to throw out somewhere. Even this, if turned in the right direction, can be used to study the multiplication table.
Count your fingers, or maybe your neighbor will have more :)
I came across this game. It consists of asking the children to show one finger at a time (for example, the thumb) and counting them, reaching 20 or 30 (depending on the number of children). Then ask all the children to put two fingers forward, thus counting by twos. Now three fingers. Then four at a time. Children love to count in fives. After all, everyone is familiar with the expression: “High five!” So easily and cheerfully we reach counting by tens. In summer you can also connect your legs. But it will be less practical, since it is only suitable for counting in fives, since not everyone can bend one toe at a time. Although, who knows, maybe at the same time you will reveal fantastic flexibility in someone. 🙂
Cross by multiplying
We divide the children into two teams. We draw a circle on the asphalt with chalk and place a stack of example cards in its center. We select one player from each team. They, measuring 30 steps, diverge in opposite directions from the circle. Players from each team take turns taking the top card from the pile and giving their answer. If the answer is correct (6? 7 = 42), then the bat card is set aside and you can run to the farthest player of your team. If an incorrect answer is given, the card is placed at the very bottom of the deck and the next one is taken until the correct answer is received. The task of each team is to transport all players to the other side to the farthest player as quickly as possible.
Now you see that you can learn the multiplication table in a variety of ways. Considering that children love colored cards, competitions and outdoor games, it would be unwise not to take advantage of this. After all, in this way you will make it clear to little future scientists that in order to learn something, it is not at all necessary to just sit hunched over textbooks and notebooks. Here’s one more (and to be honest, far from one :) proof that any action ultimately produces results.
Here is a free online game with multiplication tables. A mouse is enough to play. Choose pairs of chips with the same result. For example, 2x2 and 4. Or 6x6 and 36.
Rules of the game:
- Remove chips with the same result;
- Each level must be cleared within a certain time;
- The remaining time is shown by the indicator at the bottom;
- The higher the level, the less time is given;
- For removing the correct chips, a time bonus is given;
- You can play endlessly, the number of levels is unlimited.
If you forgot the multiplication table, you can press the button with a question mark and look at it. After this, the game will start again. Thus, if you want to score more points, play without tips!
Endless game or...
The game ends when the time allotted for the level runs out. Then a window appears with the number of points scored and levels achieved.
Who even came up with this idea - to make a game based on the Pythagorean table?
Once again playing Bejeweled, received as a gift from Origin, one programmer thought - what if we use the same or similar mechanism in an educational game. He tried it and liked it. After all, the principle remains the same - collect combinations.
Multiplication table combinations? Yes, you are laughing!
Not at all. Millions of people collect combinations of three chips in different games, and even rejoice. A in Pythagoras you need to collect combinations of just two chips. Click on one, click on the other. It doesn’t matter where they are located - the game does not impose any additional restrictions. It is only important that the value of the chips be the same.
The first levels are too easy, but I thought...
The first levels consist of only 4 chips or two pairs. This is done to quickly enter the game so that the brain can wake up and gradually work at full capacity. Every three levels the number of chips will increase until it fills the entire field.
When the chips fill the entire field and you have 40 seconds left,
Let's see if you call it too easy?
The difficulty stops increasing in the program after the chips fill the entire field. But it will increase in your brain - due to fatigue. Unless, of course, you are a genius calculator like the Soviet millionaire Koreiko.
What if the chip doesn't have a pair?
The game is made in such a way that chips always have pairs. She takes pieces of the multiplication table in the form 2x2 = 4, and then places the factors on one piece and the results on another. Thus, each level has a solution. But perhaps it’s just that you forgot something from the multiplication table. This is the test - do you remember this magic well?
I liked the game, how can I thank the developer
Show this page to as many people as possible. :)
Strategies and Tips
Why is everything so bright, like in a kaleidoscope?
The world is already full of dull multiplication tables and colorless games with them. And most importantly, colors have an additional function.
Products are in white, multipliers are in black.
All chips with multipliers are painted in lighter colors. And the font on them is black.
Chips with the result of multiplication, on the contrary, are painted in darker, more intense colors. And the font on them is white.
Moreover, the colors contain an additional hint that I, as a programmer, did not specifically plan, but it turned out naturally.
You can also win by color!
This is a secret strategy that makes the game easier by knowing the color of the winning chips.
All colors can be divided into pairs:
- Yellow Red
- Light blue - dark blue
- light green - dark green
So, paired chips with multipliers and results are always paired not only by numerical value, but also by color. For example, look at this picture
Light blue and dark blue are paired colors
If you choose a blue chip with a 4x7, the choice of paired chips is reduced to dark blue ones. At this point in the game it's 28 and 63. If you've forgotten the exact product of 4 and 7, you can randomly poke one of these dark blue tiles (very dark, actually). Not a bad strategy for those who don't like math.
So, along the way, in addition to the multiplication tables, you can train your attention and eye.
I see chips with the same numbers! Is this a bug?
This is a consequence of the fact that many products in the multiplication table are repeated. Eg, 36 can be formed as 9x4. Or like 6x6.
Two red thirty at the top is not a bug,
and the results for 5x6 and 6x5, which fell in the same series
You can remove tiles with the same numbers as pairs. But remember - after this you will have to find their factors. And comparing different multipliers is much more difficult.
Hint: chips with different multipliers, but the same result, are also counted as a pair! You can choose 3x4 and 2x6 and that will be the right pair- because these products have the same result (12).
Multiplication table used in the game
You can try to play by looking at this table. At the very least, you will train your attention :)
Adults should approach the organization of children's leisure as responsibly as possible, and students should use free minutes with special interest so as not to waste time. Most kids who are just learning the basics of arithmetic call the multiplication table a real instrument of torture. This is a useful tool that lays a solid foundation in the development of a child's intellectual abilities.
Stupid memorization is boring and uninteresting
Boring examples are easier to remember when learning takes place in a playful way. Test this effective method on yourself and get positive results very quickly.
The main differences between math toys for kids:
- Simple gameplay. To perform game manipulations, just click the mouse and get the correct answer;
- To increase the difficulty level, there is a time limit and a limit on the number of errors, exceeding which you need to start all over again;
- A fun game format makes it much easier to memorize the correct answers in columns and the basic principles of multiplication and division needed to solve simple examples.
Learn by playing with cool tutorials from Quicksave
Several persistent online classes will definitely bring the desired result. Don't miss the opportunity to test high-quality and informative games for kids for free to help them understand basic mathematical operations. Parents should be sensitive to possible difficulties when their child masters material that is incomprehensible at first glance.
Memorizing the algorithm for multiplying numbers and the child memorizing features and patterns without outside interference is a competent approach that turns a little spectacular fun into an exciting intellectual quest.
