Multiplication table for 2.3 4.5 6.7 8.9. Multiplication by four. Find an approach if the child is not in the mood

Schoolchildren find the table boring and useless. Often children get angry, upset, trying to figure out a set of numbers they do not understand. Parents can make learning easy and fun by preparing ahead of time.

The basic rule in learning the multiplication table is to interest the child. Like adults, they perceive information differently. Some children like to learn poems and songs. Others can sit quietly at the table with their parents and look at the Pythagorean table.

How to teach a child the multiplication table (picture)

Easy to remember the multiplication table for a child help:

• Cards;
• Counting figures, sticks;
• Special programs for tablet and phone;
• 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 good mood when the child is in school.

Learning the multiplication table: life hacks and videos

It is important to understand how it is more comfortable for a child to perceive information so that the process does not turn into “cramming”. Everything is very simple:

Auditory children it is better to learn new things in conversation. They like to memorize numbers by repeating examples out loud. A good option to remember the multiplication table is to learn poems, songs or watch educational videos.

Learning the multiplication table (video)

visual child learns more easily when vision and imagery are involved. They absorb information through bright drawings, coloring games that 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.

9 times table with Fixies (video)

Kinesthetic children learn through the sensations and feelings that they have when they come into contact with a new object and information. In this case, you can try the card method.

Learning the multiplication table with cards (video)

It is important to consider how your child learns best so that the process of memorizing the multiplication table will be fun and easy.

How to learn the multiplication table in 5 minutes a day

Kukina Ekaterina Georgievna

mathematics teacher

You have probably heard the opinion more than once that the level mathematics education falls.

So, when my children were in the second grade, I clearly understood why the level of mathematical 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 arises that you can no longer support with any crutches in the form of calculators.

Namely, the main problem- 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 anyway, for everyone - here is such a picture.

Multiplication table (picture)

There are even worse notebooks (for high school students), where there are no multiplication tables, but there are a bunch of meaningless formulas.

So what's wrong with this notebook? The unsuspecting parent sees that the multiplication table is on the notebook. It seems that all your life there was a multiplication table on notebooks? What's wrong?

And the problem is just that the multiplication table is NOT on the notebook.

The multiplication table, my dear readers, is this:

Sometimes the same table is even called beautiful word"table of Pythagoras". The top and left columns can be omitted, only the main rectangle.

First, it's a table. Second, it's interesting!

No child in their right mind will consider the examples written out in columns.

Not a single child, no matter how brilliant he may be, will not be able to find interesting tricks and patterns in the written examples.

Well, in general, when a 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 such a science where ordinary things are named somehow differently and you need a lot, a lot cramming, but it is impossible to understand anything. And in general, it is necessary to do "as it is said", and not "as it makes sense".

Why is the Pythagorean table better?

Firstly, it does not contain garbage and informational 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 she is constantly at hand and the child constantly stumbles upon her, he willy-nilly begins to memorize these numbers. In particular, he will never answer the question "seven of eight" with 55 - after all, the number 55 is not and never was in the table at all!

Only children with abnormal memory can memorize 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 about the diagonal are equal. You see, the human brain is just set to look for symmetry, and if it finds and notices, it is very happy. And what does it mean? This means that the product does not change from permutation of the places of the factors (or that the multiplication is commutative, to put it simply).

Pythagorean table: multiplication (picture)

You see, the child notices it himself! And what a person invented himself, he will remember forever, in contrast to what he memorized or was told.

Remember your high school math exam? You forgot all the theorems of the course, except for the one that you got, and you had to prove it to the evil teacher! Well, that's if you didn't cheat, of course. (I exaggerate, but almost always it is close to the truth).

And then the child sees that you can not learn the entire table, but only half. If we already know the line of multiplication by 3, then we do not need to memorize "eight by three", but just remember "three by eight". Half the work already.

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. trains.

In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you poke at any number and draw a rectangle from the beginning of the table to this number, then the number of cells in the rectangle is your number.

Pythagorean table: multiplication (picture)

And here the multiplication already gets a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of ​​\u200b\u200ba rectangle is equal to the product of its sides)

And you have no idea how much easier it is to divide with such a table!

In short, if your child is in the second grade, print out such a correct multiplication table for him. Hang a large one on the wall so that he looks at it when he does his homework or sits at the computer.

And print and laminate a small one for him (or write on cardboard). Let him carry it to school with him, and just keep it conveniently at hand. (it does not hurt to highlight the squares diagonally on such a table so that you can see it better)

My kids have this one. And it really helped them in the second grade and still helps a lot in math classes.

Pythagorean table: multiplication (picture)

Here's an honest word, right away GPA in mathematics will increase, and the child will stop whining that mathematics is stupid. And in addition, in the future, your child will also be easier. He will understand that it is necessary to use his brains, and not to cram. And little that he understands, he also learns to do it.

And I repeat: there is nothing wrong with examples with 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

Think of ways to reward your child. It could be the little things that make him happy.

Find an approach if the child is not in the mood

Forced to study, scream or completely deprive of entertainment - such methods beat off any desire to study. It makes sense to calmly explain the importance of classes and motivate the child.

Learn the multiplication table step by step

When a child first sees how many numbers he needs to remember, a protest arises. It is better to practice 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 careful attitude of parents is of great importance.

Talk about making mistakes

At the first failures, children lose interest, do not want to continue classes. It is important to explain that without mistakes there are no good results. Everything will surely work out.

Now you know everything about how to teach a child the multiplication table in different ways so that the stammering process is a joy.

With the best free game, learn very fast. Check it out yourself!

Learn multiplication table - game

Try our educational e-game. Using it, you will be able to decide tomorrow math problems in class at the blackboard with no answers, without resorting to the tablet to multiply the numbers. One has only to start playing, and after 40 minutes there will be an excellent result. And to consolidate the result, train several times, not forgetting the breaks. Ideally, every day (save the page so you don't lose it). game form The simulator is suitable for both boys and girls.

See the full cheat sheet below.

Multiplication directly on the site (online)

How to multiply numbers by a column (mathematics video)

To practice and learn quickly, you can also try to multiply numbers by a column.

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The multiplication table is a basic concept in mathematics, which we get acquainted with in primary school and which we then use all our lives, regardless of profession. But the children are in no hurry to memorize the endless columns by heart, especially if the task was on vacation.

website will give tips on how to easily learn the table with children and make this process fun.

Pythagorean table

Despite the fact that the task is to learn, that is, memorize, the table by heart, it is first of all important to understand the essence of the action itself. To do this, you can replace multiplication with addition: the same numbers are added as many times as we multiply. For example, 6×8 is 8 times 6.

Highlight the same values

A great helper for learning multiplication is the Pythagorean table, which also demonstrates some patterns. For example, what about t changing the places of the factors, the product does not change: 4 × 6 \u003d 6 × 4. Mark such “mirror” answers with a certain color - this will help you remember and not get confused when repeating.

It is better to start studying the Pythagorean table with the simplest and most understandable parts: multiplication by 1, 2, 5 and 10. When multiplied by one, the number remains unchanged, while multiplying by 2 gives us twice the value. All answers multiplied by 5 end either in 0 or 5. But multiplying by 10, in the answer we get a two-digit number from the digit that we multiplied and zero.

Table for fixing the result

To consolidate the results, draw an empty Pythagorean table with your child and invite him to fill in the cells with the correct answers. To do this, you only need a piece of paper, a pencil and a ruler. You need to draw a square and divide it into 10 parts vertically and horizontally. And then fill in the top line and the leftmost column with numbers from 1 to 9, skipping the first cell.

Of course, all children are individual and there is no universal recipe. The main task of a parent is to find an approach and support his child, because we all once started with such simple and complex steps at the same time.

When a student is faced with the task of learning the multiplication table, then, of course, parents want to help him and are looking for the best fast way learn the multiplication table. There are a lot of techniques, but everything needs an individual approach to your little one. We will tell you about how you can easily explain the principles of multiplying numbers to your child and help him remember it in the shortest possible time.

Most likely, it will be easiest for a student to multiply by 1 and 10. This account is given very easily to kids, since there is nothing terrible and difficult. Try drawing some examples in front of the baby, such as 1*2=2, 1*5=5, 8*1=8. In any case, the number will remain unchanged.

With the 10th it will be a little more complicated, but if you explain everything to a child of 8-9 years old, that multiplying by 10 is similar to the principle by 1, but you need to add 0 to the result, then the kid will remember it very easily. Be sure to tell your student that, having learned multiplication by 1 and by 10, he will already know the first and last line in all other columns.

Multiply by 2

With a deuce, it will also be easy, since you will tell the baby that the correct result can be obtained by adding the two proposed numbers. For example, if a child has an example of 2 * 6, then he just needs to add 6 + 6 together and get 12. After each lesson, be sure to take a break for at least an hour, and it is best to continue classes every other day.

Multiply by 3

With multiplication by three, you can try the same method as with two. You just need to explain to the child that 3 * 4 and 4 + 4 + 4 will equally equal 12. If this method is absolutely not suitable for your child, then try playing with associations. First, ask the baby to dream up and draw his associations to the numbers from 1 to 9.

After that, start making up a story for each example, and so the student will remember the 3 sign much faster. Let your child play with these drawings and make up stories for them. You can draw your own story for each example, so it will be much easier to remember.

Multiply by 4

To make it easy for your baby to remember multiplying by 4, remind him of the principle that was used when he studied columns with a deuce. But only now we will need to double the desired number and double the result. For example, 4*4= 4*2=8*2=16.

Multiplication table 4

Multiply by 5

When studying the action by 5, you should immediately draw the attention of your 8-9 year old child to the fact that on the result of multiplication in this column, all results will end either in 5 or in zero. Also note that 5 is half a dozen. Therefore, the answers will be easier to multiply the number not by 5, but by 10 and then divide the result in half. For example, we need to find the answer to the example 7*5. Try 7 * 10, it will be 70. Now divide 70 by 2 - it will be 35.

Multiply by 6

For the six, there is also a way to make memorization easy for children of 8 years old, and this column of the plate was learned in an hour. Try to remind the kid how he learned the tablet for 3 and invite him to add the same number to the result. For example, 3*5=15 means 6*5=3*5+15=30.

Multiplication table 6

Multiply by 7

If multiplying to 6 is no longer a big deal for a child of 8 years old, then understanding how to multiply by 7 will be easy for him. If you need 7 * 2, then you just need to add 7 and 7, you get 14. An example of 7 * 4 will mean that the number needs to be doubled twice and so on. Separately, you will need to write down and learn only the multiplication by 7, 8 and 9.

Multiply by 8

By analogy with the previous methods, multiplying by 8 can be compared to four, only the result will need to be doubled three times. If in our example it is written that 4 * 8, then we multiply 2 by 4, the resulting eight by two more, we get 16 and then we multiply this result by another 2 and get 32.

Multiplication table 8

Multiply by 9

There is a simple and very easy method for multiplying by 9 on your fingers. It will definitely appeal to children 8-9 years old, since you can learn it in just a few minutes, and not in an hour or two.

Ask the student to place their pens on the table, palms down. Count your fingers from left to right. So, for example, we have an example of 7*9. We count 7 fingers on the right. We bend the finger on which we stopped the count. How many fingers are not bent to the left of the seventh - six.

So, we will have six tens in the answer. How many fingers to the right of the bent one - three. This will be the number of units in the answer. So we realized that the answer is 63. Such a study of the multiplication tablet on the fingers will be useful. Do not scold the baby that he uses this method for too long. It is this method that will allow the baby to firmly and firmly remember the multiplication by 9.

Multiplication table 9

How to multiply numbers by a column

Of course, after a child of 9 years old has learned the multiplication table well, he will need to be taught to multiply two-digit ones in a column, and then three-digit numbers. Numbers that are multiplied by each other are called multipliers. They are called the first multiplier, the second multiplier, and so on. The result of multiplication will be called "product".

To multiply two numbers, you will need to arrange them in a column on top of each other so that units are above ones, tens over tens, and so on. The next step is that the top number will need to be multiplied by the digit of the bottom number. First, one is multiplied, then tens, hundreds, and so on. The result must be written below the line.

If as a result of multiplication you get a number that is more than ten, that only the last digit of the result goes under the line, and ten, if any, is written on top. Then this ten must be added to the result of multiplying ten by one. Multiplying the top number by tens and hundreds of the bottom number follows the same rules.

If you give your child the opportunity to calmly learn this or that method of memorizing the multiplication table, then he will quickly begin to count. Do not insist if the baby does not want to engage. You may well follow the lead of the child, allowing him not to repeat the table.

show him concrete examples in life, where the table can be useful to him. For example, ask your daughter to count how many sweets you need to buy so that her girlfriends all get three. It will be easy and interesting for a girl to find the answer, since this directly concerns practice and life.

In modern elementary school, the multiplication table begins to be taught in the second grade and ends in the third, and it is often given to learn the multiplication table in the summer. If you didn’t study in the summer, and the child is still “floating” in multiplication examples, we will tell you how to learn the multiplication table quickly and fun - with the help of drawings, games and even fingers.

Problems that often arise in children in connection with the multiplication table:

1. Children don't know what 7 × 8 is.
2. They do not see that the problem must be solved by multiplication (because it does not say directly: "What is 8 times 4?")
3. They do not understand that if you know that 4 × 9 = 36, then you also know what 9 × 4, 36: 4 and 36: 9 is equal to.
4. They do not know how to use their knowledge and restore a forgotten piece of the table from it.

How to quickly learn the multiplication table: the language of multiplication

Before you start learning the multiplication table with your child, it’s worth stepping back a little and realizing that a simple multiplication example can be described in a surprising number of different ways. Take the 3 × 4 example. You can read it as:

• three times four (or four times three);
• three times four;
• three times four;
• the product of three and four.

At first, it is far from obvious to the child that all these phrases mean multiplication. You can help your son or daughter if, instead of repeating yourself, you kind of casually use different language talking about multiplication. For example: "So how much is three times four? What happens if you take three times four?"

How to learn the multiplication table

The most natural way for children to learn the multiplication table is to start with the easiest and work your way up to the hardest. A reasonable sequence is:

Multiply by ten (10, 20, 30...), which children learn naturally in the process of learning to count.

Multiply by five (after all, we all have five fingers and toes).

Multiplication by two. Pairs, even numbers and doubling are familiar even to young children.

Multiply by four (after all, this is just a doubling of multiplication by two) and eight (doubling of multiplication by four).

Multiplication by nine (for this there are quite convenient tricks, about them below).

Multiply by three and six.

Multiplication by seven.

Why 3x7 equals 7x3

When helping your child memorize the multiplication table, it is very important to explain to him that the order of the numbers does not matter: 3 × 7 gives the same answer as 7 × 3. One of better ways show it clearly use an array. This is a special mathematical word denoting a set of numbers or shapes enclosed in a rectangle. Here, for example, is an array of three rows and seven columns.

*******
*******
*******

An array is a simple and visual tool to help a child understand how multiplication and fractions work. How many dots are there in a 3 by 7 rectangle? Three lines of seven elements each have 21 elements. In other words, arrays are an easy-to-understand way to visualize multiplication, in this case 3 × 7 = 21.

What if we draw the array in a different way?

***
***
***
***
***
***
***

Obviously, both arrays must have the same number of points (they do not have to be counted individually), because if the first array is rotated a quarter of a turn, it will look exactly like the second.

Look around, look nearby, in the house or on the street, for some arrays. Take a look at the cakes in the box, for example. Cakes are stacked in a 4 by 3 array. And if you rotate? Then 3 by 4.

Now take a look at the windows of the high-rise building. Wow, this is also an array, 5 by 4! Or maybe 4 by 5, how to look? As soon as you start paying attention to arrays, it turns out that they are everywhere.

If you have already taught your children the idea that 3 × 7 is the same as 7 × 3, then the number of multiplication facts that you need to remember decreases dramatically. It is worth memorizing 3 × 7 - and as a bonus, you get the answer to 7 × 3.

Knowing the commutative law of multiplication reduces the number of multiplication facts from 100 to 55 (not exactly by half due to cases of squaring, such as 3×3 or 7×7, which do not have a pair).

Each of the numbers above the dotted diagonal (for example, 5 × 8 = 40) is also present below it (8 × 5 = 40).

The table below contains another hint. Children usually begin to learn the multiplication table using counting algorithms. To figure out what 8 × 4 is, they count like this: 4, 8, 12, 16, 20, 24, 28, 32. But if you know that eight times four is the same as four times eight, then 8, 16 , 24, 32 will be faster. In Japan, children are specially taught to "put the lower number first." Seven times 3? Do not do this, count 3 times 7 better.

Learning the squares of numbers

The result of multiplying a number by itself (1×1, 2×2, 3×3, etc.) is known as square number. This is because graphically such a multiplication corresponds to a square array. If you go back to the multiplication table and look at its diagonal, you will see that it is all squares of numbers.

They have interesting feature which you can explore with your child. When listing the squares of numbers, pay attention to how much they increase each time:

Squares of numbers 0 1 4 9 16 25 36 49...
Difference 1 3 5 7 9 11 13

This curious connection between square numbers and odd numbers is a perfect example of how different types numbers are related in mathematics.

Multiplication table for 5 and 10

The first and easiest table to memorize is the 10 multiplication table: 10, 20, 30, 40...

In addition, children memorize the multiplication table for five with relative ease, and their hands and feet, visually representing four fives, help them with this.

It is also convenient that the numbers in the five times table always end in 5 or 0. (So, we know for sure that the number 3,451,254,947,815 is present in the five times table, although we cannot verify this with a calculator: on such a number simply does not fit on the screen of the device).

Children can easily double numbers. This is probably due to the fact that we have two hands with five fingers on each. However, children do not always associate doubling with multiplying by two. The child may know that if you double six, you get 12, but when you ask him what six is ​​equal to two, he has to count: 2, 4, 6, 8, 10, 12. In this case, you should remind him that six is ​​two - the same as twice six, and twice six - this is the doubled six.

Thus, if your child is good at doubling, then he essentially knows the multiplication table by two. At the same time, he is unlikely to immediately realize that with its help you can quickly imagine a multiplication table for four - for this you just need to double and double again.

Game: double walker

It is possible to adapt any game in which players roll a die so that all rolls count as doubles. This gives several advantages at once: on the one hand, children like the idea of ​​​​going twice as far with each throw as the dice shows; on the other hand, they gradually master the multiplication table by two. In addition (which is important for parents busy with other things), the game ends twice as fast.

9 Times Table: Compensation Method

One way to master the nine times table is to take the result of ten times and subtract the excess.

What is nine times seven equal to? Ten times seven is 70, subtract seven, we get 63.

7 x 9 = (7 x 10) - 7 = 63

Perhaps a quick sketch of the appropriate array will help cement this idea in the child's mind.

If you memorized the multiplication table for nine only up to "nine ten", then nine 25 will confuse you. But ten times 25 is 250, subtract 25, we get 225. 9 × 25 = 225.

Test yourself

Can you solve the 9 × 78 example mentally using the compensation method (multiplying by 10 and subtracting 78)?

There is another convenient way to master the nine times table. It uses fingers and kids love it.

Hold your hands in front of you, palms down. Imagine that your fingers (including the thumb) are numbered from 1 to 10. 1 is the little finger on the left hand (the extreme finger on your left), 10 is the little finger on the right (the extreme finger on the right).

To multiply a number by nine, bend the finger with the corresponding number. Let's say you are interested in nine 7. Bend the finger that you mentally labeled as the seventh number.

Now look at your hands: the number of fingers to the left of the curled one will give you the number of tens in the answer; in this case it is 60. The number of fingers on the right will give the number of units: three. Total: 9 × 7 = 63. Give it a try: this method works with all single digit numbers.

Multiplication table for 3 and 6

For children, the multiplication table by three is one of the most difficult. In this case, there are practically no tricks, and the multiplication table by 3 will simply have to be memorized.

The six times table follows directly from the three times table; here, again, it all comes down to doubling. If you can multiply by three, just double the result and you get a multiplication by six. So 3 x 7 = 21, 6 x 7 = 42.

Multiplication table by 7 - dice game

So, all we have left is the multiplication table for seven. There is good news. If your child has successfully mastered the tables described above, there is no need to memorize anything at all: everything is already in the other tables.

But if your child wants to learn the multiplication table for 7 separately, we will introduce you to a game that will help speed up this process.

You will need as many dice as you can find. Ten, for example, is a great number. Tell your son or daughter that you want to see which of you can add the numbers on the dice the fastest. However, let the children decide for themselves how many dice to roll. And to increase the child's chances of winning, you can agree that he must add the numbers indicated on the upper faces of the cubes, and you - those on both the upper and lower ones.

Have each child choose at least two dice and place them in a glass or mug (they are great for shaking the dice for random rolls). You only need to know how many cubes the child took.

As soon as the dice are rolled, you can immediately calculate how much the numbers on the upper and lower faces will give! How? Very simple: multiply the number of dice by 7. Thus, if three dice were drawn, the sum of the top and bottom numbers would be 21. (The reason, of course, is that the numbers on opposite sides of the die always add up to seven.)

The kids will be so amazed at how fast you can calculate that they'll want to learn this method too so they can use it someday with their buddies.

In the era of the so-called British imperial system of measures and "non-decimal" money, everyone needed to own an account up to 12 × 12 (then there were 12 pence in a shilling, and 12 inches in a foot). But even today, 12 pops up every now and then in the calculations: many people still measure and count in inches (in America this is the standard), and eggs are sold by the dozen and half a dozen.

Little of. A child who freely multiplies numbers greater than ten begins to develop an understanding of how to multiply big numbers. Knowing the multiplication tables for 11 and 12 helps to notice interesting patterns. Here is the complete multiplication table up to 12.

Note that the number eight, for example, occurs four times in the table, while 36 occurs five times. If you connect all the cells with the number eight, you get a smooth curve. The same can be said about the cells with the number 36. Indeed, if a certain number appears in the table more than twice, then all places of its occurrence can be connected by a smooth curve of approximately the same shape.

You can encourage your child to explore on their own, which will keep them busy for (maybe) half an hour or more. Print out several copies of the 12 times 12 multiplication table, and then ask him to do the following:

• colorize all cells with even numbers in red, and with odd numbers in blue;
• determine which numbers occur there most often;
• say how many different numbers are found in the table;
• answer the questions: "What is the most small number does not appear in this table? What other numbers from 1 to 100 are missing in it?

Focus with eleven

The multiplication table for 11 is the easiest to build.

1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
4 x 11 = 44
5 x 11 = 55
6 x 11 = 66
7 x 11 = 77
8 x 11 = 88
9 x 11 = 99

• Take any number from ten to 99 - let's say 26.
• Break it into two numbers and push them apart so that there is a gap in the middle: 2 _ 6.
• Add together the two digits of your number. 2 + 6 = 8 and paste what you got in the middle: 2 8 6

This is the answer! 26 x 11 = 286.

But be careful. What happens when you multiply 75 × 11?

• Splitting the number: 7 _ 5
• Add up: 7 + 5 = 12
• We insert the result in the middle and we get 7125, which is obviously wrong!

What's the matter? There is a little trick to this example that needs to be applied when the digits used to represent the number add up to ten or more (7 + 5 = 12). We add one to the first of our numbers. Therefore, 75 × 11 will not be 7125, but (7 + 1)25, or 825. So the trick is actually not as simple as it might seem.

Game: beat the calculator

The purpose of this game is to develop the skill of quickly using the multiplication table. You will need a deck of playing cards without pictures and a calculator. Decide which player will use the calculator first.

• The player with the calculator must multiply the two numbers drawn on the cards; however, he must use a calculator, even if he knows the answer (yes, this can be very difficult).
• Another player must multiply the same two numbers in their mind.
• The one who gets the answer first gets a point.
• After ten attempts, the players change places.