# Math Puzzle, Division and Multiplication Worksheet

In ideal conditions, memorizing and practical ways in mathematics are not recommended; because the main thing in mathematics is that the child creates mental schemas on his own. However, it is also wrong to say “There is no memorization in mathematics”. Because the ability to memorize is one of the marvelous features of the human mind, and avoiding using it is like unnecessarily restraining oneself. No cognitive ability of the child should be curtailed.

Memorization is sometimes the precursor of comprehension and sometimes the result. For example, a child in the third grade of primary school may learn the multiplication table spontaneously as a result of learning the concept of rhythmic counting. The child will need the multiplication table during operations and find the result by rhythmic counting. However, it makes things slow until the schema is well established. Because he will have to count rhythmically, starting from one each time. This is the disadvantage of this method. The advantage is that the child creates the mental schema for multiplication on his own.

The opposite way is also quite reasonable. First, the child is asked to memorize the multiplication table. If the child has the ability to memorize easily, he will fulfill this task in a short time. Rhythmic counting, on the other hand, will be understood by itself as he gets involved with Mathematics. In other words, in this method, it is necessary to memorize without thinking first, and the child is expected to create the necessary scheme later. The advantage of this method; child’s multiplication is very fast. However, if he doesn’t like to memorize, he may have trouble at first.

##### Some simple ways to do mental math

Division by 2: If the number to be divisible by two is one-digit, half is taken directly. If it is two-digit, half of the tens and units digits are taken separately and the results are summed. Example: If 38÷2 is to be traded; first take half of 30 (15); The result found is put in a pocket. Then half of 8 is taken (4) and this is put in the other pocket. Then the child is told: “Now add the numbers in your two pockets”. (15+4=19) Putting it in the pocket will make the process concrete in the child’s mind, so it makes it easy to remember the intermediate results.

Division by 4: The number to be divided by four is taken twice. Example: To trade 12÷4: First half of 12 is taken (6) and then half of 6 is taken. The result is 3.

Division by 8: Three times half of the number to be divided by eight is taken. Example: To trade 24÷8: First take half of 24 (12), then half of 12 (6), and then half of6. The result is 3. By the way, the child can use his fingers to remember how many times he will do the halving. When dividing by 8, he can open 3 fingers and close one finger after each division.

Division by 5: The number to be divided by 5 is divided by 10 and doubled. Example: Let’s divide 60 by 5. We divide 60 by ten (6) and we get twice 6, resulting in 12. The alternative to this operation is to double the number first, then divide by 10.

Multiplication by 5: The number to be multiplied by 5 is first multiplied by 10; then half is taken. Example: Let’s find 5 times 60. First, we multiply by ten (600) and then we get half, the result is 300. The alternative to this operation is to halve the number first, then multiply by 10.

Multiply by 15: Multiply the number by ten, add half. Example: Multiply 24 by 15. First, we multiply by ten (240); then we add half (120). (Again, pockets can be used.) 240+120=360.

Multiply by 25: First, we multiply by 100, then divide by 4. (Or vice versa) Example: Let’s multiply 18 by 25. First, we multiply by 100 (1800); then we divide by 4, that is, we halve it twice. 900 and then 450. The result is 450.

These methods can be further developed. The important thing here is to accustom the child to mentally performing the operations. Instead of teaching them all at once, it is important to show examples when appropriate. Apart from that, if the child can create their own schemas; there is no need to impose other schemes on it. Usually, after children have grasped a few methods, they begin to create other schemes themselves. As you can see, halving a number mentally, doubling it mentally, multiplying and dividing by ten in the mind are simple as well as important operations.