Do you want to have good marks in school? Math is one of the most important subjects which develop analytical thinking.

## 1. Multiplication by 9

Invite students to write a multiplication table of numbers by 9. Note that there are interesting patterns that are not mentioned in the school curriculum:

When multiplying the sequence from 1 to 9 by the number 9, the first digits in the two-digit numbers of the results increase by 1, and the second digits of the same number are successively reduced by 1.

If you write 2 columns of multiplication by 9 from 1 to 10 and from 10 to 1, the results in each row of two columns will consist of the same numbers, which will be opposite.

Lifehack for school children: how to study the multiplication table by 9:

Consider an example: calculate 9×4. To obtain a two-digit number of the result, you must reduce the digit 4 by 1 (4-1 = 3), and to obtain the second digit – subtract from 10 the digit 4 (10-4 = 6). The result is -36.

Thus, you can calculate the result of multiplying any one-digit number by 9!

## 2. Multiplication by the Japanese method

According to the requirements of NUS, the multiplication table in Ukrainian schools will be studied only from the 4th grade. But if you try to master the multiplication by the Japanese method, the tablet will be studied even by a first-grader!

Example: Multiply 2 and 4

According to mathematical theory, this means that it is necessary to calculate 2 + 2 + 2 + 2 =? or 4 + 4 =?

Alternatively, you can use the graphical method and calculate the number of intersections of the corresponding number of lines.

## 3. How easy is it to calculate the percentage of any number?

As a rule, the method of proportion is used to calculate the percentage of a certain number. It is studied in elementary school, and later often used in everyday life. And how else to simplify this mathematical operation? Light!

Example: find 40% of 250.

Decision:

It is necessary to divide both numbers by 10.

40: 10 = 4

250: 10 = 25

2) You should multiply the previously obtained results among themselves:

4×25 = 100

Thus, 40% of 250-100.

Subtraction, addition, division, multiplication – these simple mathematical operations are usually studied with children on simple examples, when the role of numbers is improvised material: counting sticks, toys, surrounding objects. But for children of the XXI century, who, just starting to walk, deftly control the functions of the tablet, can turn on a mobile phone and play interactive games, such ways of learning math are not very attractive. Especially for preschoolers and seniors, computer program developers have created interesting and useful programs.

### Kids Numbers and Math Lite

The program was created by Intellijoy, designed for preschool children and elementary school students. The application consists of several sections, where young mathematicians get acquainted with numbers, learn to count in the mind, add and subtract. The program has a user-friendly interface in Russian, easily installed on Android devices.

## Operation Math

Little children will like this application with an exciting, realistic game plot. The purpose of the mathematical “adventure” is to defeat the insidious and evil Dr. Odd. Training involves three levels, different in complexity. Tasks are interesting, presented in a bright form, giving the child the feeling that she is not learning, but playing. The application has won several US awards, is available for Android and iOS.

## Mathmateer

The application immerses the child in the world of space adventures, distant galaxies, the wonderful world of space. Unfortunately, the program is available only in English, but it trains logic, attention, memory. To begin learning, the child must choose one of 15 characters who will be his avatar-guide in the world of space and mathematics. The application is designed for boys and girls from 9 years old, works on iOS 4.3 and above.

## Geeksmath

The program is designed for students as a tutor, provides a choice of different levels of difficulty, and if there are difficulties with the tasks, you can invite an algorithm for solving them. The application allows you to track student progress by storing learning statistics. Themes have detailed descriptions in Russian, accompanied by clear examples, colorful pictures.

Mobile applications help to master mathematics, deepen mathematical knowledge, develop logic, improve attention, activate mental processes. The colorful design of the programs creates the illusion of a game where the child feels like the main character, and the task of calculation is perceived as steps on the way to victory.

### Quick Brain

This is a game of speed, it is necessary to quickly solve various mathematical problems in the mind and give the correct answers. Quick Brain involves simple mathematical operations, so it is suitable even for children. In addition, you will get math puzzles, concentration simulators and IQ. An application for training concentration, mathematical abilities, memory and oral medicine. The student’s goal in Quick Brain is to get as many correct answers as possible over a period of time. Children can compete with each other by arranging quick but intense entertainment quizzes. The application contains exercises for adding, multiplying and dividing, and is also ideal for short game breaks in the classroom. Using these applications will add variety to your lesson, improve student motivation, help distract you to get back to work and achieve your goal!

### Math theory

Probably the most comprehensive application, which collects courses in mathematics from high school to the first year of technical universities. From elementary algebra to the theory of numbers, functions and matrices.

All of them are cataloged by sections and divided into blocks. All this makes the Math theory application an ideal learning assistant.

### Math42

This is a program for schoolchildren and students, which will not only help to solve examples in mathematics, but also explain in detail the course of the decision. The application offers several solutions to each given example. A training section is available. The application can be downloaded for gadgets that run on iOS. A similar principle is in an Android application called MalMath.

### “Geogebra Classic” – a drawing without a pencil

Still building figures and graphics in a notebook? With Geogebra, you can just draw on your tablet or computer! After all, with the help of the program you can create interactive geometric structures, graphs of functions, tables, as well as analyze related statistics.

### “XSection” – acrobatics of spatial imagination

Why do we need geometry? First of all – for the development of spatial thinking. It is on the development of this skill and works “XSection”. When we draw figures on paper, we transfer three-dimensional bodies into two-dimensional space, which is not always easy to imagine a beginner who is just beginning to study geometry. Hence the problems with studying the subject.

The application contains a set of problems that cannot be solved without moving the two-dimensional image of the polygon into three-dimensional space. And the program will not allow you to create an “impossible” object, which is one of the most common mistakes of students.

The main topics of the tasks: prisms, cubes, parallelepipeds, pyramids, tetrahedra, diagonals of polygons, diagonal section, parallel and central projections, the method of internal projection, etc. The program also has a glossary of geometric terms, step-by-step instructions.

### “Kids Numbers and Math Lite” – math for the youngest

A great app for the youngest students who are just beginning to learn to count, get acquainted with numbers and learn the multiplication table. The program provides basic knowledge of mathematics, and to make it easier for children, it is divided into several categories: “Learning numbers” (can be in English), “Counting mentally”, “Largest and smallest number” (comparing numbers), “Addition and subtraction”.

### “Math Kids” – math for the smartest

Children will definitely like the application, because for the exercises they will receive stickers and will be able to watch funny scenes. For quick and correct completion of the task, children gain stars that can be exchanged for bright pictures. So, the task is to collect pictures, or even competition between classmates “who will collect more.”

The set of exercises has three levels of difficulty:

“Easy” – contains equations for addition and subtraction within 20;

“Medium” – similar exercises within 100;

“Complex” – problems of multiplication and division.

In the application you will also find a set of small (but very interesting!) Puzzles that contain tasks for comparing numbers or groups of objects, creating your own math problems by moving numbers and symbols on the screen, mini-controls, counting objects to puzzle, etc. .

Math Kids also has a monitoring feature that allows parents or teachers to track a child’s progress, change difficulty levels, and view scorecards.

### “MalMath” – those who lag behind the class

Unlike programs that can solve a problem for you, MalMath simply shows the steps to solve it. Thus, when a student does not know how to cope with a difficult task, he can use the program as a personal consultant. Of course, the most useful application will be for children who really want to understand, rather than get a solution without effort.

The application also serves as a generator of random problems in several categories (algebra, geometry, trigonometry, logarithms) and difficulty levels.

Ricardo is a freelance writer specialized in politics. He is with foreignpolicyi.org from the beginning and helps it grow. Email: richardorland4[at]gmai.com