Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Newton’s second law of motion

Let us go back to the legend of Newton and the apple. From the work on statics we will find that the apple stays on the tree as long as the apple stalk is strong enough to support the weight of the apple. As the apple grows there will come a point when the weight is too great and so the stalk will break and the apple falls. The quantity that is being added to the apple as it grows is mass. Sometimes this is confused with weight but there have now been many examples of fruits and seeds being grown inside orbiting spacecraft where every object is weightless and would float if not anchored down.

Mass is the amount of matter in a body, measured in kilograms (kg).

The reason that the apple hangs downwards on the tree, and eventually falls downwards, is that there is a force of attraction between the earth and any object that is close to it. This is the gravitational force and is directed towards the centre of the earth. We experience this as a vertical, downward force. The apple is therefore pulled downwards by the effect of gravity, commonly known as its weight. Any apple that started to grow upwards on its stalk would quickly bend the stalk over and hang down due to this gravitational effect. As the mass of the apple increases due to growth, so does the weight until the point is reached where the weight is just greater than the largest force that can be tolerated by the stalk. As a result the stalk breaks.

Now let us look at the motion of the apple once it has parted company with the tree. It still has mass, of course, as this is a fundamental property to do with its size and the amount of matter it contains. Therefore it must also have a weight, since this is the force due to gravity acting on the apple’s mass. Hence there is a downwards force on the apple which makes it start to move downwards and get faster and faster. In other words, it accelerates. What Newton showed was that the force and mass for any body were linked to this acceleration for any kind of motion, not just falling under gravity. What Newton stated as his Second Law of Motion may be written as follows.

A body’s acceleration a is proportional to the resultant force F on the body and inversely proportional to the mass m of the body.

This seems quite complicated in words but is very simple mathematically in the form that we shall use.

F = ma