Teachers should place emphasis on the use of mathematical models for representing the concrete world. Some mathematical models are open number line and diagrams through to familiarize students with math notations and numbers. Teachers can use proportional models to teach how the number and size of objects grow larger. Blocks and straw bundles are good examples of proportional models and immature minds grasp mathematical concepts more easily through them. Non-proportional models teach the multiplication of value or number which has no connection with size. Teachers refer to the use of money to explain this concept.
Teachers can use counters and number line to teach the additive properties of numbers or concepts like subtraction. Little balls are used as representative figures for counters with -- or + signs drawn inside. For example, 5 small balls with + signs represent 5. 3 small balls with -- sign on them represent 3. The representation is 5 + (-3) and the result is +2 as the plus and minus pairs cancel themselves.
To represent the addition of integers, units have to be moved either to the left or to the right on a number line. The starting point on the number line is the first number. When positive integers are added, the required numbers of units have to be moved to the right. In case of negative integers, the required numbers of units should be moved to the left. 8 + (-5) requires the student to start at 8 and 5 units have to be moved towards the left.
Hundred flats, ten rods and unit cubes make up base 10 blocks. Teachers may create thousand cubes for demonstration in front of children. Students can use 10 thousand cubes and stack them to represent a value of 10 thousand or 10000. Unit cubes also generate a list of facts on subtraction which you can demonstrate in front of your students in the following manner: 4+3 = 7, 3+4 = 7, 7-3 =4, 7-4 = 3.