This topic covers more advanced topics on integer addition and subtraction while also introducing integer multiplication and division. This series of five lessons furthers the student’s understanding of arithmetic use of the integers. Many key ideas are presented in the lessons on integer addition and subtraction. Further, integer multiplication and division is treated to show the student all of the four basic arithmetic operations with integers.
This topic continues the use of number lines in order to provide a more concrete notion of the ideas presented for the student.
This lesson first introduces the idea that the sum of two positive numbers is positive. It then goes on to show that the sum of two negative numbers is negative. The lesson then utilizes the idea of absolute values to show the idea behind adding two negative numbers. Examples show the student how to add two negative numbers by utilizing absolute values.
This lesson shows the student how to add a positive number and a negative number. The lesson uses number lines to show principles of integer addition. Absolute values are also utilized to show the student that they can find whether the sum will be positive or negative depending on the absolute value of the two addends. The student then learns that adding a positive number and a negative number can be viewed as subtraction, and uses the fact that they can find whether the sum will be positive or negative to find the solution to such problems.
This lesson utilizes the foundation of the previous two lessons. This foundation allows the student to rewrite subtraction involving integers as addition, and then find the solution to the problem with the principles they learned in the previous two lessons.
This lesson uses a pattern-based approach to show that the product of two numbers with different signs is negative, while the product of two numbers with the same sign is positive. The student is reminded of the connection between multiplication and division to learn that the same principle holds for the quotient of integers.
This lesson teaches the student to deal with more than one arithmetic operation that involves integers.