This technique shows in a concrete manner the subtraction of integers. Use pennies, dollars, apples, jelly beans or whatever is available. Give the learner a number of the objects, say 6. Tell him he has to give 4 of them back. He can count how many are left. Ask the learner to write each problem and answer on paper. For this problem, he would write 6 - 4 = 2. When he has the hang of it, give him 5 objects and tell him to give 7 of them back. As they count out the objects, they realize that they don't have enough. Have him determine how many more he would need to have the correct amount. This problem would be written 5 - 7 = -2.
Number lines are one of the best ways to help students understand and "see" the process of subtracting integers.
_________________________________________
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
For the problem 6 - 4, have the learner start at the number 6 and move 4 spaces to the left. She ends up at the number 2. When the problem is 4 - 6, she starts at 4, moves 6 spaces to the left and end up at -2. Many learners don't want to count the number 0 as they move. Tell them that 0 is an important number and cannot be skipped.
Understanding what absolute value means is critical when teaching the rules for subtracting integers. Absolute value simply means how far a number is from zero on the number line. The absolute value of 8 is 8, because it takes 8 steps to reach zero on the number line. Since it takes 8 steps to reach zero from -8 on the number line, the absolute value of -8 is also 8.
After the learner understands what happens when he subtracts integers, he should be ready for the rules and be able to apply them. There are just three rules for combining integers.
1-When both numbers are positive, add the numbers and the answer will be positive. (4 + 3 = 7)
2-When both numbers are negative, add the numbers and the answer will be negative. (-4 - 3 = -7)
3-With one positive and one negative number, subtract the smaller absolute value from the larger absolute value. The answer will have the same sign as the number with the largest absolute value.
(4 - 3 = 1, 3 - 4 = -1)