Integers and Rational Numbers
- Why should I bother learning this?
Illustrate this need by posing a problem: How would you find the average low temperature in January in Bismarck, North Dakota, where the temperature is sometimes below zero? Finding the average low temperature might, in the case of Bismarck, involve adding positive and negative numbers and dividing a negative number by a positive number.
- How can it be true that subtracting a negative number is the same as adding a positive number?
Ask students to think about being in debt. Give them an equal number of dollar-sized slips of paper in red and green. Tell them that the red slips represent debts, money owed to someone else. The green slips represent cash on hand. A red-green pair represents 0. In order to pay off a debt, you have to split up a red-green pair by giving away red debt-slips. When that happens, you have freed up some green cash-slips-you have added a positive number by subtracting a negative number!
- Why is it that when you divide a whole number by a whole number, the quotient is smaller than the dividend, but when you divide a whole number by a number less than one, the quotient is larger than the dividend?
Work with students to show a pattern to dividing by smaller and smaller numbers.
8 8 = 1
8 4 = 2
8 2 = 4
8 1 = 8
8 0.5 = ?
For the pattern to continue, the quotient must be twice 8. If you read the division as How many halves in 8?, you can see that the quotient must be 16.
Terminating and Repeating
Operations with Integers