The Number System Lesson 1 Objective: Read and write integers, and find the absolute value of an integer.

An integer is any number from the set {…, -4, -3, -2, - 1, 0, 1, 2, 3, 4, …}, where … means continues without end. Integers can be graphed on a number line. To graph an integer on the number line, draw a dot on the line at its location. Numbers that are the same distance from zero on a number line have the same absolute value. -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 Negative integers are integers less than zero. They are written with a – sign. Positive integers are integers greater than zero. They can be written with a + sign. Zero is neither negative nor positive

Write an integer for each situation 1. an average temperature of 5 degrees below normal 2. an average rainfall of 5 inches above normal.

3. Graph the set of integers {4, -6, 0} on a number line.

Evaluate each expression 4. |-4| 5. |-5| - |2|

6. Nick climbs 30 feet up a rock wall and then climbs 22 feet down to a landing area. The number of feet Nick climbs can be represented using the expression |30| + |-22|. How many feet does Nick climb?

7. Write an integer to represent a loss of 12 yards. 8 7. Write an integer to represent a loss of 12 yards. 8. Write an integer to represent 4 inches above normal.

9. Evaluate |5|. 10. Evaluate |-4| - |-3|.

11. The number of pounds Megan’s dog gained and then lost is represented by the expression |6| + |-3|. How many pounds did Megan’s dog gain and lose?

Lesson 2 Objective: add integers

Integers like 2 and-2 are called opposites because they are the same distance from 0, but on opposite sides. Two integers that are opposites are also called additive inverses. The Additive Inverse Property states that the sum of any number and its additive inverse is zero. To add integers with the same sign, add their absolute values. The sum is: - Positive if both integers are positive. - Negative if both integers are negative

To add integers with different signs, subtract their absolute values To add integers with different signs, subtract their absolute values. The sum is: -positive if the positive integer’s absolute value is greater. -negative if the negative integer’s absolute value is greater

1. Find -3 + (-2). 2. Find -26 + (-17).

3. Find 5 + (-3). 4. Find -3 + 2. 5. Find 7 + (-7).

6. Find -8 + 3. 7. Find 2 + (-15) + (-2).

8. A roller coaster starts at point A 8. A roller coaster starts at point A. It goes up 20 feet, down 32 feet, and then up 16 feet to point B. Write an addition sentence to find the height at point B in relation to point A. Then find the sum and explain its meaning.

9. Find -6 + (-3). 10. Find -34 + (-21).

11. Find 5 + (-5). 12. Find-9 + 6. 13. Find 11 + (-4) + (-11).

14. Max owes his brother $20. He gives his brother $10 one week and then the next week he gives him $5. Write an addition expression to describe this situation. Then find the sum and explain its meaning.

Lesson 3 Objective: subtract integers

1. Find 8 – 13. 2. Find -10 – 7. 3. Find 1 – (-2). 4. Find -10 – (-7).

5. Evaluate x – y if x = -6 and y = -5. 6 5. Evaluate x – y if x = -6 and y = -5. 6. Evaluate m – n if m = -15 and n = 8.

7. The temperatures on the Moon vary from -173°C to 127°C 7. The temperatures on the Moon vary from -173°C to 127°C. Find the difference between the maximum and minimum temperatures.

8. Find 2 – 15. 9. Find -13 – 8. 10. Find 12 – (-6). 11. Find -21 – (-8).

12. Evaluate g – h if g = -2 and h = -7. 13 12. Evaluate g – h if g = -2 and h = -7. 13. Evaluate a – b if a = -10 and b = 4.

14. In Mongolia, the temperature can fall to -45° Celsius in January 14. In Mongolia, the temperature can fall to -45° Celsius in January. The temperature in July may reach 40° Celsius. Find the difference between these two temperatures.

Lesson 4 Objective: multiply integers

Multiply Integers with Different Signs -The product of two integers with different signs is negative. -The Commutative Property of Multiplication states that you can multiply in any order. Multiply Integers with the Same Signs -The product of two integers with the same sign is positive. -The product of two positive integers is positive. You can use a pattern to find the sign of the product of two negative integers. -Pattern: Each product is 3 more than the previous product.

1. Find 3(-5). 2. Find -6(8). 3. Find -11(-9).

4. Find (-4)2. 5. Find -3(-4)(-2).

6. A submersible is diving from the surface of the water at a rate of 90 feet per minute. What is the depth of the submersible after 7 minutes?

7. Find 5(-4). 8. Find -3(9). 9. Find (-8)2. 10. Find (-2)(-5)(-6).

11. A mine elevator descends at a rate of 200 feet per minute 11. A mine elevator descends at a rate of 200 feet per minute. Write a multiplication expression to represent the total distance descended after 4 minutes. Then find the product and explain its meaning.

Lesson 5 Objective: divide integers

Divide Integers with Different Signs -The quotient of two integers with different signs is negative. -You can divide integers provided that the divisor is not zero. Since multiplication and division sentences are related, you can use them to find the quotient of integers with different signs. Divide Integers with the Same Signs -The quotient of two integers with the same sign is positive. -You can also use multiplication and division sentences to find the quotient of integers with the same sign.

1. Find 80 ÷ (-10). 2. Find .

3. Use the table to find the constant rate of change in centimeters per hour. Time (h) Height (cm) 1 10 2 8 3 6 4

4. Find -14 ÷ (-7). 5. Find . 6. Evaluate -16 ÷ x if x = -4.

7. The estimated Australian koala population was 1,000,000 7. The estimated Australian koala population was 1,000,000. After 10 years, there were about 100,000 koalas. Find the average change in the koala population per year. Then explain its meaning.

8. Find 51 ÷ (-3). 9. Find . 10. Find -12 ÷ (-2). 11. Find .

12. Evaluate -18 ÷ x if x = -2. 13. An October newspaper headline read that the total value of stocks held by Japanese financial institutions dropped from $987 billion to $900 billion in 6 weeks. Find the average change in value per week. Explain its meaning.