Unit 1Number Systems

Standards CCSS.Math.Content.7.NS.A.1.a Describe situations in which opposite quantities combine to make 0. CCSS.Math.Content.7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

Objectives I can describe situations where quantities combine to make 0. I can add, subtract, multiply and divide rational numbers.

Vocabulary WORD DEFINITION Rational number Integers Absolute value | |   Integers Absolute value | | the distance a number is from zero Additive inverse two numbers whose sum is zero

Question 1 Does every number have an opposite? Explain your thinking

Topic: Additive Inverse Adding the opposite of a number to that number is the additive inverse -8 + 8 = 0 3 + (-3) = 0 ¼ + (-1/4) = 0 Opposites are the same distance from zero, but in opposite directions, on the number line.

Example CCSS.Math.Content.7.NS.A.1.a Describe situations in which opposite quantities combine to make 0. Example: A hydrogen atom has one proton with a charge of +1 and one electron with a charge of -1. What is the total charge of a hydrogen atom?

Topic: Adding Integers (RULE) The sum of any integer and its opposite is equal to zero. Adding two positive integers equals a positive sum adding two negative integers equals a negative sum. To add integers with one positive sign and one negative sign do the following: Find the absolute value of each integer Subtract the lesser absolute value for the greater The sum has the same sign as the integer with the greater absolute value Example: -23 + 8 |-23| + |8| 23 – 8 = 15 -23 + 8 = -15

To add integers with one positive sign and one negative sign do the following: Find the absolute value of each integer Subtract the lesser absolute value for the greater The sum has the same sign as the integer with the greater absolute value Example: -23 + 8 |-23| + |8| 23 – 8 = 15 -23 + 8 = -15

Check Understanding 1) -97 + (-65) 2) -22 + 24

Adding Integers with a Number Line (Modeling) Rule: Start at zero Move to the first integer Find the absolute value of the second integer and move that distance If the second integer is positive, move to the right If negative, move left Example: Use a number line to add -3 + 5 = 2

Check Understanding Use a number line to add the following 1) -6 + 6 = 2) -3 + (-5) =  

Topic: Subtracting Integers To subtract an integer, add its additive inverse, which is its opposite. Example: 4 – 6 4 + (-6) = -2

Application Subtracting Integers The temperature in Caribou, Maine, was 8 degrees at noon. By 10:00 p.m. the temperature changed by -8 degrees. Find the temperature at 10:00 p.m.

Check Understanding The absolute values of two numbers that are additive inverses will ____ be the same. (always, sometimes, or never)

The sum of a number and -20 is 40. What is the number? Check Understanding The sum of a number and -20 is 40. What is the number?

Check Understanding When you add a positive number and a negative number, the positive addend will ____ be less than the sum. (always, sometimes, never)

Let’s Sum it up The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the distance from the top of Mt. McKinley to the bottom of Death Valley?

Let’s Sum it Up -- Continued

Let’s Sum it Up - Continued We can represent the elevation as an integers: The distance from the top of Mt. McKinley to the bottom of Death Valley is the same as the distance from +20,320 to -282 on the number line. We add the distance from +20,320 to 0, and the distance from 0 to -282, for a total of 20,602 feet.

Let’s Sum it Up - Continued Elevation Integer 20,320 feet above sea level +20,320 sea level 282 feet below sea level -282