1. Unit 1Number Systems

2. 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.

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

4. 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

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

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

7. 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?

8. 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 = 15
= -15

9. 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 = 15
= -15

10. Check Understanding
1) (-65) 2)

11. 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 = 2

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

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

14. 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.

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

16. 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?

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

18. 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?

19. Let’s Sum it Up -- Continued

20. 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.

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