1. Bell Ringers
Solve the following problems on a loose leaf piece of paper. 1. Draw a model to show the following expression (-5) + (-3) What is the sum of this expression? 3. While playing the additive inverse game you drew the cards 2, -5, 7, and -12. Draw a model to determine the sum. Write an equation to accompany the model. 4. Write a real world story problem to accompany the equation.

2. Addition of integers

3. solve real world problems using rational numbers.
Today I will be able to
solve real world problems using rational numbers.

4. Let’s review
Cards: Equation:

5. Counting up and down
8 + (-3) = 2 + (-4) = =

6. Think about these Questions
For the equations: and 2 + (-4) what is the distance between 2 and the sum on a number line? Does this sum lie to the right or the left on a horizontal number line? Above or below on a vertical number line?

7. Now let’s think about these questions
Given the expression , determine without finding the sum, the distance between 54 and the sum. Explain. Is the sum to the right or left of 54 on a horizontal number line? Above or below on a vertical number line?

8. Your turn
Given the expression , determine without finding the sum, the distance between 14 and the sum. Is the sum to the right or left of 14 on a horizontal number line? Is it above or below on a vertical number line?

9. Copy this question in your math journal and solve
Given the expression (-5) + 3, determine without finding the sum, the distance between (-5) and the sum. Is the sum to the right or left of (-5) on a horizontal number line? Is it above or below on a vertical number line? Draw a horizontal number line and a vertical number line to justify your answers.

10. Copy this question in your math journal and solve
Given the expression (-6) + (-2), determine without finding the sum, the distance between (-6) and the sum. Is the sum to the right or left of (-6) on a horizontal number line? Is it above or below on a vertical number line? Draw a horizontal number line and a vertical number line to justify your answers.

11. Copy this question in your math journal and solve
Given the expression (7) + (-8), determine without finding the sum, the distance between 7 and the sum. Is the sum to the right or left of 7 on a horizontal number line? Is it above or below on a vertical number line? Draw a horizontal number line and a vertical number line to justify your answers.

12. Formula for addition of integers
We can think of the addition of integers by using this formula p + q = sum: p represents the first addend and q represents the second addend. Ex: (-9) + 5 = (-4) p = (-9) q = 5 sum = (-4)

13. Identify the p’s and q’s
32 + (-9) = 23 (-15) + 10 = (-5) = 77

14. Verbal descriptions
Write and equation and create a number line model to answer the following question: the p value is 6 and the sum lies 15 units to the left of p value. What is the value of q and the sum of this verbal description? Equation:

15. Verbal descriptions
Write and equation and create a number line model to answer the following question: the p value is (-4) and the sum lies 6 units to the right of p value. What is the value of q and the sum of this verbal description? Equation:

16. Verbal descriptions
Write and equation and create a number line model to answer the following question: the p value is (-2) and the sum lies 8 units to the left of p value. What is the value of q and the sum of this verbal description? Equation:

17. Addition of Integers rules
Add rational numbers with the same sign by adding the absolute values and using the common sign.
Ex: −𝟒𝟒+(−𝟐𝟐)
Add rational numbers with opposite signs by subtracting the absolute values and using the sign of the integer with the greater absolute value.
Ex: 6 + (-18)
(-12) + 65

18. Applying this to the real world
The Schiphol Airport runway in Amsterdam is 13 feet below sea level. If I climb to the top of the control tower I increase in elevation by 57 feet. At what height above sea level am I now standing?

19. Real World
A Chinook helicopter flies to 1225 feet above sea level. The pilot then drops 243 feet in elevation and hovers. How high above sea level is the Chinook hovering?

20. Real world
New Orleans, Louisiana is 7 feet below sea level. If I climb in elevation 72 more feet to the city of Baton Rouge at what elevation would I be?

21. Check for Understanding Real World
A Blackhawk helicopter was doing maneuvers on a routine exercise. On his mission she was rise to 854 feet above sea level. Next she was to drop 61 feet in elevation and hover. What is her final elevation above sea level?

22. Check for Understanding Real World
Mike bought stock in the Boeing company. He bought it at $24 a share. One the first day the stock rose $13 a share. The next day the stock dropped $16 a share. How much money is each share now worth?

23. Check for Understanding Real World
A scuba diver dives down 323 feet below sea level to try and tag a hammer head shark. He chases the shark 40 feet toward the surface. He and the shark then dive down 15 feet, where he finally tags the shark. What is the final elevation of the scuba diver?

24. Exit Ticket
Copy the questions and answer the following problems on a loose leaf piece of paper.
Refer to the diagram on the right. Write an equation for the diagram and find the sum. What integers do the arrows represent.
Jenna and Jay are playing the integer game and below are the two cards that they drew. How to the models for these two addition problems differ on a number line? How are they the same?

25. Exit Ticket
Copy the questions and answer the following problems on a loose leaf piece of paper. 3. If the order of the cards change, how the models for these two addition problems differ on a number line? How are they the same? 4. Dawn bought a stock when it was down 12 points. The next day it rose 9 points and on the following day it fell 2 points. At how many points is the stock?