1. Big Idea #3
Develop an understanding of operations of all rational numbers and solving linear equations

2. Benchmarks Depth of Knowledge: Moderate Date Adopted or Revised: 09/07
» MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.
Depth of Knowledge: Moderate     Date Adopted or Revised: 09/07    
»  MA.7.A.3.2: Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.
»  MA.7.A.3.3: Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.
»  MA.7.A.3.4: Use the properties of equality to represent an equation in a different way and to show that two equations are  equivalent in a given context.

3. Thesis Statement
The purpose of this lesson is to work on Big Idea #3 from the 7th grade Next Generation Sunshine State Standards (NGSSS).
It says,
MA.7.A.3.1: Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers.
This lesson will be divided into 3 parts
How we’ve been taught and How we are teaching. (2 Hours)
Hands-on Math and the CRA Sequence of Instruction (2 Hours)
A Process Does not Always Tell Us Why. (2 Hours)

4. Why Do I Need to Know This? (Motivation and Real World Applications)
Thermometers have negative numbers.

5. In Chemistry For example: electrons – negative charge. 
For example:
electrons – negative charge
Protons – positive charge  
neutrons – neutral charge 
Atoms are made up of 3 types of particles electrons  , protons  and neutrons .  These particles have different properties.  Electrons are tiny, very light particles that have a negative electrical charge (-). Protons are much larger and heavier than electrons and have the opposite charge, protons have a positive charge (+).  Neutrons are large and heavy like protons, however neutrons have no electrical charge.  Each atom is made up of a combination of these particles.  Let's look at one type of atom:  

6. The World’s Tallest Building
The Burj Dubai is hardly a new phenomenon (the world has known it would be the tallest man-made structure ever back in 2004 when construction first began), but today (January 4, 2010) marks its official opening. The skyscraper — located in downtown Dubai in the United Arab Emirates — stands at an astounding 2,684 feet. To put that in perspective, New York's Empire State Building is only 1,454 feet, the Willis Tower (formerly the Sears Tower) in Chicago — the tallest building in the United States — is 1,450 feet and the Taipei 101 — the previous record holder — is roughly 2,650 feet. The project is simultaneously awe-inspiring, ridiculous, thrilling, dangerous and ostentatious, but that's the beauty of engineering. H

7. Above and Below Sea Level
What is the lowest point below sea level?
The deepest point on the ocean floors is -10,916 meters in the Mariana Trench. Trenches are the upper most parts of subduction zones and there are dozens of trench locations that are more than 5000 meters below sea level.
What is the highest point above sea level.
Answer
Mt Everest is 29,035 ft.
Mariana Trent
-10,916
Mount Everest
29,035

8. The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:
The U.S. National Debt
National debt in 1960?
$290,500,000,000
U.S. NATIONAL DEBT CLOCK
The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:

9. Floors on Elevators An elevator panel with NEGATIVE numbers.
I've spent enough time outside the US to be used to the floor numbering (and there was a time when I would have argued that it made more sense), but the salty C programmer in me is amused by the zero-indexed elevator. (Complete with negative numbers) It's the first time I've seen that. (Yes, it makes sense in a hotel with a multilingual clientele. But how many other places have you seen it?)

10. Vocabulary Words That You Need to Know
Addends, Sum, Minuend, Subtrahend, Difference, Factors, Products, Divisor, Dividend, Quotient, Mixed/Multiple Signs

11. Teaching Using Direction

12. What is ?
Start Here 4
The Answer is 2.

13. What is ?
Start Here 2
The Answer is 0.

14. What is ?
Start Here 2
The Answer is -3.

15. What is ?
Start Here …
What do you think?
The Answer is 9.

16. Adding Using Mixed/Multple
Signs

17. Mixed/Multiple Signs An addition and a positive ++
Mixed/Multiple Signs exist when two signs are together.
An addition and a positive ++
An addition and a negative +-
A subtraction and a positive - +
A subtraction and a negative - -
These problems are not difficult, they just need to be solved a little differently.

18. What is ?
Start Here 4
The Answer is -2.

19. What is ?
Start Here 1
The Answer is -4.

20. What is ?
Start Here … 4
What do you think?
The Answer is -7.

21. What is +4 + +2? I bet you know this one. The Answer is 6. 2
Start Here 2
I bet you know this one.
The Answer is 6.

22. Principles/Hypothesis Formed
When adding two integers and the signs are alike, you add and keep the sign.
2. When adding two integers and the signs are not alike, you subtract and take the largest numbers absolute value.

23. Subtracting Using Mixed/Multple
Signs

24. Principle Change Keep Change
When subtracting two integers, you keep the minuend, change the subtraction symbol to an addition symbol, and change the sign of the subtrahend to its opposite.
Keep
Change
Change

25. What is -2 - -7? What is -2 + +7? The Answer is 5.
Change to addition
Keep -2
Take the opposite of -7
What is ?
Start Here 7
The Answer is 5.

26. What is 5 - 7? What is 5 + -7? The Answer is -2.
Change to addition
Keep 5
Take the opposite of 7
What is ?
Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.
The Answer is -2.

27. What is 3 - -9? What is 3 + 9 ? The Answer is 12.
Change to
addition
Keep 3
Take the opposite of -9
What is ?
Principle: When adding two integers, and the signs are the same, you add and keep the sign.
The Answer is 12.

28. What is -5 - - 4? What is -5 + 4? The Answer is -1.
Change to addition
Keep -5
Take the opposite of -4
What is ?
Principle: When adding two integers, and the signs are not alike, you subtract and take the sign of the largest numbers absolute value.
The Answer is -1.

29. Multiplying Integers

30. Principle
When multiplying two integers and the signs are alike, the product is positive.
(+)(+) = (+)
(-)(-) = (+)
When multiplying two integers and the signs are not alike, the product is negative.
(+)(-) = (-)
(-)(+) = (-)

31. Dividing Integers

32. Principle
When multiplying two integers and the signs are alike, the product is positive.
(+)/(+) = (+)
(-)/(-) = (+)
When multiplying two integers and the signs are not alike, the product is negative.
(+)/(-) = (-)
(-)/(+) = (-)

33. Floors on Elevators Answer: 17-(-2) = 19 floors
This is an elevator panel with NEGATIVE numbers.
How far many floors have you gone up if you start at the lowest floor and go to the highest floor?
Set up the expression
Explain your reasoning
Solve the problem
I've spent enough time outside the US to be used to the floor numbering (and there was a time when I would have argued that it made more sense), but the salty C programmer in me is amused by the zero-indexed elevator. (Complete with negative numbers) It's the first time I've seen that. (Yes, it makes sense in a hotel with a multilingual clientele. But how many other places have you seen it?)
Answer: 17-(-2) =
19 floors

34. The World’s Tallest Building
How much taller is The Burj Dubai compared to The Empire State Building?
The Burj Dubai is hardly a new phenomenon (the world has known it would be the tallest man-made structure ever back in 2004 when construction first began), but today (January 4, 2010) marks its official opening. The skyscraper — located in downtown Dubai in the United Arab Emirates — stands at an astounding 2,684 feet. To put that in perspective, New York's Empire State Building is only 1,454 feet, the Willis Tower (formerly the Sears Tower) in Chicago — the tallest building in the United States — is 1,450 feet and the Taipei 101 — the previous record holder — is roughly 2,650 feet. The project is simultaneously awe-inspiring, ridiculous, thrilling, dangerous and ostentatious, but that's the beauty of engineering.
Answer: 512 – 381 = 131 meters

35. The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:
The U.S. National Debt
U.S. NATIONAL DEBT CLOCK
The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is:
If the government taxed each American $40, , approximately how many Americans would it require to pay to off our National Debt?
Answer: -12,287,322,881,897 ÷ -40, ≈ 306,666,778 Americans

36. Why Do I Need to Know This? (Motivation and Real World Applications)
What is the difference between the lowest and the highest temperature reading on the thermometer?
Thermometers have negative numbers.
Answer: 120 – (-40) = 160°F

37. Above and Below Sea Level
What is the difference between the highest point above sea level and the lowest point below sea level?
Mount Everest
29,035
What is the lowest point below sea level?
The deepest point on the ocean floors is -10,916 meters in the Mariana Trench. Trenches are the upper most parts of subduction zones and there are dozens of trench locations that are more than 5000 meters below sea level.
What is the highest point above sea level.
Answer
Mt Everest is 29,035 ft.
Mariana Trent
-10,916
Answer: 29,035 – (-10,916) = 39,951