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

2. Benchmarks » 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. Depth of Knowledge: Moderate Date Adopted or Revised: 09/07 » MA.7.A.3.3: Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients. Depth of Knowledge: Moderate Date Adopted or Revised: 09/07 » 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. Depth of Knowledge: Moderate Date Adopted or Revised: 09/07

3. Thesis Statement http://www.neirtec.org/activities/applets/numberline.htm The purpose of this lesson is to work on Big Idea #3 from the 7 th 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) http://www.labsafety.com/images/xl/Weather- Thermometer-40-to-LSS_i_LBM37561Z.jpg

5. In Chemistry Protons – positive charge neutrons – neutral charge. electrons – negative charge For example:

6. The World’s Tallest Building H http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestD M_468x525.jpg

7. Above and Below Sea Level http://www.treehugger.com/mariana%20trench.jpg http://www.thetravelpeach.com/asia- vacations/everest-mount.jpg Mariana Trent -10,916 Mount Everest 29,035

8. The U.S. National Debt U.S. N ATIONAL D EBT C LOCK The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is: http://www.brillig.com/debt_clock/

9. Floors on Elevators An elevator panel with NEGATIVE numbers.

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

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

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

14. What is -1 - 2? Start Here 2 The Answer is -3.

15. What is +5 + 4? Start Here The Answer is 9. … What do you think?

17. Mixed/Multiple Signs 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 +2 + -4? Start Here 4 The Answer is -2.

19. What is -5 + +1? Start Here 1 The Answer is -4.

20. What is -3 + -4? Start Here 4 The Answer is -7. … What do you think?

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

22. Principles/Hypothesis Formed 1.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.

24. Principle 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

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

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

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

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

30. Principle 1.When multiplying two integers and the signs are alike, the product is positive. (+)(+) = (+) (-)(-) = (+) 2.When multiplying two integers and the signs are not alike, the product is negative. (+)(-) = (-) (-)(+) = (-)

31. Why does a positive times a negative equal a negative? 4 3 = 12 4 2 = 8 4 1 = 4 4 0 = 0 4 -1 = ? The Answer is -4. So a positive times a negative is a negative.

32. But why does a negative times a negative equal a positive? -4 3 = -12 -4 2 = -8 -4 1 = -4 -4 0 = 0 -4 -1 = ? The Answer is 4. So a negative times a negative is a positive. Well, knowing a positive times a negative is a negative, also means that a negative times a positive is a negative, so again…

34. Principle 1.When multiplying two integers and the signs are alike, the product is positive. (+)/(+) = (+) (-)/(-) = (+) 2.When multiplying two integers and the signs are not alike, the product is negative. (+)/(-) = (-) (-)/(+) = (-)

36. Floors on Elevators 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? (1)Set up the expression (2)Explain your reasoning (3)Solve the problem Answer:17-(-2) = 19 floors

37. The World’s Tallest Building http://img.dailymail.co.uk/i/pix/2007/07_02/WorldsTallestD M_468x525.jpg How much taller is The Burj Dubai compared to The Empire State Building? Answer: 512 – 381 = 131 meters

38. The U.S. National Debt U.S. N ATIONAL D EBT C LOCK The Outstanding Public Debt as of 09 Jan 2010 at 01:30:59 PM GMT is: http://www.brillig.com/debt_clock/ If the government taxed each American $40, 068.00, approximately how many Americans would it require to pay to off our National Debt? Answer: -12,287,322,881,897 ÷ -40,068.00 ≈ 306,666,778 Americans

39. Why Do I Need to Know This? (Motivation and Real World Applications) http://www.labsafety.com/images/xl/Weather- Thermometer-40-to-LSS_i_LBM37561Z.jpg What is the difference between the lowest and the highest temperature reading on the thermometer? Answer: 120 – (-40) = 160°F

40. Above and Below Sea Level http://www.treehugger.com/mariana%20trench.jpg http://www.thetravelpeach.com/asia- vacations/everest-mount.jpg Mariana Trent -10,916 Mount Everest 29,035 What is the difference between the highest point above sea level and the lowest point below sea level? Answer: 29,035 – (-10,916) = 39,951