1. copyright©amberpasillas2010

2. Emily’s mother is an accountant. One day, Emily heard her Mom talking to a client on the phone. During the conversation, her Mom used the phrases “ in the red ” and “ in the black ”. That evening at dinner, Emily asked her Mom what the terms meant. Here is what her Mom said:

3. copyright©amberpasillas2010 “When people in business talk about income and expenses, they often use colors to describe the numbers they are dealing with. Black refers to profits or income. Red refers to losses or expenses. A company that is making money is “ in the black. ” POSITIVE INTEGERS. A company that is losing money or owes money is “ in the red.” NEGATIVE INTEGERS.

4. copyright©amberpasillas2010 One positive and one negative has a value of zero because they cancel each other out. +– This is called a NEUTRAL FIELD or a ZERO BANK.

5. copyright©amberpasillas2010 Emily was studying Integers in her Math class & thought she could use these ideas of “ in the black ” and “ in the red ” to model the addition of positive & negative integers. Her model uses a positive black and a negative red. Each black represents +1 and each red represents -1. For example, this shows a value of +5: + + + + +

6. copyright©amberpasillas2010 We can show +5 using more than 5 tiles. + –+++++ +–++–+++++–++–++++ They also don’t need to be in a straight line.

7. copyright©amberpasillas2010 This shows a value of -6 – – – – – – – ––+ – – – + – – So does this! It has 2 zeros!

8. copyright©amberpasillas2010 1) Put in the 1 st number of + or – 2) Add the 2 nd number of + or – 3) Balance out what you have 5) The leftovers are the final answer 4) One + balances out one – When a + and – cancel each other out it is called a NEUTRAL FIELD or ZERO BANK

9. copyright©amberpasillas2010 To represent 3 + 2 Put +3 in Put +2 in Since all the signs are the same you just figure out your answer. 3 + 2 = 5 + + + +

10. copyright©amberpasillas2010 To represent -4 + -3 Put – 4 in Put – 3 in Since all the signs are the same you just figure out your answer. -4 + -3 = -7 – – – – –

11. copyright©amberpasillas2010 To represent 5 + -2 Put + 5 in Put – 2 in 2 positives cancel out with 2 negatives. 5 + -2 = 3 – + + + Equalize, or balance out, what you have. +

12. copyright©amberpasillas2010 To represent -3 + 4 Put -3 in Put +4 in -3 + 4 = 1 + + + –––––– Equalize, or balance out, what you have. + 3 positives cancel out with 3 negatives.

13. copyright©amberpasillas2010 Take Out Your Study Guide !!!

14. copyright©amberpasillas2010 Integers are the set of numbers including positive whole numbers, negative whole numbers and zero. Negative Positive * Negative integers are less than zero *Positive integers are greater than zero * The integer zero is neither positive or negative #3 -5 -4 -3 -2 -1 0 1 2 3 4 5 < >

15. copyright©amberpasillas2010 Steps To Add Integers 1) Put in the 1 st number of + or – 2) Add the 2 nd number of + or – 3) Balance out what you have 5) The leftovers are the final answer #4 4) One + balances out one – When a + and – cancel each other out it is called a NEUTRAL FIELD or ZERO BANK

16. copyright©amberpasillas2010 Hyperlinked Website Below Goes With Lesson Hands on Model on the INTERNET http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html