1. Bell Work
Explain why the location of point A(1, -2) is different than the location of point B(-2, 1).
**Answer in complete thought sentences.

2. Adding Integers

3. Using Counters to Add/Subtract Integers
Let represent our Positive Integers
Let represent our Negative Integers
Pair up with to create “ZERO pairs” since 1+(-1) = 0, the remaining counters will represent the left over amounts.
Example:
Thus we have 2 positive tokens left, so the answer would be -3+5 = 2.

4. Use counters to find the following sums:
5+6
-4+3
-2+7
-5+(-2)
-7+2
Check your answers with a number line

6. Tricks: Adding same-sign numbers
If you are adding integers with the same sign (ex: 5+5), you simply add their absolute values and keep the sign.
5+5 = 10
-6+(-2) = -8
-2+-3 = -5

7. Practice
Give an example of an addition sentence containing at least four integers whose sum is zero.
Explain how you know whether a sum is positive, negative, or zero without actually adding.

8. Using Counters to Subtract Integers
Let represent our Positive Integers
Let represent our Negative Integers
Example: -3 –2
1) Begin with the counters of the first integer given (-3)
2) Add the zero pairs determined by the number of the second integer.
3)Then, remove the positive or negative chips determined by the 2nd integer (+2). Create zero pairs and count the remaining!
Why can we add these zero pairs?
-3 –2 = -5

9. Using a number line
Show on a number line. Can we rewrite the expression to make it addition?
How could we show -3 –(-2)? Hint think of assets and debts.

10. Use counters or a number line to solve the following expressions:
5-6
-4-(-3)
-2-7
-5-(-2)
-7-2

11. Trick: Subtracting Integers
Rewrite subtracting a positive as adding a negative: 5-7 = 5+(-7)
Taking away a debt is a good thing! 9-(-5) = 9+5
If the numbers have the same signs, add the absolute values and keep the sign.
-5-15 = -5+(-15) = -20
If the numbers have opposite signs, subtract the two numbers and keep the sign of the number with the highest absolute value!
9-12 = 9+(-12) think: 12-9 =3, but 12 is larger so -3!

12. Evaluate an Expression
Evaluate x-y if x=12 and y =7
Replace x and y with the numbers above and solve:
x-y
12-7
12+ (-7) 5

13. Integer Video

14. 1-3B/C Multiply Integers

15. How do I write 5+5+5 as multiplication?

16. How do I write 6+6+6+6+6 as multiplication?

17. How do I write
(-6)+(-6)+(-6)+
(-6)+(-6)?
as multiplication?

18. Explore Multiplying with Counters
The number of students who bring their lunch to Phoenix middle School has been decreasing at a rate of 4 students per month. What integer represents the total change after three months?
So what do we need to find?
The integer -4 represents a decrease of 4 students each month. After 3 months, the total change will be 3(-4) Use counters to model 3 groups of 4 negative counters.

19. Model 3 x (-4) Place 3 sets of 4 negative counters on the mat.
How many negative counters do we have?
What does this represent?

20. Use counters to find -2 x (-4)
If the first factor is negative, you will need to remove counters front the mat.

22. Now try representing (-3)(2).
Draw it!
With your partner, figure out how you could represent 4x2 on a number line.
Now try representing (-3)(2).

23. Write it!! The RULES: Ways to express multiplication:
x, parenthesis, ∙
For even numbers of factors:
Same (like) signs = POSITIVE
Different (unlike) signs = NEGATIVE
Or draw a triangle…
Example: 3(4) =12
(-2)x(-7) = 14
(3)(-4) = -12
2(-7) = -14

24. Use the Triangle + − −

25. But what about the EXPONENTS?
(8)2 = ?
(-8)2 = ?
Write the rule for powers of 2!
(2)3 = ?
(-2)3 = ?
Write the rule for powers of 3!
Try powers of 4 and 5. Is there a pattern?

26. Explain Your Reasoning
Evaluate (-1)50. Explain your reasoning.
Explain when the product of three integers is positive.

27. 1-3D Divide Integers

28. Integers- Part 2! Division

29. The Rules: Same as Multiplication!
Division can be written in two ways: ÷ or by a fraction (top divided by the bottom number)
We call the answer to a division problem a Quotient
For 2 factors:
Like signs = POSITIVE
Unlike signs = NEGATIVE

30. Multiplication/Division ONLY
Try this:
(3)(-4)(4) ÷(-12) = # of negatives: 2
(24 ÷(-3))(7) ÷ 2 = # of negatives: 1
(-2)(-2)(4)(-2) ÷(-4)= # of negatives: 4
(7)(-2)(16 ÷(-8))(-3)= # of negatives: 3
If your problem has only multiplication or division (no addition or subtraction signs) what do you notice about even and odd number of negatives?
1) 4 2) ) 8 4)-84

31. Evaluating Expressions
Rewrite the equation using given numbers. Make sure to plug into variables using (), especially when the number is negative!
Ex: Let x = -8 and y = 5.
xy ÷ (-10) =
(-8)(5) ÷ (-10) =
(-40) ÷ (-10) = 4

32. Evaluating Expressions
2) = -9 Note: (10-x)/(-2)  notice you simplify the top first in order of operations, then divide last!

33. Review of all Rules!
Addition: Same sign: add and keep the sign Different sign: subtract and keep the sign of the number with the largest absolute value Subtraction: Change minus sign to a plus and flip the sign of the 2nd number: Ex: 5-2 become 5+(-2) or 6- (-2) becomes 6+2, then follow the addition rules. ____________________________________________________ Multiplication/Division: Like sign: Positive Unlinke sign: Negative If it is all multiplication/Division, even negatives= positive odd negatives = negative

34. Check Your Understanding
Page 63 #1-9 Rally Coach
* Remember: One sheet of paper for the pair. Take turns coaching and writing.