Explain why the location of point A(1, -2) is different than the location of point B(-2, 1).

**Answer in complete thought sentences.

Bell Work

Adding 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: -3 + 5

Thus we have 2 positive tokens left, so the answer would be -3+5 = 2.

Using Counters to Add/Subtract Integers

1. 5+62. -4+33. -2+74. -5+(-2)5. -7+2

Check your answers with a number line

Use counters to find the following sums:

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

Tricks: Adding same-sign numbers

1. Give an example of an addition sentence containing at least four integers whose sum is zero.

2. Explain how you know whether a sum is positive, negative, or zero without actually adding.

Practice

Let represent our Positive Integers Let represent our Negative Integers

Example: -3 –21) 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!

Using Counters to Subtract Integers

-3 –2 = -5

Why can we add these zero pairs?

Show -3 -2 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.

Using a number line

1. 5-62. -4-(-3)3. -2-74. -5-(-2)5. -7-2

Use counters or a number line to solve the following expressions:

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!

Trick: Subtracting Integers

Evaluate x-y if x=12 and y =7 Replace x and y with the numbers above and solve:

x-y 12-712+ (-7)5

Evaluate an Expression

http://www.teachertube.com/video/integers-121930

Integer Video

1-3B/C Multiply Integers

How do I write5+5+5

as multiplication?

How do I write6+6+6+6+6

as multiplication?

How do I write(-6)+(-6)+(-6)+

(-6)+(-6)?

as multiplication?

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.

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?

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

remove counters front the mat.

Draw it!

With your partner, figure out how you could represent 4x2

on a number line.

Now try representing (-3)(2).

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) = -122(-7) = -14

Use the Triangle

+

−−

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?

Explain Your Reasoning

1) Evaluate (-1)50. Explain your reasoning.

2) Explain when the product of three integers is positive.

1-3D Divide Integers

Integers- Part 2! Division

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

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?

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

Evaluating Expressions

2)

= -9

Note: (10-x)/(-2) notice you simplify the top first in order of operations, then divide last!

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

Check Your Understanding

Page 63 #1-9 Rally Coach

* Remember: One sheet of paper for the pair. Take turns coaching and writing.