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.

Adding Integers

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

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

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

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.

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

Using a number line 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.

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

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!

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

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

1-3B/C Multiply Integers

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

How do I write 6+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.

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).

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

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 Evaluate (-1)50. Explain your reasoning. 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? 1) 4 2) -28 3) 8 4)-84

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.