## Wednesday, March 16, 2011

### Van's Great Big Book of Integers

CHAPTER 1
Grade 7 Integer Review

• You can use a number line to model an integer.
• You can also use "integer chips"to represent integers.(Integer chips are coloured disk used to represent integers;positive integers are usually red and negative integers are usually blue.).

• When subtaracting that isnt there,use a zero pair.([For example,-6 + 2=?] [use six negative chips and 2 positive chips....remove zero pairs.Then,you are left with -4.][-6 + 2 = -4])

Integer ala Grade 7

(+4) + (-4)= 0 (you have 4 and you owe 4,how are left? A=0)

Standard Form

(+4) + (-4) -remove the brackets(brackets are just training wheels)

= 4 - 4 -pure standard form

Removing negative part of a zero pair

Ex.10 - (-4)=? (when a term is in a bracket,remove it by using zero pairs and turn it to a positive integer)

Use 10 positive chips and 4 negative chips.Use zero pairs for the negative chips and remove the negatives.Now, you are left with 10 positive chips and another group of 4 positive chips.Add 4 and 10.(Any integer subtraction can be completed by adding the opposite integer).10 -(-4)= 10 + (+4) = 14

Star Statements

-3 -(-7)=4 (explanation:(-)integer minus another (-) integer is positive.If we use integer chips,use zero pairs for -7 and remove the negatives.Use the 3 negative chips as zero pairs for the 7positive chips.Now, you are left with 4 positive chips.)

-3-7=-10 (explanation:subtraction:adding a negative integer)

3-7=-4 (explanation:Make zero pairs.You are left with 4 negative chips)

3+7=10 (explanation:Just add them because they have the same sign[add their chips])

-3+7=4 (explanation:Make zero pairs.You are left with 4 positive chips)

CHAPTER 2

Multiplying Integers

SIGN RULES (NEGATIVE SIGNS)

Even=when you have even number of negative factors,the product is positive

Odd=when you have an odd number of negative factors,the product is negative

STANDARD FORM

(2) x (-4) -remove the multiplication sign

(2)(-4) or 2(-4) -standard form of a multiplication statement

Examples of multiplication statements

a.(+4) x (+2)=8 (multiply [(+) x (+) = (+)])

b.(+5) x (-2) =-10 (multiply[(+) x (-) = (-)])

c.(-4) x (+2)=-8 (multiply[(-) x (+) =(-)])

d.(-6)x (-1) = 6 (multiply [(-) x (-) =(+)])

Another set of examples

(+2) x (+3) = 6 (Make 2 groups of 3 positive chips)

(+2) x (-3) =-6 (Make 2 groups of 3 negative chips)

(-2) x (+3)= -6 (You can change the position of terms to (+3) x (-2) or use zero pairs)

(-2) x (-3)= 6 (make two groups of -3 and apply sign rules)

Chapter 3

Dividing Integers

Two types of division

Partative Division- making parts

Ex. 6 /2=3 (make two parts of six)
(+)(+)(+)(+)(+)(+)
[(+)(+)(+) ] [(+)(+)(+)]

Quotative Division-sharing your total with groups

(-6) / 2 =-3

share 6 with 2 groups

(-1,-1,-1)=-3 (-1,-1,-1)=-3

Check by using Multiplicative Inverse

(multiply the quotient by the divisor)

(-3)(2)=-6

(2)(-3)=-6

SIGN RULES

When you have an odd number of (-) signs in a division question,the quotient is always negative.

(-6) / 2 = -3 Check:(-3)(2)=6 -multiplicative inverse and use multiplication sign rules

6 / (-2) =-3 Check:(-3)(-2)= 6

When you have an even number of (-) or (+) signs in a division question,the quotient is always positive

6 / 2 = 3 Check:(3)(2)=6

-6 /-2 =3 Check:(3)(-2)=-6

CHAPTER 4

ORDER OF OPERATIONS WITH INTEGERS

Order of Operations

B- BRACKETS
E-EXPONENT
D-DIVISION
M-MULTIPLICATION
S-SUBTRACTION

-Solve terms in brackets first

-Multiply and Divide from left to right

-Add and subtract from left to right

EX.

(+5) x(-3) + (-6) / (+3)

- [15] + [-6 / 3]

-(15) + (-2)

- (-17)