### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

### Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# math

chapter1

by

Tweet## Kremble Bailey

on 11 January 2013#### Transcript of math

MY MATH PROJECT

BY: KREMBLE BAILEY VOCABULARY WORDS: LESSON1-1

* QUANTITY~ anything that can be measured or counted. ex. a dozen is another way to describe a quantity of 12 eggs.

*VARIABLE~ a symbol, usually a letter, that represents one or more numbers. ex. k is the variable in the equation 14-k=5

*ALEBRAIC EXPRESSION~ a mathematical phrase that includes one or more variables. ex. 6+x is an algebraic expression.

*NUMERICAL EXPRESSION~ a mathematical phrase involving numbers and operaion symbols, but no variables. ex. 6+7 EXAMPLES WRITING EXPRESSIONS WITH ADDITION AND SUBTRACTION

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.14 more than k{k+14} B. 14 less a number x {14-x}

WRITING EXPRESSIONS WITH MULTIPLICATION AND DIVISION

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.43 times a number j{43j} B. the quotient of a number b and 22{b/22}

WRITING EXPRESSIONS WITH TWO OPERATIONS

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A. 6 more than twice a number a{6+2a} B. 3 less than the quotient of 5 and a number c{5/c-3} C. the product of 7 and the sum of a number k and 6{7(k+6)}

USING WORDS FOR AN EXPRESSIONS

6k{three times a number k} CHAPTER 1 VOCABULARY WORDS :LESSON1-2

*POWER~ the base ad the exponent of an expression of the form 2^3. ex.6^7

*EXPONENT~a number that shows repeated multiplication. ex.5^6 :the exponent 6 indicates that 5 is used as a factor 6 times.

*BASE~a number that is multiplied repeatedly.ex.2^3 :the base 2 is used as a factor 3 times.

*SIMPLIFY~to replace an expression with its simplest name or form.ex.3+5=8,so 8 is the simplest form.

*EVALUATE~to substitute a given number for each variable, and then simplify.ex. to evaluate 3x+4 for x=2,substitute 2 for x and simplify 3(2)+4=6+4=10 EXAMPLES SIMPLIFYING POWERS

What is the simplified form of the expression?:A. 5^6{5^6=5×5×5×5×5×5=78,125

B.(0.2)^3{(0.2)^3=0.0016}

SIMPLIFYING NUMERICAL EXPRESSIONS

What is the simplified form of the expression?:

A.

(10-4)^3÷2 (10-4)^3÷2=6^3÷2=216÷2=108

EVALUATING ALGEBRAIC EXPRESSIONS

What is the value of the expression for k=5 and s=2 A. K^2+K-14÷S^2{5^2+5-14÷2^2=25+5-14÷4=25+5-3=30-3=27} VOCABULARY WORDS:LESSON1-3

*SQUARE ROOT~ a number a is the square root of a number b if a"^"=b ex. 7^2= 49, so 7 is the square root.

*RADICAND~ the expression under the radical symbol. ex.the radicand of the radical expression √x+2 is x+2.

*RADICAL~together the radical symbol and radicand form a radical.ex.√a

*PERFECT SQUARE~the square of an integer. ex.the numbers 1,4,9,16,25,36... are perfect squares ecause they are the squares of integers.

*SET~a well-defined collection of objects.ex.{...,-3,-2,-1,0,1,1,2,3...}

*ELEMENT OF A SET~members of a set. ex.cats and dogs are elements of the set of mammals.

*SUBSET~ a subset of a set consists of elements from the given set.ex. if B={1,2,3,4,5,6,7} and A ={1,2,5}, then A is a subset of B.

*RATIONAL NUMBERS~a real number that can be written as a ratio of two integers. Rational numbers in decimal form are terminating or repeating. ex. 2/3,1.548,and 2.292929

*NATURAL NUMBERS~ the counting numbers.ex. 1,2,3...

*WHOLE NUMBERS~the nonnegative numbers.ex.0,1,2,3,.....

*INTEGERS~whole numbers and their opposites.ex. ...-3,-2,-1,0,1,2,3...

*IRRATIONAL NUMBERS~a number that cannot be written as a ratio of two integers. Irrational numbers in decimal form are nonterminating and nonrepeating.ex.

*REAL NUMBERS~a number that is either rational or irrational. ex.5,-3,0.666,0

*INEQUALITY~a mathematical sentence that compares the values of two expressions using an inequality symbol.ex.3<7 SIMPLIFYING SQUARE ROOT EXPRESSIONS

What is the simplified form of each expression.

A. 81/=9 {9^2=81, so 9 is the square root of 81.

B.9/16=3/4{(3/4)^2= 9/16, so 3/4 is the square root of 9/16.

CLASSIFYING REAL NUMBERS

To which subsets of the real numbers does each number belong?

A.15={ natural numbers, hole numbers, integers, rational numbers.

B. -1.4583{rational numbers

(since -1.4583 is a terminating decimal)}

C. √57={irrational numbers(since 57 is not a perfect square)} VOCABULARY WORDS:LESSON1-4

*EQUIVALENT EXPRESSIONS~algebraic expressions that have the same value for all values of the variable(s). ex.6a +7a and 13a are equivalent expressions.

*DEDUCTIVE REASONING~ a process of reasoning logically from given facts to a conclusion. ex.based on the fact that the sum of any two even numbers is even, you can deduce that the product of any whole number and any even number is even.

*COUNTEREXAMPLE~ an example showing that a statement is false.

example statement: all apples are red

counter ex. a Granny Smith apple is green. VOCABULARY WORDS: LESSON 1-5

*ABSOLUTE VALUE~the distance that a number is from zero on a number line. ex. -5 is 5 units from 0, so |-7| =7

*OPPOSITES~ a number that is the same distance from 0 on the number line as a given number, but lies in the opposite direction. ex. -4 and 4 are opposites.

*ADDITIVE INVERSES~ the opposite or additive inverse of any number a is -a. The sum of opposites is 0. ex. -6 and 6 are additive inverses because -6+6=0. IDENTIFYING PROPERTIES

What properties is illustrated by each statement?

A.14*0=0{Zero property of multiplication}

B.(y+6)+28=y+(6+28){Associative property of addition}

C.6x+0=6x{Identity property of addition}

WRITING EQUIVALENT EXPRESSIONS

Simplify each expression.

A.6(5n)=(6*5)n{associative property of multiplication}

30n{simplify}

B.(3+8b)+6=(8b+3)+6{commutative property of addition}

(8b+3)+6

8b+(3+6){associative property of addition}

8b+9{simplify}

C.4xy/y=4x*y/1*y{rewrite denominator using identity property of multiplication}

4x/1*y/y{use rule for multiplying fraction}

4x*1{x/1=x and y/y=1}

4x{identity property of multiplication} -3 -2 -1 0 1 2 3 4 5 -4 -5 6 7 USING NUMBER LINE MODELS

What is each sum? Use a number line. 3+2 start at 3 3+2=5 A. B. 3+(-2) 0 -1 -2 -3 -4 1 2 3 4 3+(-2)=1 C. -3+2 0 1 2 3 4 -1 -2 -3 -4 -3+2=-1 VOCABULARY WORDS:

LESSON 1-6

*MULTIPLICATIVE INVERSE~given a nonzero rational number a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero number and its multiplicative inverse is 1.ex. 4/3 is the multiplicative inverse of3/4 because 3/4*4/3=1

*RECIPROCAL~given a nonzero rational number a/b, the reciprocal, or multiplicative inverse, is b/a. the product of a nonzero number and its reciprocal is 1. ex. 2/5 and 5/2 are reciprocals because 2/5*5/2=1. MULTIPLYING REAL NUMBERS

What is each product?

A.5(-9)=-45 {the product of two numbers with different signs is negative.}

B.24(0.5)=12{the produt of two numbers with the same sign is positve.}

SIMPLIFYING SQUARE ROOT EXPRESSIONS

What is the simplified form of each expression? A.-√169=-13{(-13)^2=169, so -√169=-13}

B.√1/36=1/6{(1/6)^2=1/36, so 1/36=1/6}

DIVIDING FRACTIONS

What is the value of x/y when x=3/4 and y=2/3?

x/y=x÷y=-3/4÷(-2/3)=-3/4×(-3/2)=9/8 VOCABULARY WORDS:

LESSON1-7

*DISTRIBUTIVE PROPERTY~For all real number a, b , and c: a(b+c)=ab+ac

(b+c)a=ba+ca a(b-c)=ab-ac (b-c)a=ba-ca

ex.3(19+4)=3(19)+3(4)

(19+4)3=19(3)+4(3)

7(11-2)=7(11)-7(2)

(11-2)7=11(7)-2(7)

*TERM~a number, variable, or the product or quotient of a number and one or more variables. ex.the expression: 5x+y/2-8 has three terms: 5x,y/2, and-8.

*CONSTANT~a term that has no variable factor. ex.in the expression 4x+13y+17, 17 is the constant term.

*COEFFICIENT~the numerical factor when a term has a variable. ex. in the expression 2x+3y+16, 2 and 3 are coefficients.

*LIKE TERMS~terms with exactly the same variable factors in a variable expression. ex. 4y and 16y are like terms. SIMPLIFYING FRACTIONS

What is the simplified form of each expression?

A. 3(x+8){3(x+8)=3(x)+3(8) distributive property

=3+24 simplify}

B.(5b-4)(-7) {(5b-4)(-7)= 5b(-7)-4(-7)

=-35b+24

REWRITING FRACTION EXPRESSIONS

What sum or difference is equivalent to 7x+2/5?

7x+2/5=1/5(7x+2)

=1/5(7x)+1/5(2)

=7/5x+2/5

USING THE MULTIPLICATION PROPERTY OF -1

What is the simplified form of -(2y-3x)?

-(2y-3x)=-1(2y-3x)

=(-1)(2y)+(-1)(-3x)

=-2y+3x VOCABULARY WORDS:

LESSON1-8

*EQUATION~ a mathematical sentence that uses an equal sign(=). ex. x+5=3x-7

*OPEN SENTENCE~ an equation that contains one or more variables and may be true or false depending on the value of its variables. ex.5+x=12 is an open sentence.

*SOLUTION OF AN EQUATION~ any value or values that make an equation true. ex.3 is the solution of the equation 4x-1=11 CLASSIFYING EQUATIONS

Is the equation true, false, or open?

A.14+6=11+9{true, because both expressions equal 20.}

B.9×5=48{false, because 9×5=45 and 45≠48}

C.6x-12=18{open, because it has a variable}

IDENTIFYING SOLUTIONS OF AN EQUATION

Is x=9 a solution of the equation 52=5x+11?

52=5x+11

52=5(9)+11

52≠56

no, x=9 is not a solution of the equation 52=5x+11. VOCABULARY WORDS:

LESSON1-9

*SOLUTION OF AN EQUATION~a solution of a two-variable equation with the variables x and y is any ordered pair(x,y) that makes the equation true. ex.(4,1) is one solution of the equation x=4y

*INDUCTIVE REASONING~making conclusions based on observed patterns. IDENTIFYING SOLUTIONS OF A TWO-VARIABLE EQUATION

Is (5,9) a solution of the equation y=2x?

y=2x

9=2×5

9≠10 EXAMPLES EXAMPLES EXAMPLES EXAMPLES EXAMPLES

Full transcriptBY: KREMBLE BAILEY VOCABULARY WORDS: LESSON1-1

* QUANTITY~ anything that can be measured or counted. ex. a dozen is another way to describe a quantity of 12 eggs.

*VARIABLE~ a symbol, usually a letter, that represents one or more numbers. ex. k is the variable in the equation 14-k=5

*ALEBRAIC EXPRESSION~ a mathematical phrase that includes one or more variables. ex. 6+x is an algebraic expression.

*NUMERICAL EXPRESSION~ a mathematical phrase involving numbers and operaion symbols, but no variables. ex. 6+7 EXAMPLES WRITING EXPRESSIONS WITH ADDITION AND SUBTRACTION

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.14 more than k{k+14} B. 14 less a number x {14-x}

WRITING EXPRESSIONS WITH MULTIPLICATION AND DIVISION

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A.43 times a number j{43j} B. the quotient of a number b and 22{b/22}

WRITING EXPRESSIONS WITH TWO OPERATIONS

WHAT IS THE ALGEBRAIC EXPRESSION FOR THE WORD PHRASE?:A. 6 more than twice a number a{6+2a} B. 3 less than the quotient of 5 and a number c{5/c-3} C. the product of 7 and the sum of a number k and 6{7(k+6)}

USING WORDS FOR AN EXPRESSIONS

6k{three times a number k} CHAPTER 1 VOCABULARY WORDS :LESSON1-2

*POWER~ the base ad the exponent of an expression of the form 2^3. ex.6^7

*EXPONENT~a number that shows repeated multiplication. ex.5^6 :the exponent 6 indicates that 5 is used as a factor 6 times.

*BASE~a number that is multiplied repeatedly.ex.2^3 :the base 2 is used as a factor 3 times.

*SIMPLIFY~to replace an expression with its simplest name or form.ex.3+5=8,so 8 is the simplest form.

*EVALUATE~to substitute a given number for each variable, and then simplify.ex. to evaluate 3x+4 for x=2,substitute 2 for x and simplify 3(2)+4=6+4=10 EXAMPLES SIMPLIFYING POWERS

What is the simplified form of the expression?:A. 5^6{5^6=5×5×5×5×5×5=78,125

B.(0.2)^3{(0.2)^3=0.0016}

SIMPLIFYING NUMERICAL EXPRESSIONS

What is the simplified form of the expression?:

A.

(10-4)^3÷2 (10-4)^3÷2=6^3÷2=216÷2=108

EVALUATING ALGEBRAIC EXPRESSIONS

What is the value of the expression for k=5 and s=2 A. K^2+K-14÷S^2{5^2+5-14÷2^2=25+5-14÷4=25+5-3=30-3=27} VOCABULARY WORDS:LESSON1-3

*SQUARE ROOT~ a number a is the square root of a number b if a"^"=b ex. 7^2= 49, so 7 is the square root.

*RADICAND~ the expression under the radical symbol. ex.the radicand of the radical expression √x+2 is x+2.

*RADICAL~together the radical symbol and radicand form a radical.ex.√a

*PERFECT SQUARE~the square of an integer. ex.the numbers 1,4,9,16,25,36... are perfect squares ecause they are the squares of integers.

*SET~a well-defined collection of objects.ex.{...,-3,-2,-1,0,1,1,2,3...}

*ELEMENT OF A SET~members of a set. ex.cats and dogs are elements of the set of mammals.

*SUBSET~ a subset of a set consists of elements from the given set.ex. if B={1,2,3,4,5,6,7} and A ={1,2,5}, then A is a subset of B.

*RATIONAL NUMBERS~a real number that can be written as a ratio of two integers. Rational numbers in decimal form are terminating or repeating. ex. 2/3,1.548,and 2.292929

*NATURAL NUMBERS~ the counting numbers.ex. 1,2,3...

*WHOLE NUMBERS~the nonnegative numbers.ex.0,1,2,3,.....

*INTEGERS~whole numbers and their opposites.ex. ...-3,-2,-1,0,1,2,3...

*IRRATIONAL NUMBERS~a number that cannot be written as a ratio of two integers. Irrational numbers in decimal form are nonterminating and nonrepeating.ex.

*REAL NUMBERS~a number that is either rational or irrational. ex.5,-3,0.666,0

*INEQUALITY~a mathematical sentence that compares the values of two expressions using an inequality symbol.ex.3<7 SIMPLIFYING SQUARE ROOT EXPRESSIONS

What is the simplified form of each expression.

A. 81/=9 {9^2=81, so 9 is the square root of 81.

B.9/16=3/4{(3/4)^2= 9/16, so 3/4 is the square root of 9/16.

CLASSIFYING REAL NUMBERS

To which subsets of the real numbers does each number belong?

A.15={ natural numbers, hole numbers, integers, rational numbers.

B. -1.4583{rational numbers

(since -1.4583 is a terminating decimal)}

C. √57={irrational numbers(since 57 is not a perfect square)} VOCABULARY WORDS:LESSON1-4

*EQUIVALENT EXPRESSIONS~algebraic expressions that have the same value for all values of the variable(s). ex.6a +7a and 13a are equivalent expressions.

*DEDUCTIVE REASONING~ a process of reasoning logically from given facts to a conclusion. ex.based on the fact that the sum of any two even numbers is even, you can deduce that the product of any whole number and any even number is even.

*COUNTEREXAMPLE~ an example showing that a statement is false.

example statement: all apples are red

counter ex. a Granny Smith apple is green. VOCABULARY WORDS: LESSON 1-5

*ABSOLUTE VALUE~the distance that a number is from zero on a number line. ex. -5 is 5 units from 0, so |-7| =7

*OPPOSITES~ a number that is the same distance from 0 on the number line as a given number, but lies in the opposite direction. ex. -4 and 4 are opposites.

*ADDITIVE INVERSES~ the opposite or additive inverse of any number a is -a. The sum of opposites is 0. ex. -6 and 6 are additive inverses because -6+6=0. IDENTIFYING PROPERTIES

What properties is illustrated by each statement?

A.14*0=0{Zero property of multiplication}

B.(y+6)+28=y+(6+28){Associative property of addition}

C.6x+0=6x{Identity property of addition}

WRITING EQUIVALENT EXPRESSIONS

Simplify each expression.

A.6(5n)=(6*5)n{associative property of multiplication}

30n{simplify}

B.(3+8b)+6=(8b+3)+6{commutative property of addition}

(8b+3)+6

8b+(3+6){associative property of addition}

8b+9{simplify}

C.4xy/y=4x*y/1*y{rewrite denominator using identity property of multiplication}

4x/1*y/y{use rule for multiplying fraction}

4x*1{x/1=x and y/y=1}

4x{identity property of multiplication} -3 -2 -1 0 1 2 3 4 5 -4 -5 6 7 USING NUMBER LINE MODELS

What is each sum? Use a number line. 3+2 start at 3 3+2=5 A. B. 3+(-2) 0 -1 -2 -3 -4 1 2 3 4 3+(-2)=1 C. -3+2 0 1 2 3 4 -1 -2 -3 -4 -3+2=-1 VOCABULARY WORDS:

LESSON 1-6

*MULTIPLICATIVE INVERSE~given a nonzero rational number a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero number and its multiplicative inverse is 1.ex. 4/3 is the multiplicative inverse of3/4 because 3/4*4/3=1

*RECIPROCAL~given a nonzero rational number a/b, the reciprocal, or multiplicative inverse, is b/a. the product of a nonzero number and its reciprocal is 1. ex. 2/5 and 5/2 are reciprocals because 2/5*5/2=1. MULTIPLYING REAL NUMBERS

What is each product?

A.5(-9)=-45 {the product of two numbers with different signs is negative.}

B.24(0.5)=12{the produt of two numbers with the same sign is positve.}

SIMPLIFYING SQUARE ROOT EXPRESSIONS

What is the simplified form of each expression? A.-√169=-13{(-13)^2=169, so -√169=-13}

B.√1/36=1/6{(1/6)^2=1/36, so 1/36=1/6}

DIVIDING FRACTIONS

What is the value of x/y when x=3/4 and y=2/3?

x/y=x÷y=-3/4÷(-2/3)=-3/4×(-3/2)=9/8 VOCABULARY WORDS:

LESSON1-7

*DISTRIBUTIVE PROPERTY~For all real number a, b , and c: a(b+c)=ab+ac

(b+c)a=ba+ca a(b-c)=ab-ac (b-c)a=ba-ca

ex.3(19+4)=3(19)+3(4)

(19+4)3=19(3)+4(3)

7(11-2)=7(11)-7(2)

(11-2)7=11(7)-2(7)

*TERM~a number, variable, or the product or quotient of a number and one or more variables. ex.the expression: 5x+y/2-8 has three terms: 5x,y/2, and-8.

*CONSTANT~a term that has no variable factor. ex.in the expression 4x+13y+17, 17 is the constant term.

*COEFFICIENT~the numerical factor when a term has a variable. ex. in the expression 2x+3y+16, 2 and 3 are coefficients.

*LIKE TERMS~terms with exactly the same variable factors in a variable expression. ex. 4y and 16y are like terms. SIMPLIFYING FRACTIONS

What is the simplified form of each expression?

A. 3(x+8){3(x+8)=3(x)+3(8) distributive property

=3+24 simplify}

B.(5b-4)(-7) {(5b-4)(-7)= 5b(-7)-4(-7)

=-35b+24

REWRITING FRACTION EXPRESSIONS

What sum or difference is equivalent to 7x+2/5?

7x+2/5=1/5(7x+2)

=1/5(7x)+1/5(2)

=7/5x+2/5

USING THE MULTIPLICATION PROPERTY OF -1

What is the simplified form of -(2y-3x)?

-(2y-3x)=-1(2y-3x)

=(-1)(2y)+(-1)(-3x)

=-2y+3x VOCABULARY WORDS:

LESSON1-8

*EQUATION~ a mathematical sentence that uses an equal sign(=). ex. x+5=3x-7

*OPEN SENTENCE~ an equation that contains one or more variables and may be true or false depending on the value of its variables. ex.5+x=12 is an open sentence.

*SOLUTION OF AN EQUATION~ any value or values that make an equation true. ex.3 is the solution of the equation 4x-1=11 CLASSIFYING EQUATIONS

Is the equation true, false, or open?

A.14+6=11+9{true, because both expressions equal 20.}

B.9×5=48{false, because 9×5=45 and 45≠48}

C.6x-12=18{open, because it has a variable}

IDENTIFYING SOLUTIONS OF AN EQUATION

Is x=9 a solution of the equation 52=5x+11?

52=5x+11

52=5(9)+11

52≠56

no, x=9 is not a solution of the equation 52=5x+11. VOCABULARY WORDS:

LESSON1-9

*SOLUTION OF AN EQUATION~a solution of a two-variable equation with the variables x and y is any ordered pair(x,y) that makes the equation true. ex.(4,1) is one solution of the equation x=4y

*INDUCTIVE REASONING~making conclusions based on observed patterns. IDENTIFYING SOLUTIONS OF A TWO-VARIABLE EQUATION

Is (5,9) a solution of the equation y=2x?

y=2x

9=2×5

9≠10 EXAMPLES EXAMPLES EXAMPLES EXAMPLES EXAMPLES