Pre-Algebra CHAPTER 1 – Order of Operations ... Warm-up: Write each as an algebraic expression. 1)...

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CHAPTER 1: TOOLS FOR ALGEBRA AND GEOMETRY

Pre-Algebra

Chapter 1: WRITE THIS DOWN IN YOUR PLANNER 1-2 PEMDAS and Divisibility Rules

FRIDAY - QUIZ 1A

1-3 Variables and Expressions

1-4 Variables and Equations

1-5 Distribution Property

FRIDAY - Quiz 1B

1-7 Ordered Pairs

1-8 Solving Equations Using Inverse Operations

FRIDAY - Quiz 1C

1-9 Inequalities

1-10 Gathering and Recording Data

FRIDAY - Chapter 1 Test

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1.2 – Order of Operations

OBJ: To re-examine the basic tools for Algebra:

To choose the appropriate method of computation

To use variables and algebraic properties

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1.2 – Order of Operations P – Parenthesis

E – Exponents

M – Multiply

D- Divide

A – Add

S - Subtract

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Example: 5(2+6) – 8 x 4 =

5(8) – 8 x 4 = 40 – 32=

Answer = 8

PEMDAS (Order of Operations)

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Parentheses 3(5 + 4) =

Exponents 6-2²

Add/Sub. Family

Mult./Div. Family

Order of Operations PEMDAS

http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Order of Operations.pdfOprder

http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Order of Operations.pdfOprder

Divisibility Rules

CHAPTER 1 Kruska


OBJ: To evaluat e expressions con t ain ing var iab les and t ranslat e verb al p h rases in t o algeb raic expressions.

Warm -up : Find t he value o f each exp ressions:

1. 72 + 12 =

35 + 7

2. 54 – 42 ÷ 7 =

3. 36 ÷ 9 ∙ 3=

4. 37 + 38 =

30 – 5

5. 3[(18 – 3) + 4(5 + 7)] =

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Answers: 1. 2 2. 48 3. 12 4. 3 5. 189

Vocabulary Quiz - FRIDAY


Not es:

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“Expression”

•An expression is a phrase, a sentence fragment.

•You simplify an expression.

•An expression has no relation

symbol. 1. a number less than five = 5 - x

2. five less than a number = x - 5


Math Vocabulary

Mathematics (math) is the study of numbers, quantities, shapes, and space using mathematical processes, rules, and symbols.

CHAPTER 1 Kruska Vocabulary Quiz - FRIDAY

Math Vocabulary

Kruska Vocabulary Quiz - FRIDAY

Math Vocabulary

Algorithm:

A step-by-step mathematical procedure used to find an answer.


Math Vocabulary

Coefficient

A number that multiplies a variable.

For example, 9 is the coefficient in 9x.


Math Vocabulary

Denominator

The bottom number in a fraction.

The denominator represents the number of parts into which the whole is divided.

For example, 6 is the denominator in the fraction .


Math Vocabulary

Equation

A mathematical statement used to show that two expressions are equal.

It contains an equals sign.

For example, 16 - 9 = 7 (the expression 16 - 9 and the expression 7 are equal).


Math Vocabulary

Greatest Common Factor (greatest common divisor)

The largest number that will divide two or more other numbers equally.

For example, the greatest common factor of 32 and 48 is 16.


Math Vocabulary

Improper Fraction (mixed fractions)

A fraction that has a larger numerator than denominator.

For example, is an improper fraction.


Math Vocabulary

Inverse Operations

Opposite or reverse operations.

Addition and subtraction are inverse operations, as are multiplication and division.


Math Vocabulary

Negative Number

A number that is less than zero.

A minus sign is used to show that a number is negative.

For example, -12 is a negative number.


Math Vocabulary

Numerator

The top number in a fraction.

The numerator represents the number of parts of the whole.

For example, 5 is the numerator in the fraction .


Math Vocabulary

Ordinal Number

A number that shows place or position, as in 2nd place.


Math Vocabulary

Positive Number

A number that is greater than zero.

While a minus sign is used to signify a negative number, the absence of a minus sign signifies a positive number.


Math Vocabulary

Prime Number

A number that can be divided evenly only by itself and 1.

For example, 7 is a prime number.


Math Vocabulary

Square Number

A number that results from multiplying another number by itself.

For example, 49 is the square of 7 (7 x 7 = 49).


7 x 7

49

Math Vocabulary

Square Root of a Number

A number that is multiplied by itself to produce a square number.

For example, 7 is the square root of 49. It is designated by the symbol √.


Math Vocabulary

Variable

A quantity that can change or vary, taking on different values.

It is typically represented by a letter of the alphabet.

For example x is the variable in 9x (x can be any number that is being multiplied by 9).



Kruska

Assignment:

p. 19 (11-14, 16 – 26 EVEN)

1-4 Properties

OBJ: To iden t if y p ropert ies of add it ion and

m ult ip licat ion and use t hem t o solve p rob lem s.

Warm -up : Evaluat e each expression if :

a= 4, b= 2, and c= 3

1. a + bc

2. 4a + b ∙ b

3. ac

b

4. 7a – (2c + b)

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Answers: 1. 10 2. 20 3. 6 4. 20


1-4 Properties Notes:

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1-4 Propert ies

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Assignment:

p 25

(16-48 x4)

1-5 Distributive Property

OBJ: To sim p lif y algebraic expressions using t he

d ist r ibu t ive p ropert y

Warm -up : Nam e t he p rop er t y:

1. (ab)c = a(bc)

2. (7 + 4) 0 = 0

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Answers: 1. Associative Prop.

Of Mult. 2. Mult. Prop. Of Zero



NOTES: The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

Take a look at the problem below. • 2(3 + x) • 2(3) + 2(x) • 6 + 2x

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Notes:

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1-5 Distibution Property

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Assignment:

p 28

(15-33 x3)


OBJ: To iden t if y and so lve open sen t ences

Warm -up : Sim p lif y each exp ression:

1. 4q + q

2. 4m + 6m + 3

3. 24a + a + 16

4. 9(r + 7) + 12r

5. 6(x + y) + 4(2x + 3y)

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Answers: 1. 5q 2. 10m + 3 3. 25a + 16 4. 21r + 63 5. 14x + 18y


Chapter 1 – Update!

1-2 PEMDAS and Divisibility Rules

FRIDAY - QUIZ 1A (DONE)


1-4 Properties


FRIDAY - Quiz 1B (DONE)


1-8 Solving Equations Using Inverse Operations

FRIDAY - Quiz 1C (THIS FRIDAY)

1-9 Inequalities

1-10 Gathering and Recording Data

FRIDAY - Chapter 1 Test (NEXT FRIDAY!)

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Notes:

ADDING your like t erm s

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http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Combining Like Terms.pdf

1-6 Variables and Equations Determine which equation is true by

replacing the variable with -1.

A. 5 + x = 4

B. 5 + x = 5

C. 5 + x = 9

D. 5 + x = 10

Determine which equation is true by replacing the variable with 3.

A. 6x + 4 = 16

B. 3x + 1 = 10

C. 6x = 8

D. 2x + 2 = 8

Which of the numbers is the solution of x ÷ 4 – 2 = 5?

A. 32

B. 28

C. 26

D. 30

Solve 11 = 2m - 3 mentally.

A. 4

B. 22

C. 7

D. 12

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Kruska

Assignment:

p 34

(15-33 x3)

1-8 Solving Equations OBJ: To use inverse operat ions t o so lve equat ions

and solve p rob lem s using equat ions

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Answers: 1) 10-5 2) 14/7 3) u – 17 4) 14/2 5) x + 6 6) x ∙ 7

7) q + 8 8) 6²

Equation Quiz - FRIDAY

Warm -up : Writ e each as an algebraic expression .

1) t he dif f erence o f 10 and 5

2) t he quot ient o f 14 and 7

3) u decreased by 17

4) half o f 14

5) x increased by 6

6) t he product o f x and 7

7) t he sum o f q and 8

8) 6 squared

9) t w ice q

10) t he product o f 8 and 12

1-8 Solving Equations Notes:

Solve f o r var iab le using INVERSE OPERATIONS

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Using Inverse Operations Just like with “PEMDAS”

M/D House

A/S House

The operation that reverses the effect of another operation. Example: Addition and subtraction

are inverse operations

Another Example: Multiplication and division are inverse operations.

http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/One-Step Equations.pdf

1-8 Solving Equations

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Assignment:

p 44

(12-13 & 18 - 39 x3)

1-9 Inequalities OBJ: To w rit e and so lve inequalit ies

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Answers: 1) r = 2 2) x = 17 3) w = 24 4) y = 13.69 5) d = 7

Equation Quiz - FRIDAY

Warm -up : Writ e each as an algebraic expression .

1) 5 + r = 7

2) 34 = 2x

3) 2 = 4) 4.37 = y – 9.32

5) d + 48 = 55

Weekly Schedule

Monday – 1.9 Inequalities

Tuesday – Quiz Reviews

Block – Review Math Lab

Friday – Chapter 1 Test

PROGRESS REPORTS

NEXT WEEK!

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1-9 Inequalities Notes:

Solve INEQUALITIES

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http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multi-Step Inequalities.pdf

1-9 Inequalities

Graphing the Inequality: Draw your number line

--------I--------------I-----------------I--------

1 2 3

Mark this point with the appropriate notation (an open dot indicating that the point x = 2 was NOT included in the solution)

Then you'd shade everything to the right, because "greater than" meant "everything off to the right".

The steps for graphing two-variable linear inequalities are very much the same.

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x > 2

1-9 Inequalities

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Assignment:

p 48 (13-21 ALL

& 22-26 Evens - GRAPH EACH ANSWER)

Math Lab – Chapter 1 Review

Section A – (IND)

p58 (9-35 ODD)

Section B – (ME)

p 60 (63 – 68 ALL)

Section C – (GROUP)

p 58-59 (30-49 & 56-62)

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Pre-Algebra CHAPTER 1 – Order of Operations ... Warm-up: Write each as an algebraic expression. 1)...

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