1. ~ Chapter 1 ~ Algebra I Algebra I Tools of Algebra
Lesson Using Variables
Lesson Exponents & Order of Operations
Lesson Exploring Real Numbers
Lesson Adding Real Numbers
Lesson Subtracting Real Numbers
Lesson Multiplying & Dividing Real Numbers
Lesson The Distributive Property
Lesson Properties of Real Numbers
Lesson Graphing Data on the Coordinate Plane
Chapter Review

2. Chap 1 Diagnosing Readiness Answers
Lesson 1-1
Using Variables
Chap 1 Diagnosing Readiness Answers
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3. Using Variables Lesson 1-1 Notes
Variable – a symbol that represents one
or more numbers.
Examples – x, y, q, r, s, n …
Algebraic Expression – a mathematical
phrase that can include numbers, variable,
and operation symbols. (no equal sign)
Examples ~ 2n , , n , 27x – 4y … 9
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4. Lesson 1-1 Using Variables Notes Lesson 1-1 Using Variables Notes
Writing an Algebraic Expression
Add – Terms -> sum, altogether, more than,
greater than…
Subtract – terms -> difference, minus,
less than…
Multiply – terms -> product, times,
multiplied by, twice, triple…
Divide – terms -> quotient, divided by,
half, third…
Writing an Algebraic Expression
Add – Terms -> sum, altogether, more
than, greater than…
Subtract – terms -> difference, minus,
less than…
Multiply – terms -> product, times,
multiplied by, twice, triple…
Divide – terms -> quotient, divided by,
half, third…
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5. Using Variables Lesson 1-1 Notes Examples: Five more than a number
The difference of five and a number
5 - x
Five less than x
x - 5
The product of five and a number 5n
The quotient of a number and five
n ÷ 5
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6. Using Variables Lesson 1-1 Notes More complex algebraic expressions:
Two times a number plus five
2n + 5
Seven less than five times a number
5x - 7
Four more than the quotient of a number and six
(n ÷ 6) + 4
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7. Using Variables Lesson 1-1 Notes
Equation – a mathematical sentence that uses an equal sign. (Ex: 2+3 = 5, 4x=8,…)
Open sentence – an equation that contains one or more variables. (Ex: 2x=8, 3x+2y = 10)
Writing an Equation
Track One Media sells all CD’s for $12 each. Write an equation for the total cost of a given number of CD’s.
Know: The total cost is 12 times the number of CD’s
Define: Let n = of CD’s Let c = total cost
Write: c = 12n or 12n = c
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8. Using Variables Lesson 1-1 Notes Number of Hours Total Pay 4 $32 6 $48
$64 10
$80
Know:
Number of hours times 8 equals the total pay
Define:
Let n = number of hours Let t = total pay
Write:
8n = t or t = 8n
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9. Notes – Practice Problems
Lesson 1-1
Using Variables
Notes – Practice Problems
the quotient of 6.3 and b
6.3 ÷ b
s minus ten
s - 10
9 less than a number
n - 9
The sum of twice a number and thirty-one
2x + 31
The product of one half of a number and one fourth of the same number
½ n ( ¼ n)
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10. Lesson 1-1
Using Variables
Homework
Practice 1-1 ~ all ~
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11. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Daily Math Review
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12. Using Variables Lesson 1-1 Homework - Answers ?????? Questions ???????
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?????? Questions ???????

13. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Notes
Simplify – replace an expression with its simplest name or form.
Exponents – A number that shows repeated multiplication. (In 24 ~ 4 is the exponent)
Base – The number that is multiplied repeatedly in a power. (In 24 ~ 2 is the base)
Power – has two parts, a base and an exponent, and has the form an.
Order of operations – GEMS – (1) grouping symbols; (2) Exponents; (3) Multiply & Divide (left to right) (4) Subtract & Add (left to right)
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14. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Notes
Simplifying a Numerical Expression
25 – 8 *
* 4 – 22
3 + 5 – 6 ÷ 2
6 – 10 ÷ 5 3 2 4 1 18 3 2 4 1 18 2 3 1 5 2 1 4
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15. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Notes
Evaluating an Algebraic Expression
3a – 23 ÷ b for a = 7 and b = 4
3 * 7 – 23 ÷ 4
Example: A shirt costs $22.85 plus sales tax. What is the total cost of the shirt?
Expression - p + p * r
( p = price; r = tax)
c = $ $22.85(0.07) = $ $ =
c = $24.45 2 4 3 1 19
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16. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Practice
3 * 6 – 42 ÷ 2
4 * ÷ 22
÷ 10
Evaluate the following for c = 2 and d = 5
4c – 2d ÷ c c4 – d * 2
d + 6c ÷ – d2 + cd * 3
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17. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Notes
Expressions with parenthesis
15(13 – 7) ÷ (8 - 5) (5 + 3) ÷ 2 + (52 – 3)
15(6) ÷ (3) (8) ÷ 2 + (25 – 3)
90 ÷
Expressions with Exponents
(cd)2 for c = 7 & d = 19
(7 * 19)2
(133)2 = 17,689
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18. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Notes
m2n for m = 5 & n = 4
52 * 4 = 25 * 4 = 100
Evaluate the following for m=3, q=4, p=7
qp2 + q2p m(pq)2
4* *7 3(7*4)2
4* *7 3(28)2
= (784) = 2,352
Simplifying an expression
2[(13-7)2 ÷3] 24
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19. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Practice
5[4 + 3(22+1)] 28 ÷ [(19 -7) ÷ 3]
5[4 + 3(4+1)] 28 ÷ [(12) ÷ 3]
5[4 + 3(5)] 28 ÷ [4] = 7
5[4 + 15]
5[19] = 95
9 + [4 – (10 – 9)2]3
9 + [4 – (1)2]3
9 + [4 – 1]3
9 + [3]3
= 36
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20. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Homework
Practice ~ even ~
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21. Exploring Real Numbers
Lesson 1-3
Exploring Real Numbers
Daily Math Review
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22. Exponents & Order of Operations
Lesson 1-2
Exponents & Order of Operations
Homework - Answers
?????? Questions ???????
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?????? Questions ???????

23. Exploring Real Numbers
Lesson 1-3
Notes
Natural Numbers – counting numbers ~ 1, 2, 3… (not 0)
Whole Numbers – non-negative integers ~ 0, 1, 2, 3, 4…
Integers – whole #’s & their opposites ~ …-2, -1,0,1,2…
Rational Numbers – numbers that can be written as a/b where b ≠ 0. Decimal form is a terminating or repeating decimal.
Irrational Numbers – numbers that cannot be expressed in the form a/b where a & b are integers. (Ex ~ π, √10, …)
Classify the following
integer, rational number rational number
/12
natural number, whole number, rational number
integer, rational number
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24. Exploring Real Numbers
Lesson 1-3
Notes
Counterexample – Any example that proves a statement false…
All Whole numbers are rational numbers T or F
All integers are whole numbers. T or F
The square of a number is always greater than the number. T or F
All whole numbers are integers. T or F
No fractions are whole numbers. T or F
Inequality
(>, <, ≥ , ≤ , ≠ ~ used to compare the value of two expressions)
Ordering fractions
Write fractions as a decimal and then compare
Find the common denominator, convert, and then compare
Absolute value – distance a number is from l-19l = l22l = 22
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25. Lesson 1-4 Notes Adding Real Numbers
Identity Property of Addition - n + 0 = n, for every real number n.
Inverse Property of Addition – n + (-n) = 0
(additive inverse is the opposite of a number)
Rules for Adding
Numbers with the same signs – add and keep the sign.
Numbers with different signs – subtract, answer takes the sign of the number with the greatest absolute value.
Examples
-7 + (-4)
-3/4 + (-1/2) 8/9 + (-5/6)
-1 ¼ 1/18
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26. Adding & Subtracting Real Numbers
Lesson 1-4 & 1-5
Notes
Evaluating Expressions
-n for n = t + (-4.3) for t = -7.1
Matrix
Subtracting Real Numbers
Leave, change, opposite… (then use the rules for addition)
3 – 5 = 3 + (-5) = (-5) = = 8
¾ - (-11/12) =
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27. Subtracting Real Numbers
Lesson 1-5
Notes
Absolute Values
l 5-11 l = l 7 – 8 l =
Evaluating Expressions
-a – b for a = -3 & b = -5
-(-3) – (-5) = = 8
Subtract with Matrices _
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28. Homework Real Numbers Practice 1-3 - every 3rd problem
Lesson 1-3, 1-4, & 1-5
Real Numbers
Homework
Practice every 3rd problem
Practice 1-4 – every 3rd problem
Practice 1-5 – every 3rd problem & #35
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29. Lesson 1-4
Adding Real Numbers
Daily Math Review
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30. Lesson 1-3 & 1-4
Real Numbers
Homework - Answers
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31. Homework - Answers Real Numbers Lesson 1-5 ?????? Questions ???????
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?????? Questions ???????

32. Multiplying & Dividing Real Numbers
Lesson 1-6
Notes
Identity Property of Multiplication ~ 1 * n = n
Multiplication Property of Zero ~ n * 0 = 0
Multiplication Property of -1 ~ -1 * n = -n
Rules for Multiplying & Dividing
Like/same signs – answer is positive.
Different signs – answer is negative.
Simplifying Expressions
-6 * -5 = ( -15/3) = * 4.1 =
(-2) (3/4)2
-(4*4*4) (-2)(-2)(-2)(-2) ( ¾ * ¾)
/16
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33. Multiplying & Dividing Real Numbers
Lesson 1-6
Notes
Evaluating Expressions
-(cd) (-2)(-3)(cd) for c= -8 and d= -7
-(-8*(-7)) (-2)(-3)(-8*(-7))
3x ÷ 2z + y ÷ z+x/2y for x = 8, y = -5, & z = -3
3(8) ÷ 2(-3) + (-5) ÷ [2(-3) + (8)]/2(-5)
24 ÷ (-6) + (-5/10) [-6 + 8]/-10
-4 + (-1/2) /-10
-4 ½ /5
Inverse Property of Multiplication ~ a ≠ 0, a (1/a) = 1
x/y x = -3/4 and y = -5/2
-3/4 ÷ (-5/2) (the reciprocal or multiplicative inverse is used)
-3/4 x (-2/5) = 6/20 = 3/10
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34. Properties of Real Numbers
Lesson 1-8
Notes
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35. The Distributive Property
Lesson 1-7
Notes
Distributive Property ~ a(b + c) = ab + ac; (b + c)a = ba + ca
a(b – c) = ab – ac; (b – c)a = ba – ca
Simplifying Expressions
13(103) = 13( ) (98) =
= 13(100) + 13(3) =
= 1339
6(m + 5) (3-7t) ( c)(3)
6m – 14t c
Terms, constants, and coefficients…
6a2 – 5ab + 3b – (a2, ab, and b are all unlike terms)
Like terms are combined to simplify an expression…
3x2 + 5x y + 6y w3 - 3w3
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36. Multiplying & Dividing Real Number & The Distributive Property
Lesson 1-6 & 1-7
Notes & Homework
Writing an Expression…
-2 times the quantity t plus 7
-2(t + 7)
The product of 14 and the quantity 8 plus w
14(8 + w)
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37. Properties of Real Numbers
Lesson 1-8
Notes
Commutative Property of Addition ~ a + b = b + a
Commutative Property of Multiplication ~ a * b = b * a
Associative Property of Addition ~ (a + b) + c = a + (b + c)
Associative Property of Multiplication ~ (a * b) * c = a * (b * c)
Identity Property of Addition ~ a + 0 = a
Identity Property of Multiplication ~ a * 1 = a
Inverse Property of Addition ~ a + (-a) = 0
Inverse Property of Multiplication ~ a (1/a) = 1
Distributive Property
Multiplication Property of Zero
Multiplication Property of -1
Identify the property… = m = m np = pn =2
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38. Properties of Real Numbers
Lesson 1-8
Notes
Using Deductive Reasoning – logically justifying the reason (the why) for each step in simplifying an expression using properties, definitions, or rules.
Simplify the expression… Justify each step
7z – 5(3 + z)
Step Reason
7z – z Distributive Property
7z +(-15) + (-5z) Rules for subtraction
7z + (-5z) + (-15) Commutative property of addition
2z + (-15) addition of like terms
2z – rules for subtraction
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39. Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9
Notes
2(3t – 1) + 2
Step Reason
6t – Distributive property
6t +(-2) Rules/defn of subtraction
6t addition
Homework
Practice 1-7 & 1-8 even;-)
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40. Subtracting Real Numbers
Lesson 1-5
Subtracting Real Numbers
Quiz Lesson 1-1 to 1-4
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41. Properties of Real Numbers
Lesson 1-8
Notes
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42. Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9
Properties of Real Numbers & Graphing on the Coordinate Plane
Homework Answers
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43. Graphing on the Coordinate Plane
Lesson 1-9
Notes
Graphing Data on the Coordinate Plane
A coordinate plane has an x-axis (horizontal)
and a y-axis (vertical)
An ordered pair (x, y) are the numbers that
identify the specific location of a point.
y-axis
(0,0)
origin
origin
(-,+)
(+,+)
Quadrant II
Quadrant I
x-axis
Quadrant IV
Quadrant III
(+,-)
(-,-)
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44. Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9
Notes
Identifying & Graphing Points
Use the (x, y) location to identify the location of a point.
Graph C(0,3); D (2,4); E(-1,-4); F(-3,0)
Quadrant? (-2,0) (4,-1) (-3,-5) (2.7,3.6)
Can we find the dimensions of a shape when we graph it?
Scatter Plot
Graph that relates data of two different sets. Scattered points do not form a line. (Usually graphed in Quadrant I)
A trend line can show trend of the data in a scatter plot.
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45. Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9
Properties of Real Numbers & Graphing on the Coordinate Plane
Practice
Homework
Practice 1-8 & 1-9 odd
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46. Properties of Real Numbers & Graphing on the Coordinate Plane
Lesson 1-8 & 1-9
Properties of Real Numbers & Graphing on the Coordinate Plane
Homework Answers
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47. Daily Math Review
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48. Algebra I
Algebra I
~ Chapter 1 ~
Chapter Review
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49. Algebra I
Algebra I
~ Chapter 1 ~
Chapter Review
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