1. UNIT TWO: CLASSIFYING REAL NUMBERS
LEARNING TARGET 1: I CAN CLASSIFY WHAT IS A REAL NUMBER.

2. TODAY: AUGUST 30, 2017
DO NOW!
AGENDA:
A ______________ SHOWS THE RELATIONSHIP BETWEEN SETS.
(VENN DIAGRAM, LINE PLOT)
WRITE EACH FRACTION AS A DECIMAL.
2/9         
4 3/8
WRITE EACH DECIMAL AS A FRACTION.
   0.6
   5.75
DO NOW!
UNIT TWO PROGRESS MONITORING CHART
CLASSIFYING REAL NUMBERS
PRACTICE!

3. WHAT IS REAL?! WHAT IS A SET? NULL/EMPTY, FINITE, INFINITE
REAL NUMBERS
WHAT IS A SET?
NULL/EMPTY, FINITE, INFINITE
REAL NUMBER SUBSETS
NATURAL NUMBERS
WHOLE
INTEGERS
RATIONAL NUMBERS
IRRATIONAL NUMBERS
REAL NUMBERS
RATIONAL NUMBERS
IRRATIONAL NUMBERS
INTEGERS
WHOLE
NATURAL

4. TODAY: AUGUST 31, 2017 DO NOW! AGENDA:
FOR EACH NUMBER, IDENTIFY IF IT IS A RATIONAL OR IRRATIONAL NUMBER. IF IT IS A RATIONAL NUMBER, IDENTIFY WHICH SUBSET IT BELONGS TO, AS WELL.
-73 5/9 18π .33 √2
DO NOW!
INTERSECTION OF SETS
PRACTICE!

5. REAL NUMBERS CONT…
INTERSECTION OF SETS- A SET OF ELEMENTS (NUMBERS) THAT ARE IN BOTH A AND B.
UNION- A SET OF ALL ELEMENTS (NUMBERS) THAT ARE IN A AND B.
CLOSURE- WHEN A SET OF NUMBERS IN AN OPERATION ARE BOTH MEMBERS OF THE SET.
COUNTEREXAMPLE- AN EXAMPLE THAT PROVES A STATEMENT IS FALSE.

6. TODAY: SEPTEMBER 5, 2017 DO NOW! AGENDA: DO NOW! LATE/MISSING WORK
USING THE FOLLOWING NUMBERS, PLACE THEM IN THEIR APPROPRIATE PLACE IN THE CHART WE MADE THE OTHER DAY IN OUR NOTES.
-5, 2, 18, 15
LABEL THE FOLLOWING SETS AS A UNION, AN INTERSECTION, OR A COUNTEREXAMPLE.
…40, 44, 48, 52, 56, 60, 64
56, 57, 58, 59
DO NOW!
LATE/MISSING WORK
CLASSIFYING REAL NUMBERS ACTIVITY

7. TODAY: SEPTEMBER 6, 2017
DO NOW!
AGENDA:
DETERMINE THE PRIME FACTORIZATION FOR THE FOLLOWING NUMBERS:
WHEN TWO NUMBERS ARE MULTIPLIED, THE RESULT IS CALLED THE __________ (QUOTIENT/PRODUCT)
MULTIPLY:
4.5(0.23) ( 2 9 )
DO NOW!
MINI-CONFERENCES
CLASSIFYING REAL NUMBERS ACTIVITY

8. TODAY: SEPTEMBER 11, 2017
DO NOW!
AGENDA:
SIMPLIFY:
3 5 ∙ ∙ ∙7 1 4
DO NOW!
CLASSIFYING REAL NUMBERS WORKSHEET
UNDERSTANDING VARIABLES AND EXPRESSIONS NOTES

9. LEARNING TARGET 2: I UNDERSTAND VARIABLES AND EXPRESSIONS.
UNIT TWO: lesson two
LEARNING TARGET 2: I UNDERSTAND VARIABLES AND EXPRESSIONS.

10. VARIABLES AND CONSTANTS
VARIABLE- A SYMBOL (LETTER) USED TO REPRESENT AN UNKNOWN NUMBER.
CONSTANT- A QUANTITY WHOSE VALUE DOES NOT CHANGE.
FACTOR- WHEN TWO OR MORE QUANTITIES ARE MULTIPLIED, THEY ARE EACH A FACTOR OF THE PRODUCT.
COEFFICIENT- THE NUMERIC FACTOR OF A PRODUCT INCLUDING A VARIABLE.
6 AND 3 ARE CONSTANTS
X IS A VARIABLE
6 – 3x
4xy
X AND Y ARE THE FACTORS
4 IS THE COEFFICIENT

11. 7vw
-5rst cd
71wz
28y

12. TERMS OF AN EXPRESSION 4x (y + 2) -8 3x + 2y – 10
PARTS OF AN EQUATION THAT ARE SEPARATED BY A + OR – SIGN ARE CALLED TERMS OF AN EXPRESSION.
THIS INCLUDES TERMS INSIDE OF PARENTHESES (WITH + OR -)
YOU CAN REFER TO A PARTICULAR TERM OF AN EXPRESSION BY ITS PLACEMENT WITHIN THE EXPRESSION.
NUMBERED FROM LEFT TO RIGHT
4x     (y + 2)     -8    
3x + 2y – 10
X – 4xym     xy

13. 6xy + 57w – 24x
           
1m + 3mn – 5t - 9

14. TODAY: SEPTEMBER 12, 2017 DO NOW! AGENDA:
LABEL THE FOLLOWING WITH EACH EXPRESSION:
TERM(S)
COEFFICIENT(S)
VARIABLE(S)
4xy + (2x – 2y) + 7 6m – m +( 2 3 +m)
DO NOW!
VARIABLES AND EXPRESSIONS WORKSHEET
PRODUCT PROPERTY OF EXPONENTS NOTES
PRODUCT PROPERTY OF EXPONENTS WORKSHEET

15. TODAY: SEPTEMBER 13, 2017 IN THE TERM 4x, x IS THE ___________?
DO NOW!
AGENDA:
IN THE TERM 4x, x IS THE ___________?
(VARIABLE/COEFFICIENT)
SIMPLIFY:
(1.2)(0.7) (0.5)(11)(0.9)
( 1 2 )( 4 5 )( )
DO NOW!
VARIABLES AND EXPONENTS WORKSHEET
PRODUCT PROPERTY OF EXPONENTS NOTES
PRODUCT PROPERTY OF EXPONENTS WORKSHEET

16. Unit two: lesson three
LEARNING TARGET 3: I CAN SIMPLIFY EXPRESSIONS USING THE PRODUCT PROPERTY OF EXPONENTS. 

17. EXPONENTS 5 3 BASE EXPONENT
BASE OF A POWER- THE NUMBER USED AS A FACTOR.
EXPONENT- INDICATES HOW MANY TIMES THE BASE IS USED AS A FACTOR.
EXPONENT
BASE
5 3

18. (0.3) ( 1 2 )

19. PRODUCT OF PROPERTY OF EXPONENTS
IF m AND n ARE REAL NUMBERS AND x ≠ 0, THEN x m ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛
𝑥 5 ∙ 𝑥 7 ∙ 𝑥 2
𝑥 5+7+2
𝑥 14

20. 𝑚 3 ∙ 𝑚 2 ∙ 𝑚 4 ∙ 𝑛 6 ∙ 𝑛 𝑎 2 ∙ 𝑏 2 ∙ 𝑐 2 ∙ 𝑎 2 ∙ 𝑏 2

21. MAGNITUDE
ORDER OF MAGNITUDE- THE NEAREST POWER OF TEN TO A GIVEN QUANTITY.
CAN BE USED TO ESTIMATE WHEN PERFORMING CALCULATIONS MENTALLY.

22. EXPONENTS 5 3 EXPONENTS CAN BE USED TO SHOW REPEATED MULTIPLICATION.
BASE OF POWER- NUMBER USED AS A FACTOR
EXPONENT- INDICATES HOW MANY TIMES THE BASE IS USED AS A FACTOR.
EXPONENT
5 3
BASE

23. (0.3) ( 1 2 )

24. PRODUCT PROPERTY OF EXPONENTS
IF m AND n ARE REAL NUMBERS AND x ≠ 0, THEN 𝑥 𝑚 ⋅

25. LEARNING TARGET 4: I CAN USE ORDER OF OPERATIONS
UNIT TWO: LESSON 4
LEARNING TARGET 4: I CAN USE ORDER OF OPERATIONS

26. ORDER OF OPERATIONS 2∙ (3) 2 6
SIMPLIFY- TO SIMPLIFY AN EXPRESSION MEANS TO PERFORM ALL OPERATIONS.
COULD PRODUCE MULTIPLE ANSWERS WITHOUT RULES CONCERNING THE ORDER IN WHICH OPERATIONS ARE PERFORMED.
2∙ (3) 2 6

27. ORDER OF OPERATIONS
WORK INSIDE GROUPING SYMBOLS
SIMPLIFY POWERS AND ROOTS
MULTIPLY AND DIVIDE
ADD AND SUBTRACT FROM LEFT TO RIGHT

28. 2∙ (3) 2 6
(10∙3)+7∙(5+4) (2∙3−2) 2 2
4 3 +9÷3−2∙ (3) 2

29. COMPARING EXPRESSIONS
WE CAN COMPARE EXPRESSIONS USING <, >, OR =
1.5+3 ÷ (18+8) 2 −8÷4

30. LEARNING TARGET 5: I CAN FIND ABSOLUTE VALUE BY ADDING REAL NUMBERS.
Unit two: lesson 5
LEARNING TARGET 5: I CAN FIND ABSOLUTE VALUE BY ADDING REAL NUMBERS.

31. ABSOLUTE VALUE:
ABSOLUTE VALUE- THE DISTANCE OF A NUMBER FROM THE NUMBER ZERO ON A NUMBER LINE.
TAKE THE NUMBER 4.
4 = 4
-4 = 4

32. −

33. RULES FOR ADDING REAL NUMBERS
ADDING NUMBERS WITH THE SAME SIGN
TO ADD NUMBERS WITH THE SAME SIGN, ADD THEIR ABSOLUTE VALUES. THE SUM WILL HAVE THE SAME SIGN AS THE ADDENDS.
EXAMPLES: = = (-2) = = - 5
ADDING NUMBERS WITH DIFFERENT SIGNS
TO ADD NUMBERS WITH DIFFERENT SIGNS, FIND THE DIFFERENCE OF THEIR ABSOLUTE VALUES. THE SUM WILL HAVE THE SIGN OF THE ADDEND WITH THE GREATER VALUE.
EXAMPLES: (-2) = = (-3) + 2 = = - 1

34. (-12) (-19) + (-8) (3.2) + (-5.1)

35. LEARNING TARGET 6: I CAN SUBTRACT REAL NUMBERS.
UNIT 2: LESSON 6
LEARNING TARGET 6: I CAN SUBTRACT REAL NUMBERS.

36. OPPOSITES AND ADDITIVE INVERSES
OPPOSITES- TWO NUMBERS WITH THE SAME ABSOLUTE VALUE BUT DIFFERENT SIGNS.
ADDITIVE INVERSE- ANOTHER NAME FOR THE OPPOSITE OF A NUMBER.
THE SUM OF A NUMBER AND ITS OPPOSITE IS ALWAYS 0.
INVERSE PROPERTY OF ADDITION
FOR EVERY REAL NUMBER a, a + (-a) = (-a) + a = 0
EXAMPLE: (-5)= 0

37. RULES FOR SUBTRACTING REAL NUMBERS
TO SUBTRACT A NUMBER, ADD ITS INVERSE. THEN FOLLOW THE RULES FOR ADDING REAL NUMBERS.
EXAMPLE: – 5= 3 + (-5)= -2

38. (-12) – 12 (-19) – (-8) 3.2 – (-5.1) (− 3 5 ) −(− 1 5 )
(-12) – (-19) – (-8) – (-5.1) (− 3 5 ) −(− 1 5 )

39. ADDING AND SUBTRACTING REAL NUMBERS:
WHEN SOLVING A PROBLEM CONTAINING ADDITION AND SUBTRACTION OF SIGNED NUMBERS:
BEGIN BY WRITING THE PROBLEM AS ADDITION ONLY.
NEXT, GROUP AND ADD TERMS WITH LIKE SIGNS
LAST, ADD TERMS WITH UNLIKE SIGNS.
− − 2 5 −(− 4 5 )

40. − − 2 5 −(− 4 5 )
WRITE THE PROBLEM AS ADDITION.
− −
GROUP THE TERMS WITH LIKE SIGNS.
− −
ADD NUMBERS WITH LIKE SIGNS. −
ADD.
− 4 5

41. 3.16+ −1.22 − − 5 8 − 1 8
− −3.75

42. UNIT 2: LESSON 7
LEARNING TARGET 7: I CAN SIMPLIFY AND COMPARE EXPRESSIONS WITH SYMBOLS OF INCLUSION

43. MATH LANGUAGE: SYMBOLS OF INCLUSION
( ) PARENTHESES
[ ] BRACKETS
{ } BRACES
a 𝑏 FRACTION BAR
x ABSOLUTE-VALUE SYMBOLS
INCLUDE- FRACTION BARS, ABSOLUTE-VALUE SYMBOLS, PARENTHESES, BRACES, AND BRACKETS.
INDICATE WHICH NUMBERS, VARIABLES, AND OPERATIONS ARE PART OF THE SAME TERM.

44. SIMPLIFYING EQUATIONS WITH SYMBOLS OF INCLUSION
MATHEMATICAL EXPRESSION CAN INCLUDE NUMBERS, VARIABLES, OPERATIONS, AND SYMBOLS OF INCLUSION.
EXPRESSIONS INSIDE OF SYMBOLS OF INCLUSION ARE CONSIDERED A SINGLE TERM.
TO SIMPLIFY AN EXPRESSION WITH MULTIPLE SYMBOLS OF INCLUSION, BEGIN WITH THE INNERMOST SYMBOL OF INCLUSION AND WORK OUTWARD.

45. HOW MANY SYMBOLS OF INCLUSION ARE THERE IN THIS EQUATION?
HOW WOULD YOU SIMPLIFY THE EQUATION?
( 2𝑥 ) −2𝑦
2y IS ALSO A SINGLE TERM.
( 2𝑥 ) IS CONSIDERED A SINGLE TERM.

46. 9 – 4 – 6 5∙2+[3+ 6−8 ]

47. ORDER OF OPERATIONS AND SYMBOLS OF INCLUSION
IT IS IMPORTANT TO FOLLOW THE ORDER OF OPERATIONS AT ALL TIMES, ESPECIALLY WHEN WORKING INSIDE SYMBOLS OF INCLUSION.
BEGIN WITH THE INNERMOST SYMBOL OF INCLUSION AND WORK OUTWARD.
TO SIMPLIFY A RATIONAL EXPRESSION, THE NUMERATOR AND DENOMINATOR MUST BE SIMPLIFIED FIRST.
3 + 5∙[(9− 3) 2 −6]

48. [5∙ 4+ 2) ∙5 2

49. COMPARE: (<,>, =) 12+[5 7− 5) 3 −14 [ 9− 5) 2 +7 − 3 3

50. LEARNING TARGET 8: I CAN USE UNIT ANALYSIS TO CONVERT MEASURES.
UNIT 2: LESSON 8
LEARNING TARGET 8: I CAN USE UNIT ANALYSIS TO CONVERT MEASURES.

51. UNIT ANALYSIS: 12 𝑖𝑛. 1 𝑓𝑡. 1 𝑚 100 𝑐𝑚. 3 𝑓𝑡. 1 𝑦𝑑. 1 𝑚𝑖. 1760 𝑦𝑑.
A PROCESS FOR CONVERTING MEASURES INTO DIFFERENT UNITS.
A UNIT RATIO, OR CONVERSION FACTOR, COMPARES 2 MEASURES THAT NAME THE SAME AMOUNT.
UNIT RATIOS ARE ALWAYS EQUAL TO 1
SINCE THE PRODUCT OF 1 AND A NUMBER IS ALWAYS THAT NUMBER, A UNIT RATIO MULTIPLIED BY A MEASURE WILL ALWAYS NAME THE SAME AMOUNT.
12 𝑖𝑛. 1 𝑓𝑡 𝑚 100 𝑐𝑚 𝑓𝑡. 1 𝑦𝑑 𝑚𝑖 𝑦𝑑.

52. A cheetah ran at a rate of 105,600 yards per hour
A cheetah ran at a rate of 105,600 yards per hour. How fast did the cheetah run in miles per hour?

53. LEARNING TARGET 9: EVALUATING AND COMPARING ALGEBRAIC EXPRESSIONS.
UNIT 2: LESSON 9
LEARNING TARGET 9: EVALUATING AND COMPARING ALGEBRAIC EXPRESSIONS.

54. EVALUATION:
NUMERIC EXPRESSION: AN EXPRESSION THAT CONTAINS ONLY NUMBERS AND OPERATIONS.
ALGEBRAIC EXPRESSION: AN EXPRESSION WITH VARIABLES AND/OR NUMBERS THAT USES OPERATIONS.
ALSO CALLED A VARIABLE EXPRESSION.
EVALUATE: TO SUBSTITUTE VALUES FOR THE VARIABLES AND TO SIMPLIFY USING ORDER OF OPERATIONS.

55. EVALUATE THE EXPRESSION WHEN x=3 AND a=1. 3x- 4x +ax
EVALUATE THE EXPRESSION FOR y=2 AND z=4 3(𝑧− 𝑦) 2 −4 𝑦 3

56. COMPARE THE EXPRESSION WHEN a = 4 AND b = 3. USE <,>, AND =.
3 𝑎 2 +2𝑏−4 𝑏 𝑎 2 𝑏 2