Day 1: Solving Equations Goal: To solve equations in one
variable that contain more than one operation Standard: Prior
Standard Guiding Question: How do I solve an equation for a
variable? Materials: Pencil, Folder, Student Packet
Slide 4
Adding and Subtracting Fractions When you add or subtract
fractions, you need a common denominator Adding and Subtracting
Decimals 13.34 + 12 When you add or subtract decimals, make sure
you line the decimals up. Dividing Fractions To give dividing
fractions a try, flip the second and multiply. Reflection Starters:
I know or I need to work on Menta l Math Math Review Day 1
Slide 5
Access: Apply the correct order of operations: A)7 x 4 + 3 = B)
(1 + 3) 2 9 3 + 6 = C)12 6 x 2 + 7 = D) 24 12 2 x 3 + 7 =
Slide 6
One-Step Equations: A)3 + x = 7B) -10 = x 4 Try: C) X 9 = 11 D)
-5 x = 10 E) -13 = x 4F) 17 = 6 - x
Word Problems: Josie bought 4 cases of sports drinks for an
upcoming meet. After talking to her coach she bought three more
cases spending an additional $6.95 on additional items. Her
receipts totaled $74.15. Write and solve an equation to find out
how much each case of sports drink costs.
Slide 10
Work Time: Work through pages 3 and 4 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 11
Multiplication Timed Test: -Page 5 of your packet tear in half
and remove one from the packet You have five minutes to fill in as
much as you can Go = Start, Stop = hands up! Highlight the ones you
did not know
Slide 12
Exit Slip: (on a half-sheet of scratch paper) A)5x 9 = 17 B)
Make sure it has your name and turn it in!
Slide 13
Day 2: Solving Equations Goal: To solve equations that have
variables on both sides Standard: Prior Standard Guiding Question:
How do I solve an equation for a variable? Materials: Pencil,
Folder, Student Packet
Slide 14
Adding and Subtracting Fractions When you add or subtract
fractions, you need a common denominator Adding and Subtracting
Decimals 45 9.867 When you add or subtract decimals, make sure you
line the decimals up. Dividing Fractions To give dividing fractions
a try, flip the second and multiply. Reflection Starters: I know or
I need to work on Menta l Math Math Review Day 2
Slide 15
Access: Solve the equation: A)3x 9 = 11B) C)
Slide 16
Solve the equation: A)3d + 8 = 2d 17B) t + 5 = t 19 C) 5 (t 3)
= -1 + (2 3) D) x + 4 6x = 6 - 5xE)-8x + 6 + 9x = -17 + x
Work Time: Work through pages 7 and 8 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 20
Multiplication Timed Test: -Page 5 of your packet tear out of
packet You have five minutes to fill in as much as you can Go =
Start, Stop = hands up! Highlight the ones you did not know
Slide 21
Exit Slip: (on a half-sheet of scratch paper) Previous Material
(PM): A)5y 9 = 16 New Material (NM): B) 3x 8 = 6 2xC) 6x = 5x 10
Make sure your name is on it, and turn it in!
Slide 22
Day 3: Solving Inequalities Goal: To solve multi-step
inequalities AND to solve inequalities that contain variables on
both sides. Standard: Prior Standard Guiding Question: How do I
solve an inequality for a variable? Materials: Pencil, Folder,
Student Packet
Slide 23
Adding and Subtracting Fractions When you add or subtract
fractions, you need a common denominator Adding and Subtracting
Decimals 15.87+ 1.9 When you add or subtract decimals, make sure
you line the decimals up. Dividing Fractions To give dividing
fractions a try, flip the second and multiply. Reflection Starters:
I know or I need to work on Menta l Math Math Review Day 3
Slide 24
Access: Solve the equation: A)3x + 9 = x 8 B) 7 4x = 6x + 2 C)
7x = 10x - 1
Slide 25
Solve: - 3x > 9 Check a Number. What is the rule when
solving inequalities?
Slide 26
Solve the inequality and graph the solution: A)2m + 1 > 13B)
2d + 21 11 C) D) 4 X > 3(4 2)
Slide 27
Solve the inequality and graph the solution: E) 4r 9 > 7F) 3
5 2x G)-4x 8 > 16H) I) 12 (x 3) + 2x 6
Slide 28
Solve the inequality and graph the solution: J) 2x > 4x 6K)
5(4 x) 3(2 + x)
Work Time: Work through pages 9 and 10 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 31
Multiplication Timed Test: -Page 11 of your packet tear out of
packet You have five minutes to fill in as much as you can Go =
Start, Stop = hands up! Highlight the ones you did not know
Slide 32
Exit Slip: (on a half-sheet of scratch paper) Previous Material
(PM): A)2r + 20 = 200B) 3(2x 5) = 2(3x 2) New Material (NM): C) 2 +
(-6) > -8p D) 3(1-x) 3(x + 2) Make sure your name is on it, and
turn it in!
Slide 33
Day 4: Graphing Linear Functions Goal: To solve for a variable
AND To graph linear functions using tables or equations Standard:
9.2.1.8 Make Qualitative statements about the rate of change of a
function based on its graph or table of values 9.2.2.3 Sketch
graphs of linear, quadratic and exponential functions and translate
between graphs, tables and symbolic representations. Know how to
use graphing technology to graph these functions. Guiding Question:
What and how are the many ways I can graph a line? Materials:
Pencil, Folder, Student Packet
Slide 34
Adding and Subtracting Fractions When you add or subtract
fractions, you need a common denominator Adding and Subtracting
Decimals 1.309+ 134.8 When you add or subtract decimals, make sure
you line the decimals up. Dividing Fractions To give dividing
fractions a try, flip the second and multiply. Reflection Starters:
I know or I need to work on Menta l Math Math Review Day 4
Slide 35
Access: Graph the points on a coordinate plane: A (5, 6) B (-1,
-3) C (4, -9) D (-1.5, 0)
Slide 36
Solve for a variable: A)2x - 3y = 12 B) 2x + y = 8 Try: C) 5y =
5x - 10 D) 2y - 6y = -8
Slide 37
What is a function? What makes a function linear? How can I
graph a line? Table, Slope and Intercept, x-and y- intercepts, and
slope-intercept form
Work Time: Work through pages 13 and 14 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 45
Multiplication Timed Test: -Page 11 of your packet tear out of
packet You have five minutes to fill in as much as you can Go =
Start, Stop = hands up! Highlight the ones you did not know
Slide 46
Exit Slip: (on a half-sheet of scratch paper) New Material
(NM): Solve for y: A)7y + 14x = 28 B) -5y = 2x + 7 Graph: A)B) y =
-3x C) y = 2 D) 3x - 2y = 6 Make sure your name is on it, and turn
it in!
Slide 47
Day 5: Graphing Linear Inequalities Goal: To graph linear
inequalities using tables or equations. AND To write equations to
describe lines. Standard: 9.2.4.4 Represent relationships in
various contexts using systems of linear inequalities; solve them
graphically. Indicate which parts of the boundary are included in
and excluded from the solution set using solid and dotted lines.
Guiding Question: How do I graph a linear inequality? AND How can I
write equations of lines? Materials: Pencil, Folder, Student
Packet
Slide 48
Adding and Subtracting Fractions Adding and Subtracting
Decimals A)67.8 + 5.23 B)71 8.09 Dividing Fractions Math Review Day
5 QUIZ
Slide 49
Access: Graph: A)y = 3x - 2 B) C) y = -2x + 5
Slide 50
Write an equation with the following information: A)Slope =,
y-intercept = 4 B) Slope = 4, y-intercept = Try: C) Slope =,
y-intercept = 4 D) slope = 3, y-intercept = 2
Slide 51
E) Slope: -4 and contains (-1, -2) F) Slope: and contains (5,
1) Try: G) Slope = -4, and contains (0, 3) H) Slope = 1 and
contains (-1, -4)
Slide 52
I)Contains (1, -4) and (3, 2) J) contains (4, -7) and (0, 5)
Try: K) contains (2, -3) and (4, 1) L) Contains (0, 1) and (-2,
9)
Slide 53
How are parallel lines related? How are perpendicular lines
related? M) Parallel to y = -3x + 5, contains (6, -2) N)
Perpendicular to y = -2x + 4, contains (-2, 5) Try: O) Parallel to
y = x - 6, contains (-1, 2) P) Perpendicular to y = 5 - 3x,
contains (2, -4)
Slide 54
Graph the inequality: A)y - 2x + 6 B) y < 3x -3 C) y > 4x
+ 7
Slide 55
Try: D) y 2 - 3x E) 3x - 2y > 6 F) y x + 5 G) y > 3x + 1
H) y > 2/3x - 1
Slide 56
Work Time: Work through pages 15 and 16 in your packet Exit
Slip at: _________
Slide 57
Exit Slip: (on a half-sheet of scratch paper) Previous Material
(PM): Solve for y: A)6x - y = 10 B) 4y = 4x - 8 New Material (NM):
Write the equation: A)Contains (1, 2) and (-3, 4) B) slope: -2,
contains (0, 3) Graph: A)Y x - 2 B) y < 2x + 3 Make sure your
name is on it, and turn it in!
Slide 58
Solve the proportion: "Make sure x is in the numerator and
solve" Find 10%, 20%, 50% and 100%: 80 "Find 10% by moving the
decimal one place, and use it to find the others. Percent Problems:
What is 15% of 40? "Write an equation, is =, of x, and solve for
x." Reflection Starters: I know or I need to work on Menta l Math
Math Review Day 6
Slide 59
Day 6: Exponents Goal: To simplify expressions containing
exponents. AND to evaluate expressions Standard: Standard 9.2.3:
Generate equivalent algebraic expressions involving polynomials and
radicals; use algebraic properties to evaluate expressions. Guiding
Question: How can I evaluate expressions? AND How do I use exponent
properties to simplify expressions? Materials: Pencil, Folder,
Student Packet
Slide 60
Access: What does 2 2 mean? 2 3 ? 2 4 ? (x + 2) 2 ?
Slide 61
Simplifying Exponential Expressions: -no negative exponents
-same base does not appear more than once -no powers, products or
quotients are raised to powers (ie no parenthesis) -numerical
coefficients are relatively prime
Slide 62
Integer Exponents: Zero Exponent: x 0 = 1 Negative Exponent: x
-n = Simplify: A)4 -3 B) 7 0 Try: C) (-5) -4 D) -2 -3 E)2r 0 m -3
F) G)
Slide 63
Product of Powers: a m a n = a m+n Power of a Power: (a m ) n =
a mn Power of a Product: (xy) m = x m y m Simplify: A)(x 2 ) 5 B)n
6 n 2 C) (2t) 5 D) (a 2 b 2 ) 5 (a - 5 ) 2 Try: E) (2 3 ) 3 F) (3 6
) 0 G) (p 4 q 2 ) 7 H) (-4x 3 ) 4 I)(ab) 3 (ab) -2
Slide 64
Quotient of Powers: Positive Power of a Quotient: Negative
Power of a Quotient: Simplify: A) B) Try) C) D) E) F)
Slide 65
Evaluate each Expression for the given variable: A)2x + 3 for x
= 7 B)4x+8; x=-2 C) p 0 for p = 9 D) x -3 y for x = 4 and y = -2
Try) E) 3n - 5 for n = 7 F)-5t - 15; t = 1 G) t -6 for t = 2 H) (5
d) -7 for d = 6 I)r 0 s -2 for r=8 and s = 10
Slide 66
Work Time: Work through pages 17 and 18 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 67
Multiplication Timed Test: -Page 19 of your packet tear out of
packet You have five minutes to fill in as much as you can Go =
Start, Stop = hands up! Highlight the ones you did not know
Slide 68
Exit Slip: (on a half-sheet of scratch paper) NM: Simplify each
expression: A)x^4/y^-6 B) 8f -4 g 0 C) (m 3 n 3 ) 5
D)(x^3y^4/xy^5)^-3 Make sure your name is on it, and turn it
in!
Slide 69
Day 7: Polynomials Goal: To simplify polynomial expressions by
adding or subtracting Standard: 9.2.3.2 Add, subtract and multiply
polynomials; divide a polynomial by a polynomial of equal or lower
degree. Guiding Question: How do I simplify polynomials
expressions? AND how do I add or subtract polynomials expressions?
Materials: Pencil, Folder, Student Packet
Slide 70
Solve the proportion: "Make sure x is in the numerator and
solve" Find 10%, 20%, 50% and 100%: 53 "Find 10% by moving the
decimal one place, and use it to find the others. Percent Problems:
13 is what percent of 52? "Write an equation, is =, of x, and solve
for x." Reflection Starters: I know or I need to work on Menta l
Math Math Review Day 7
Slide 71
Access: Put a circle on those that are alike in each set: A)
2x, 4, -10x, 7x 2, 9x, 15 B) 8, -5x, 11, x 2, 12x 3, 14, -8 C) 14x
4, 9x, 9x 2, 14x 2, -13, 6x 2, x 5
Slide 72
What is a polynomial? Word Problems: A tourist accidentally
drops her lip balm off the Golden Gate Bridge. The bridge is 220
feet from the water of the bay. The height of the lip balms is
given by the polynomial -16t 2 +220, where t is the time in
seconds. How far above the water will the lip balm be after 3
seconds?
Slide 73
Try: The surface area of a cone is approximated by the
polynomial 3.14r 2 + 3.14rl, where r is the radius and l is the
slant height. Find the approximate surface area of a cone that has
radius of 6 cm and slant height 10cm.
Slide 74
Add or Subtract: A)12p 3 + 11p 2 + 8p 3 B) 5x 2 - 6 - 3x + 8
Try: C) t 2 + 2s 2 4t 2 s 2 D) 10m 2 n + 4m 2 n 8m 2 n
Work Time: Work through pages 21 and 22 in your packet
Multiplication test at: ______ Exit Slip at: _________
Slide 78
Multiplication Timed Test: -Page 19 of your packet tear out of
packet You have five minutes to fill in as much as you can Go =
Start, Stop = hands up! Highlight the ones you did not know
Slide 79
Exit Slip: (on a half-sheet of scratch paper) NM: Add or
Subtract: A) 7m 2 + 3m + 4m 2 B) (r 2 + s 2 ) - (5r 2 + 4s 2 ) C)
(10pq + 3p) + (2pq - 5p + 6pq) D) (14d 2 - 8) +(6d 2 - 2d + 1) Make
sure your name is on it, and turn it in!
Slide 80
Day 8: Polynomials Goal: To simplify polynomial expression by
multiplying. Standard: 9.2.3.2 Add, subtract and multiply
polynomials; divide a polynomial by a polynomial of equal or lower
degree. Guiding Question: How can I multiply polynomials?
Materials: Pencil, Folder, Student Packet
Slide 81
Solve the proportion: "Make sure x is in the numerator and
solve" Find 10%, 20%, 50% and 100%: 65 "Find 10% by moving the
decimal one place, and use it to find the others. Percent Problems:
45 is 33% of what number? "Write an equation, is =, of x, and solve
for x." Reflection Starters: I know or I need to work on Menta l
Math Math Review Day 8
Slide 82
Access: Simplify using exponent properties: A) x 2 x 4 B) 3x(4x
3 ) C) 2x 2 - 9x + x 2 D) -7x 3 + 9x + 18x 3 - 10x
Work Time: Work through pages 23 and 24 in your packet Exit
Slip at: _________
Slide 88
Exit Slip: (on a half-sheet of scratch paper) NM: Multiply:
A)(6s 2 t 2 )(3st) B)4xy 2 (x + y) C)(x + 2)(x - 8) D)(2x - 7)(x 2
+ 3x - 4) E) 6mn (m 2 + 10mn -2) F) (2x - 5y)(3x + y) Make sure
your name is on it, and turn it in!
Slide 89
Day 9: Factoring Goal: To factor polynomials by using the
greatest common factor Standard: 9.2.3.3 Factor common monomial
factors from polynomials, factor quadratic polynomials, and factor
the difference of two squares. Guiding Question: How do I find the
greatest common factor of a polynomial? Materials: Pencil, Folder,
Student Packet
Slide 90
Solve the proportion: "Make sure x is in the numerator and
solve" Find 10%, 20%, 50% and 100%: 90 "Find 10% by moving the
decimal one place, and use it to find the others. Percent Problems:
What is 22% of 31? "Write an equation, is =, of x, and solve for
x." Reflection Starters: I know or I need to work on Menta l Math
Math Review Day 9
Slide 91
Access: Simplify: A)2(w + 1) B) 3x(x 2 - 4) C) (x + 3)(x + 8)
Write the prime factorization (factor tree) A) 20 B) 50 C) 17 D)
38
Slide 92
What is the greatest common factor: A)100 and 60 B) 26 and 52
C) 18 and 27 Try) D) 12 and 16 E) 15 and 25 F)55 and 121
Slide 93
Find the GCF of the pair of monomials: A) 15x 3 and 9x 2 B) 8x
2 and 7y 3 C)3x 3 and 6x 2 Try: D) 18g 2 and 27g 3 E) 16a 6 and 9b
F) 8x and 7x 2
Slide 94
Word Problems: A cafeteria has 18 chocolate milk cartons and 24
regular milk cartons. The cook wants to arrange the cartons with
the same number of cartons in each row. Chocolate and regular milk
will not be in the same row. How many rows will there be if the
cook puts the greatest possible number of cartons in each row?
Slide 95
Try: Samantha is making beaded necklaces using 54 glass beads
and 18 clay beads. She wants each necklace to have the same number
of beads, but each necklace will have only one type of bead. If she
puts the greatest number of beads on each necklace, how many
necklaces can she make?
Work Time: Work through pages 25 and 26 in your packet Exit
Slip at: _________
Slide 99
Exit Slip: (on a half-sheet of scratch paper) PM: Multiply A)
2x(3x 2 + 9x - 8) B) (x - 6)(x+6) NM: Find the GCF: A)18 and 75 B)
12x and 28x 3 Factor: A)16x + 20x 3 B) 4m 4 12m 3 + 8m C) 7k(k-3) +
4(k-3) Make sure your name is on it, and turn it in!
Slide 100
Day 10: Factoring Goal: To factor quadratic trinomials of the
form x 2 + bx + c Standard: 9.2.3.3 Factor common monomial factors
from polynomials, factor quadratic polynomials, and factor the
difference of two squares. Guiding Question: How does FOIL help me
factor trinomials? Materials: Pencil, Folder, Student Packet
Slide 101
Solve the proportion: Find 10%, 20%, 50% and 100%: A) 30 B) 41
Percent Problems: A)15 is what percent of 80? B)What is 9% of 72?
Reflection Starters: I know or I need to work on Math Review Day 10
QUIZ
Slide 102
Access: A)What two numbers add or subtract to 6 and multiply to
8? B) What two numbers add or subtract to -1 and multiply to 42? C)
What two numbers add or subtract to 5 and multiply to -6? D) What
two numbers add or subtract to 14 and multiply to 24?
Slide 103
Factor: A)x 2 + 6x + 5 B) x 2 + 6x + 9 C)x 2 - 8x + 15 Try: D)
x 2 + 8x + 12 E) x 2 - 5x + 6 F) x 2 + 13x + 42
Slide 104
G) x 2 + x -20 H) x 2 - 3x - 18 I) x 2 + 7x - 18 Try: J) x 2 +
2x - 15 K) x 2 - 6x + 8 L) x 2 - 8x - 20 How would you know if the
trinomial is not factored correctly?
Slide 105
Work Time: Work through page 27 in your packet Exit Slip at:
_________
Slide 106
Exit Slip: (on a half-sheet of scratch paper) NM: Explain in
your own words how to factor x 2 + 9x + 14. Show how to check your
answer. Factor: A)x 2 - 11x + 30 B) x 2 + 10x + 9 C) x 2 - 6x -27
D) x 2 + 14x 32 Make sure your name is on it, and turn it in!
Slide 107
Day 11: Factoring Goal: To factor quadratic trinomials of the
form ax 2 + bx + c Standard: 9.2.3.3 Factor common monomial factors
from polynomials, factor quadratic polynomials, and factor the
difference of two squares. Guiding Question: How does FOIL help me
factor trinomials? Materials: Pencil, Folder, Student Packet
Slide 108
Order the Fractions from least to greatest: "To order
fractions, they must have a common denominator." Order the Decimals
from least to greatest: 0.88, 0.8, 8, 0.81 "When ordering decimals
compare each place value" Prime Factorization: 24 "What prime
numbers multiply to make the number?" Reflection Starters: I know
or I need to work on Menta l Math Math Review Day 11
Slide 109
Access: Find the product: A)(x-2)(2x+7) B) (3y +4)(2y+9)
Factor: A) x 2 + 4x - 32 B)z 2 + 15z + 36
Work Time: Work through page 28 in your packet Exit Slip at:
_________
Slide 114
Exit Slip: (on a half-sheet of scratch paper) NM: Factor each
trinomial: A)5x 2 + 17x + 6 B) 2x 2 + 5x - 12 C) 6x 2 - 23x + 7 D)
-4x 2 + 11x + 20 E) -2x 2 + 7x - 3 F) 8x 2 + 27x + 9 Make sure your
name is on it, and turn it in!
Slide 115
Day 12: Quadratics Goal: To identify and graph a quadratic
function. Standard: 9.2.1.8 Make qualitative statements about the
rate of change of a function, based on its graph or table of
values. Guiding Question: How can I graph a quadratic using a
table? Materials: Pencil, Folder, Student Packet
Slide 116
Order the Fractions from least to greatest: "To order
fractions, they must have a common denominator." Order the Decimals
from least to greatest: 13.876, 13.901, 11.875, 13.87 "When
ordering decimals compare each place value" Prime Factorization: 30
"What prime numbers multiply to make the number?" Reflection
Starters: I know or I need to work on Menta l Math Math Review Day
12
Slide 117
Access: Evaluate x 2 + 5x for x = 4 and x = -3 What is Domain?
What is range?
Slide 118
Tell whether each function is a quadratic. Explain: A){(-2,
-9), (-1, -2), (0, -1), (1, 0), (2, 7)} B) y = 7x + 3 C) y 10x 2 =
9 Try: D) {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)} E) y + x = 2x
2
Slide 119
Use a table of values to graph each quadratic function A)y = x
2 B) y = -4x 2 Try: C) y = x 2 + 2 D) y = -3x 2 + 1
Slide 120
Tell whether the graph of each quadratic function opens up or
down. Explain: A)y x 2 = x - 3 B) y = 5x 3x 2 Try: C) f(x) = -4x 2
- x + 1 D) y 5x 2 = 2x - 6
Slide 121
Identify the vertex of each parabola. The give the maximum or
minimum value of the function. Find the domain and Range.
Slide 122
Try:
Slide 123
Work Time: Work through pages 29 and 30 in your packet Exit
Slip at: _________
Slide 124
Exit Slip: (on a half-sheet of scratch paper) NM: A)Is y = -x -
1 quadratic? Explain. B) Graph using a table of values y = 1.5x 2
C)Identify the vertex D) Does the function have a minimum or
maximum? What is it? E) Find the domain and range Make sure your
name is on it, and turn it in!
Slide 125
Day 13: Quadratics Goal: To find the axis of symmetry, vertex
and zeroes of a quadratic function. Standard: 9.2.1.5 Identify the
vertex, line of symmetry and intercepts of the parabola
corresponding to a quadratic function, using symbolic and graphical
methods, when the function is expressed in the form f (x) = ax 2 +
bx + c, in the form f (x) = a(x h) 2 + k, or in factored form.
Guiding Question: How can I find the axis of symmetry, zeroes and
vertex of a quadratic function? Materials: Pencil, Folder, Student
Packet
Slide 126
Order the Fractions from least to greatest: "To order
fractions, they must have a common denominator." Order the Decimals
from least to greatest: 0.7, 0.77, 0.707, 0.717 "When ordering
decimals compare each place value" Prime Factorization: 17 "What
prime numbers multiply to make the number?" Reflection Starters: I
know or I need to work on Menta l Math Math Review Day 13
Slide 127
Access: Find the x-intercept of each linear function: (hint y =
0) A)y = 2x - 3 B) y = 3x + 6 Evaluate each quadratic function for
the given input values A)y = -3x 2 + x - 2, when x = 2 B) y = x 2 +
2x + 3, when x = -1
Slide 128
Find the zeros of each quadratic function from its graph. Check
your answer. Try:
Slide 129
Find the axis of symmetry of each parabola: Try: C) y = -3x 2 +
10x + 9 D) y = x 2 + x + 3 Try: E) y = x 2 + 4x - 7 F) y = 3x 2 -
18x + 1
Slide 130
Find the vertex: B)y = -3x 2 + 6x - 7 C) y = 5x 2 - 10x +3 Try:
D)y = -5x 2 + 10x + 3 E) y = x 2 + 4x - 7 F) y = -x 2 + 6x - 1
Slide 131
Word Problems: The graph of f(x) = -0.6x 2 + 0.6x + 10.26 can
be used to model the height in meters of an arch support for a
bridge, where the x-axis represents the water level and x
represents the distance in meters from where the arch support
enters the water. Can a sailboat that is 14 meters tall pass under
the bridge? Explain.
Slide 132
Try: The height of a small rise in a roller coaster track is
modeled by f(x) = -0.07x 2 + 0.42x + 6.37, where x is the distance
in feet from a support pole at ground level. Find the height from
the rise.
Slide 133
Work Time: Work through pages 31 and 32 in your packet Exit
Slip at: _________
Slide 134
Exit Slip: (on a half-sheet of scratch paper) NM: A)Find the
zeros and axis of symmetry of the parabola. Find the axis of
symmetry and vertex: A)y = 3x 2 + 12x + 8 B) y = -x 2 + 8x + 16 C)
y = x 2 + 7x Make sure your name is on it, and turn it in!
Slide 135
Day 14: Quadratics Goal: To graph a quadratic function using
the axis of symmetry, vertex and zeroes. Standard: 9.2.2.3 Sketch
graphs of linear, quadratic and exponential functions, and
translate between graphs, tables and symbolic representations. Know
how to use graphing technology to graph these functions. Guiding
Question: How can I graph a quadratic function? Materials: Pencil,
Folder, Student Packet
Slide 136
Order the Fractions from least to greatest: "To order
fractions, they must have a common denominator." Order the Decimals
from least to greatest: 15.409, 14.509, 15.4, 14.609 "When ordering
decimals compare each place value" Prime Factorization: 32 "What
prime numbers multiply to make the number?" Reflection Starters: I
know or I need to work on Menta l Math Math Review Day 14
Slide 137
Access: Find the axis of symmetry: A)y = 4x 2 - 7 B) y = x 2 -
3x + 1 Find the vertex: A) y = x 2 + 4x + 5 B) y = 3x 2 + 2
Slide 138
Graph the Quadratic Function: Step 1: Find the axis of symmetry
Step 2: Find the vertex Step 3: Find the y-intercept Step 4: Find
two points on the same side of the axis of symmetry as the point
containing the y-intercept.
Slide 139
Graph: A)y = 3x 2 - 6x + 1 B)y = 2x 2 + 6x + 2 C) y + 6x = x 2
+9
Slide 140
Try: D) y = x 2 - 2x - 3 E) y = 2x 2 + 2x - 4 F) y = x 2 + 4x -
8 G) y + x 2 + 5x + 2 = 0
Slide 141
Word Problems: The height in feet of a basketball can be
modeled by f(x) = -16x 2 + 32x, where x is the time in seconds
after its thrown. Find the basketball's maximum height and the time
it takes the basketball to reach this height. Then find how long
the basketball is in the air.
Slide 142
Try: The height in feet of a golf ball that is hit from the
ground can be modeled by the function f(x) = -16x 2 + 96x, where x
is the time in seconds after the ball is hit. Find the ball's
maximum height and the time it takes the ball to reach this height.
Then find how long the ball is in the air.
Slide 143
Work Time: Work through pages 33 and 34 in your packet Exit
Slip at: _________
Slide 144
Exit Slip: (on a half-sheet of scratch paper) NM: Graph: A)y =
-2x 2 - 8x + 4 B) y = x 2 - 8x C) y = 3x 2 + 12x + 9 D) The height
in feet of a fireworks shell can be modeled by h(t) = -16t 2 +
224t, where t is the time in seconds after it is fired. Find the
maximum height of the shell, the time it takes to reach its maximum
height, and the length of time the shell is in the air. Make sure
your name is on it, and turn it in!
Slide 145
Day 15: Data Goal: To organize data in various graphs. AND To
describe the central tendency of data. Standard: 9.4.1.1 Describe a
data set using data displays, including box-and-whisker plots;
describe and compare data sets using summary statistics, including
measures of center, location and spread. Measures of center and
location include mean, median, quartile and percentile. Measures of
spread include standard deviation, range and inter-quartile range.
Know how to use calculators, spreadsheets or other technology to
display data and calculate summary statistics. Guiding Question:
How can I organize data? AND What can the measures of central
tendency tell me about a set of data? Materials: Pencil, Folder,
Student Packet
Slide 146
Order the Fractions from least to greatest: Order the Decimals
from least to greatest: A)0.01, 0.1, 0.11, 0.101 B) 16.7, 16.07,
15.7, 16.32 Prime Factorization: A) 18 B)72 Reflection Starters: I
know or I need to work on Math Review Day 15 QUIZ
Slide 147
Access: Write the percent: A) B) Put the data set in order from
least to greatest: A) 2.4, 5.1, 3.7, 2.1, 3.6, 4.0, 2.9, B) 5, 5,
6, 8, 7, 4, 6, 5, 9, 3, 6, 6, 9
Slide 148
Read and Interpret the graph: A)What casserole was ordered the
most? B) About how many orders were placed? C) About how many more
tuna noodle casseroles were ordered than king ranch casserole? D)
About what percent of the total orders were baked ziti?
Slide 149
A)Which feature received the same satisfaction rating for each
SUV? B)B) Which SUV received a better rating for mileage?
Slide 150
A)At what time was the humidity the lowest? B) During which
4-hour time period did the humidity increase the most?
Slide 151
A)In which months did station A charge more than station B B)
During which month(s) did the stations charge the same for
gasoline?
Slide 152
A) Which ingredients are present in equal amounts?
Slide 153
Stem and Leaf plots: The number of defective widgets in batches
of 1000 are given below. Use the data to make a stem-and-leaf plot.
14, 12, 8, 9, 13, 20, 15, 9, 21, 8, 13, 19
Slide 154
Try) The temperatures in degrees Celsius for two weeks are
given below. Use the data to make a stem-and-leaf plot. 7, 32, 34,
31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31
Slide 155
Frequency Tables and Histograms: The numbers of students
enrolled in Western Civilization classes at a university are given
below. Use the data to make a frequency table with intervals and
then a histogram: 12, 22, 18, 9, 25, 31, 28, 19, 22, 32, 14
Slide 156
Try: The number of days Maria's last 15 vacations are listed
below. Use the data to make a frequency table and then a histogram:
4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12
Slide 157
Measures of Central Tendency: Mean: Median: Mode: Rico scored
74, 73, 80, 75, 67 and 55 on six history tests. Find the mean,
median and mode. Which value best describes Rico's scores?
Slide 158
Try: Josh scored 75, 75, 81, 84 and 85 on five tests. Find the
mean, median and mode. Which value best describes the score Josh
received most often? Which value best describes Josh's scores?
Slide 159
Box-and-Whisker Plot: Quartiles: Interquartile Range (IQR): The
numbers of runs scored by a softball team at 19 games are given.
Use the data to make a box-and-whisker plot: 3, 8, 10, 12, 4, 9,
13, 20, 15, 10, 5, 11, 5, 10, 6, 7, 6, 11
Slide 160
Try: Use the data to make a box-and-whisker plot: 13, 14, 18,
13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23
Slide 161
Misleading Graphs: Explain why this graph is misleading:
Slide 162
Try: Explain why this graph is misleading:
Slide 163
Exit Slip: (on a half-sheet of scratch paper) A) The number of
people at a caterer's last 12 parties are given below. 16, 18, 17,
19, 15, 25, 18, 17, 18, 16, 17, 19 i)Use the data to make a
frequency table with intervals. ii) Use your frequency table to
make a histogram B) The daily high temperatures on 14 consecutive
days in one city were: 59, 49, 48, 46, 47, 51, 49, 43, 35, 52, 51,
51, 51, and 38 i)Find the mean, median and mode of the temperature
ii)Which value describes the average high temperature for the 14
days? iii) Which value best describes the high temperature?
Explain. C) Use the data in B to make a box-and-whisker plot.
Slide 164
Day 16: Data and Probability Goal: To determine the
experimental or theoretical probability of an event. Standard:
9.4.3.1 Select and apply counting procedures, such as the
multiplication and addition principles and tree diagrams, to
determine the size of a sample space (the number of possible
outcomes) and to calculate probabilities. Guiding Question: How can
I determine the probability of an event? Materials: Pencil, Folder,
Student Packet
Slide 165
Conversions: How many inches are in 6 feet? "When converting
make sure your labels cancel Time: "The short hand on the clock
gives the hour, the long hand gives the minute" Find the perimeter:
"Perimeter is the distance around an object" Reflection Starters: I
know or I need to work on Math Review Day 16 Menta l Math
Slide 166
Access: Write the percent: A)3/10 B) 18/90 Write the fraction:
A)40% B) 35% Write the decimal: A) 18% B) 1/5
Slide 167
Experiment: Trial: Outcome: Sample Space: Identify the sample
space and the outcome of A)rolling a number cube. A)Flipping a
coin
Slide 168
Event: Probability:
Slide 169
Write impossible, unlikely, as likely as not, likely, or
certain to describe each event. A)A shoe selected from a pair of
shoes fits the right foot B) Katrina correctly guesses the last
digit of a phone number C) Max pulls a green marble from a bag of
all green marbles D) A radomonly selected month contains the letter
R
Slide 170
Try: Write impossible, unlikely, as likely as not, likely or
certain to describe the event: A)Anthony rolls a number less than 7
on a standard number cube. B) A coin lands heads up C) There are 31
days in August D) You roll a 10 on a standard number cube.
Slide 171
Experimental Probability: An experiment consists of spinning a
spinner. Use the results in the table to find the experimental
probability of each event: A)the spinner lands on orange B) The
spinner does not land on orange. Green15 Orange10 Purple8
Pink7
Slide 172
A manufacturer inspects 500 strollers and finds 498 have no
defects A)what is the experimental probability that a stroller
chosen at random has no defects? B) The manufacturer shipped 3500
strollers to a distribution center. Predict the number of strollers
that are likely to have no defects.
Slide 173
Try: One game of bowling consists of ten frames. Elyse usually
rolls 3 strikes in each game. A)What is the experimental
probability that Elyse will roll a strike on any frame? B) Predict
the number of strikes Elyse will throw in 18 games.
Slide 174
Theoretical Probability: An experiment consists of rolling a
number cube. Find the theoretical probability of each outcome:
A)rolling a 5 B)rolling an odd number C) rolling a number less than
3
Slide 175
Try: Find the Theoretical probability of each: A)flipping 2
coins and both landing on heads B) rolling a number divisible by 3
on a number cube You have a 1/50 chance of winning, what is the
probability of not winning?
Slide 176
A box contains only red, black and white blocks. The
probability of choosing a red block is 1/4, the probability of
choosing a black block is 1/2. What is the probability of choosing
a white block? Try: The probability of randomly choosing a blue
marble from a bag of 5 blue marbles, 8 red marbles and 7 yellow
marbles?
Slide 177
Exit Slip: (on a half-sheet of scratch paper) A) The neighbor's
dog barked at Tana the last 4 out of 5 times she walked by the
house. i) What is the experimental probability that the dog barks
at Tana when she walks past the house? ii) Predict the number of
times the dog will bark at Tana if she walks past the house 45
times. B) Find the theoretical probability of randomly choosing B
from the letters in ALGEBRA. C) The probability that it will be
sunny is 15%. What is the probability that it will not be
sunny?
Slide 178
Day 17: Data and Probability Goal: To find the probability of
independent or dependent events AND To solve problems involving
permutations and combinations. Standard: 9.4.3.1 Select and apply
counting procedures, such as the multiplication and addition
principles and tree diagrams, to determine the size of a sample
space (the number of possible outcomes) and to calculate
probabilities. Guiding Question: How can I find the probability of
an event? AND How can I determine the amount of times an event will
occur? Materials: Pencil, Folder, Student Packet
Slide 179
Conversions: How many feet are in 3.5 yards? "When converting
make sure your labels cancel Time: "The short hand on the clock
gives the hour, the long hand gives the minute" Find the perimeter:
"Perimeter is the distance around an object" Reflection Starters: I
know or I need to work on Math Review Day 17 Menta l Math
Slide 180
Access: Find the theoretical probability of each outcome.
A)rolling a 6 on a number cube B) rolling on an odd number on a
number cube C) flipping a coin and it landing heads up
Slide 181
Independent Event: Dependent Event: Tell whether each set of
events is independent or dependent. Explain your answer. : A)You
select a card from a standard deck of cards and hold it. A friend
selects another card from the same deck B)You flip a coin and it
lands heads up. You flip the same coin and it lands heads up
again.
Slide 182
Try: Tell whether each set of events is independent or
dependent. Explain your answer, A)A number cube lands showing an
odd number. It is rolled a second time and lands showing a 6. B)
One students in your class is chosen for a project. Then another
student in the class is chosen.
Slide 183
Probability of Independent Events: If A and B are independent
events, then P(A and b) = P(A) P(B) A) An experiment consists of
randomly selecting a marble from a bag, replacing it and selecting
another marble. The bag contains 3 red marbles, and 12 green
marbles. What is the probability of selecting a red marble, and
then a green marble? B) A coin is flipped 4 times, what is the
probability of flipping 4 heads in a row?
Slide 184
Try: An experiment consists of spinning the spinner twice. What
is the probability of spinning two odd numbers?
Slide 185
Probability of Dependent Events: If A and B are dependent
events, then P(A and B) = P(A) P(B after A) A) A snack cart has 6
bags of pretzels and 10 bags of chips. Grant selects a bag at
random, and then Iris selects a bag at random. What is the
probability that Grant will select a bag of chips?
Slide 186
Try: A bag has 10 red marbles, 12 white marbles and 8 blue
marbles. Two marbles are randomly drawn from the bag. What is the
probability of drawing a blue marble and then a red marble?
Slide 187
Fundamental Counting Principle: If there are m ways to choose a
first item and n ways to choose a second item after the first item
has been chosen, then there are mn ways to choose both items. A) A
voicemail system password is 1 letter followed by a 3-digit number
less than 600. How many different voicemail passwords are
possible?
Slide 188
Try) A sandwich can be made with 3 different types of bread, 5
different meats and 2 types of cheese. How many types of sandwiches
can be made if each sandwich consists of one bread, one meat, and
one cheese?
Slide 189
Compound Event: Combination: Permutation:
Slide 190
Tell whether each situation involves combinations or
permutations. Then give the number of possible outcomes. A)An
English test contains 5 different essay questions labeled A, B, C,
D and E. You are supposed to choose 2 to answer. How many different
ways are there to do this? B) A family of 3 plans to sit in the
theater. How many ways can the family be seated in 3 seats
Slide 191
Try: A)Ingrid is stringing three different types of beads on a
bracelet. How many ways can she use one bead of each type to string
the next three beads? B) Nathan wants to order a sandwich with two
of the following ingredients: mushroom, eggplant, tomato and
avocado. How many different sandwiches can Nathan choose?
Slide 192
Factorial: A) Four people need to be selected from a class of
15 to help clean up campus. How many different ways can the 4
people be chosen?
Slide 193
Try: A basketball team has 12 members who can play any
position. How many different ways can the coach choose 5 starting
players?
Slide 194
Exit Slip: (on a half-sheet of scratch paper) A)Tell whether
the set of events is independent or dependent and explain your
answer: flipping two different coins and each coin landing showing
heads B)Eight cards are numbered from 1 to 8 and placed in a box.
ne card is selected at random and not replaced. Another card is
randomly selected. What is the probability that both cards are
greater than 5? C) You are ordering a triple-scoop ice-cream cone.
There are 18 flavors to choose from and you dont care which flavor
is on the top, middle, or bottom. How many different ways can you
selected a triple-scoop ice-cream cone?
Slide 195
Day 18: Exponential Functions Goal: To evaluate, identify and
graph exponential functions. Standard: 9.2.4.2 Represent
relationships in various contexts using equations involving
exponential functions; solve these equations graphically or
numerically. Know how to use calculators, graphing utilities or
other technology to solve these equations. Guiding Question: How
can I graph, evaluate and identify exponential functions?
Materials: Pencil, Folder, Student Packet
Slide 196
Conversions: How many feet are in 1.2 miles? "When converting
make sure your labels cancel Time: "The short hand on the clock
gives the hour, the long hand gives the minute" Find the perimeter:
"Perimeter is the distance around an object" Reflection Starters: I
know or I need to work on Math Review Day 18 Menta l Math
Slide 197
Access: Simplify each expression: A) 3 -2 B) 5 4 C) 2(3) 3 D)
2/3(3) 4
Slide 198
Exponential Function: A)The function f(x) = 500(1.035) x models
the amount of money in a certificate of deposit after x years. How
much money will there be in 6 years? B) The function f(x) =
200,000(0.98) x, where x is the time in years, models the
population of a city. What will the population be in 7 years?
Slide 199
Try: The function f(x)= 1500 (0.995) x, where x is the time to
years, models a prairie dog population. How many prairie dogs will
there be in 8 years?
Slide 200
Tell whether each set of ordered pairs satisfies and
exponential function. Explain your answer. A) {(-1, 1.5), (0, 3),
(1, 6), (2, 12)} B) {(-1, -9), (1, 9), (3, 27), (5, 45)}
Slide 201
Try: Tell whether the set of ordered pairs satisfies an
exponential function. Explain your answer: {(- 1, 1), (0, 0), (1,
1), (2, 4)}
Slide 202
Graph: A)y = -1/4 (2) x B)-1(1/4) x C) y = 4(0.6) x
A)A sculpture is increasing in value at a rate of 8% per year,
and its value in 2000 was $1200. Write an exponential growth
function to model this situation. The find the sculpture's value
in2006. B) Write a compound interest function to model the
situation, then find the balance after the given number of years.
$1200 invested at a rate of 3.5% compound quarterly; 4 years
Slide 206
Try: A)The original value of a painting is $9000 and the value
increases by 7% each year. Write an exponential growth function to
model this situation. Then find the painting's value in 15 years.
B) The population of a town is decreasing at a rate of 3% per year.
In 2000, there were 1700 people. Write an exponential decay
function to model the situation. Then find the population in
2012.
Slide 207
General Forms of Functions: Linear: Quadratic:
Exponential:
Slide 208
Look for a pattern in the data set to determine which model
best describes the data:
Slide 209
Try:Look for a pattern in the data set to determine which model
best describes the data:
Slide 210
Exit Slip (on a half-sheet of scratch paper) A)The function y =
11.6(1.009) x models residential energy consumption in quadrillion
Btu where x is the number of years after 2003. What will
residential energy consumption be in 2013? B) Graph y = -0.5(3) x
C) What kind of model best describes the data set?
Slide 211
Slide 212
Day 19: Review Goal: To review the last 18 days in preparation
for the Final! Standard: See Days 1 to 18. Guiding Question: How
can I study for the Final? Materials: Pencil, Folder, Student
Packet
Slide 213
Conversions: How many inches are in 5.5 feet? "When converting
make sure your labels cancel Time: "The short hand on the clock
gives the hour, the long hand gives the minute" Find the perimeter:
"Perimeter is the distance around an object" Reflection Starters: I
know or I need to work on Math Review Day 19 Menta l Math
Slide 214
Access: Look over your packet, exit slips, and notes. Create
three questions you have still in this class?
Slide 215
Ask questions. - Teacher answer - Student answer - work in
pairs to answer Do you need some work time to complete the packet?
How can I study for the final?
Slide 216
Sample Problem for Final (this question is NOT on the final)
Part I: Short Answer 1)Simplify the expression: 6 (8 + 1) x 9 3
Part II: Multiple Choice 1)Simplify the expression: 6 (8 + 1) x 9 3
A) -9 B) -21 C) -25 D) -3
Slide 217
Make 5 to 15 practice problems for a friend. Include the short
answer and multiple choice. Trade to take home and study!
Slide 218
Exit Slip: (on a half-sheet of paper) Quick Write: How can I
study for the test? How will I know I am prepared?
Slide 219
Day 20: Final Goal: To show what you have learned at summer
school! Standard: See Days 1 to 18. Guiding Question: Will I pass
this class? Materials: Pencil! GOOD LUCK!