swbat… review exponents tues, 4/9 agenda 1. wu (10 min) 2. exponent review (25 min) warm-up: 1....
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SWBAT… review exponents Tues, 4/9
Agenda 1. WU (10 min)2. Exponent review (25 min)
Warm-Up:1. Write your HW in your planner for the week
2. Write the formula for the area of a rectangle
3. Write the formula for the area of a triangle
4. Write the formula for the area of a circle
5. Write the formula for the circumference of a circle
6. Write the formula for the volume of a rectangular prism
See agenda
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New unit on Polynomials & Exponents SWBAT…n Identify the difference between monomials,
binomials and trinomials.n Apply and explain the rules of exponents (7rules) n Add and subtract polynomials.n Multiply a monomial by a polynomial.n Solve equations with polynomials.n Multiply two binomials using the FOIL method.
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A monomial is an algebraic expression consisting of only one term.
A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –)
Examples of monomials: 3, s, 3s, 3sp, 3s2p
Open Ended: Write 3 different examples of monomials
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Polynomials
A polynomial is a monomial or the sum or difference of monomials
Some polynomials have special names: A monomial has one termA binomial is the sum or difference of two
monomialsA trinomial is the sum or difference of three
monomials
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz
-6.5
6x3 + 4x + x + 3
3ab5
Fill out the chart above!Fill out the chart above!
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz Yes; 4y – 5xz is the difference of two monomials.
Binomial
-6.5
6x3 + 4x + x + 3
3ab5
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz Yes; 4y – 5xz is the difference of two monomials.
Binomial
-6.5 Yes; -6.5 is a constant Monomial
6x3 + 4x + x + 3
3ab5
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz Yes; 4y – 5xz is the difference of two monomials.
Binomial
-6.5 Yes; -6.5 is a constant Monomial
6x3 + 4x + x + 3
3ab5
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz Yes; 4y – 5xz is the difference of two monomials.
Binomial
-6.5 Yes; -6.5 is a constant Monomial
6x3 + 4x + x + 3 Yes; 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials
Trinomial
3ab5
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Expression Is it a polynomial?
Explain
Monomial, binomial, or trinomial?
4y – 5xz Yes; 4y – 5xz is the difference of two monomials.
Binomial
-6.5 Yes; -6.5 is a constant Monomial
6x3 + 4x + x + 3 Yes; 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials
Trinomial
3ab5 Yes; one term with the product of a coefficient and variables.
Monomial
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Exponent Review
Ms. Sophia Papaefthimiou
Infinity HS
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Definition of an exponent
An exponent tells how many times a number is multiplied by itself.
34
= (3)(3)(3)(3) = 81
34
BaseExponent
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How to read an exponent
Three to the fourth power
34
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How to read an exponent (cont’d)
Three to the 2nd power or Three squared
32
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How to read an exponent (cont’d)
Three to the 3rd power or Three cubed
33
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Exponents are often used in area problems to show the units are squared
Area = (length)(width)
Area = (30 ft)(15 ft) = 450 ft 215ft
30ft
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A = π(8cm)2
A = 64π cm2
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Exponents are often used in volume problems to show the units are cubed
Volume = (length)(width)(height)
Volume = (20cm)(10cm)(10cm) = 2,000 cm3
10
10
20
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What is the exponent?
(5)(5)(5)(5) = 54
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What is the answer?
53
= 125
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What is the base and the exponent?
(7)(7)(7)(7)(7) = 7 5
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What is the base and the exponent?
(x)(x)(x)(x)(x)(x) =x 6
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What the base and the exponent?
(a)(a)(a)(b)(b)(c) =a 3b2c
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What the base and the exponent?
aaabbc = a 3b2c
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What the base and the exponent?
(4)(x)(x)(y) = 4x 2y
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What the base and the exponent?
(4xxyyyy)(8xxy) = 32 x 4y 5
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Compute: (-4)2
Answer: (-4)(-4) = 16
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Calculate: -42
Answer: -(4)(4) = -16
PEMDAS
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Simplify: n2 when n = -5
Answer: (-5)2 = (-5)(-5) = 25
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Simplify: -n2 when n = -5
Answer: -(-5)2 = -(-5)(-5) = -25
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Compute: (-6)2
Answer: (-6)(-6) = 36
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Compute: -62
Answer: -(6)(6) = -36
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Compute: -(-6)2
Answer: -(-6)(-6) = -36
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Simplify: (x + 3)2
Answer: (x + 3)(x + 3) x2 + 6x + 9
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Compute: 02
Answer: (0)(0) = 0
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Compute: 20
Answer: 1Yes, it’s 1; explanation will follow
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WHY is anything to the power zero "1"
36 = 72935 = 243 34 = 81 33 = 27 32 = 9 31 = 3
30 = 1
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Laws of Exponents
nmn
m
m
mm
mmm
mnnmnmnm
nnn
n
xx
x
y
x
y
xyxxy
xxxxx
xx
orx
xx
.7
.6.5
.4.3
11.21.1 0
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Zero Exponent Property (1)Words: Any nonzero number raised to the zero
power is equal to 1.
Symbols: For any nonzero number a, a0 = 1.
Examples:
1.) 120 = 1
2.)
3.)1
0
c
b
17
20
Open Ended: Create a problem that satisfies this property!
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Let’s practice
Simplify each expression:
1. (-4)0
2. -40 (Recall PEMDAS - Exponents first!)
3. (5x)0 5x0
4. -(-4.9)0 (Recall PEMDAS – Exponents first!)
5. [(3x4y7z12)5 (–5x9y3z4)2]0
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Negative Exponent Property (2)
Words: For any nonzero number a and any integer n,
a-n is the reciprocal of an.
Also, the reciprocal of a-n = an.
Symbols: For any nonzero number a and any integer n,
Examples:
nnn
n aa
anda
a 11
25
1
5
15
22 3
3
1m
m
Open Ended: Create a problem that satisfies this property!Use any number for a and n.
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52
152 32
Examples
24
1
24 16
112
12
1
4848
1
4096
1
3)2(
1
3)2( )2)(2)(2(
1
8
1
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2
2
7
2
06 yx
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SWBAT… compute problems involving zero & negative exponents Fri, 4/27
Agenda 1. Review problems Zero & Negative Exponent Property (20 min)
2. Practice – hw#1 (15 min)
3. Quiz (10 min)
WARM-UP
1. (5x)0
2. 5x0
3.4.
HW: Quiz corrections
0)( iouPapaefthimSophia3)2(
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22
1
1
8
4
1
1
8 2228
Examples (cont’d)
24
4 24
1
1
4 244 164 64
0)6(9 )1(9 9
2
2
8
2
2
2
8
1
1
2
22
82
1 64
4
1 16
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SWBAT… simplify problems using the first 5 exponent laws Wed, 5/2Agenda
1. WU (5 min)
2. Review HW#1 (15 min) and Review HW#2 (20 min)
3. Exit slip (5 min)
Warm-Up: Simplify:
03 )2(32 d
29