chapter 5 expressions. day….. 1.exponents 2.order of operations 3.numerical expressions...
TRANSCRIPT
![Page 1: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/1.jpg)
Chapter 5
Expressions
![Page 2: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/2.jpg)
Day…..
1. Exponents
2. Order of Operations
3. Numerical Expressions
4. Algebraic Properties
5. Distributive Property
![Page 3: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/3.jpg)
Day 1
![Page 4: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/4.jpg)
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation. Ex. 4x + 3
Expressions that have the same value. Ex. 5+9 = 20-6
Numerical Expression -
Algebraic Expressions -
Order of Operations-
Equivalent Expressions-
Evaluate-
Properties -
To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
A combination of numbers and operations. Ex. 10 + 5 - 8
The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)
Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.
Variable -A letter or symbol used to represent an unknown number.
![Page 5: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/5.jpg)
I Can….
Write and evaluate expressions involving
exponents
![Page 6: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/6.jpg)
Exponent
Essential Understanding:• Exponents are a shorthand way to show how many
times a number, called the base, is multiplied times itself.
• A number with an exponent is said to be "raised to the power" of that exponent.
• The "Laws of Exponents” come from three ideas:1. The exponent says how many times to use the number in
a multiplication. 2. A negative exponent means divide, because the opposite
of multiplying is dividing3. A fractional exponent like 1/n means take the nth root
![Page 7: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/7.jpg)
Laws of Exponents
Law: Examples:① x1 = x 61 = 6② x0 = 1 70 = 1③ x-1 = 1/x 4-1 = ¼④ xmxn = xm+n x2x3 = x2+3 = x5
⑤ xm/xn = xm-n x6/x2 = x6-2 = x4
⑥ (xm)n = xmn (x2)3 = x2×3 = x6
⑦ (xy)n = xnyn (xy)3 = x3y3
⑧ (x/y)n = xn/yn (x/y)2 = x2 / y2
⑨ x-n = 1/xn x-3 = 1/x3
![Page 8: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/8.jpg)
Wrap it Up
• Review
• Questions
• Exit Tickets
![Page 9: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/9.jpg)
Day 2
![Page 10: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/10.jpg)
Bell WorkComplete the provide page in your book.
![Page 11: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/11.jpg)
Homework Check
![Page 12: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/12.jpg)
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation. Ex. 4x + 3
Expressions that have the same value. Ex. 5+9 = 20-6
Numerical Expression -
Algebraic Expressions -
Order of Operations-
Equivalent Expressions-
Evaluate-
Properties -
To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
A combination of numbers and operations. Ex. 10 + 5 - 8
The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)
Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.
Variable -A letter or symbol used to represent an unknown number.
![Page 13: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/13.jpg)
I Can….
Solve expressions involving multiple
operations.
![Page 14: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/14.jpg)
Order of OperationsEssential Understanding: Order of operation is the rule that states the order in which an expression or equation is solved. You can remember this order with simple mnemonic devices such as “Please Excuse My Dear Aunt Sally”. Where as:
P stands for parenthesis
E stands for Exponents
M stands for multiply
D stands for divide
A stands for addition
S stands for subtraction
Examples:
1) 4+6*8-6(12-9) =
2) 14-8+5*5+102=
![Page 15: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/15.jpg)
Wrap it Up
• Review
• Questions
• Exit Tickets
![Page 16: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/16.jpg)
Day 3
![Page 17: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/17.jpg)
Bell WorkDirections: Use your knowledge of the order of operations to simplify each expression.
I. 17 + 3 * 6 – 1 + 10II. 42 + 10 – 5III. 12 * 4 * 2 3 + 50 – 11IV. 6 + 21 * 5 – 3 * 7 + 9V. 1 + 2 + 3 * 4 * 5 6 + 7 – 8 * 9
Justify your response.
![Page 18: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/18.jpg)
Homework Check
![Page 19: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/19.jpg)
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation. Ex. 4x + 3
Expressions that have the same value. Ex. 5+9 = 20-6
Numerical Expression -
Algebraic Expressions -
Order of Operations-
Equivalent Expressions-
Evaluate-
Properties -
To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
A combination of numbers and operations. Ex. 10 + 5 - 8
The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)
Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.
Variable -A letter or symbol used to represent an unknown number.
![Page 20: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/20.jpg)
I Can….
Solve expressions involving multiple
operations.
![Page 21: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/21.jpg)
Order of Operations
![Page 22: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/22.jpg)
Your Turn….
• Clear your desk of everything but a pencil.
![Page 23: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/23.jpg)
Wrap it Up
• Review
• Questions
• Exit Tickets
![Page 24: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/24.jpg)
Day 4
![Page 25: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/25.jpg)
Homework Check
![Page 26: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/26.jpg)
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation. Ex. 4x + 3
Expressions that have the same value. Ex. 5+9 = 20-6
Numerical Expression -
Algebraic Expressions -
Order of Operations-
Equivalent Expressions-
Evaluate-
Properties -
To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
A combination of numbers and operations. Ex. 10 + 5 - 8
The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)
Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.
Variable -A letter or symbol used to represent an unknown number.
![Page 27: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/27.jpg)
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
![Page 28: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/28.jpg)
I Can….
Apply the properties of operations to generate
equivalent expressions.
![Page 29: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/29.jpg)
Algebraic PropertiesEssential Understanding:
Algebraic properties can be used to rewrite expressions or generate equivalent expressions. For instance, the expression 3+4+2 can be rewritten like this 4+3+2 using commutative property of addition to rearrange the numbers.
Examples of other algebraic properties:I. 1 x 4 x 3 = 4 x 3 x 1 -_____________________II. (6 + 3) +8 = (8 +3) + 6-____________________III. 9 x (3 x 2) = (9 x 3) x 2-____________________IV. 4(3 – 2)-______________________
![Page 30: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/30.jpg)
Watch This• Associative property: http://
learnzillion.com/lessons/137-combine-parts-of-an-expression-using-the-associative-property ( 5 mins)
• Commutative property: http://learnzillion.com/lessons/2357-the-commutative-property (3 mins)
![Page 31: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/31.jpg)
Group Work
Please take out your maker boards
![Page 32: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/32.jpg)
Wrap it Up
• Review
• Questions
• Exit Tickets
![Page 33: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/33.jpg)
Day 5
![Page 34: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/34.jpg)
pOp Quiz
• Take out a pencil and a calculator
• Clear everything else from your desk
![Page 35: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/35.jpg)
Bell WorkDirections: Use your knowledge of associative and commutative properties to rewrite the following expressions.
I. 3 * 3 * 8
II. 5 + 7 + 9 + 6
III. 2 * (7 * 6)
IV. 5 + (4 + 3)
V. 4 + 5 + 6 – 2
VI. 15 3
Justify Your Methods
![Page 36: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/36.jpg)
Homework Check
![Page 37: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/37.jpg)
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation. Ex. 4x + 3
Expressions that have the same value. Ex. 5+9 = 20-6
Numerical Expression -
Algebraic Expressions -
Order of Operations-
Equivalent Expressions-
Evaluate-
Properties -
To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
A combination of numbers and operations. Ex. 10 + 5 - 8
The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)
Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.
Variable -A letter or symbol used to represent an unknown number.
![Page 38: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/38.jpg)
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
![Page 39: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/39.jpg)
I Can….
Apply the properties of operations to simplify
expressions.
![Page 40: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/40.jpg)
Distributive Property
Essential Understanding:Distributive property can be used to rewrite algebraic expressions by multiplying the number outside the parenthesis by each number, term, or variable inside. For instance the expression 3(p+2) can be rewritten as 3p + 6
Examples:I. 2(3+7)II. (6-3)3III. 5(3+6d)IV. (4-a)8V. (5b+6c)8VI. 9(ab + 4c)
![Page 41: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/41.jpg)
Watch This• Distributive property: http://learnzillion.com/lessons/2338-create-an-equivalent-expression-using-the-standard-algorithm ( 5 mins)
![Page 42: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/42.jpg)
Puzzle TimeBefore we begin…….1. Complete an exit ticket.2. Pack up everything except for your
pencil.3. Sit quietly unit everyone is ready.
![Page 43: Chapter 5 Expressions. Day….. 1.Exponents 2.Order of Operations 3.Numerical Expressions 4.Algebraic Properties 5.Distributive Property](https://reader035.vdocuments.us/reader035/viewer/2022062222/5697c00a1a28abf838cc7759/html5/thumbnails/43.jpg)
Wrap it Up
• Review
• Questions
• Exit Tickets