Transcript 11-4 PPT

5 Minute Check
Complete on your homework. Write an algebraic
expression to represent the following.
1. Malinda goes bowling on Saturday. She bowls three
games and pays $2 for shoe rental.
2. Kyle has 5 more than one fourth as many Legos as Tom.
3. Moesha’s music library has 17 more than 2 times the
songs as Damian’s.
4. Ciera has three more the one half the number of purses
as Aisha.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
1. Malinda goes bowling on Saturday. She bowls three
games and pays $2 for shoe rental.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
1. Malinda goes bowling on Saturday. She bowls three
games and pays $2 for shoe rental.
3g + $2, g = the cost of each game
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
2. Kyle has 5 more than one fourth as many Legos as Tom.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
2. Kyle has 5 more than one fourth as many Legos as Tom.
L ÷ 4 + 5, L = Number of Legos
L
4
+5
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
3. Moesha’s music library has 17 more than 2 times the
songs as Damian’s.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
3. Moesha’s music library has 17 more than 2 times the
songs as Damian’s.
2D + 17, D = the number of songs in Damian’s library.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
4. Ciera has three more the one half the number of purses
as Aisha.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
4. Ciera has three more the one half the number of purses
as Aisha.
A ÷ 2 + 3 , A = the number of purses Aisha has.
Or
𝐴
2
+3
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
5 Minute Check
Complete in your notebook. Write an algebraic
expression to represent the following.
Mid Chapter Check
Log onto my website and click on the Quia link to
begin the Chapter 6.6 quiz.
Username is first name last name 371 (no spaces, no
capitals). Username is the proper name as used in
Progress Book.
Password is the student ID.
You will have a maximum of 25 minutes.
When complete, work on Accum Rev 6 or Compass
Learning.
5 Minute Check
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Tuesday, Nov 4
Lesson 6.6.5
Algebra: Properties
Algebra: Properties
Objective: To use properties to simplify
expressions.
Algebra: Properties
Math properties are statements that are true
for any number.
Algebra: Properties
Commutative Property (CP) - The order in
which two or more numbers are added or
multiplied does not change the sum or
product.
e.g. 9 + 7 = 7 + 9
a+b=b+a
e.g. 3 · 2 = 2 · 3
a·b=b·a
The word commute means to move around.
Algebra: Properties
Associative Property (AP) - The way in
which three numbers are grouped when they
are added or multiplied does not change the
sum or product.
e.g.
9 + (7+ 5) = (9 + 7) + 5
3 · (2 · 4)= (3 · 2) · 4
a + (b+ c) = (a + b) + c
a · (b · c) = (a · b) · c
The word associate means group.
Algebra: Properties
Distributive Property (DP) – To multiply a
sum by a number, multiply each addend by
the number outside the parenthesis.
e.g. 4 · (3 + 1) = 4 · 3 + 4 · 1= 12 + 4 = 16
e.g. 4 · (a + 1) = 4 · a + 4 · 1 or 4a + 4
The word distribute means to share.
Algebra: Properties
Identity Properties (IP) - The sum of an
addend and zero is the addend. The product
of a factor and one is the factor.
e.g. 9 + 0 = 9
a+0=a
3·1=3
a·1=a
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
15 + ( 5 + 8) and (15 + 5) + 8
How can we do this?
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
15 + ( 5 + 8) and (15 + 5) + 8
To determine if expressions are equal,
perform the operations using the order of
operations, then compare the answers.
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
15 + ( 5 + 8) and (15 + 5) + 8
15 + 13
20 + 8
28
=
28, so
15 + ( 5 + 8) = (15 + 5) + 8,
AP
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
(20 - 12) - 3 and 20 – (12 – 3)
Do this on your own.
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
(20 - 12) - 3 and 20 – (12 – 3)
8 - 3
20 - 9
5
≠
11
AP is not true for subtraction.
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
34 + 0 and 34
Do this on your own.
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
34 + 0 and 34
34 = 34
IP
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
20 ÷ 5 and 5 ÷ 20
Do this on your own.
Algebra: Properties
Determine if the two expressions are
equivalent. If so, tell what property is
applied. If not, explain why.
20 ÷ 5 and 5 ÷ 20
4
≠
¼
CP does not work for division.
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
6 + ( 4 + a)
Do this on your own.
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
6 + ( 4 + a)
AP essentially says if we have all addition or
all multiplication we can remove the
parenthesis.
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
6 + ( 4 + a)
6+4+a
Can we perform any
operations?
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
6 + ( 4 + a)
6 + 4 + a = 10 + a
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
7 · (t · 3)
Do this on your own.
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
7 · (t · 3)
7 · t · 3 = 21t
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
3 + (z + 5)
Algebra: Properties
Use one or more properties to rewrite each
expression as an expression that does not
have parenthesis.
3 + (z + 5)
3+z+5= 8+z
Algebra: Properties
In recent years the Kansas Jayhawks had 15
guards, 4 forwards and 3 centers on their
roster. Write two equivalent expressions
using the Associative Property that can be
used to find the total number of players on
their roster.
Do this on your own.
Algebra: Properties
In recent years the Kansas Jayhawks had 15
guards, 4 forwards and 3 centers on their
roster. Write two equivalent expressions
using the Associative Property that can be
used to find the total number of players on
their roster.
(15 + 4) + 3 and 15 + ( 4 + 3)
Algebra: Properties
At a gymnastics meet a gymnast scored an
8.95 on the vault and a 9.2 on the uneven
bars. Write two equivalent expressions using
the Commutative Property that can be used
to find the total score.
Do this on your own.
Algebra: Properties
At a gymnastics meet a gymnast scored an
8.95 on the vault and a 9.2 on the uneven
bars. Write two equivalent expressions using
the Commutative Property that can be used
to find the total score.
8.95 + 9.2 and 9.2 + 8.95
Algebra: Properties
Determine whether (18 + 35) x 4 = 18 + 35 x 4
is true or false. Explain.
Algebra: Properties
Determine whether (18 + 35) x 4 = 18 + 35 x 4
is true or false. Explain.
False; using the order of operations,
(18 + 35) x 4 = 212
18 + 35 x 4 = 158
Algebra: Properties
A counterexample is an example showing that
a statement is not true. Provide a
counterexample to the following statement.
Division of whole numbers is commutative.
Algebra: Properties
A counterexample is an example showing that
a statement is not true. Provide a
counterexample to the following statement.
Division of whole numbers is commutative.
Sample answer
24 ÷ 12 = 2 and 12 ÷ 24 = 0.5
2 ≠ 0.5
Algebra: Properties
Agenda Notes
Homework –
Homework Practice 6.6.5
Due Wednesday, Nov 5
Chapter 6.6 Test – Monday, Nov 10
Accum Rev 6 Due Nov 10