unit 1 expressions

Unit 1 Expressions

Thursday Sept 10, 2020 Activator • Grab all of the papers, folder, & Cal

• Sign your name

• Find/pick your assigned seat• New Student Form• Introductions • Classroom Tour

Today’s Objective Unit 1Lesson 1

Students will be able to acclimate with their new group

and simplify expressions.

SyllabusOverview • Presentations (10%)• Homework Packet (20%)• Classroom Notes (30%)• Tests (40%)

Thursday Sept 10, 2020 Activator

Classwork worksheet (30%)Before you get sent to the hall, how many times can you get into trouble? 3 What do you have to do in the hall? SheetHow long do you have to stay in the hall?3-5 minutes, Go to the bathroom/drink

Today’s New Vocab (1 of 4)How do I earn extra credit?Raising your hand to ask a question. Raising your hand to answer another students question. So, NOT by answering Mr. V’s questions.

What do I do with the chips?You should hold onto the chips until test day to buy extra credit. Two chips can buy you a small piece of candy.

Today’s New Vocab (2 of 4)6 + 6 + 6 = 18Each Star Point = 14 + 4 + 6 = 14Each Fan Blade = 13 + 3 – 4 = 2Each hour = 13 + 2(10) = 23Multiply first

Today’s New Vocab (3 of 4)

4x + 2x – 9x Question

Does the answer get an equal sign? No

Combine (Add or Subtract) the following expression (No equal sign).

-3x Answer

No equal sign in the question,No equal sign in the answer.

Super Important

The sum of 7x - 8 and -9x is

7x - 8 - 9x 7x - 9x - 8

Commute (switch the order)

-2x - 8 Combine Like Terms


7x - 8 + -9x Can a number have two signs? No

Where do I stand? 3 spotsHow long? Less than 30 seconds

Do I get a reward? Yes, 1 chipIs it part of my grade? Yes, 10%

Presentation Time

I will now demonstrate.

Work Period

Meet your group members

What did your group members do this summer?

Does anyone want to switch seats or groups?

Thursday Sept 10, 2020 Work Period

Thursday Sept 10, 2020 Exit Question

.

What is your favorite movie quote and why?

Monday Sept 14, 2020 Activator

Simplify the expression.

C + C + C + C + C + C + C 3c + 4C

7c Joke of the DaySail the 7 seas

Today’s Objective

Students will be able to simplify expressions with two variables.

Unit 1Lesson 2

Today’s New Vocab (1 of 4)What is a variable?

What is an expression?

It is an unknown number. For example, we usually use x or y.

A mathematics problem without an = sign.

If it doesn’t have an = , don’t write = .

Today’s New Vocab (2 of 4)Simplify the expression.

4x + 5x


4x + 5y 9x 4x + 5y

The 4 and 5 can only be combined when the variables are the same.

Today’s New Vocab (3 of 4)Combine Like Terms (CLT) means Simplify

4x + 2x + 5y – 9y 4x + 5y + 2x – 9y

6x - 4y

CommutativeChange order

CLTDoes the answer get an equal sign? No

Today’s New Vocab (4 of 4)Combine Like Terms (CLT) means Simplify

4x + 2x + 5y – 9y - 34x + 5y - 3 + 2x – 9y

6x - 4y - 3

Commutative

CLT


Monday Sept 14, 2020 Work Period Write an expression that represents

the number of yards in x feet?

Convert 12 feet to yards.

12 𝑓𝑒𝑒𝑡

3 𝑓𝑒𝑒𝑡 𝑖𝑛 𝑎 𝑦𝑎𝑟𝑑= 4 yards

𝑥

3

Monday Sept 14, 2020 Exit Question

5x - 3

Which expression is simplified correctly? Left

2x5x - 3

5x - 3 5x - 3

Explain why. NOT LIKE TERMS

-15x

5x and -3 are NOT like terms. So, they stay side by side. One number has an x and the other number does not.

Wednesday Sept 16, 2020 Activator

2(4) 2(-7) Question #1 Question #2

Simplify the expressions.

Distributing is the same as multiplying.

Question #3

2(x)

8 -14 2x

Today’s Objective

Students will be able to distribute.

Unit 1Lesson 3

(1 of 4)

Distribute

Definition

Example(s) Non-Example(s)

Facts

to multiply It removes the ( ).

3(x) 3(4)3x 12

3

𝑥𝑜𝑟

𝑥

3

Today’s New Vocab (2 of 4)Simplify the following expression.

-4(-3) -3(-4)

Same answer or different answers?+12 +12

Same. Why? Multiplication is commutative

-3(x) x(-3) -3x -3x

Always write the number in front of the variable.

Today’s New Vocab (3 of 4)Simplify the following expressions.

-8(4+5) -8(4) - 8(5)

Same answer or different answers? Same

-32 - 40 -72 -72

This is called the Distributive Property.The -8 is multiplied by both numbers.

-8(9)


-5(4y) + 4y(-5) -20y + -20y-20y - 20y

-40y

DistributeMultiply signs

Combine Like Terms

Which expression represents "5 subtracted

from the product of 7 and x"? Left

Wednesday Sept 16, 2020 Work Period

7(x) - 5 -5(7x)or

5 Subtracted from 7xis the same as

7x - 5

This says -5 times 7x.

Wednesday Sept 16, 2020 Exit TicketKonnor wants to burn 10 calories per minute while exercising in the gym.

Write an expression for this situation.

10x or 10m or 600h10 times the number of minutes.60 minutes (10) is 600 calories per hour.

Friday Sept 20, 2020 Activator

3(540)

Simplify the following expression.

3(500 + 40)

Same answer or different answers? SameWhy? The distributive property

1,620 1,500 + 120 1,620

Today’s Objective

Students will be able to double distribute.

Unit 1Lesson 4


5(-6x) 5(-6x + 2)

-30x -30x + 10

Distribute/Multiply to remove the ( ).

Today’s New Vocab (2 of 4)What is the product of 3(3x + 4)?

3(3x) + 3(4)

9x + 12 Distribute (Multiply)

Don’t have to write this step.

Can you combine the 9x and 12? NOWhy? They are not LIKE TERMS.

Today’s Misconception (3 of 4)

5 – 3(2x – 9)Simplify the following expression.

5 – 6x + 27Distribute

5 + 27 - 6x Commutative

32 – 6xCombine Like Terms


-3(5𝑥 − 7𝑦)Distribute

-15𝑥 + 21𝑦

Can you combine -15x +21𝑦? NoWhy? Not like terms (variables).

Friday Sept 20, 2020 Work Period

.

Simplify the following expression.

6g – 8 – 8g - 3

6g – 8g – 8 - 3

-2g – 11

2(3g – 4) – (8g + 3) Distribute

Commute

Combine (CLT)

Friday Sept 20, 2020 Exit Ticket

.

Which are equivalent (The same)?

6x + 4 and 2(3x + 2) and 6x + 22(3x) + 2(2)

6x + 4

2(3x + 2) is the same as 6x + 4

Tuesday Sept 22, 2020 Activator

Multiply.

x y

2 6

4 12

line 3xWhen x = 2, what does y = _6_ ?

When x = 4, what does y = _12_ ?

3(2)

3(4)

Today’s Objective

Students will be able to evaluate (substitute).

Unit 1Lesson 5

Mon(D) Tue(A) Wed (B) Thur(C) Fri(D)Lesson 1.4

Double Distribute

x Lesson 1.5Substitution

x Lesson 1.6Commute

NextMon(A)

NextTue(B)

NextWed(C)

NextThur(D)

NextFri(A)

x Lesson 1.7Simplify

x ReviewUnit 1

x

Announcements• Grab Folder and Calculator everyday• Open House: Thursday, Sept. 26th 6-8pm• Study Guide Answers for Unit 1 are on my website.

• Test #1 Monday, Sept 30th

• HW #1 due on Test Day.• Save 20 chips for Test Day for MAX 5% EC.

(1 of 4)

Evaluate

Definition

Example(s) Non-Example(s)

Facts

to determine the number using substitution

The answer will be a number

If a=3, what is 2a?

2(3) is 6

x + 4 = 5

x = 1-4 -4 This is

solving.

Today’s New Vocab (2 of 4)Evaluate the expression

when A = -2 and B = -3 and C = -4.

B - 515A 12 ÷ 𝐶

15(-2) (-3) - 5 12 ÷ (−4)

-30-8

-3 - 5 12 ÷−4

-3


when A = 3 and B = 4 and C = 5.

A + B A(B) A+BC

(3) + (4)

7

(3)(4)

12

(3)+(4)(5)3+20

23


when x = 7 and y = 8 and z = 9.

-4y + x 6z – 10y-4(8) + (7)

-32 + 7-25

6(9) - 10(8)54 - 80

-26

https://www.youtube.com/watch?v=YgHV9_3iqdM

Video 1:30

https://www.youtube.com/watch?v=YgHV9_3iqdM

.

What is f(5) and g(4), if g(x) = 3x and f(x) = 2x +1 ?

g(4) = 3(4) g(4) = 12

f(5) = 2(5) +1 f(5) = 10 +1

f(5) = 11

Tuesday Sept 22, 2020 Work Period

Tuesday Sept 22, 2020 ET #1

.

Evaluate the function f(x) = -2x + 4 when x = 6. f(6) = -2(6) + 4

f(6) = -12 + 4

f(6) = -8

Tuesday Sept 22, 2020 ET #2

https://www.youtube.com/watch?v=c-I7ysCe25U Video 4:25-5:45

How much (distance), d, can you travel if you go 55 miles per hour (Rate) for 3 hours (Time)?

D = RTD = (55)(3)D = 165 miles

https://www.youtube.com/watch?v=c-I7ysCe25U

Thursday Sept 24, 2020 ActivatorWrite in the missing number

using the commutative property.

9 + x = -3 + 9What is x?

(8)(x) = (x)(8)What is x?

The commutative property switchesthe order of the number.

-3 unknown number

Today’s Objective

Students will be able to use all properties including the commutative property.

Unit 1Lesson 6

Mon(D) Tue(A) Wed (B) Thur(C) Fri(D)Lesson 1.4

Double Distribute

x Lesson 1.5Substitution

x Lesson 1.6Commute

NextMon(A)

NextTue(B)

NextWed(C)

NextThur(D)

NextFri(A)

x Lesson 1.7Simplify

x ReviewUnit 1

x

Today’s New Vocab (1 of 4)Is this an example of the commutative property? NO

10 + (9 + 3) = (10 + 9) + 3

Is the order of the number different? NO

10 + (12) = (19) + 3

22 = 22

10 + 9 + 3 = 10 + 9 + 3 No, this is called the Associative property. The

(inside) moves.

https://www.youtube.com/watch?v=7e9r8_VOO-8 0:30-2:30 Video

https://www.youtube.com/watch?v=7e9r8_VOO-8

Today’s New Vocab (2 of 4)Is Division an example of the commutative property?

6

3=

3

6

𝑥

4=

4

𝑥

Does 2 = 0.5? Is x divided by 4

equal to 4 divided by x?

NO

NONO

When dividing, the bigger number does NOT ALWAYS go on top. Some answers this year will be decimals and fractions.

Today’s New Vocab (3 of 4)Is this an example of the commutative property?

10 - 4 = 4 - 10 X – 10 = 10 - X6 = -6

10 – 4 = -4 + 10

No

6 = 6YESX - 10 = -10 + x

No, not commutative

YES, commutative

Today’s New Vocab (4 of 4)Is this an example of the commutative property? YES

12 + (9 + x) = (9 + x) + 12A + (B) = (B) + A

Yes, CommutativeThe order switched.


(A) + (B) = (B) + (A)


The inside of ( ) did not change. The order of the groups changed.

https://www.youtube.com/watch?v=H1zsWdHC_V8 1:30 at end

https://www.youtube.com/watch?v=H1zsWdHC_V8

Thursday Sept 24, 2020 Work Period

.

A family drove t miles on Tuesday and w miles on Wednesday. Write an expression for the total number of miles driven.

t + w w + t or

Both expressions are the same, because of the commutative property.

.

Thursday Sept 24, 2020 Exit Ticket Do and explain each step. 2(x + 4x)2x + 8x

8x + 2x10x

Distribute

Commutative

Combine Like Terms

Remove ( )

Switch order

(Add or Subtract)

Monday Sept 29, 2020 Activator Which is the distributive property?Which is the commutative property?

(3x + 5) = (5 + 3x) 3(x + 5) = 3x + 15Commutative Distributive

Why? Order changed

Why? ( ) disappeared

Today’s Objective

Students will be able to simplify multistep expressions.

Unit 1Lesson 7

Mon(A) Tue(B) Wed (C) Thur(D) Fri(A)x Lesson 1.7

Simplifyx Review

Unit 1x

NextMon(B)

NextTue(C)

NextWed(D)

NextThur(A)

NextFri(B)

Test 1Expressions

x Lesson 2.1One-StepEquations

x Lesson 2.2Two-StepEquations


2(-x) 2(-x) - 4 2(-x – 4)

-2x -2x - 4 -2x – 8

Are any of the expressions equivalent (same)? No

Which one property was done to all 3 expressions?

Distributive


6 + 2(-x - 4) - 5xSimplify the following expression.

-2x - 5x + 6 - 86 - 2x - 8 - 5x

-7x - 2

Distribute

Commute

Combine (CLT)


6[-3(4 - x) - 2x]6[-12 + 3x - 2x]

-72 + 6x6[-12 + 1x]

What are the brackets?

It is another set of ( ) in the same problem. [ ] are the same as ( ).

Today’s New Vocab (4 of 4)Evaluate the following expression

-72 + 6x when x = 11 when x = -11

-72 + 6(11) -72 + 66

-6

-72 + 6x -72 + 6(-11) -72 - 66

-138

Same answer

or different answers?

Different because you substituted different numbers.

Monday Sept 29, 2020 Work Period

.

Andy bought a small computer for $360. Each week, w, he pays $30. Write an expression that could be used to find out how much money he still owes after 8 weeks? Then, determine how much money he has left after 8 weeks.

$360 – $30ww = 8 $360 – $30(8)

$360 – $240

$120

After 8 weeks, Andy still owes

$120.

Monday Sept 29, 2020 Exit Ticket

.

Evaluate the expression when x = 3.

-2(x – 7)-2(x – 7)-2x + 14 -2[(3) – 7]

-2[3 – 7]

8-2[-4]

-2(3) + 14-6 + 14

8

Do you substitute

first or distribute

first?

Either

Thursday Oct 2, 2020 Activator

#1

Equivalent meansthe same as

Today’s Objective

Students will be able toreview all objectives in Unit 1.

Unit 1Review

Mon(A) Tue(B) Wed (C) Thur(D) Fri(A)x Lesson 1.7

Simplifyx Assembly

5th Periodx

NextMon(B)

NextTue(C)

NextWed(D)

NextThur(A)

NextFri(B)

ReviewUnit 1

x Test 1Expressions

x Lesson 2.1and

Lesson 2.2

Announcements• Study Guide Answers for Test 1 are on my website.

• Test #1 on Wednesday• HW #1 due Wednesday

• Absent work is due on Wednesday• Save 20 chips for Test Day for MAX 5% EC.• Read through the Testing Rules

• Unit #1 Test: 10% Question #19 all others are 5%

Today’s New Vocab (1 of 4)#14

#10


4(-6x-7) +3(8-x)-24x -28 +24 -3x-24x -3x -28 +24

-27x -4#18 What is the first step called?

Distribute

Thursday Oct 2, 2020 Exit Ticket

.

#11

• Show Mr. V absent work and Testing Rules• Turn in Classwork Packet and HW Packet• Max 20 chips for +5 Extra Credit• +3 Extra Credit for Perfect Attendance• Unit #1 Test 10% Question #19 all others are 5%

• You must receive at least a 65%, or you must stay after school to complete it.

• Tutoring Today, Monday 2:45-3:45

Monday Oct 5, 2020 Test #1

unit 1 expressions

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