students will be able to simplify and expand with exponents

Today’s Objective Students will be able to simplify

and expand with exponents.

Lesson 1.2

Monday July 6, 2020 Activator

What does the little number (exponent) mean?

It is the number of times that you multiply.

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)Expand and Evaluate 46

The base is the number that gets multiplied. The exponent is number of times the base gets multiplied.

What is the base? 4What is the exponent? 6What is the answer?Evaluated. 4,096

(4)(4)(4)(4)(4)(4)

Today’s New Vocab (3 of 4)Expand and simplify 𝑥5(𝑥3)(x)

What do you do with the exponents? When you are multiplying variables, you ADD the exponents.

Expand (x)(x)(x)(x)(x)(x)(x)(x)(x)

When in doubt, expand it out !!! 𝑥5+3+1 𝑥9or

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

(3y)(3y)(3y)(3y)(3y)

Does the answer get an = sign? No why?

(3)(3)(3)(3)(3)(y)(y)(y)(y)(y)

(3)5(𝑦)5 or (3𝑦)5

Monday July 6, 2020 Word Period

(1) Expand and write 23(42) is equivalent to:

(2) What is the product of 6𝑥3 and (2𝑥)5 ?

(3) What is the product of 3𝑎2𝑏 and 2𝑎𝑏3 ?Hint: Can not add Exponents from Different variables

(2)(2)(2)(4)(4) is 128

(6)(x)(x)(x)(2x)(2x)(2x(2x)(2x) is 192𝑥8

(3)(a)(a)(b)(2)(a)(b)(b)(b) is 6𝑎3𝑏4

.

Monday July 6, 2020 Exit Question

𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 3𝑥2𝑦 𝑎𝑛𝑑 −4𝑥𝑦3 ?

(3𝑥2𝑦) (−4𝑥𝑦3)

What does product mean? Multiply

3𝑥2𝑦 (−4𝑥𝑦3)3 −4 𝑥2(𝑥)𝑦(𝑦3)

−12𝑥3𝑦4

Does the answer get an equal sign?

No, Why?

Today’s Objective Students will be able to apply

the distributive property to expressions.

Lesson 1.4

Tuesday July 7, 2020 Activator

3(542)

Simplify the following expression.

3(500 + 40 + 2)

Same answer or different answers? Why?

1,626 1,500 + 120 + 6

1,626

Today’s New Vocab (1 of 4)Simplify the following expression.

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

-30x -30x + 10

Multiply to remove the ( )

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

3( 4𝑥2 + 5𝑥 − 7)Distribute to remove the ( ) parentheses. 12𝑥2 + 15𝑥 − 21

Can you combine 12𝑥2 + 15𝑥? NoWhy? Not like exponents (terms)

Today’s New Vocab (3 of 4)

16𝑦 − 24

8

Simplify the following expression.

2𝑦 − 3

Divide both by 8

16

8𝑦 −

24

8

Today’s New Vocab (4 of 4)

−4(6𝑥 + 12)

3

Simplify the following expression.

−24𝑥 − 48

3

Distribute to remove the ( )

Divide both the -24 and -48 by 3

−24

3𝑥 −

48

3

-8x - 16

Tuesday July 7, 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)

Tuesday July 7, 2020 Exit Ticket

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Are the following equivalent? No

3(5+x) = 15 + x3(5) + 3(x) = 15 + x

15 + 3x = 15 + xS/he did not distribute the 3 to the x.

Today’s Objective Students will be able to

multiply (Double Distribute) using the box method.

Lesson 1.5

Wednesday July 8, 2020 Activator

x + x x (x) Question #1 Question #2

Simplify the expressions.

When you multiply variables, you ADD the exponents.

Question #3

x (2x)

2x 𝑥2 2𝑥2

Today’s Misconception (1 of 4)

5(x) + 5(4)

Simplify the following expression.

5 (x + 4)

5x + 20

+5x +205x + 4

Today’s New Vocab (2 of 4)

+200 +30

+40 +6

Simplify the expression.

(12)(23)(10+2)(20+3)Write down all boxes

10

+2

+320

200 + 30 + 40 + 6276 answer

Combine Like Terms

Today’s New Vocab (3 of 4)

𝒙𝟐 -4x

+4x -16

Simplify the expression.

(x + 4)(x - 4)Write down all boxes

x

+4

-4x

𝑥2- 4x + 4x - 16𝑥2+ 0x - 16 answer Combine Like Terms

Today’s New Vocab (4 of 4)

𝟏𝟓𝒙𝟐 +20x

-6x -8

Simplify the expression.

(5x - 2)(3x + 4)Write down all boxes

5x

-2

+43x

15𝑥2+20x - 6x - 815𝑥2+ 14x - 8 answer

Combine Like Terms

Wednesday July 8, 2020 Work Period

.

𝟑𝒙𝟐 -21x

+2x -14

3x

-7x

+2

3𝑥2-21x +2x - 143𝑥2-19x - 14

Write down the boxes.

Wednesday July 8, 2020 Exit Ticket

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Does 2(3x + 4) = 6x + 8 for all numbers?

Pick any number at random and substitute it in for both x’s.

If x = 5, is it true? Yes, it is true for all numbers.

2(3(5)+ 4) = 6(5) + 8

2(15+ 4) = 30 + 8

38 = 38

2(19) = 38

Today’s Objective

Students will be able write expressions and equations in words.

Lesson 1.7

Wednesday July 8, 2020 Activator Write each phrase as an algebraic expression.

15 less than 40 15 less than x

40 - 15

With less than you need to remember to switch the order.

x - 15

40 minus 15 x minus 15

Today’s New Vocab (1 of 4)Write a verbal expression for each algebraic expression.

12x

12 times x The product of 12 and x12 multiplied by x

15

𝑦

15 divided by y

The quotient of 15 and y

Today’s New Vocab (2 of 4)Write a verbal expression for each algebraic expression.

4𝑥2- 7 4(𝑥2- 7) Seven less than

the product of four and x squared

Four times the quantity of seven

less than x squaredOr four times x squared minus seven

Today’s New Vocab (3 of 4)Translate the sentence into an equation.

The product of 15 and x is 30

15(x) = 30

5 more than a third of x is 7

5 +1

3𝑥 = 7

15 times x is 30

Today’s New Vocab (4 of 4)Determine if the following are commutative or associative or neither.

7 + x = x + 7 Commutative

5 + (3 + x) = (5+3)+ x Associative

The order changes. The ( ) changes.

6(4) = (4)6

The order changes.(1)(2*9)=(1*2)(9) The ( ) changes.

Wednesday July 8, 2020 Work Period

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The difference of a number and one multiplied by two is negative eight.

2 ( x – 1 ) = - 8

Translate the sentence into an equation.

Wednesday July 8, 2020 Exit Ticket

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The zoo must put a new tracking bracelet on each leg of

the animals at the Zoo in the Bronx. It has inhabitants of birds (2 legs) and cats (4 legs). If the Zoo contains a 78 birds and 82 cats, how many Bracelets need to be purchased.

78(2L) + 82(4L)

156L + 328L 484L

They need to buy 484 Bracelets.

Today’s Objective

Students will be able to review lesson from Unit #1.

Unit 1 Review

Thursday July 9, 2020 Activator

#8 Write in Expanded form. (No parentheses)

(5𝑥6)4

(5𝑥6)(5𝑥6)(5𝑥6)(5𝑥6)(5)(5)(5)(5)(𝑥6)(𝑥6)(𝑥6)(𝑥6)

625𝑥24

#13Today’s New Vocab (1 of 4)

Today’s New Vocab (2 of 4)#4

Combine Like Terms

The binomial (7𝑥 + 4)2 𝑖𝑠 …

Today’s New Vocab (3 of 4)

#10

Today’s New Vocab (4 of 4)#15

Thursday July 9, 2020 Work Period

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#18 and #19

Thursday July 9, 2020 Exit Ticket

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#16 Which are equivalent? 6x + 4 and 2(3x + 2) and 6x + 2

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

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