grade 6 accelerated standard 7.eei.5 understand and apply ... › cms › lib › sc02209149 ›...

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Grade 6 Accelerated Day 3

Standard 7.EEI.5 Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property) to simplify numerical expressions that include whole-number exponents.

Learning Targets I Can Statements

I can apply the laws of exponents.

Essential Question(s) How can the laws of exponents be applied in real-world situations?

Resources You will need a pair of scissors and a glue stick to complete this assignment. All answers should be written on the page provided.

Learning Activities or Experiences

1. Complete at least 3 topics of your ALEKS pathway. (if available)

2. Review attached notes and complete the “Exponent Rules Puzzle.”

3. Complete the “Today’s Thought” activity.

NOTE: For additional practice aligned to your grade for SC READY review please refer to the 6th grade level

assignments.

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Lesson Notes

Exponent Rules Puzzle

1. Cut out the nine puzzle pieces.

2. Pair up the matching expressions (each non-simplified expression

has a matching simplified expression).

3. When complete, the puzzle will be a

three-by-three square. Glue your

final arrangement on the page

provided. GOOD LUCK!

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Exponent Rules Puzzle Solution

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Today’s Thought

1. What is the value of the expression 𝟖𝟔÷𝟖𝟑

𝟒𝟎÷𝟒𝟐 ?

a. 16

b. 32

c. 512

d. 4,096

2. Which value is 𝟕𝟐⋅𝟕𝟎∙𝟑𝟑

𝟑𝟐 simplified?

a. 0

b. 49

c. 147

d. 210

3. What is the value of (𝟗𝟐 × 𝟗𝟎)2 ?

a. 90

b. 93

c. 94

d. 95

For problems 4 – 6, you will need to simplify each expression.

4. (2𝒙𝟒𝒚𝟒)3

5. 𝒙𝟑𝒚𝟑⋅𝒙𝟑

𝟒𝒙𝟐

6. (𝟓𝒂𝟒𝒃𝟑)0

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Standard 7.EEI.2 Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.


I can write algebraic expressions and their equivalent forms to represent real-world situations.

Essential Question(s) How can writing and identifying equivalent forms of algebraic expressions assist with understanding real-world situations.

Resources No additional resources needed. However, all answers should be written on a separate sheet of paper.



2. Review attached notes and complete the practice problems.

3. Complete the exercises titled “You Try It”.



assignments.

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Algebraic Expressions Lesson Notes

What is an algebraic expressions?

An algebraic expression is a combination of integer constants, variables, exponents and algebraic operations such as addition, subtraction, multiplication and division. 5x, x + y, x-3

and more are examples of algebraic expression. ... A variable is a letter used to represent an

unknown value.

There are a variety of ways to write an algebraic expression to represent a given situation in

mathematics. Let’s take a look at an example.

Alvin wants to take his two sons to the carnival that’s in town this weekend.

Admission for each adult is $7 and children pay $5 to get in.

All rides cost $2 no matter your age.

Help Alvin to write an expression he can use to figure out his total cost once the kids

decide how many rides they want to get on. Let “r” represent number of rides.

Expression #1: $7 + $5(2) + $2r

Expression #2: $7 + $10 + $2r

Expression #3: $17 + 2r

You Try It

It is school supply time and Marie is almost finished with her supply list. The only items

left to get are ink pens and notebook paper. So she notices that one teacher like for

students to write on wide-rule paper and the other wants college-rule paper. They both

want her to have four packs of paper each. The wide rule is on sale for $.75 and the

college rule cost $1.25. Marie has $10 remaining to spend. Help her to write an

expression to figure out how much she has to spend on the ink pens.

First Expression:

Equivalent Expression:

Stretch Your Thinking: How much can Marie spend on her ink pens?

Here are three examples of ways you represent this situation mathematically.

All expression are correct because they are equivalent.

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Today’s Thought

1. A teacher goes to an office supply store and purchases 3 packs of red markers, 5 packs of black markers,

and 4 packs of blue markers. The cost of each pack of markers is $1.70. The expression 1.70 x 3 + 1.70 x

4 represents the total amount of money the teacher spends on markers. Which is another way the

teacher spends on markers?

a. 1.70 + 3 + 5 + 4

b. 1.70 x 3 x 5 x 4

c. 1.70 + (3 x 5 x 4)

d. 1.70 x (3 + 5 + 4)

2. Eva takes a taxi to and from work. The taxi charges a flat rate of $2.60 and $1.20 for each mile. Eva gives

her friend, who lives d miles away from her work, a ride home in the taxi. Evan then travels m miles more

in the taxi before reaching her home. Which statement is true about the amount Eva pays for the taxi?

a. Eva pays 1.20 (m – d) + 2.60 dollars, which is equivalent to 1.20m - 1.20d + 2.60.

b. Eva pays 1.20(m + d) + 2.60 dollars, which is equivalent to 1.20m + 1.20d + 2.60.

c. Eva pays 1.20(m – d) + 2.60 dollars, which is equivalent to 1.20m - d + 2.60.

d. Eva pays 1.20(m + d) + 2.60 dollars, which is equivalent to 1.20m + d + 2.60.

3. A teacher writes the scenario on the board.

Amber sells bags at 20% more than the price that it costs her to make them.

The teacher asks four students to write an expression representing the price at which Amber sells a

bag that costs her $c to make. The table shows the students’ responses. Which student(s) is (are)

correct?

Student Response

Charlie c + 0.2c

Deborah c – 0.2c

Rosario 1.2c

Vincent 0.98c

a. Only Charlie

b. Only Deborah

c. Both Charlie and Rosario

d. Both Deborah and Vincent

4. Craig and Madison spend d dollars on dinner and then tip the server 18%. Which expressions represent

the total cost of Craig and Madison’s dinner? Select ALL that apply.

a. 0.82d

b. 1.18d

c. d + 0.18

d. d + 0.18d

e. d + 1.18

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Standard 7.EEI.3 Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.


I can apply order of operations to multi-step real-world problems.

Essential Question(s) How important is order of operation when working through multi-step situations? Can changing the order of solving a multi-step mathematical problem still achieve the same outcome?

Resources No additional resources needed. However, all answers should be written on a separate sheet of paper.



2. Review attached notes and complete the “You Try It.”



assignments.

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Lesson Notes

When applying order of operations with numerical expressions the acronym PEMDAS often

comes to mind. You many know it as “Please Excuse My Dear Aunt Sally.”

Parenthesis

Exponents

Multiplication (from left to right)

Division (from left to right)

Addition (from left to right)

Subtraction (from left to right)

So, what does order of operations look like when there is an unknown, a variable? This now

makes it an algebraic expression or equation. There is not an acronym but you can refer to

some steps to organization your thought process that will allow you to work through the

mathematical situation.

Parenthesis – this could be the distributive property

Exponents – evaluate all powers

Addition / Subtraction – isolate your variable using inverse operations

Multiplication / Division – isolate your variable using inverse operations

NOTE: All steps are with the understanding, if applicable. Not all equations will have every

element of this process. Also, this provides a basic process. As the mathematical situations

grow in complexity so will your process. For example, you may be required to combine like terms

multiple times when solving an equation.

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Let’s Take a Look

Christopher is making a bookshelf. Each shelf needs to be 3 ½ feet long. Each side of the

bookshelf needs to be 5 ½ feet tall. He has a 25-foot board that will be exactly enough wood if

he cuts precisely. How many shelves will be on the bookshelf?

Let x represent our unknown which is the number of bookshelves. The following equations

represents our mathematical situation.

2 (5 ½) + 3 ½ x = 25

Let’s use the steps above to solve the equation.

Equation Explanation

2 (51

2) + 3

1

2𝑥 = 25 Original Equation

11 + 31

2𝑥 = 25 Parenthesis

11 – 11 + 31

2𝑥 = 25 – 11 Addition / Subtraction

31

2𝑥 = 14 Simplify

31

2

31

2

𝑥 = 14

31

2

Multiplication / Division

x = 4 Simplify to Solve

So it looks like Christopher will be able to make four shelves on his bookshelf.

You Try It

Francis earns $3.50 an hour mowing lawns. He also gets $10 a week allowance. Bella earns $5.25

an hour babysitting and spends $11 a week on books. If Francis and Bella work the same number

of hours a week and have the same amount of money at the end of each week, for how many

hours a week do they each work?

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Today’s Thought

1. Denise is training for a race. She plans to increase the distance she runs by 20% each week. Denise runs 5 miles the 1st week.

5(1.2)x-1

If x represents the number of weeks Denise runs, how many miles does she run during the 3rd week? a. 5.2 miles b. 6 miles c. 7 miles d. 7.2 miles

2. At a local flower shop, corsages are on sale. Each corsage costs $10, but the florist will sell every third

corsage purchased at a 60% discount. To save money, a group of 12 friends, going to a school dance, decide to purchase corsages together. How much will it cost to buy 12 corsages? a. $84 b. $96 c. $104 d. $120

3. The table shows the changes in the amount of money in Christopher’s bank account in the last four weeks.

Week Change in Amount

1 -$58.47

2 $36

3 -$15.82

4 $24

If Christopher has $79.14 left in his bank account after the four weeks, how much did he have originally? a. $93.43 b. $80.67 c. $64.85 d. $55.15

4. A lifeguard earns $12 per hour working during the summer. The lifeguard works a total of 52 hours and

spends 80% of the money earned on a video game system. Which statement is true?

a. The lifeguard has about $500 left after earning $624 and spending about $125 of that on the video game system.

b. The lifeguard has about $500 left after earning $624 and spending about $499 of that on the video game system.

c. The lifeguard has about $125 left after earning $624 and spending about $125 of that on the video game system.

d. The lifeguard has about $125 left after earning $624 and spending about $499 of that on the video game system.

Grade 6 Grade Level Day 4 (MRS. CINDY WORKMAN)

MR. RONEL TURQUESA

STANDARD:

6.GM.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by

composing into rectangles or decomposing into triangles and other shapes; apply these techniques in

the context of solving real-world and mathematical problems.

LEARNING TARGETS AND/OR I CAN STATEMENT:

I can... Use formulas to find area of triangles, Quadrilaterals, and polygons

Essential Question: How can we use the area of squares and rectangles to determine the area of triangles, trapezoids, and rhombus?

RESOURCES: No additional resources needed. However, all answers should be written on a separate

sheet of paper

LEARNING ACTIVITIES AND/OR EXPERIENCES


2. Review attached notes and complete the practice problems below.

3. Complete the “The Language of Geometry”

Grade 6 Grade Level and Accelerated Day 5 (MRS. CINDY WORKMAN)

MR. RONEL TURQUESA

STANDARD:

6.GM.4 Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find

the surface area and to solve real-world and mathematical problems


I can... Find the surface area using rectangles and triangles

Essential Question: How can we construct 3-dimensional figures out of triangles and rectangles to figure out the area? How can we use area of 2-dimensional figures to find the surface area of 3-

dimensional figure?


sheet of paper



2. Review attached notes and complete the practice problems below.

3. Complete A KIM Chart, pick 10

Key Terms protractor (13.1) compass (13.1) straightedge (13.1) sketch (13.1) draw (13.1)

construct (13.1) triangle (13.1) equilateral triangle (13.1) isosceles triangle (13.1) scalene

triangle (13.1) equiangular triangle (13.1) acute triangle (13.1) right triangle (13.1) obtuse

triangle (13.1) quadrilateral (13.1) opposite sides (13.1) consecutive sides (13.1) square (13.1)

rectangle (13.1) rhombus (13.1) parallelogram (13.1) kite (13.1) trapezoid (13.1) isosceles

trapezoid (13.1) polygon (13.1) regular polygon (13.1) irregular polygon (13.1) pentagon (13.1)

hexagon (13.1) heptagon (13.1) octagon (13.1) nonagon (13.1) decagon (13.1) altitude of a

parallelogram (13.3) height of a parallelogram (13.3) altitude of a triangle (13.3) height of a

triangle (13.3) bases of a trapezoid (13.4) legs of a trapezoid (13.4) altitude of a trapezoid (13.4)

height of a trapezoid (13.4) congruent polygons (13.6) apothem (13.6)

https://www.mathworksheets4kids.com/surface-area/nets/customary/counting-squares-1.pdfhttps://www.mathworksheets4kids.com/surface-area/nets/customary/drawing-nets-1.pdf

https://www.mathworksheets4kids.com/surface-area/counting-squares/customary/isometric-dot-paper-1.pdfhttps://www.mathworksheets4kids.com/surface-area/counting-squares/customary/draw-rectangular-prism-1.pdf

SURFACE AREA VOCABULARY BUILDING (MATHCHING WORDS AND THEIR MEANING)

A B

prism a polyhedron with two congruent faces that lie in

parallel planes, where the other faces are

parallelograms.

bases congruent faces that lie in parallel planes

lateral faces parallelograms formed by connecting the

corresponding vertices of bases in a prism.

right prism a prism where each lateral edge is perpendicular

to both bases.

https://www.mathworksheets4kids.com/surface-area/counting-squares/customary/rectangular-prism-moderate-1.pdf

oblique prisms Prisms that have lateral edges that are not

perpendicular to the bases.

surface area of a polyhedron The sum of the areas of the faces.

lateral area of a polyhedron The sum of the areas of the lateral faces

net The two-dimensional representation of all of a

prism's faces.

cylinder A solid with congruent circular bases that lie in

parallel planes.

right cylinder A cylinder where the segment joining the centers

of the bases is perpendicular to the bases.

lateral area of a cylinder The area of a cylinder's curved surface and equal

to the product of the circumference and the

height.

surface area of a cylinder Equal to the sum of the lateral area and the areas

of the two bases.

Theorem: Surface Area of a Right Prism S = 2B + Ph, where B is the area of a base, P is the

perimeter of a base, and h is the height.

Theorem: Surface Area of a Right Cylinder S = 2B + Ch, where B is the area of a base, C is the

circumference of a base, r is the radius of a base,

and h is the height.

pyramid A polyhedron in which the base is a polygon and

the lateral faces are triangles with a common

vertex.

lateral edge The intersection of two lateral faces of a pyramid.

base edge The intersection of the base of a pyramid and a

lateral face.

altitude or height The perpendicular distance between the base and

the vertex

regular pyramid This has a regular polygon for a base and its

height meets the base at its center.

slant height of a regular pyramid The altitude of any lateral face.

circular cone This has a circular base and a vertex that is not in

the same plane as the base.

right cone The height meets the base at its center

slant height of a right cone The distance between the vertex and a point on

the base edge

lateral surface of a cone all segments that connect the vertex with points

on the base edge

Theorem: Surface Area of a Regular Pyramid S = B +1/2(Pl), where B is the area of the base, P is

the perimeter of the base, and l is the slant height

Theorem: Surface Area of a Right Cone S = (pi)r-squared + (pi)rl, where r is the radius of

the base and l is the slant height


MR. RONEL TURQUESA

STANDARD:

6.GM.2 Use visual models (e.g., model by packing) to discover that the formulas for the volume of a

right rectangular prism (𝑎 = 𝑎𝑎ℎ, 𝑎 = 𝑎ℎ) are the same for whole or fractional edge lengths. Apply these

formulas to solve real-world and mathematical problems


I Can... Compute volume by using visual models

Essential Question: Does finding volume require a 2-D or 3-D figure?


sheet of paper



2. Review attached notes and complete the practice problems below (pick 5 each page)

3. Complete Volume (Words)


MR. RONEL TURQUESA

STANDARD:

6.EEI.1 Write and evaluate numerical expressions involving whole-number exponents and positive

rational number bases using the Order of Operations.


I Can... Identify and explain the differences between an expression and equation; Understand

expressions and equations and their relation to algebra; Identify all parts of an expression; Use real

world scenarios to solve equations.

Essential Question: How can we identify the numerical value of a variable? How can we write expressions to represent real-world scenarios? How can we use and write real-world scenarios to

represent equivalent expressions?


sheet of paper



2. Review attached notes and complete the practice problems below

3. Summarize PEMDAS

https://www.google.com/url?sa=i&url=https://www.pinterest.com/pin/351773420865647208/&psig=AOvVaw3qYD-OmIZ7LByyQs2nzATe&ust=1584401813529000&source=images&cd=vfe&ved=0CAIQjRxqFwoTCOD-6u3SnegCFQAAAAAdAAAAABAL


MR. RONEL TURQUESA

STANDARD:

6.EEI.2 Extend the concepts of numerical expressions to algebraic expressions involving positive

rational numbers.

a. Translate between algebraic expressions and verbal phrases that include variables.

b. Investigate and identify parts of algebraic expressions using mathematical terminology, including

term, coefficient, constant, and factor.


I can...Identify and explain the differences between an expression and equation; Understand

expressions and equations and their relation to algebra.

Essential Question: How can I identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor?


sheet of paper




3. Study all problems completed


MR. RONEL TURQUESA

STANDARD:

6.EEI.5 Understand that if any solutions exist, the solution set for an equation or inequality consists of

values that make the equation or inequality true.


I can... Solve for a solution set that will make an equation true; Understand how to write expressions

using real world situations; Use inequalities to compare expressions.

Essential Question: How can we use inequalities to compare algebraic expressions? How can we use a pan model to develop the conceptual understanding of solving equations involving one step? How can

we use equations, tables, and graphs, to represent and solve real-world problems?


sheet of paper




3. Study all problems completed


MR. RONEL TURQUESA

STANDARD:

6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic

expressions in real-world and mathematical situations.


I can... Use inequalities to compare expressions.

Essential Question: How can we use inequalities to compare algebraic expressions?


sheet of paper



2. Review attached notes and complete the practice problems.

3. Study all problems completed.

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