Boot Camp - Exponents & Roots · BOOT CAMP Level 2 Mastery A Name: 1.) 81 2.) 144 3.) 256 4.) 400 5.) !!1 6.) 125 Specialist (Perfect Squares & Perfect CuBes) EXPONENTS & ROOTS BOOT

© 21st Century Math Projects


Title: Exponents and Roots Boot Camp

Standard Focus: Operations Time Range: 3-‐5 Days

Supplies: Calculator

Topics of Focus:

-‐ Evaluating Expressions with Exponents and Roots

-‐ Word Problems

Benchmarks:

6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.

8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Procedures: A. To start, give the Pre-‐Assessment to students. The rows of problems correspond to the Levels. The first row is Level 1, the second row is Level 2 and so on ending with the sixth row Level 6.

If students miss questions on a level, that is where to have them start. If they finish the entire thing without making a mistake they will start on Level 7.

We like to use stickers or stamps to sign off on their mastery of a level. Regardless the age of students, they like this too.

In my experience, it works well to have students on similar levels work through problems together.

B. Once they complete a Practice assignment, they can take the Mastery Test. There are two versions of each test provided. If they pass the mastery test (you set the threshold – I like to use 90%) then they can move onto the next level. If they do not then they can repeat that Practice Assignment.

I like to let students take a Practice Assignment home so they can walk in and take a Mastery Test the next day.

C. Once a student completes all the levels, they become a teacher. A tutor for a student or a small group instructor generally works well.

The goal is that the students get differentiated practice on perhaps the most important math skill of all.


EXPONENTS AND ROOTS

BOOT CAMP Name_____________________

INSIGNIA RANK MASTERY !

Private

Specialist

Corporal

Sergeant

Staff Sergeant

Lieutenant

Captain

Major

Colonel

General


Basic Training

(Pre-Assessment)

EXPONENTS & ROOTS BOOT CAMP Placement Test

Name:

1.)

7!

2.)

2! + 9!

3.)

3!×4!

4.) 121

5.) 196

6.) 125!

7.)

−8 !

8.)

5× −2 !

9.) 15! ÷ −5 !

10.)

Which two integers is 130 between?

11.)

Fill in the statement with “>” or “<” 6.4 ____ 35

12.)

Fill in the statement with “>” or “<”

48____ 7

13.) −

13

!

14.)

35

!

−710

!

15.)

34

!

÷67

!

16.)

75

17.)

32

18.)

200


Private (Evaluate Exponent

Expressions)

EXPONENTS & ROOTS BOOT CAMP

Level 1 Practice

Name:

1.) 3!

2.) 2!

3.) 4!

4.) 5+ 1!

5.) 2! + 6!

6.) 7! − 2!

7.) 2! − 3!

8.) 9! − 3!

9.) 8!×11!

10.) 2!×5!

11.) 2!×2!

12.) 8! ÷ 8!

13.) 12! ÷ 6!

14.) 10+ 4 !

15.) 21− 17 !



Expressions)


Level 1 Mastery A

Name:

1.)

3!

2.)

2! + 5!

3.)

11! − 3!

4.)

3!×4!

5.)

10! ÷ 5!

6.)

37− 31 !


Expressions)


Level 1 Mastery B

Name:

1.)

2!

2.)

4! + 7!

3.)

15! − 3!

4.)

2!×4!

5.)

15! ÷ 3!

6.)

19− 4 !


Specialist (Perfect

Squares & Perfect CuBes)


Level 2 Practice

Name:

1.) 16

2.) 121

3.) 1

4.) 9

5.) 324

6.) 100

7.) 49

8.) 36

9.) 25

10.) 0

11.) 64

12.) 196

13.) 64!

14.) 8!

15.) 216!


Specialist

(Perfect Squares & Perfect CuBes)


Level 2 Mastery A

Name:

1.) 81

2.) 144

3.) 256

4.) 400

5.) 1!

6.) 125!

Specialist (Perfect

Squares & Perfect CuBes)


Level 2 Mastery B

Name:

1.) 36

2.) 100

3.) 196

4.) 361

5.) 729!

6.) 343!


Corporal (Integer Bases)


Level 3 Practice

Name:

1.) −1 !

2.)

−2 !

3.)

−3 !

4.)

−2 ! + 4!

5.)

7! + −5 !

6.)

−2 ! + −3 !

7.)

−3 ! − 3!

8.)

4! − −4 !

9.) −2 ! − −2 !

10.)

−7 !×2!

11.)

3!× −2 !

12.)

−3 ! ÷ 3!

13.)

10! ÷ −4 !

14.)

−5− 3 !

15.)

−3 ×3 !




Level 3 Mastery A

Name:

1.) −5 !

2.)

−4 !

3.)

−2 ! + −3 !

4.)

−4 ! − −5 !

5.)

7!× −3 !

6.)

6! ÷ −3 !



Level 3 Mastery B

Name:

1.) −7 !

2.)

−5 !

3.)

−5 ! + −4 !

4.)

−7 ! − −3 !

5.)

−2 !×5!

6.)

−8 ! ÷ 2!


Sergeant (Estimating

Square Roots)


Level 4 Practice

Name:

1.)


2.)


3.)


4.) Which two integers is 60 between?






10.) Fill in the statement with “>” or “<”

2 ____ 8

11.) Fill in the statement with “>” or “<” 11 ____ 3

12.) Fill in the statement with “>” or “<”

3.5 ____ 17

8.173− 1.297






Square Roots)


Level 4 Mastery A

Name:

1.)


2.)


3.)




6.) Fill in the statement with “>” or “<” 83 ____ 10.3


Square Roots)


Level 4 Mastery B

Name:

1.)


2.)


3.)






Staff Sergeant

(Fraction Bases)


Level 5 Practice

Name:

1.) 13

!

2.) −12

!

3.) 25

!

4.) 32

!

+ 6

5.) 2+

14

!

6.) 45

!

+15

!

7.) 73

!

− 2

8.) 4! − −

56

!

9.) 34

!

−18

!

10.) 73

!

×6!

11.) 14

!

× −23

!

12.) 95

!

×103

!

13.) 411

!

÷ −2 !

14.) 35

!

÷65

!

15.) −18

!

÷74

!


Staff Sergeant

(Fraction Bases)


Level 5 Mastery A

Name:

1.)

25

!

2.) −

34

!

3.) 3! + −

12

!

4.) −12

!

− −54

!

5.) −14

!

×83

!

6.) −13

!

÷79

!

Staff Sergeant

(Fraction Bases)


Level 5 Mastery B

Name:

1.)

37

!

2.) −

23

!

3.)

14

!

+ 4!

4.) −12

!

−25

!

5.) 37

!

×149

!

6.) 65

!

÷ −25

!


Lieutenant (Simplifying

Square Roots)


Level 6 Practice

Name:

1.)

27

2.)

72

3.)

18

4.) 75

5.) 98

6.) 108

7.) 300

8.) 192

9.) 80

10.) 245

11.) 2 112

12.) 3 486

13.) 3 252

14.) 2 243

15.) 5 450



Square Roots)


Level 6 Mastery A

Name:

1.) 45

2.) 128

3.) 98

4.) 200

5.) 4 605

6.) 3 50


Square Roots)


Level 6 Mastery B

Name:

1.) 28

2.) 63

3.) 80

4.) 245

5.) 3 363

6.) 2 405


Captain

(Mixed-Up)


Level 7 Practice

Name:

1.)

11!

2.)

25! + 4!

3.)

8!×2!

4.) 81

5.) 225

6.) 1000!

7.)

−3 !

8.)

−2 !×4!

9.) 20! ÷ −4 !

10.)


11.)

Fill in the statement with “>” or “<” 5.9 ____ 39

12.)

Fill in the statement with “>” or “<” 99____ 11

13.)

34

!

14.)

27

!

−314

!

15.)

15

!

×53

!

16.)

147

17.)

175

18.)

3 98


Captain

(Mixed-Up)


Level 7 Mastery A

Name:

1.) 2! + 6!

2.) 256

3.) −3 !×2!

4.) Fill in the statement with “>” or “<” 2.9 ____ 10

5.) 32

!

−12

!

6.) 243

Captain

(Mixed-Up)


Level 7 Mastery B

Name:

1.) 5! + 2!

2.) 169

3.) −9 ! ÷ 3!

4.) Fill in the statement with “>” or “<” 189 ____ 15.2

5.) 54

!

+12

!

6.) 162


Major

(Challenging)


Level 8 Practice

Name:

Simplify the expressions.

1.)

5!

2.)

𝑥!

3.)

9!

4.)

6!!

5.)

𝑚!!

6.)

4𝑛!

Solve for the unknowns.

7.)

2! = 16

8.)

3! = 27

9.)

2×4! = 32

10.) 5!!! = 25

11.) 9𝑦 = 81

12.) 3 𝑧 = 21


Major

(Challenging)


Level 8 Mastery A

Name:

1.)

Simplify 11!

2.)

Simplify 𝑥!𝑦!!

3.)

Solve 9! = 81.

4.)

Solve 6 𝑦 = 96.

Major

(Challenging)


Level 8 Mastery B

Name:

1.)

Simplify 13!

2.)

Simplify 𝑚!𝑛!!

3.)

Solve 4! = 64.

4.)

Solve 3 𝑦 = 15.


Colonel (Word)


Level 9 Practice

Name:

1.) Alex can read 3! pages of books per day. How many pages can he read in 4! days?

2.) There are 2 boxes of apples. There are 5! apples in the first box and 2! apples in the second box. How many apples are there in total?

3.) A bus travel 8! miles in 2! hours. What is the distance it traveled per hour?

4.) A warehouse can fit 12! crates. There are 9! crates in the warehouse. How many more crates can be fit in the warehouse?

5.) A web site is getting 6! visitors in 2! minutes. What is the average visitors per minute?

6.) Write the expression (with exponents) of the volume of a cube with length, width and height of 8cm. Evaluate the expression.


Colonel (Word)


Level 9 Mastery A

Name:

1.) A store has 10! boxes of crackers. In each of the box, there are 2! packs of crackers. How many packs of crackers in total do they have in store?

2.) A newly invented electric vehicle can travel up to 5! km after it is fully charged. After the initial charge, the car travels for 3! km. What is the distance it can travel before the next charge?

3.) Maggie has a piece of construction paper in square shape with width of 6 inches and she wants to cut out a smaller square with the width of 4 inches. Write the expression (with exponents) to show the area of paper left after she cut out the smaller square. Evaluate the expression.

Colonel (Word)


Level 9 Mastery B

Name:

1.) A computer can finishes 10! calculations per second. How many calculations can it complete in 3! seconds?

2.) A total of 8! gallons of water is to be stored in 4! of containers. How much water will be store in each container?

3.) Emma is going to paint 5 square shapes on a wall. If the length of each of the squares is 2 feet, write the expression (with exponents) to show the total area she needs to paint. Evaluate the expression.


General (Teacher)

EXPONENTS & ROOTS BOOT CAMP Level 10

Congratulations! You have successfully mastered how to compute with exponents and roots. Given your acumen for this particular skill you have been promoted to the post of General. A General is an individual who is responsible for leading a number of people. They must be a role model, leader and teacher. You now have the opportunity to impact an individual in a very meaningful way. Using exponents and roots is a backbone of high school and college mathematics and if you are able to help a classmates master this skill, you will be empowering their math skills.

You are now working collaboratively the only Exponent and Root Boot Camp Five-Star General, your teacher. Good luck to you!


Decimals

BOOT CAMP ANSWER GUIDE

Pre-Test

1.) 49 7.) 64 13.) −127

2.) 89 8.) -‐40 14.) −137500

3.) 144 9.) −95

15.) 147256

4.) 11 10.) 11 and 12 16.) 5 3 5.) 14 11.) > 17.) 4 2 6.) 5 12.) < 18.) 10 2

Level Practice Mastery A Mastery B

1

1 9 2 8 3 16 4 6 5 38 6 17 7 55 8 54 9 968 10 100 11 128 12 8 13 4 14 196 15 64

1 27 2 41 3 40 4 144 5 8 6 216

1 128 2 113 3 198 4 512 5 125 6 225


2

1 4 2 11 3 1 4 3 5 18 6 10 7 7 8 6 9 5 10 0 11 8 12 14 13 4 14 2 15 6

1 9 2 12 3 16 4 20 5 1 6 5

1 6 2 10 3 14 4 19 5 9 6 7

3

1 -‐1 2 4 3 -‐27 4 20 5 -‐76 6 -‐11 7 -‐54 8 0 9 -‐96 10 392 11 36 12 9

13 1252

14 64 15 81

1 25 2 -‐64 3 -‐11 4 -‐9 5 3969 6 -‐8

1 49 2 -‐125 3 41 4 76 5 -‐200 6 8

4

1 1 and 2 2 4 and 5 3 7 and 8 4 7 and 8 5 9 and 10 6 11 and 12 7 13 and 14 8 14 and 15 9 15 and 16 10 < 11 > 12 < 13 < 14 < 15 <

1 3 and 4 2 5 and 6 3 6 and 7 4 > 5 < 6 <

1 5 and 6 2 7 and 8 3 10 and 11 4 < 5 < 6 <


5

1 19

2 −132

3 8125

4 334

5 3316

6 69125

7 319

8 3581216

9 1332

10 196

11 1144

12 120

13 −1242

14 320

15 1343

1 425

2 916

3 718

4 − !"!"

5 −827

6 −349

1 949

2 −827

3 25716

4 −57200

5 49

6 −452

6

1 3 3 2 6 2 3 3 2 4 5 3 5 7 2 6 6 3 7 10 3 8 8 3 9 4 5 10 7 5 11 8 7 12 27 6 13 18 7 14 18 3 15 75 2

1 3 5 2 8 2 3 7 2 4 10 2 5 44 5 6 15 2

1 2 7 2 3 7 3 4 5 4 7 5 5 33 3 6 18 5


7

1 121 2 41 3 256 4 9 5 15 6 10 7 -‐27 8 -‐2048 9 25 10 5 and 6 11 < 12 <

13 2764

14 128

15 145

16 7 3 17 5 7 18 21 2

1 44 2 16 3 -‐216 4 <

5 258

6 9 3

1 33 2 13 3 9 4 <

5 2916

6 9 2

8

1 5 2 𝑥 3 81 4 6 5 𝑚 6 2𝑛 7 4 8 3 9 2 10 1 11 729 12 49

1 11 2 𝑥𝑦 3 2 4 256

1 13 2 𝑚!𝑛 3 3 4 25

9

1 576 2 41 3 64 4 63 5 162

6 8! cm3

512 𝑐𝑚!

1 16000 2 2396 km

3 6! − 4! sq. in ch 20 sq. inch

1 27000 2 16 gallons

3 5×2! sq. ft. 20 sq. ft.

Documents

Boot Camp - Exponents & Roots · BOOT CAMP Level 2 Mastery A Name: 1.) 81 2.) 144 3.) 256 4.) 400 5.) !!1 6.) 125 Specialist (Perfect Squares & Perfect CuBes) EXPONENTS & ROOTS BOOT