Boot Camp - Exponents & Roots · BOOT CAMP Level 2 Mastery A Name: 1.) 81 2.) 144 3.) 256 4.) 400...
Transcript of Boot Camp - Exponents & Roots · BOOT CAMP Level 2 Mastery A Name: 1.) 81 2.) 144 3.) 256 4.) 400...
© 21st Century Math Projects
© 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.
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EXPONENTS AND ROOTS
BOOT CAMP Name_____________________
INSIGNIA RANK MASTERY !
Private
Specialist
Corporal
Sergeant
Staff Sergeant
Lieutenant
Captain
Major
Colonel
General
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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
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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 !
© 21st Century Math Projects
Private (Evaluate Exponent
Expressions)
EXPONENTS & ROOTS BOOT CAMP
Level 1 Mastery A
Name:
1.)
3!
2.)
2! + 5!
3.)
11! − 3!
4.)
3!×4!
5.)
10! ÷ 5!
6.)
37− 31 !
Private (Evaluate Exponent
Expressions)
EXPONENTS & ROOTS BOOT CAMP
Level 1 Mastery B
Name:
1.)
2!
2.)
4! + 7!
3.)
15! − 3!
4.)
2!×4!
5.)
15! ÷ 3!
6.)
19− 4 !
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Specialist (Perfect
Squares & Perfect CuBes)
EXPONENTS & ROOTS BOOT CAMP
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!
© 21st Century Math Projects
Specialist
(Perfect Squares & Perfect CuBes)
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 CAMP
Level 2 Mastery B
Name:
1.) 36
2.) 100
3.) 196
4.) 361
5.) 729!
6.) 343!
© 21st Century Math Projects
Corporal (Integer Bases)
EXPONENTS & ROOTS BOOT CAMP
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 !
© 21st Century Math Projects
Corporal (Integer Bases)
EXPONENTS & ROOTS BOOT CAMP
Level 3 Mastery A
Name:
1.) −5 !
2.)
−4 !
3.)
−2 ! + −3 !
4.)
−4 ! − −5 !
5.)
7!× −3 !
6.)
6! ÷ −3 !
Corporal (Integer Bases)
EXPONENTS & ROOTS BOOT CAMP
Level 3 Mastery B
Name:
1.) −7 !
2.)
−5 !
3.)
−5 ! + −4 !
4.)
−7 ! − −3 !
5.)
−2 !×5!
6.)
−8 ! ÷ 2!
© 21st Century Math Projects
Sergeant (Estimating
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
Level 4 Practice
Name:
1.)
Which two integers is 3 between?
2.)
Which two integers is 17 between?
3.)
Which two integers is 50 between?
4.) Which two integers is 60 between?
5.) Which two integers is 93 between?
6.) Which two integers is 133 between?
7.) Which two integers is 180 between?
8.) Which two integers is 221 between?
9.) Which two integers is 230 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
13.) Fill in the statement with “>” or “<” 26 ____ 7
14.) Fill in the statement with “>” or “<” 5 ____ 28
15.) Fill in the statement with “>” or “<” 32 ____ 7
© 21st Century Math Projects
Sergeant (Estimating
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
Level 4 Mastery A
Name:
1.)
Which two integers is 10 between?
2.)
Which two integers is 27 between?
3.)
Which two integers is 48 between?
4.) Fill in the statement with “>” or “<” 37 ____ 5
5.) Fill in the statement with “>” or “<” 7 ____ 80
6.) Fill in the statement with “>” or “<” 83 ____ 10.3
Sergeant (Estimating
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
Level 4 Mastery B
Name:
1.)
Which two integers is 33 between?
2.)
Which two integers is 58 between?
3.)
Which two integers is 102 between?
4.) Fill in the statement with “>” or “<” 114 ____ 13
5.) Fill in the statement with “>” or “<” 9 ____ 90
6.) Fill in the statement with “>” or “<” 123 ____ 14
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Staff Sergeant
(Fraction Bases)
EXPONENTS & ROOTS BOOT CAMP
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
!
© 21st Century Math Projects
Staff Sergeant
(Fraction Bases)
EXPONENTS & ROOTS BOOT CAMP
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)
EXPONENTS & ROOTS BOOT CAMP
Level 5 Mastery B
Name:
1.)
37
!
2.) −
23
!
3.)
14
!
+ 4!
4.) −12
!
−25
!
5.) 37
!
×149
!
6.) 65
!
÷ −25
!
© 21st Century Math Projects
Lieutenant (Simplifying
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
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
© 21st Century Math Projects
Lieutenant (Simplifying
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
Level 6 Mastery A
Name:
1.) 45
2.) 128
3.) 98
4.) 200
5.) 4 605
6.) 3 50
Lieutenant (Simplifying
Square Roots)
EXPONENTS & ROOTS BOOT CAMP
Level 6 Mastery B
Name:
1.) 28
2.) 63
3.) 80
4.) 245
5.) 3 363
6.) 2 405
© 21st Century Math Projects
Captain
(Mixed-Up)
EXPONENTS & ROOTS BOOT CAMP
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.)
Which two integers is 30 between?
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
© 21st Century Math Projects
Captain
(Mixed-Up)
EXPONENTS & ROOTS BOOT CAMP
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)
EXPONENTS & ROOTS BOOT CAMP
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
© 21st Century Math Projects
Major
(Challenging)
EXPONENTS & ROOTS BOOT CAMP
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
© 21st Century Math Projects
Major
(Challenging)
EXPONENTS & ROOTS BOOT CAMP
Level 8 Mastery A
Name:
1.)
Simplify 11!
2.)
Simplify 𝑥!𝑦!!
3.)
Solve 9! = 81.
4.)
Solve 6 𝑦 = 96.
Major
(Challenging)
EXPONENTS & ROOTS BOOT CAMP
Level 8 Mastery B
Name:
1.)
Simplify 13!
2.)
Simplify 𝑚!𝑛!!
3.)
Solve 4! = 64.
4.)
Solve 3 𝑦 = 15.
© 21st Century Math Projects
Colonel (Word)
EXPONENTS & ROOTS BOOT CAMP
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.
© 21st Century Math Projects
Colonel (Word)
EXPONENTS & ROOTS BOOT CAMP
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)
EXPONENTS & ROOTS BOOT CAMP
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.
© 21st Century Math Projects
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!
© 21st Century Math Projects
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
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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 <
© 21st Century Math Projects
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
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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.