grade 8 calendar and summer packet 2018-2019 · 2019-05-23 · fractions packet created by mlc @...
TRANSCRIPT
East Orange School District Division of Curriculum Services
GRADE 8 CALENDAR and SUMMER PACKET
2018-2019
East Orange School District Division of Curriculum Services
Dear students, We are excited that you have successfully completed your grade 7 mathematics course.
In order to continue your learning cycle through the summer, you will find a July and August calendar, with an accompanying summer packet of exciting math problems for your enjoyment over the summer. If followed correctly, you will learn more about growth mindset in mathematics, your learning style, how to manage your time, test taking strategies, and prerequisite skills that you should master before September. The purpose of the summer packet is to review the topics you have already mastered in math and to make sure that you are prepared for the class you are about to enter.
The packet contains a brief summary and explanation of the topics so you don’t need to worry if you don’t have your math book. You will find many sample problems, which will be great practice for you before you try your own problems. There are also video links to websites that can explain the material even better. The explanations are divided into sections to match the sample problems so you should be able to reference the examples easily.
It is mandatory that you complete this packet before the school year starts so that you can be sure that you are ready. The answers will be available to you when you return back to school.
East Orange School District Division of Curriculum Services
Directions:
➢ Complete this entire packet by writing your answers in the spaces provided. If needed, create a personal and fun math journal by stapling several pieces of paper together or use a notebook or binder with paper. Be creative and decorate the cover to show math in your world.
➢ Each problem should have a clear and complete answer for all problems, showing all mathematical work.
➢ Be neat and organized. ➢ Be ready to submit your work during the first week of school.
Note: Playing board and card games are a good way to reinforce basic computation skills and mathematical reasoning. Try to play board and card games at least once a week. Some suggested games to play are: Monopoly, Chess, War, Battleship, Mancala, Dominoes, Phase 10, Yahtzee, 24 Challenge, Sudoku, Connect Four, and Risk.
LOOKING FOR HELP?
TRY THESE INTERNET RESOURCES.
www.purplemath.com www.youtube.com/mathdoris
www.khanacademy.org www.ixl.com
East Orange School District Division of Curriculum Services
July 2018 Topic Assignment Website
Week 1
Day 1
Growth Mindset
Watch “Four Boosting Messages from Jo
Boaler and her Students”
https://www.youcubed.org/resources/four-boosting-messages-jo-students/
Watch “Tour of Mathematical Connections”
https://www.youcubed.org/resources/tour-mathematical-connections/
Learning Styles Discover your learning style
http://www.educationplanner.org/students/self-assessments/learning-
styles.shtml
Click on “Answer 20 Questions”
Day 2 Time Management Learn how to manage your time.
https://bigfuture.collegeboard.org/get-started/inside-the-classroom/8-ways-
to-take-control-of-your-timehttp://guides.frederick.edu/studys
kills
Day 3
Reducing Math Anxiety
Learn how to reduce your math anxiety (if
any)
http://www.radford.edu/content/LARC/home/learning-guides/math/math-
anxiety.html
Day 4 Growth Mindset Watch “Rethinking Giftedness”
https://www.youcubed.org/rethinking-giftedness-film/
Day 5 Tips for Studying
and Doing Your Homework
Watch a video on the best ways to study and
complete HW https://youtu.be/bR8i4y5VlaQ
Week 2 Day 1 Order of
Operations Complete problems 1-25 https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-
East Orange School District Division of Curriculum Services
algebra-order-of-operations/v/introduction-to-order-of-
operations
Day 2 Operations with Signed Numbers
Complete problems 1-12 for Adding &
Subtracting Signed Numbers
AND
Complete problems 1-12 Multiplying and Dividing
Signed Numbers
https://www.khanacademy.org/math/in-sixth-grade-math/integers-
india/subtraction-integers-number-line/v/adding-subtracting-negative-
numbers
https://www.khanacademy.org/math/arithmetic-home/negative-numbers/mult-
divide-negatives/v/multiplying-and-dividing-negative-numbers
Day 3 Rounding Numbers Complete problems 1-10
https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-
rounding-decimals/v/rounding-decimals
Day 4 Multiplying and Dividing Fractions
Complete problems 1-18
Complete problems 1-15
https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-
review-multiply-fractions/v/multiplying-fractions
https://www.khanacademy.org/math/ari
thmetic/fraction-arithmetic/arith-review-dividing-fractions/v/dividing-
fractions-example
Day 5 TAKE A BREAK
Play a Math Game https://www.youcubed.org/resource/apps-games/
Week 3 Day 1 Adding and Subtracting Fractions
Complete problems 1-27 https://www.khanacademy.org/math/ari
thmetic/fraction-arithmetic/arith-review-adding-subtracting-
East Orange School District Division of Curriculum Services
frac/v/adding-fractions-with-like-denominators
https://www.khanacademy.org/math/in-sixth-grade-math/fractions-1/addition-
subtraction-fractions/v/adding-fractions-with-unlike-denominators
https://www.khanacademy.org/math
/arithmetic/fraction-arithmetic/arith-review-add-sub-
fractions/v/subtracting-small-fractions-with-unlike-denominators
Day 2 Evaluating
Expressions Complete problems 1-16
https://www.khanacademy.org/math/algebra/introduction-to-
algebra/alg1-substitution/v/evaluating-
expressions-in-two-variables
Day 3 Combining Like Terms Complete problems 1-12
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equivalent-
exp/cc-6th-combining-like-terms/v/combining-like-terms-1
https://www.khanacademy.org/math/cc-
sixth-grade-math/cc-6th-equivalent-exp/cc-6th-combining-like-
terms/v/combining-like-terms-2
Day 4 Graphing Complete problems 1-20
https://www.khanacademy.org/math/basic-geo/basic-geo-coord-plane/coordinate-
plane-4-quad/v/plot-ordered-pairs
https://www.khanacademy.org/math/8th-engage-ny/engage-8th-module-4/8th-
East Orange School District Division of Curriculum Services
module-4-topic-b/v/graphs-of-linear-equations
Day 5 TAKE A BREAK
Play a Math Game https://www.youcubed.org/resource/apps-games/
Week 4
Day 1 Solving Equations Complete problems 1-24
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-add-sub-equations/v/adding-and-subtracting-the-same-thing-from-
both-sides
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-mult-div-equations/v/solving-
one-step-equations-2
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-mult-div-equations/v/simple-
equations
Day 2 Inequalities Complete problems 1-4 AND 1-6
https://www.khanacademy.org/math/algebra/one-variable-linear-
inequalities/alg1-inequalities/v/plotting-inequalities-on-a-number-line
Day 3 Algebraic
Translations Complete problems 1-10
AND 1-5
https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-
writing-expressions/v/writing-expressions-with-variables-examples
Day 4 Word Problems Complete problems 1-10
https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-
expressions/pre-algebra-alg-expression-word-problems/v/writing-
East Orange School District Division of Curriculum Services
basic-expressions-from-word-problems-examples
https://www.khanacademy.org/math/pr
e-algebra/pre-algebra-equations-expressions/pre-algebra-alg-
expression-word-problems/v/more-fancy-expressions-from-word-problems
Day 5 TAKE A BREAK
Play a Math Game https://www.youcubed.org/resource/apps-games/
Week 5
Day 1 Father’s Day Breakfast Complete the full Activity
Day 2 For Three! Complete the full Activity
Day 3 Sequel Complete the full Activity
East Orange School District Division of Curriculum Services
August 2018 Topic Assignment Website
Week 1
Day 1 Percent and
decimal Complete problems 1-8
Sewing Activity
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/modal/v/converting-fractions-
to-decimals-example https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-decimals-to-fractions/v/converting-
fractions-to-decimals-example https://www.khanacademy.org/math/ari
thmetic-home/arith-review-decimals/decimals-to-
fractions/v/converting-fractions-to-decimals
Day 2 Decimal and Percent
Complete problems 9-16 Percents Cards
Week 2
Day 1
Percent and Fraction
Fraction and Percent
Complete problems 17-26
Complete problems 27-34
Day 2 Proportions Complete problems 1-22
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-
rates/pre-algebra-write-and-solve-proportions/v/find-an-unknown-in-a-
proportion
Day 3 Proportion word
problems Complete problems 1-8
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-
rates/pre-algebra-write-and-solve-proportions/v/writing-proportions
Day 4
Day 5 TAKE A BREAK
Play a Math Game https://www.mathgames.com/play/mathleaper.html
Week 3 Day 1 Multiplying Complete problems 1-26 https://www.khanacademy.org/math/p
East Orange School District Division of Curriculum Services
Exponents re-algebra/pre-algebra-exponents-radicals/pre-algebra-
exponents/v/introduction-to-exponents
Day 2 Dividing
Exponents Complete problems 1-20
https://www.khanacademy.org/math/algebra/rational-exponents-and-
radicals/alg1-exp-prop-review/v/multiplying-and-dividing-
powers-with-integer-exponents
Day 3 Powers of Exponents Complete problems 1-18
https://www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-rules-
part-1
Day 4 Scientific Notation Complete problems 1-32
https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-scientific-notation/v/scientific-notation-i
Day 5 TAKE A BREAK
Play a Math Game https://www.mathgames.com/grade8
Week 4
Day 1 Area of quadrilaterals Complete problems 1-14
https://www.khanacademy.org/math/basic-geo/basic-geometry-shapes/basic-geo-quadrilaterals/v/quadrilateral-overview
https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-area/v/perimeter-and-area-basics
Day 2 One step word problems Complete problems 1-8
https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-
expressions/pre-algebra-alg-
East Orange School District Division of Curriculum Services
expression-word-problems/v/writing-basic-expressions-from-word-
problems-examples
Day 3
Two step
equations with integers
Complete problems 1-24
https://www.khanacademy.org/math/algebra/one-variable-linear-
equations/alg1-two-steps-equations-intro/v/why-we-do-the-same-thing-to-
both-sides-two-step-equations
Day 4 Two step
equations with decimals
Complete problems 1-18
https://www.khanacademy.org/math/algebra/one-variable-linear-
equations/alg1-two-steps-equations-intro/v/why-we-do-the-same-thing-to-
both-sides-two-step-equations
Day 5
TAKE A BREAK Play a Math Game
https://www.mathgames.com/play/kingofmath.html
Week 5
Day 1 2 step word
problems Complete problems 1-8
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-linear-eq-word-probs/v/basic-linear-equation-word-problem
Day 2 Multi-step equations
Complete problems 1-20
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations-intro/v/solving-equations-1
Day 3 Get Ready for School!
Fractions Packet Created by MLC @ 2003 page 18 of 42
7
1
1
1
1
8
1
10
Multiplication and Division of Fractions Worksheets When multiplying fractions, simply multiply the numerators (top number of the fractions) together and multiply the denominators (bottom number of the fractions) together. It is good practice to check to see if any of the numbers can cancel. Canceling is done when the numerator and denominator can be divided evenly by the same number. Note: canceling can happen top-to-bottom and/or diagonally but never across.
Ex. 1: 62
32
21 this product can be canceled. Divide the numbers in the
fraction by 2 to get the canceled answer 31
2622 .
The fractions in Ex. 1 can cancel before they are multiplied. Ex. 1:
31
32
21
The 2’s cancel by dividing by 2. Cross them out and place 1’s close by. Now multiply the top numbers together, then the bottom numbers. The product is the final answer.
Ex. 2: 1000100
4035 can be rewritten as
807
101
87
1000100
4035
Cancel by dividing by 5. Then cancel by dividing by 100. Multiply and get the product.
Ex. 3: 31
3 can be written like. 111
31
13 Cancel by dividing by 3. Finally,
multiply to find the product.
Fractions Packet Created by MLC @ 2003 page 19 of 42
Exercise 1 (answers on page 40) Multiply these fractions. Cancel and simplify if possible.
1. 32
81
2. 54
21 3.
1110
53
4. 43
98
5. 212
107 6.
75
43
7. 87
95
8. 31
6 9. 995
10. 21
10
11. 1231 12.
108
1615
13. 1312
87
14. 31
96 15.
43
105
16. 2423
1716 17.
3020
165 18.
10050
109
Fractions Packet Created by MLC @ 2003 page 21 of 42
2
1
Dividing Fractions When dividing fractions, invert (turn over) the fraction to the right of the (“divide by”) symbol. Cancel (if possible) then multiply.
Ex. 1: 32
34
21
43
21
Ex. 2: 253
51
53
15
53
553
Exercise 3 (answers on page 40) Divide these fractions. Cancel if necessary and simplify
1. 65
32
2. 21
109 3.
41
43
4. 227
119
5. 61
52 6.
43
21
7. 41
87
8. 61
51 9.
1615
85
10. 85
1615
11. 43
127 12.
89
98
13. 83
2 14. 21
6 15. 443
Fractions Packet Created by MLC @ 2003 page 32 of 42
Adding and Subtracting of Fractions When adding or subtracting, there must be a common denominator. If the denominators are different:
(a) Write the problem vertically (top to bottom) (b) Find the LCD (c) Change to equivalent fractions (by building) (d) Add or subtract the numerators (leave the denominators the same) (e) Simplify and reduce, if possible
Ex. 1: 54
51
53
The denominators are the same. Add the numerators, keep
the denominator. This fraction cannot be simplified or reduced.
Ex. 2: 41
21 ?
4341
41
42
21
Ex. 3: 31
85 ?
247
248
31
2415
85
Ex. 4: 43
32 ?
125
11217129
43
128
32
Ex. 5: 31
1511 ?
52
156
155
31
1511
1511
The denominators are different numbers.
Therefore, change to equivalent fractions.
See page 25
Simplifying and reducing completes addition and subtraction problems. See page 25 & 27
Fractions Packet Created by MLC @ 2003 page 33 of 42
Exercise 4 (answers on page 41) Add or subtract the following fractions. Simplify and reduce when possible.
1) 73
72
2) 141
149 3)
63
61
4) 41
53
5) 21
32 6)
21
54
7) 63
42
8) 83
65 9)
32
97
10) 21
43
11) 31
53 12)
32
87
13) 41
125
14) 21
119 15)
65
1211
16) 31
21
17) 41
65 18)
31
109
19) 51
208
20) 61
1514 21)
83
74
22) 21
126
23) 32
98 24)
85
1612
25) 61
73 26)
106
54 27)
32
132
Father’s Day Breakfast Surprise
This Sunday is Father’s Day. I looked up a recipe for something that I’m sure that my dad will love and I’m going to surprise him. I already bought the fresh blueberries and I’m going to make blueberry muffins. This is going to be great. But … I couldn’t find any measuring cups in the kitchen. I could only find a small cup that was marked ¼ cup. 1. Here is my recipe. Would you please help me figure out how many of these little ¼ cups to fill to make these muffins? Ingredients • 2 cups fresh blueberries • 2 and 1/2 cups all-purpose flour • 4 teaspoons baking powder • 1 teaspoon salt • 1/4 cup margarine • 1-1/2 cups white sugar • 2 eggs • 1 teaspoon vanilla extract • 1 cup milk Cooking Instructions 1. Preheat oven to 375 degrees F (190 degrees C). Grease 12 muffins tins, or line
cups with paper liners. 2. Sprinkle 1/4 cup flour over blueberries, and stir to coat berries thoroughly. 3. In a small bowl, whisk together 2 cups flour, baking powder and salt. 4. In a large bowl, cream margarine, and gradually mix in sugar. Beat eggs, and stir
into creamed mixture along with vanilla. Stir in milk alternately with flour mixture, mixing well after each addition. Fold in berries. Fill muffin cups 2/3 full with batter.
Bake for 25 minutes. http://recipes.kaboose.com/blueberry-muffins.html
Ingredients* Number*of*¼*cups*or*fraction*of*¼*cups*flour* *blueberries* *baking*powder* *salt* *margarine* *white*sugar* *vanilla*extract* *milk* *eggs* Don’t*have*to*measure*in*¼*cups*
*Hint:**16*Tablespoons*=*1*cup** 3*teaspoons*=*1*Tablespoon***
2.*How*many*¼*cups*would*I*need*to*use*for*any*number*(n)*of*cups*of*blueberries?***********3.**How*would*your*answers*(number*of*¼*cups*needed*for*each*item)*in*the*table*change*if*you*only*had*a*½*cup*measuring*cup?**********4.**How*would*your*answers*(number*of*¼*cups*needed*for*each*item)*in*the*table*change*if*you*only*had*a*1/8*cup*measuring*cup?************************
Brought*to*you*by*www.YUMMYMATH.com*
ForThree!
1.TheNBAgamehaschangeddramaticallyoverthepastseveralyears.Teamsareshootingmorethreepointshotsandatahigherpercentagethaneverbefore.TheClevelandCaviliersandGoldenStateWarriorshavemetforfourstraightyearsintheNBAFinalsandbothteamshavereliedheavilyonthethreetogetthemthereanddominatetheleague.Takealookatthegraphbelowandmakeatleasttwomathematicalobservations.
file://localhost/FromtheWallStreetJournal-https/::www.wsj.com:articles:the-first-shots-of-the-nbas-3-point-revolution-1523542076
2.Areallshotscreatedequal?Onthefollowingpageisascalemodelofabasketballcourt.Thethreepointarcisthegiant,almosthalfciclesurroundingthebasket.Useyourgeometyskillstoapproximatethedistancefromplacesalongthethreepointline.Besuretolabelandgivethedistanceinfeetforeachspotonthethreepointlinethatyoufound.Areallshotsalongthethreepointarcthesamedistance?Ifnot,wherewouldyoufindtheshortestthreepointshots?
3.Thepicturebelowshowsthedifferentzonesonabasketballcourt.Herearethefieldgoalpercentagesforeachthreepointzone.1Howdotheshootingpercentagescomparewiththecourtdistancesforeachtypeofshot?Consideringthedistancesanddatadoesthismakesense?
http://82games.com/locations.htm
4.Shouldteamsshoot3’sor2’s?Asof2016teamsweremaking35%ofthreepointshotswhilemaking49%oftwopointshots.2Withthosepercentagesandshotvalues,whichshouldgetyoumorepointsovertime–atwoorathree?Defendyourreasoning.
5.StephCurryhasmade43.6%ofhis3’soverhiscareer(asof2018).ShaquilleO’Nealmade58.3%ofhis2’soverhiscareer.3Whichplayerscoresmoreonaverageperpossession?
BroughttoyoubyYummymath.com
1http://82games.com/locations.htm2http://www.businessinsider.com/nba-three-point-shooting-2016-33https://www.basketball-reference.com/
1and5corner3’s–42.5%2and4wing3’s–34.9%3straightup3’s–38.8%
SequelMoreandmorenewmoviestodayaresequelstoearlier,successfulmovies.Aresequelsasgoodastheoriginalfilm?Whatkindoffactorsordatawouldyouconsidertoanswerthisquestion?
ThetablebelowgivestheMetacritic1scorefromarandomsampleofmoviesandtheirsequels.
MovieSeries Original SequelToyStory&ToyStory2 92 88SpiderMan&SpiderMan2 73 83MonstersInc.&MonstersU 78 65NightattheMuseum&NightattheMuseum:BattlefortheSmithsonian 48 42Shrek&Shrek2 84 75StarWars&EmpireStrikesBack 91 78PiratesoftheCaribbean:TheCurseoftheBlackPearl&PiratesoftheCaribbean:DeadMan'sChest 63 53
XMEN&X2 64 68HarryPotterandthePhilosopher'sStone&HarryPotterandthePrisonerofAzkaban(1st&3rdPotterMovies) 64 82
PrincessDiaries&PrincessDiaries2 52 43HowtoTrainYourDragon&HowtoTrainYourDragon2 74 76HungerGames&HungerGamesCatchingFire 67 75
1.Use measuresofcentraltendencyandvariability(mean,median,mode,range,MADorinterquartilerange)tocomparetheMetacriticscoresoftheoriginalsandthesequels.
2.Createplotstocomparethetwodatasets,considerahistogram,boxandwhiskerplotorothers.
3.Useyourdataanalysistomakeacasefortheoriginalmoviesbeingbetter.
4.Useyourdataanalysistomakeacaseforthesequelsbeingbetter.
5.Howcanweimproveonourdataanalysisoforiginalsmoviesandtheirsequels?Howcanwecomparethemwithmorecertainty?1Metacriticisawebsitethataggregatesreviewsofmovies,games,musicandotherentertainments.
BroughttoyoubyYummymath.com
East Orange School District Division of Curriculum Services
Grade 6 –2009 Copyright © 2009 by Mathematics Assessment Resource Service. All rights reserved.
4
Sewing
This problem gives you the chance to: • use mathematics in a real life situation Amy is sewing some pants for herself. This is the rule for how much fabric she needs to buy. • Measure from your waist to the finished length of the pants • Double this measurement • Add 8 inches 1. Amy’s measurement from her waist to the finished length of the pants is 35 inches. How many inches of fabric does she need? _____________________________ 2. Fabric is actually sold not in inches, but in yards. Each yard is 36 inches. The smallest amount you can buy is a quarter of a yard. So, if you want one yard and 25 inches you have to buy one and three quarter yards. How much fabric must Amy buy for the pants? _____________________________ 3. Chris is also making some pants for herself. She buys fabric, thread, buttons and a zipper. Complete Chris’s bill
$
21/4 yards of fabric at $5 a yard
2 spools thread at 35¢ a spool
3 buttons at 25¢ each
Zipper 60¢
Total before sales tax
Sales tax at 8% (round this to nearest cent)
Total
10
East Orange School District Division of Curriculum Services
Grade 6 – 2008 Copyright © 2008 by Mathematics Assessment Resource Service
All rights reserved.
47
Percent Cards
This problem gives you the chance to: • relate fractions, decimals and percents
Mrs. Lopez makes sets of cards for her math class.
All the cards in a set have the same value.
1. Complete these sets of cards.
!
3
4
!
0.75
!
75
100
!
75%
Simple
fraction
Decimal Percent
fraction Percent
Set A
!
2
5
!
40
100
!
40%
!
65%
!
3
8
!
0.65
Set B
Set C
Set D
Grade 6 – 2008 Copyright © 2008 by Mathematics Assessment Resource Service
All rights reserved.
48
2. Show
!
2
5, 65% and
!
3
8 on the number line below.
0 100%
!
3
4
7
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
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Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Exponents and Multiplication
Simplify. Your answer should contain only positive exponents.
1)
42 ⋅
42
2)
4 ⋅
42
3)
32 ⋅
32
4)
2 ⋅
22 ⋅
22
5)
2
n4 ⋅
5
n4
6)
6
r ⋅
5
r2
7)
2
n4 ⋅
6
n4
8)
6
k2 ⋅
k
9)
5
b2 ⋅ 8
b 10)
4
x2 ⋅ 3
x
11)
6
x ⋅
2
x2
12)
6
x ⋅
6
x3
-1-
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13)
7
v3 ⋅
10
u3
v5 ⋅
8
u
v3
14)
9
x
y2 ⋅
9
x5
y2
15)
6
m3
n3 ⋅
8
m2
n3
16)
6
x2 ⋅
6
x3
y4
17)
7
u2
v5 ⋅
9
u
v3
18)
uv ⋅
4
u
v5
19)
10
x
y3 ⋅
8
x5
y3
20)
3
u4
v5 ⋅
7
u2
v3
21)
(
2
x2)2
22)
(
p4)4
23)
(
k3)4
24)
(7
k)2
25)
(
x2)3
26)
(
2
b2)4
-2-
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Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Exponents and Division
Simplify. Your answer should contain only positive exponents.
1)
54
5
2)
3
33
3)
22
23
4)
24
22
5)
3
r3
2
r6)
7
k2
4
k3
7)
10
p4
6
p8)
3
b
10
b3
9)
8
m3
10
m3
10)
7
n3
2
n5
-1-
©p a2q0k1F20 AKSugtSap FSwoRf8tNw2aJr7eN bLfLLCl.3 b UAglslU mreifgdhutPs8 5rPejs8efrovme3dt.I X kMXaudsez nwXiwt2hh jI1n9fbi9nMigtoeR TP1r6eY-yApljg1e4bqrtaw.R Worksheet by Kuta Software LLC
11)
2
n2
n12)
8
x3
10
x5
13)
12
x3
9
y8
14)
14
x4
y7
6
x5
y4
15)
11
u4
17
u7
v9
16)
4
y4
14
y
x8
17)
12
y
x4
10
y
x8
18)
18
x8
y8
10
x3
19)
5
n8
20
n8
20)
16
y
x4
9
x8
y2
-2-
©T b2q0u1B22 fKguvtvaJ 5SJozfFt4wRadrue3 lLDLxCC.U p rADlyl2 xreiEgShOtPso trveGsneorSvqeTdw.K G FM6akdgeP dwFiqtLh5 qIenYfHiLn6iftAew hPTrFeq-LAvlSgReybmrmaS.R Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Powers of Products and Quotients
Simplify. Your answer should contain only positive exponents.
1)
(
3
a2)3
2)
(
2
n4)4
3)
(
3
x4)4
4)
(
6
b2)2
5)
(
7
y4)2
6)
(
3
a
b4)4
7)
(
2
x4
y4)3
8)
(
5
m
n3)3
9)
(
x2
y2)2
10)
(
6
y
x4)2
11)
(
u4
v3)2
12)
(
2
x4
y4)4
13)
(
3
x2 ⋅
2
x2)2
14)
(
2
p3 ⋅ 2
p)2
15)
(
4
n3 ⋅
n2)2
16)
(
3
x ⋅ 2
x)2
17)
(
4
x4 ⋅
x4)3
18)
(
4
n4 ⋅
n)2
©V E2R0h1E2M vK0u4tAaM eS3oyfutmwJaMrSeu vLuLCCm.n z CAtlslf PrriPgNhFtust Crkens1eTrHvqeHdO.4 N XMQaddiec TwmiGt2hi lI7nOfRi3nxiDtEeW xAql1ghe8barOar g1k.O Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________Writing in Scientific Notation
Write each number in scientific notation.
1) 0.000006 2) 5400000
3) 60 4) 0.009
5) 6.7 6) 0.0000002
7) 2000000 8)
71 ×
103
9) 48900 10) 0.0000009
11)
0.63 ×
101
12)
33 ×
10−3
13) 0.000216 14) 0.0042
15)
0.15 ×
10−2 16) 4.8
-1-
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Write each number in standard notation.
17)
0.9 ×
10−1
18)
2 ×
10−1
19)
2 ×
105
20)
804 ×
102
21)
2.66 ×
104
22)
1.5 ×
10−2
23)
7.75 ×
10−1
24)
8.3 ×
107
25)
9.5 ×
107
26)
1.71 ×
107
27)
0.9 ×
10−3
28)
38 ×
102
29)
7.5 ×
10−5
30)
4 ×
100
31)
8.4 ×
105
32)
4 ×
10−5
-2-
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Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Area of Squares, Rectangles, and Parallelograms
Find the area of each.
1) 2 m
7.7 m
2)
1 in
1 in
3) 6.9 in
2.4 in
4) 6 in
8 in
5) 1.5 yd
4 yd
6)
4 in
5.9 in
7)
18.7 yd
6 yd
18.7 yd
8)
5.8 m
6 m
5.8 m5 m
6 m
-1-
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9)
3 m 6.6 m
10)
14.9 ft15.1 ft
14.9 ft
7 ft
15.1 ft
11)
10.2 cm
14.2 cm
10.2 cm
12)
18.8 m
15.2 m20 m
13)
18 in
19 in
18 in
19 in
14)
18 mi 18 mi
18 mi
-2-
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
©h X230q1q2V WKhuKtDaJ vSGoPfvtIwZanroeJ sLdLnCy.o W KAHlklX zrUiigJhTtgsz ErteusveerXvIeIdX.i s sMKaTd0eq 4wQi0tLh2 eI0n4f6i4ncirt6el SPkrfen-WAfl1g1eUbWrhaX.P Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Two-Step Equations With Decimals
Solve each equation.
1)
m
2.8 − 4.9 = −7.11
2)
0.4
x + 3.9 = 5.78
3)
−10.5 +
m
11.57 = −2.748
4)
9.2
r + 5.514 = 158.234
5)
v
10.44 − 2.9 = −4.422
6)
−5.4 −
7.8
x = −78.408
7)
k − 2.6
5.2 = −0.418
8)
−8.38
v + 10.71 = 131.382
-1-
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9)
2.8 +
x
3.1 = 2.709 10)
n − 12.9
6.1 = −0.377
11)
−7.3 +
r
9.2 = −0.739 12)
−13.3 +
k
11.796 = −0.296
13)
12.1 +
a
4.9 = 7.071 14)
−13.9 +
b
12.8 = −13.306
15)
12.84 +
x
2.89 = −2.166
16)
3.649 +
12.3
v = 146.329
17)
−3.8 −
13.4
p = −460.60618)
r − 8.7
3.6 = 3.722
-2-
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services
East Orange School District Division of Curriculum Services