Sponge Activity #1 for Mathematical Properties for UIL ...Sponge Activity #1 for Mathematical Properties for UIL Number Sense Lesson Goal: Students will learn to use the commutative,

SpongeActivity#1forMathematicalPropertiesforUILNumberSense

LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesinwaystosolvemathproblemsusingNumberSenseTests.Time:Nomorethan15minutes.Course:AlgebraI&AlgebraIITEKSAddressed:AlgebraI(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:

1. Pencil.2. Practiceproblems(attached)3. AnswerKey(attached)

Procedures:

ThisActivity(Includinggradingtime)shouldtakenolongerthan15minuteseitheratthebeginningorendoftheclassperiod.Ifthisworkistobegraded,giveextrapointsforspeed.

1. GivetheProblemWorksheettoeachStudent.2. TimetheStudentstakingtheWorksheet.(Nomorethan10min.)3. GradetheWorksheetpointingoutthehintsforeachproblem.

Lesson#1Workeachoftheseproblemsasquicklyaspossible.

Estimate#10toplusorminus10%.

AnswerstoLesson#1

1) Addbystartingontheleftandworkingtotheright.2) Multiplyingby11

a. Putazeroinfrontandinbackofthenumberb. (020090)c. Addpairsofdigitsstartingontheright.d. 0+9,9+0,0+0,0+2,2+0

3) Subtractwithborrowing.4) Dividingby25

a. 1/25=4/100b. Multiply2010by4c. MoveDecimalPlace2unitsleft.

5) Leave,Change,Flip

a.

€

35

x158

b. Cancelthe5’s

c.

€

31

x38

=98

6) MakeImproper

a.

€

4x2 23

= 4x83

=323

=10 23

7)

€

16% =16100

=425

8) OrderofOperationsa. 3+(4x5‐6)÷7b. 3+(20‐6)÷7c. 3+14÷7d. 3+2e. 5

9) Memorize1/8=.125;3(.125)=.37510) Estimation

a. Roundtothenearest100b. 2000+2000+2900=6900


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraI&AlgebraIITEKSAddressed:AlgebraI(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#2

1) Noticethatanswerwillbenegativea. ‐2010+231b. Subtractwithborrowing.

2)

€

38

x49

=12

x13

=16

3) LongDivisiona. Writeanswertothenearestpenny.

4) ChangeMixedNumbertoDecimala. 2.01‐2.1+21b. ‐.09+21c. 20.91

5) ChangeDecimaltoFraction

a.

€

49

÷3

10

b. Leave,Change,Flip

c.

€

49

x103

=4027

6)

€

44% =44

100=

1125

7) OrderofOperations(DivideFirsttoMakeeasier)a. 9x6÷3‐6+9b. 9x2‐6+9c. 9x3‐6d. 27‐6=21

8) UsebackwardsFOIL(RighttoLeft)a. 3x4=12

i. (Write2Carry1)b. 4x4+3x3+1=16+9+1=26

i. (Write6Carry2)c. 3x4+2=14

i. (Write14)9) Factor(Answerisnegative)

a. (63‐82)15b. (‐19)15c. UseReverseFOILd. 9x5=45

i. Write5Carry4e. 1x5+1x9+4=18

i. Write8Carry1f. 1x1+1=2

10) Estimationa. Roundtothenearest10b. 750‐940+840c. 750‐100=650


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraI&MathModelsTEKSAddressed:MathModels(2)(B)Thestudentusesgraphicalandnumericaltechniquestostudypatternsandanalyzedata.Thestudentisexpectedtoanalyzenumericaldatausingmeasuresofcentraltendency,variability,andcorrelationinordertomakeinferences.AlgebraI(4)(B)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedtousethecommutative,associative,anddistributivepropertiestosimplifyalgebraicexpressions.MaterialsNeeded:


Procedures:





AnswerstoLesson#3

11) Memorizesquaresto35a. 172=289

12) Conversionsa. 8oz=½poundb. 3x1.1=3.30

13) GCDa. 3x16=48b. 3x19=57

i. GCD=314) UseRemainders

a. 58/4remainder2b. 79/4remainder3c. 66/4remainder2d. 2+3+2=7;7/4remainder3

15) 4pecks=1bushela. 2½x4=10

16) OrdertheDataa. 1,1,2,2,3,3,4,5b. Averageof2&3is2.5

17) Memorizeprimesto100a. 97

18) Memorizecubesto20a. 113=1331

19) 2010÷5=40220) Estimation

a.

€

1243 ≈ 35 b. Round3421to3400c. 35x3500=122500


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraIorAlgebraIITEKSAddressed:AlgebraI(4)(B)(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedtousethecommutative,associative,anddistributivepropertiestosimplifyalgebraicexpressions.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#4

1) Subtractwithborrowinga. 2210‐1030=1180

2)

€

710

x5

14=

12

x12

=14

3) Multiplyingby11a. Putazeroinfrontandinbackofthenumberb. (03260)c. Addpairsofdigitsstartingontheright.d. 0+6,6+2,2+3,3+0


a.

€

524

x43

=56

x13

=5

18

b. Cancelthe5’s

5)

€

36% =36

100=

925

6) OrderofOperationsa. (2+3)‐5÷6x4b. 5‐5÷6x4

c. 5‐

€

103

d.

€

153−

103

e.

€

53

7) MemorizeSquaresto35a. 172=289


i. (Write0Carry3)b. 6x6+5x5+3=36+25+3=64


i. (Write36)9) MemorizeCubesto20

a. 93=72910) Estimation

a. Roundtothenearest100b. 3200+4000‐5100=2100


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraIandAlgebraIITEKSAddressed:AlgebraI(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#5

1) Add2010+201+20=22312) Divideby5isthesameasmultiplyby2anddivideby10

a. 20.1x

€

210=4.02

3) SwitchnumbersWriteNegative,Subtracta. ‐358+112

4)

€

815

x9

10=

45

x35

=1225

5) Memorizefractionstopercentsto1/16

a.

€

138

÷1

16

b.

€

118

x161

=111

x21

= 22

6) Divideby9;adddigitsa. 2+1+3+4+7+1+1=19b. 1+9=10c. 1+0=1

7) OrderofOperationsa. 4÷(5+6‐7)x8b. 4÷(4)x8c. 1x8=8

8) ChangetoFractions

a.

€

4415

+7615

=12015

= 8

9) Memorizefractionstopercentsto1/16i. .0625(7)=.43.75%

10) Estimationa. Roundtothenearest100b. 7800‐900+100=7000


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraIorAlgebraIITEKSAddressed:AlgebraI(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#6

1) Add2010‐424+508a. 508‐424=84b. 2010+84=2094

2)

€

825

x1516

=15

x32

=3

10

3) Dividingby2.5isthesameasmultiplyingby

€

410

a. 201x

€

410=

€

80410

= 80.40

4)

€

2 13

+ 315

= 2 515

+ 3 315

= 5 815

5) 48%=

€

48100

=1225

6) Divideby9;adddigitsa. 2+0+1+0=3

7) 1‐1÷2+3x5

a. 1‐

€

12+3x5

b.

€

12+3x5

c.

€

12+15

d. 15

€

12



i. (Write4Carry1)b. 7x7+2x2+1=49+4+1=54


i. (Write19)10) Estimation

a. Roundtothenearest1000b. 11000+2000=13000


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraITEKSAddressed:(4)(A)(B)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedtofindspecificfunctionvalues,simplifypolynomialexpressions,transformandsolveequations,andfactorasnecessaryinproblemsituations;usethecommutative,associative,anddistributivepropertiestosimplifyalgebraicexpressions.MaterialsNeeded:


Procedures:





AnswerstoLesson#7

1) Add38+459+6712=72092) Leave,Change,Flip

a.

€

2435

x74

=65

3) Teen’sRule245x16a. 6x5=30

i. Write0Carry3b. 6x4+5+3=32

i. Write2Carry3c. 6x2+4+3=19

i. Write9Carry1d. 6x0+2+1=3

4) Switchandwritenegativesigna. ‐123.4+7.65=‐115.75

5)

€

14

x34

x81

=32

6) 72%=

€

72100

=1825

7) OrderofOperationsa. 10‐8x6÷4+2b. 10‐12+2=0

8)

€

351.5

+641.5

=703

+128

3=

1983

= 66

9)

€

−5 16

+ 315

= −4 3530

+ 3 630

= −12930

10) Estimationa. Roundsmallnumberstothenearest10b. ‐260=80=340c. Roundtonearest100d. 1300‐300=1000


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraIITEKSAddressed:AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#8



13)

€

2460

=4

10= 40%

14) UsebackwardsFOIL32x23(RighttoLeft)a. 2x3=6

i. Write6b. 3x3+2x2=13


i. (Write7)15) SumofOddnaturalnumbers

a. Add1tothelastnumberi. 23+1=24

b. Divideby2i. 24/2=12

c. Squarei. 122=144

16) CrossMultiplya. 16x11=176b. 13x13=169

c. 176isbiggerso

€

1113isbigger

17) Divideby9;adddigitsa. 2+0+1+0=3

18) MCDLXIVa. 1000+500‐100+50+10+5‐1=1464

19)

€

14

x2000 = 500lbs

a. 500x16=800020) Estimation

a. Roundnumberstothenearest10b. 240x150c. Halfof240is120d. 240+120=360e. 360x100=36000


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraI&AlgebraIITEKSAddressed:AlgebraI(3)(A)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedto:usetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations.MaterialsNeeded:


Procedures:





AnswerstoLesson#9

1) Collectthepositiveintegersa. 3141‐2718+1618b. 4759‐2718=2041


a.

€

35x2521

=11x57

=57

3) Multiply4x15=60a. Writeanswertothenearestpenny.

4)

€

2225

x44

=88

100= 88%

5) ChangeDecimaltofraction

a. .08333…=

€

112

b.

€

76x

121

= 7x2 =14

6) ChangeMixedNumbertoDecimala. 3.4+2.3‐1=4.7

7) Changetofractions

a.

€

7725

+12325

=20025

= 8


i. (Write0Carry2)b. 5x5+4x4+1=25+16+2=43


i. (Write24)9) OrderofOperations

a. 8÷4‐2+4x8b. 2‐2+32=32

10) Estimationa. Roundtothenearest100b. 2500+3600+1000=7100


LessonGoal:Studentswilllearntousethecommutative,associative,anddistributivepropertiesindifferentwaystosolvemathproblemsusingNumberSenseTests.Time:NoMorethan15MinutesCourse:AlgebraI,Geometry,AlgebraIITEKSAddressed:Geometry(1)(A)Geometricstructure.Thestudentunderstandsthestructureof,andrelationshipswithin,anaxiomaticsystem.Thestudentisexpectedtodevelopanawarenessofthestructureofamathematicalsystem,connectingdefinitions,postulates,logicalreasoning,andtheorems.AlgebraI(3)(A)(B)(4)(B)Foundationsforfunctions.Thestudentunderstandshowalgebracanbeusedtoexpressgeneralizationsandrecognizesandusesthepowerofsymbolstorepresentsituations.Thestudentisexpectedto:usesymbolstorepresentunknownsandvariables;andlookforpatternsandrepresentgeneralizationsalgebraically.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedtousethecommutative,associative,anddistributivepropertiestosimplifyalgebraicexpressions.AlgebraII(2)(A)(B)Foundationsforfunctions.Thestudentunderstandstheimportanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblemsandusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressionsandsolveequationsandinequalitiesinproblemsituations.Thestudentisexpectedtousetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressionsandtotransformandsolveequations;andcomplexnumberstodescribethesolutionsofquadraticequations.MaterialsNeeded:


Procedures:



Lesson#10Workeachoftheseproblemsasquicklyaspossible.Estimate#20toplusorminus10%.

AnswerstoLesson#10



13) ForLCMfirstfindtheGCDa. 3x16=48b. 3x19=57

i. GCD=3c. 48(57)÷3=912

14) UseRemaindersa. 34/9remainder7b. 56/9remainder2c. 78/9remainder6d. 7x2‐6=8;remainder8

15) 1acre=43,560sqft16) Mode=Most=317) 555x111=6160518) Memorizeprimesto100

a. 31,37b. Primes=2

19) 4.5/6=.7520) Estimation

a. Memorizesquaresto35b. 26x34c. (30‐4)(30+4)d. 900‐16=884

Documents

Sponge Activity #1 for Mathematical Properties for UIL ...Sponge Activity #1 for Mathematical Properties for UIL Number Sense Lesson Goal: Students will learn to use the commutative,