SECONDARY MATH I // MODULE 1

SEQUENCES – 1.2

Mathematics Vision Project

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1.2

READY

Topic:UsingfunctionnotationToevaluateanequationsuchas𝑦 = 5𝑥 + 1 whengivenaspecificvalueforx,replacethevariablexwiththegivenvalueandworktheproblemtofindthevalueofy.Example:Findywhenx=2.Replacexwith2.𝑦 = 5 2 + 1 = 10 + 1 = 11. Therefore,y=11whenx=2.Thepoint 2, 11 isonesolutiontotheequation𝑦 = 5𝑥 + 1.Insteadofusing𝑥 𝑎𝑛𝑑 𝑦inanequation,mathematiciansoftenwrite𝑓 𝑛 = 5𝑛 + 1becauseitcangivemoreinformation.Withthisnotation,thedirectiontofind𝑓 2 ,meanstoreplacethevalueof𝑛with2andworktheproblemtofind𝑓 𝑛 .Thepoint 𝑛, 𝑓 𝑛 isinthesamelocationonthegraphas 𝑥, 𝑦 ,where𝑛describesthelocationalongthex–axis,and𝑓 𝑛 istheheightofthegraph.Giventhat𝒇 𝒏 = 𝟖𝒏 − 𝟑and𝒈 𝒏 = 𝟑𝒏 − 𝟏𝟎,evaluatethefollowingfunctionswiththeindicatedvalues.

1.𝑓 5 = 2.𝑔 5 = 3.𝑓 −4 = 4.𝑔 −4 =

5.𝑓 0 = 6.𝑔 0 = 7.𝑓 1 = 8.𝑔 1 =

Topic:LookingforpatternsofchangeCompleteeachtablebylookingforthepattern.

9. Term 1st 2nd 3rd 4th 5th 6th 7th 8thValue 2 4 8 16 32

10. Term 1st 2nd 3rd 4th 5th 6th 7th 8thValue 66 50 34 18

11. Term 1st 2nd 3rd 4th 5th 6th 7th 8thValue 160 80 40 20

12. Term 1st 2nd 3rd 4th 5th 6th 7th 8thValue -9 -2 5 12

READY, SET, GO! Name PeriodDate

SECONDARY MATH I // MODULE 1

SEQUENCES – 1.2

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

1.2

SET

Topic:Usevariablestocreateequationsthatconnectwithvisualpatterns.

Inthepicturesbelow,eachsquarerepresentsonetile.

13.DrawStep4andStep5.

Thestudentsinaclasswereaskedtofindthenumberoftilesinafigurebydescribinghowtheysawthe

patternoftileschangingateachstep.Matcheachstudent’swayofdescribingthepatternwiththe

appropriateequationbelow.Notethat“s”representsthestepnumberand“n”representsthenumberof

tiles.

(a)𝒏 = 𝟐𝒔 − 𝟏 + 𝒔 − 𝟏 (b)𝒏 = 𝟑𝒔 − 𝟐 (c)𝒏 = 𝒔 + 𝟐 𝒔 − 𝟏

14._____Danexplainedthatthemiddle“tower”isalwaysthesameasthestepnumber.Healsopointed

outthatthe2armsoneachsideofthe“tower”containonelessblockthanthestepnumber.

15._____Sallycountedthenumberoftilesateachstepandmadeatable.Sheexplainedthatthenumber

oftilesineachfigurewasalways3timesthestepnumberminus2.

stepnumber 1 2 3 4 5 6

numberoftiles 1 4 7 10 13 16

16._____Nancyfocusedonthenumberofblocksinthebasecomparedtothenumberofblocksabovethebase.Shesaidthenumberofbaseblocksweretheoddnumbersstartingat1.Andthenumberoftilesabovethebasefollowedthepattern0,1,2,3,4.Sheorganizedherworkinthetableattheright.

Stepnumber #inbase+#ontop

1 1+0

2 3+1

3 5+2

4 7+3

5 9+4

Step 2 Step 3 Step 1 Step 4 Step 5

SECONDARY MATH I // MODULE 1

SEQUENCES – 1.2

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

1.2

GO

Topic:ThemeaningofanexponentWriteeachexpressionusinganexponent.17.6×6×6×6×6 18.4×4×4 19.15×15×15×15 20.!

!× !!

A)Writeeachexpressioninexpandedform.B)Thencalculatethevalueoftheexpression.21.7!

A)B)

22.3!A)B)

23.5!A)B)

24.10!A)B)

25.7(2)!A)B)

26.10 8! A)B)

27.3 5 !A)B)

28.16 !!

!

A)B)