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
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)
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