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Transcript of of add o i isEa.Ex IM · two rows wide as a surround for the tables and serving carts. Below is an...
y ftpIga ssffEfop t 30 of add 30
oi isEa.Exe
l2Icgi3IM F at or timesa
M 423123 4 481,24
1948 4
times 4
SECONDARY MATH I // MODULE 1
SEQUENCES – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
/HVVRQ�� Checkerboard Borders
A Develop Understanding Task
Inpreparationforbacktoschool,theschooladministrationplanstoreplacethetileinthecafeteria.Theywouldliketohaveacheckerboardpatternoftilestworowswideasasurroundforthetablesandservingcarts.Belowisanexampleoftheborderthattheadministrationisthinkingofusingtosurroundasquare5x5setoftiles.A. Findthenumberofcoloredtilesinthecheckerboardborder.Trackyourthinkingandfinda
wayofcalculatingthenumberofcoloredtilesintheborderthatisquickandefficient.Bepreparedtoshareyourstrategyandjustifyyourwork.
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Page 1
z s 8g 5 5 28tiles
28 10
a 5 5ve a 4x4
Is 13
24 1423 a la n is 3 322 20 18 16
SECONDARY MATH I // MODULE 1
SEQUENCES – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
B. Thecontractorthatwashiredtolaythetileinthecafeteriaistryingtogeneralizeawaytocalculatethenumberofcoloredtilesneededforacheckerboardbordersurroundingasquareoftileswithanydimensions.Torepresentthisgeneralsituation,thecontractorstartedsketchingthesquarebelow.
FindanexpressionforthenumberofcoloredbordertilesneededforanyNxNsquarecenter.
N
N
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1.1 Checker Boarders -- Recursive Patterns
X Y
in.am mMmminmiasma 4 4 24HA 4 Won
no 44 naMt MA
MO KA Ake MKma MM NA M
M.µMmMmm
mm 3 m3x3mWh mun m in 20M M M M
Tiles
2 2 163 3 20 44X4 245 5 2g 7 46 6 32
1.1 Checker Boarders -- Recursive Patterns
# Numbers Start Explanation in Words
Explanation with Next/Now
Recursive Function
1 8, 5, 2, -1…
2 12, 6, 3, 3/2…
3 5, 11, 17, 23, 29…
4 ½, 3/2, 9/2, 27/2
5 7, 2, -3, -8 ….
These patterns can also be written as NEXT = NOW * # Or NEXT = NOW + # Example: 7, 10, 13
Recursive Functions START can be written as NOW can be written as NEXT can be written as
So 7, 10, 13… can be written as
Start Explanation in Words Explanation
with Next/Now Recursive Function
1st Pattern
88 g ADDing 3 Next _Now 1 3 fcn fCn 1 3
3 3 3 Start _Is f 1 D88 12 times Yz Next _NOW LEE f n _Hn DEEK'late Start _1 2 f 17 12
Yutaka 5 Adding6 Next_NOW fin fCn 1 the
start _5 f D 5
12 times 3
Next_NOW 03 fcnt fcnD.ISart YzfCD Yz
575 7 Adding 5 Next _Now An fCn DEE
Start _7 f 1 7
as f If n Df n
373 f n f n 1 3 fu 7
I 2 I iz
i a'itADDING2
Next _Now 2 fin fcn DtzStart 3 f 1 3
1.1 Checker Boarders -- Recursive Patterns
Start Explanation in Words Explanation with Next/Now
Recursive Function
Start Explanation in Words Explanation with Next/Now
Recursive Function
Start Explanation in Words Explanation with Next/Now
Recursive Function
1.1 Checker Boarders -- Recursive Patterns
Start Explanation in Words Explanation with Next/Now
Recursive Function
Start Explanation in Words Explanation with Next/Now
Recursive Function
Start Explanation in Words Explanation with Next/Now
Recursive Function
Start Explanation in Words Explanation with Next/Now
Recursive Function
(e)
(f)
(g)
SECONDARY MATH I // MODULE 1
SEQUENCES – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
/HVVRQ��
READY
Topic:RecognizingSolutionstoEquations
Thesolutiontoanequationisthevalueofthevariablethatmakestheequationtrue.Intheequation9! + 17 = −19, "a”isthevariable.Whena=2,9! + 17 ≠ −19, because 9 2 + 17 = 35. Thus! = 2 is NOT a solution.However,when! = −4, the equation is true 9 −4 + 17 = −19.Therefore,! = −4mustbethesolution.Identifywhichofthe3possiblenumbersisthesolutiontotheequation.
1. 3! + 7 = 13 (! = −2; ! = 2; ! = 5) 2. 8 − 2! = −2 (! = −3; ! = 0; ! = 5)
3. 5 + 4! + 8 = 1 (! = −3;! = −1;! = 2) 4. 6! − 5 + 5! = 105 (! = 4; ! = 7; ! = 10)
Someequationshavetwovariables.Youmayrecallseeinganequationwrittenlikethefollowing:! = 5! + 2.Wecanletxequalanumberandthenworktheproblemwiththisx-valuetodeterminetheassociatedy-value.Asolutiontotheequationmustincludeboththex-valueandthey-value.Oftentheansweriswrittenasanorderedpair.Thex-valueisalwaysfirst.Example: !, ! .Theordermatters!
Determinethey-valueofeachorderedpairbasedonthegivenx-value.
5. ! = 6! − 15; 8, , −1, , 5, 6. ! = −4! + 9; −5, , 2, , 4,
7. ! = 2! − 1; −4, , 0, , 7, 8. ! = −! + 9; −9, , 1, , 5,
READY, SET, GO! Name Period Date
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SECONDARY MATH I // MODULE 1
SEQUENCES – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
/HVVRQ��
SET
Topic:UsingaconstantrateofchangetocompleteatableofvaluesFillinthetable.Thenwriteasentenceexplaininghowyoufiguredoutthevaluestoputineachcell.9. Yourunabusinessmakingbirdhouses.Youspend$600tostartyourbusiness,anditcostsyou$5.00
tomakeeachbirdhouse.
#ofbirdhouses 1 2 3 4 5 6 7
Totalcosttobuild
Explanation:
10. Youmakea$15paymentonyourloanof$500attheendofeachmonth.
#ofmonths 1 2 3 4 5 6 7
Amountofmoneyowed
Explanation:
11. Youdeposit$10inasavingsaccountattheendofeachweek.
#ofweeks 1 2 3 4 5 6 7
Amountofmoneysaved
Explanation:
12. Youaresavingforabikeandcansave$10perweek.Youhave$25whenyoubeginsaving.
#ofweeks 1 2 3 4 5 6 7
Amountofmoneysaved
Explanation:
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SECONDARY MATH I // MODULE 1
SEQUENCES – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
/HVVRQ��
GO
Topic:GraphLinearEquationsGivenaTableofValues.Graphtheorderedpairsfromthetablesonthegivengraphs.
13.! !
0 3
2 7
3 9
5 13
14.! !
0 14
4 10
7 7
9 5
15.! !
2 11
4 10
6 9
8 8
16.! !
1 4
2 7
3 10
4 13
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